%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW293+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 : n006.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 05:31:03 PM UTC 2026
% Result : Theorem 38.94s 22.22s
% Output : CNFRefutation 43.74s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_6014)
% Comments :
%------------------------------------------------------------------------------
fof(fact_of__int__num,axiom,
! [X101,X10] :
( class_Rings_Oring__1(X10)
=> ( ( X101 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hAPP(c_Int_Oring__1__class_Oof__int(X10),X101) = c_Groups_Ozero__class_Ozero(X10) )
& ( X101 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Int_Oring__1__class_Oof__int(X10),X101) = hAPP(c_Groups_Ouminus__class_Ouminus(X10),hAPP(c_Int_Oring__1__class_Oof__int(X10),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X101))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Int_Oring__1__class_Oof__int(X10),X101) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X10),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X10,X10)),tc_fun(tc_Int_Oint,X10)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,X10),X10),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X10,X10)),tc_fun(tc_Int_Oint,X10)),tc_Int_Oint),c_COMBB(tc_fun(X10,X10),X10,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X10,tc_fun(tc_fun(X10,X10),X10),tc_Int_Oint),c_HOL_OLet(X10,X10)),c_Int_Oring__1__class_Oof__int(X10)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X10,X10),tc_fun(X10,X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,X10)),tc_fun(tc_fun(X10,X10),tc_fun(X10,X10)),tc_Int_Oint),c_COMBS(X10,X10,X10)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X10,X10),tc_fun(X10,tc_fun(X10,X10))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,X10)),tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_fun(X10,X10))),tc_Int_Oint),c_COMBB(X10,tc_fun(X10,X10),X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_fun(X10,X10)),tc_Int_Oint),c_If(X10)),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(X10,X10,X10),c_Groups_Oplus__class_Oplus(X10)),c_COMBI(X10))))),hAPP(hAPP(c_COMBC(X10,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X10),c_Groups_Oplus__class_Oplus(X10)),hAPP(hAPP(c_COMBS(X10,X10,X10),c_Groups_Oplus__class_Oplus(X10)),c_COMBI(X10)))),c_Groups_Oone__class_Oone(X10))))),c_Divides_Odivmod__int(X101,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,
! [X105,X93,X94] :
( class_Rings_Olinordered__idom(X94)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),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(X94),X105),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X94))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__sum__power2__lt__zero) ).
fof(fact_power2__less__0,axiom,
! [X84,X94] :
( class_Rings_Olinordered__idom(X94)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X94))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__less__0) ).
fof(fact_zmod__number__of__Bit1,axiom,
! [X144,X133] :
( ( 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),X133)))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X133))) = 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),X144),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)))),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),X133)))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X133))) = 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),X144)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)))),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,
! [X133,X144] :
( 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),X144)))
=> ( ( 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),X133)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144))))
=> c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)) = 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),X133)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144))) )
& ( ~ 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),X133)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144))))
=> c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133),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),X144)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg__eqn__number__of) ).
fof(fact_negDivAlg__eqn__1__number__of,axiom,
! [X133] :
( 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),X133)))
=> ( ( 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),X133))))
=> c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)) = 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),X133))) )
& ( ~ 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),X133))))
=> c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)),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),X133)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg__eqn__1__number__of) ).
fof(fact_posDivAlg__eqn__number__of,axiom,
! [X133,X144] :
( 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),X144)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)) = 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),X133)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133),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),X144)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg__eqn__number__of) ).
fof(fact_posDivAlg__eqn__1__number__of,axiom,
! [X133] :
( 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),X133)))
=> ( ( 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),X133)))
=> c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)) = 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),X133)))
=> c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)),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),X133)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg__eqn__1__number__of) ).
fof(fact_negDivAlg__eqn,axiom,
! [X84,X92] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X92))
=> ( ( 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),X84),X92)))
=> c_Divides_OnegDivAlg(X84,X92) = 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),X84),X92)) )
& ( ~ 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),X84),X92)))
=> c_Divides_OnegDivAlg(X84,X92) = hAPP(c_Divides_Oadjust(X92),c_Divides_OnegDivAlg(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)))),X92))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg__eqn) ).
fof(fact_posDivAlg__eqn,axiom,
! [X84,X92] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X92))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),X92))
=> c_Divides_OposDivAlg(X84,X92) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),X92))
=> c_Divides_OposDivAlg(X84,X92) = hAPP(c_Divides_Oadjust(X92),c_Divides_OposDivAlg(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)))),X92))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg__eqn) ).
fof(fact_power__number__of__odd__number__of,axiom,
! [X168,X131,X10] :
( class_Int_Onumber__ring(X10)
=> ( ( 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),X131)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X168)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X131))) = hAPP(hAPP(c_HOL_OLet(X10,X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X168)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X131))),hAPP(hAPP(c_COMBS(X10,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X10),c_Groups_Otimes__class_Otimes(X10)),hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X168)))),c_COMBI(X10))) )
& ( ~ 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),X131)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X168)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X131))) = c_Groups_Oone__class_Oone(X10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__number__of__odd__number__of) ).
fof(fact_power__number__of__odd,axiom,
! [X73,X131,X10] :
( class_Int_Onumber__ring(X10)
=> ( ( 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),X131)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),X73),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X131))) = hAPP(hAPP(c_HOL_OLet(X10,X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X73),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X131))),hAPP(hAPP(c_COMBS(X10,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X10),c_Groups_Otimes__class_Otimes(X10)),hAPP(c_Groups_Otimes__class_Otimes(X10),X73))),c_COMBI(X10))) )
& ( ~ 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),X131)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),X73),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X131))) = c_Groups_Oone__class_Oone(X10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__number__of__odd) ).
fof(fact_zpower__number__of__odd,axiom,
! [X73,X131] :
( ( 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),X131)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X73),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X131))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X73),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X131))),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),X73))),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),X131)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X73),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X131))) = 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,
! [X16,X177,X10] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X10,X10),X177)),c_Transitive__Closure_Ortrancl(X10,X177)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X16)),c_Transitive__Closure_Otrancl(X10,X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_irrefl__tranclI) ).
fof(fact_dvd_OatLeastatMost__psubset__iff,axiom,
! [X141,X18,X38,X39] :
( 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),X39,X38)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X18,X141)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X39),X38))
| ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X18),X39))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X38),X141))
& ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X18),X39))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X39),X18)) )
| ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X38),X141))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X141),X38)) ) ) ) )
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X18),X141)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastatMost__psubset__iff) ).
fof(fact_acyclic__def,axiom,
! [X177,X10] :
( c_Wellfounded_Oacyclic(X10,X177)
<=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X3)),c_Transitive__Closure_Otrancl(X10,X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__def) ).
fof(fact_zdiv__number__of__Bit1,axiom,
! [X144,X133] :
( ( 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),X133)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X144))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X133))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)) )
& ( ~ 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),X133)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X144))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X133))) = 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),X144)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__number__of__Bit1) ).
fof(fact_acyclicI,axiom,
! [X177,X10] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X3)),c_Transitive__Closure_Otrancl(X10,X177)))
=> c_Wellfounded_Oacyclic(X10,X177) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclicI) ).
fof(fact_nat__number__of__Bit1,axiom,
! [X131] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X131)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X131)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X131)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X131)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X131)),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,
! [X42,X97] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X97)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X42)))
=> c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X97),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X42)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X97)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X97)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X42))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X97)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X42)))
=> c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X97),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X42)) = 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,
! [X133,X94] :
( ( class_Int_Onumber__ring(X94)
& class_Int_Oring__char__0(X94) )
=> ~ c_Int_Oiszero(X94,hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OBit1(X133))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iszero__number__of__Bit1) ).
fof(fact_not__iszero__Numeral1,axiom,
! [X94] :
( class_Int_Onumber__ring(X94)
=> ~ c_Int_Oiszero(X94,hAPP(c_Int_Onumber__class_Onumber__of(X94),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,
! [X42,X144] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),X42)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X42) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),X42)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X144))),X42) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__nat__number__of__add) ).
fof(fact_upt__Suc,axiom,
! [X119,X120] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X120),X119))
=> c_List_Oupt(X120,hAPP(c_Nat_OSuc,X119)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X120,X119)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X119),c_List_Olist_ONil(tc_Nat_Onat))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X120),X119))
=> c_List_Oupt(X120,hAPP(c_Nat_OSuc,X119)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__Suc) ).
fof(fact_upt__rec,axiom,
! [X119,X120] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),X119))
=> c_List_Oupt(X120,X119) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X120),c_List_Oupt(hAPP(c_Nat_OSuc,X120),X119)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),X119))
=> c_List_Oupt(X120,X119) = 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,
! [X144] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X144),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),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),X144),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X144)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__diff__1) ).
fof(fact_nat__number__of__add__1,axiom,
! [X144] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X144),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),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),X144),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X144)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__add__1) ).
fof(fact_nat__1__add__number__of,axiom,
! [X144] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X144),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),X144)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X144),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),X144)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X144)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1__add__number__of) ).
fof(fact_Suc__nat__number__of,axiom,
! [X144] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X144)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__nat__number__of) ).
fof(fact_adjust__def,axiom,
! [X38] : c_Divides_Oadjust(X38) = 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)),X38))))),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)),X38))))),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,
! [X103] : c_Int_Osucc(c_Int_OBit0(X103)) = c_Int_OBit1(X103),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_succ__Bit0) ).
fof(fact_Bit0__def,axiom,
! [X103] : c_Int_OBit0(X103) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X103),X103),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit0__def) ).
fof(fact_diff__bin__simps_I2_J,axiom,
! [X103] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X103),c_Int_OMin) = c_Int_Osucc(X103),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I2_J) ).
fof(fact_prod__fun__imageE,axiom,
! [X196,X1,X2,X195,X125,X18,X13,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),X18),hAPP(c_Set_Oimage(tc_prod(X125,X195),tc_prod(X10,X13),c_Product__Type_Omap__pair(X125,X10,X195,X13,X2,X1)),X196)))
=> ~ ! [X3,X90] :
( X18 = hAPP(hAPP(c_Product__Type_OPair(X10,X13),hAPP(X2,X3)),hAPP(X1,X90))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X125,X195)),hAPP(hAPP(c_Product__Type_OPair(X125,X195),X3),X90)),X196)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod__fun__imageE) ).
fof(fact_divmod__int__pdivmod,axiom,
! [X162,X101] :
( ( X101 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odivmod__int(X101,X162) = 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)) )
& ( X101 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( ( X162 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odivmod__int(X101,X162) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X101) )
& ( X162 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odivmod__int(X101,X162) = 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,X162))),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)),X162)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X101))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X162),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(X101,X162)),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),X162))))),c_Divides_Opdivmod(X101,X162)))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__pdivmod) ).
fof(fact_apsnd__def,axiom,
! [X2,X10,X125,X13] : c_Product__Type_Oapsnd(X13,X125,X10,X2) = c_Product__Type_Omap__pair(X10,X10,X13,X125,c_Fun_Oid(X10),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apsnd__def) ).
fof(fact_divmod__int__code,axiom,
! [X162,X101] :
( ( X101 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odivmod__int(X101,X162) = 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)) )
& ( X101 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( ( X162 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odivmod__int(X101,X162) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X101) )
& ( X162 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odivmod__int(X101,X162) = 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,X162))),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,X101)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X162))),c_Divides_Opdivmod(X101,X162)),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),X162))))),c_Divides_Opdivmod(X101,X162)))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__code) ).
fof(fact_Nitpick_Oplus__frac__def,axiom,
! [X177,X158,X10] : c_Nitpick_Oplus__frac(X10,X158,X177) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X10),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(X10),X158),hAPP(c_Nitpick_Odenom(X10),X177))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,X10),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,X10),tc_Int_Oint),c_Nitpick_Ofrac(X10)),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(X10),X158))),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(X10),X158))))),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(X10),X177))),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(X10),X177)))))),c_COMBI(tc_Int_Oint))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Oplus__frac__def) ).
fof(fact_Nitpick_Odenom__def,axiom,
! [X10] : c_Nitpick_Odenom(X10) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X10,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Odenom__def) ).
fof(fact_Nitpick_Onum__def,axiom,
! [X10] : c_Nitpick_Onum(X10) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X10,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Onum__def) ).
fof(fact_reflcl__set__eq,axiom,
! [X25,X16,X177,X10] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_prod(X10,X10)),tc_fun(X10,tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X10),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool),X10),c_member(tc_prod(X10,X10)))),c_Product__Type_OPair(X10,X10)))),X177)),c_fequal),X16),X25))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X177),c_Relation_OId(X10)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reflcl__set__eq) ).
fof(fact_rtrancl__empty,axiom,
! [X10] : c_Transitive__Closure_Ortrancl(X10,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool))) = c_Relation_OId(X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__empty) ).
fof(fact_adjust__eq,axiom,
! [X177,X158,X38] : hAPP(c_Divides_Oadjust(X38),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X158),X177)) = 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),X177),X38)),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)))),X158)),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)))),X158)),X177))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_adjust__eq) ).
fof(fact_trancl__insert,axiom,
! [X177,X16,X25,X10] : c_Transitive__Closure_Otrancl(X10,hAPP(hAPP(c_Set_Oinsert(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X25),X16)),X177)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X10,X177)),hAPP(c_Set_OCollect(tc_prod(X10,X10)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X10,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X10,X10),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool),X10),c_member(tc_prod(X10,X10))),hAPP(hAPP(c_COMBC(X10,X10,tc_prod(X10,X10)),c_Product__Type_OPair(X10,X10)),X25))),c_Transitive__Closure_Ortrancl(X10,X177))))),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X10,X10),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool),X10),c_member(tc_prod(X10,X10))),hAPP(c_Product__Type_OPair(X10,X10),X16))),c_Transitive__Closure_Ortrancl(X10,X177)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__insert) ).
fof(fact_trancl__unfold__left,axiom,
! [X177,X10] : c_Transitive__Closure_Otrancl(X10,X177) = hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X177),c_Transitive__Closure_Ortrancl(X10,X177)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__unfold__left) ).
fof(fact_map__add__map__of__foldr,axiom,
! [X286,X102,X13,X10] : c_Map_Omap__add(X10,X13,X102,c_Map_Omap__of(X10,X13,X286)) = c_List_Ofoldr(tc_prod(X10,X13),tc_fun(X10,tc_Option_Ooption(X13)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,tc_fun(tc_fun(X10,tc_Option_Ooption(X13)),tc_fun(X10,tc_Option_Ooption(X13)))),hAPP(hAPP(c_COMBC(X10,tc_fun(X13,tc_Option_Ooption(X13)),tc_fun(X13,tc_fun(tc_fun(X10,tc_Option_Ooption(X13)),tc_fun(X10,tc_Option_Ooption(X13))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X13),tc_fun(tc_fun(X10,tc_Option_Ooption(X13)),tc_fun(X10,tc_Option_Ooption(X13)))),tc_fun(tc_fun(X13,tc_Option_Ooption(X13)),tc_fun(X13,tc_fun(tc_fun(X10,tc_Option_Ooption(X13)),tc_fun(X10,tc_Option_Ooption(X13))))),X10),c_COMBB(tc_Option_Ooption(X13),tc_fun(tc_fun(X10,tc_Option_Ooption(X13)),tc_fun(X10,tc_Option_Ooption(X13))),X13)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_Option_Ooption(X13)),tc_fun(tc_Option_Ooption(X13),tc_fun(X10,tc_Option_Ooption(X13)))),tc_fun(tc_Option_Ooption(X13),tc_fun(tc_fun(X10,tc_Option_Ooption(X13)),tc_fun(X10,tc_Option_Ooption(X13)))),X10),c_COMBC(tc_fun(X10,tc_Option_Ooption(X13)),tc_Option_Ooption(X13),tc_fun(X10,tc_Option_Ooption(X13)))),hAPP(c_COMBC(tc_fun(X10,tc_Option_Ooption(X13)),X10,tc_fun(tc_Option_Ooption(X13),tc_fun(X10,tc_Option_Ooption(X13)))),c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)))))),c_Option_Ooption_OSome(X13))),X286,X102),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__map__of__foldr) ).
fof(fact_foldr__foldl,axiom,
! [X39,X290,X2,X10,X13] : c_List_Ofoldr(X13,X10,X2,X290,X39) = hAPP(c_List_Ofoldl(X10,X13,hAPP(c_COMBC(X13,X10,X10),X2),X39),hAPP(c_List_Orev(X13),X290)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldr__foldl) ).
fof(fact_sum__power2__le__zero__iff,axiom,
! [X25,X16,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X16),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(X10),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(X10)))
<=> ( X16 = c_Groups_Ozero__class_Ozero(X10)
& X25 = c_Groups_Ozero__class_Ozero(X10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__power2__le__zero__iff) ).
fof(fact_transpose_Opsimps_I3_J,axiom,
! [X328,X290,X16,X10] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X10)),c_List_Otranspose__rel(X10)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290)),X328)))
=> c_List_Otranspose(X10,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290)),X328)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X16),c_List_Oconcat(X10,hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_Olist__case(tc_List_Olist(X10),X10,c_List_Olist_ONil(X10),hAPP(hAPP(c_COMBB(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_List_Olist(X10)),X10),c_COMBK(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_COMBC(X10,tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_OCons(X10)),c_List_Olist_ONil(X10))))),X328)))),c_List_Otranspose(X10,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X10)),X290),c_List_Oconcat(tc_List_Olist(X10),hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_List_Olist(tc_List_Olist(X10))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X10)),X10,c_List_Olist_ONil(tc_List_Olist(X10)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X10),tc_List_Olist(tc_List_Olist(X10))),X10),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_List_Olist(tc_List_Olist(X10)),tc_List_Olist(tc_List_Olist(X10))),c_List_Olist_OCons(tc_List_Olist(X10))),c_List_Olist_ONil(tc_List_Olist(X10)))))),X328))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose_Opsimps_I3_J) ).
fof(fact_concat__conv__foldl,axiom,
! [X328,X10] : c_List_Oconcat(X10,X328) = hAPP(c_List_Ofoldl(tc_List_Olist(X10),tc_List_Olist(X10),c_List_Oappend(X10),c_List_Olist_ONil(X10)),X328),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__conv__foldl) ).
fof(fact_transpose_Osimps_I3_J,axiom,
! [X328,X290,X16,X10] : c_List_Otranspose(X10,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290)),X328)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X16),c_List_Oconcat(X10,hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_Olist__case(tc_List_Olist(X10),X10,c_List_Olist_ONil(X10),hAPP(hAPP(c_COMBB(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_List_Olist(X10)),X10),c_COMBK(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_COMBC(X10,tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_OCons(X10)),c_List_Olist_ONil(X10))))),X328)))),c_List_Otranspose(X10,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X10)),X290),c_List_Oconcat(tc_List_Olist(X10),hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_List_Olist(tc_List_Olist(X10))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X10)),X10,c_List_Olist_ONil(tc_List_Olist(X10)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X10),tc_List_Olist(tc_List_Olist(X10))),X10),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_List_Olist(tc_List_Olist(X10)),tc_List_Olist(tc_List_Olist(X10))),c_List_Olist_OCons(tc_List_Olist(X10))),c_List_Olist_ONil(tc_List_Olist(X10)))))),X328))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose_Osimps_I3_J) ).
fof(fact_odd__power__less__zero,axiom,
! [X42,X84,X94] :
( class_Rings_Olinordered__idom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),c_Groups_Ozero__class_Ozero(X94)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),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)))),X42)))),c_Groups_Ozero__class_Ozero(X94))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__power__less__zero) ).
fof(fact_rel__compE,axiom,
! [X54,X177,X125,X284,X13,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),X284),hAPP(hAPP(c_Relation_Orel__comp(X10,X125,X13),X177),X54)))
=> ~ ! [X3,X90,X159] :
( X284 = hAPP(hAPP(c_Product__Type_OPair(X10,X13),X3),X159)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X125)),hAPP(hAPP(c_Product__Type_OPair(X10,X125),X3),X90)),X177))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X125,X13)),hAPP(hAPP(c_Product__Type_OPair(X125,X13),X90),X159)),X54)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__compE) ).
fof(fact_odd__0__le__power__imp__0__le,axiom,
! [X42,X84,X94] :
( class_Rings_Olinordered__idom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),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)))),X42)))))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X84)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__0__le__power__imp__0__le) ).
fof(fact_evaln__elim__cases_I7_J,axiom,
! [X77,X20,X54,X39,X19,X48] :
( c_Natural_Oevaln(c_Com_Ocom_OCall(X48,X19,X39),X54,X20,X77)
=> ~ ! [X67] :
( X77 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X67),hAPP(c_Natural_Ogetlocs,X54))),X48),hAPP(hAPP(c_Natural_Ogetlocs,X67),c_Com_ORes))
=> ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X19),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X54),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X39,X54)),X20,X67) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I7_J) ).
fof(fact_power2__diff,axiom,
! [X105,X93,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X93),X105)),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(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),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(X94),X105),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(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X93)),X105)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__diff) ).
fof(fact_power2__sum,axiom,
! [X105,X93,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X93),X105)),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(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),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(X94),X105),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(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X93)),X105)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__sum) ).
fof(fact_dvd_OgreaterThan__iff,axiom,
! [X101,X113] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X113),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)))),X101)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X101),X113))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X113),X101)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OgreaterThan__iff) ).
fof(fact_dvd_OlessThan__iff,axiom,
! [X101,X113] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X113),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)))),X101)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X113),X101))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X101),X113)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OlessThan__iff) ).
fof(fact_Nitpick_Osetsum_H__def,axiom,
! [X2,X154,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> c_Nitpick_Osetsum_H(X10,X13,X2,X154) = hAPP(c_List_Omonoid__add__class_Olistsum(X13),hAPP(hAPP(c_List_Omap(X10,X13),X2),c_Hilbert__Choice_OEps(tc_List_Olist(X10),hAPP(hAPP(c_COMBS(tc_List_Olist(X10),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X10)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X10)),c_fequal),c_List_Oset(X10))),X154))),c_List_Odistinct(X10))))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> c_Nitpick_Osetsum_H(X10,X13,X2,X154) = c_Groups_Ozero__class_Ozero(X13) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Osetsum_H__def) ).
fof(fact_sum__power2__gt__zero__iff,axiom,
! [X25,X16,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X16),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(X10),X25),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
<=> ( X16 != c_Groups_Ozero__class_Ozero(X10)
| X25 != c_Groups_Ozero__class_Ozero(X10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__power2__gt__zero__iff) ).
fof(fact_transpose__aux__max,axiom,
! [X328,X13,X290,X10] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290))),c_List_Ofoldr(tc_List_Olist(X13),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X13)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X13))),X328,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(X10)),X290)),c_List_Ofoldr(tc_List_Olist(X13),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X13)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(X13),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X13)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X13)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(X13),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X13)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X13),tc_List_Olist(X13),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X13)))),X328),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,
! [X113,X290,X154,X10] : hAPP(hAPP(c_List_Omap(tc_prod(X10,tc_Nat_Onat),X10),c_Product__Type_Ofst(X10,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X10,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X10,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(X10,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X10,tc_Nat_Onat))),X154)),hAPP(hAPP(c_List_Ozip(X10,tc_Nat_Onat),X290),c_List_Oupt(X113,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X113),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290)))))) = hAPP(hAPP(c_List_Omap(tc_prod(X10,tc_Nat_Onat),X10),c_Product__Type_Ofst(X10,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X10,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X10,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(X10,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X10,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(X10,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(X10,tc_Nat_Onat))),X113))),X154)),hAPP(hAPP(c_List_Ozip(X10,tc_Nat_Onat),X290),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__shift__lemma) ).
fof(fact_sorted__list__of__set__range,axiom,
! [X20,X102] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X102),X20)) = c_List_Oupt(X102,X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__list__of__set__range) ).
fof(fact_Random_Osimps,axiom,
! [X202,X1,X10,X203] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X203),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
=> c_Random__Sequence_ORandom(X10,X1,X203,X202) = 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(X10)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X10)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X203),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
=> c_Random__Sequence_ORandom(X10,X1,X203,X202) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X10,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(X10)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(X1,X202)),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(X10)))),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(X10)))),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(X10)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(X10,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(X10)))),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(X10)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(X10,X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X203),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X202))),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(X10)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X10))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X10)))),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(X10)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(X10,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(X10)))),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(X10)))),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(X10))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X10)))),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(X10)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X10)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X10))))),tc_prod(X10,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(X10)),hAPP(hAPP(c_COMBB(X10,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X10)))),tc_prod(X10,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(X10)),c_Product__Type_Ofst(X10,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,
! [X144,X97] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X97)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)) = 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)))),X97)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__div__eq__add3__div__number__of) ).
fof(fact_Suc__div__eq__add3__div,axiom,
! [X42,X97] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X97)))),X42) = 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)))),X97)),X42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__div__eq__add3__div) ).
fof(fact_New__DSequence_Opos__not__seq__def,axiom,
! [X113,X200] : hAPP(c_New__DSequence_Opos__not__seq(X200),X113) = c_Lazy__Sequence_Ohb__not__seq(hAPP(X200,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)))),X113))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__not__seq__def) ).
fof(fact_mem__splitE,axiom,
! [X166,X18,X125,X13,X73,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X73),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X13,X125,tc_fun(X10,tc_HOL_Obool)),X18),X166)))
=> ~ ! [X3,X90] :
( X166 = hAPP(hAPP(c_Product__Type_OPair(X13,X125),X3),X90)
=> ~ hBOOL(hAPP(hAPP(c_member(X10),X73),hAPP(hAPP(X18,X3),X90))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__splitE) ).
fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
! [X168,X154,X16,X73,X2,X13,X10] :
( c_Finite__Set_Ofun__left__comm(X10,X13,X2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X13,X2,X73,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)),X168))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ~ ! [X90] :
( X168 = hAPP(hAPP(X2,X16),X90)
=> ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X13,X2,X73,X154),X90)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__insertE) ).
fof(fact_int__of__code,axiom,
! [X103] :
( ( X103 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_Code__Numeral_Oint__of,X103) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( X103 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> ( ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X103,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,X103) = 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),X103),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,X103,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,X103) = 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),X103),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,
! [X105,X93,X94] :
( class_Rings_Olinordered__idom(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),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(X94),X105),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,X13,X154,X10] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),hAPP(c_Set_Oimage(X10,X13,X2),X154)))
=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
& ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X154))),hAPP(hAPP(c_COMBC(X10,X13,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X13,tc_fun(X13,tc_HOL_Obool),X10),c_fequal),X2)),hAPP(X2,X3)))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pigeonhole__infinite) ).
fof(fact_concat__eq__concat__iff,axiom,
! [X289,X290,X10] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),X3),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X10),tc_List_Olist(X10)),X290),X289))))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X10),tc_List_Olist(X10),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_Nat_Onat),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X10),tc_Nat_Onat),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),tc_List_Olist(X10)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X10))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X10)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X10))))),c_Nat_Osize__class_Osize(tc_List_Olist(X10)))),X3)) )
=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),X290) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),X289)
=> ( c_List_Oconcat(X10,X290) = c_List_Oconcat(X10,X289)
<=> X290 = X289 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__eq__concat__iff) ).
fof(fact_concat__injective,axiom,
! [X289,X290,X10] :
( c_List_Oconcat(X10,X290) = c_List_Oconcat(X10,X289)
=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),X290) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),X289)
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),X3),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X10),tc_List_Olist(X10)),X290),X289))))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X10),tc_List_Olist(X10),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_Nat_Onat),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X10),tc_Nat_Onat),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),tc_List_Olist(X10)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X10))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X10)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X10))))),c_Nat_Osize__class_Osize(tc_List_Olist(X10)))),X3)) )
=> X290 = X289 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__injective) ).
fof(fact_nat__rec__add__eq__if,axiom,
! [X20,X168,X2,X39,X10] : hAPP(c_Nat_Onat_Onat__rec(X10,X39,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)),X20)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X10),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X168))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X10,X10),hAPP(hAPP(c_COMBC(tc_Int_Oint,X10,tc_fun(X10,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_fun(X10,X10)),tc_Int_Oint),c_If(X10)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(X10,X39,X2),X20))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X10,X10),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X10,X10),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)),X20))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,tc_Int_Oint),c_Nat_Onat_Onat__rec(X10,X39,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)),X20))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__rec__add__eq__if) ).
fof(fact_add__Min__right,axiom,
! [X103] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X103),c_Int_OMin) = c_Int_Opred(X103),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Min__right) ).
fof(fact_neg__zmod__mult__2,axiom,
! [X92,X84] :
( 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,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)))),X92)),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_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),X92),c_Groups_Oone__class_Oone(tc_Int_Oint)),X84))),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,
! [X92,X84] :
( 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),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)))),X92))),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_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X92),c_Groups_Oone__class_Oone(tc_Int_Oint))),X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__zdiv__mult__2) ).
fof(fact_pos__zdiv__mult__2,axiom,
! [X92,X84] :
( 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),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)))),X92))),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_Divides_Odiv__class_Odiv(tc_Int_Oint),X92),X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__zdiv__mult__2) ).
fof(fact_eq__number__of__Suc,axiom,
! [X20,X168] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168) = hAPP(c_Nat_OSuc,X20)
<=> 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(X168))),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)),X20))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__number__of__Suc) ).
fof(fact_Suc__eq__number__of,axiom,
! [X168,X20] :
( hAPP(c_Nat_OSuc,X20) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)
<=> 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(X168))),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)),X20))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__number__of) ).
fof(fact_Nitpick_Ocard_H__def,axiom,
! [X154,X10] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> c_Nitpick_Ocard_H(X10,X154) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_Hilbert__Choice_OEps(tc_List_Olist(X10),hAPP(hAPP(c_COMBS(tc_List_Olist(X10),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X10)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X10)),c_fequal),c_List_Oset(X10))),X154))),c_List_Odistinct(X10)))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> c_Nitpick_Ocard_H(X10,X154) = 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,
! [X113,X230] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X230))
=> 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)),X230))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X113)))) = 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)),X230))),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,X113))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__less__Suc2) ).
fof(fact_power2__le__imp__le,axiom,
! [X105,X93,X94] :
( class_Rings_Olinordered__semidom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),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(X94),X105),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(X94),c_Groups_Ozero__class_Ozero(X94)),X105))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X105)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__le__imp__le) ).
fof(fact_power2__less__imp__less,axiom,
! [X105,X93,X94] :
( class_Rings_Olinordered__semidom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),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(X94),X105),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(X94),c_Groups_Ozero__class_Ozero(X94)),X105))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X105)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__less__imp__less) ).
fof(fact_vimage__if,axiom,
! [X160,X13,X141,X154,X18,X10] :
( ( hBOOL(hAPP(hAPP(c_member(X10),X18),X154))
=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X141),X154))
=> hAPP(c_Set_Ovimage(X13,X10,hAPP(hAPP(c_COMBC(X13,X10,X10),hAPP(hAPP(c_COMBC(X13,X10,tc_fun(X10,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_fun(X10,X10)),X13),c_If(X10)),hAPP(hAPP(c_COMBC(X13,tc_fun(X13,tc_HOL_Obool),tc_HOL_Obool),c_member(X13)),X160))),X18)),X141)),X154) = c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X141),X154))
=> hAPP(c_Set_Ovimage(X13,X10,hAPP(hAPP(c_COMBC(X13,X10,X10),hAPP(hAPP(c_COMBC(X13,X10,tc_fun(X10,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_fun(X10,X10)),X13),c_If(X10)),hAPP(hAPP(c_COMBC(X13,tc_fun(X13,tc_HOL_Obool),tc_HOL_Obool),c_member(X13)),X160))),X18)),X141)),X154) = X160 ) ) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X18),X154))
=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X141),X154))
=> hAPP(c_Set_Ovimage(X13,X10,hAPP(hAPP(c_COMBC(X13,X10,X10),hAPP(hAPP(c_COMBC(X13,X10,tc_fun(X10,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_fun(X10,X10)),X13),c_If(X10)),hAPP(hAPP(c_COMBC(X13,tc_fun(X13,tc_HOL_Obool),tc_HOL_Obool),c_member(X13)),X160))),X18)),X141)),X154) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X13,tc_HOL_Obool)),X160) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X141),X154))
=> hAPP(c_Set_Ovimage(X13,X10,hAPP(hAPP(c_COMBC(X13,X10,X10),hAPP(hAPP(c_COMBC(X13,X10,tc_fun(X10,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_fun(X10,X10)),X13),c_If(X10)),hAPP(hAPP(c_COMBC(X13,tc_fun(X13,tc_HOL_Obool),tc_HOL_Obool),c_member(X13)),X160))),X18)),X141)),X154) = c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__if) ).
fof(fact_pos__zmod__mult__2,axiom,
! [X92,X84] :
( 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,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)))),X92)),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_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,X92,X84))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__zmod__mult__2) ).
fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
! [X144,X97] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X97))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)) = 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)))),X97),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mod__eq__add3__mod__number__of) ).
fof(fact_zero__le__even__power_H,axiom,
! [X42,X84,X94] :
( class_Rings_Olinordered__idom(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),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)))),X42)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__even__power_H) ).
fof(fact_Suc__mod__eq__add3__mod,axiom,
! [X42,X97] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X97))),X42) = 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)))),X97),X42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mod__eq__add3__mod) ).
fof(fact_mod__Suc__eq__mod__add3,axiom,
! [X42,X97] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X97,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X42)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X97,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)))),X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__Suc__eq__mod__add3) ).
fof(fact_div__Suc__eq__div__add3,axiom,
! [X42,X97] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X97),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X42)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X97),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)))),X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__Suc__eq__div__add3) ).
fof(fact_trancl__Int__subset,axiom,
! [X54,X177,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X177),X54))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X10,X177)),X54)),X177)),X54))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X10,X177)),X54)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__Int__subset) ).
fof(fact_setprod__gen__delta,axiom,
! [X18,X38,X39,X216,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X216))
=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X39),X216))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),hAPP(hAPP(c_COMBC(X10,X13,X13),hAPP(hAPP(c_COMBS(X10,X13,tc_fun(X13,X13)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X13,tc_fun(X13,X13)),X10),c_If(X13)),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X39))),X38)),X18)),X216) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),hAPP(X38,X39)),hAPP(hAPP(c_Power_Opower__class_Opower(X13),X18),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X216)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X216))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),hAPP(hAPP(c_COMBC(X10,X13,X13),hAPP(hAPP(c_COMBS(X10,X13,tc_fun(X13,X13)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X13,tc_fun(X13,X13)),X10),c_If(X13)),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X39))),X38)),X18)),X216) = hAPP(hAPP(c_Power_Opower__class_Opower(X13),X18),hAPP(c_Finite__Set_Ocard(X10),X216)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__gen__delta) ).
fof(fact_setsum__delta,axiom,
! [X38,X39,X216,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X216))
=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X39),X216))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),hAPP(hAPP(c_COMBC(X10,X13,X13),hAPP(hAPP(c_COMBS(X10,X13,tc_fun(X13,X13)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X13,tc_fun(X13,X13)),X10),c_If(X13)),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X39))),X38)),c_Groups_Ozero__class_Ozero(X13))),X216) = hAPP(X38,X39) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X216))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),hAPP(hAPP(c_COMBC(X10,X13,X13),hAPP(hAPP(c_COMBS(X10,X13,tc_fun(X13,X13)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X13,tc_fun(X13,X13)),X10),c_If(X13)),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X39))),X38)),c_Groups_Ozero__class_Ozero(X13))),X216) = c_Groups_Ozero__class_Ozero(X13) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__delta) ).
fof(fact_setprod__delta,axiom,
! [X38,X39,X216,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X216))
=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X39),X216))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),hAPP(hAPP(c_COMBC(X10,X13,X13),hAPP(hAPP(c_COMBS(X10,X13,tc_fun(X13,X13)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X13,tc_fun(X13,X13)),X10),c_If(X13)),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X39))),X38)),c_Groups_Oone__class_Oone(X13))),X216) = hAPP(X38,X39) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X216))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),hAPP(hAPP(c_COMBC(X10,X13,X13),hAPP(hAPP(c_COMBS(X10,X13,tc_fun(X13,X13)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X13,tc_fun(X13,X13)),X10),c_If(X13)),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X39))),X38)),c_Groups_Oone__class_Oone(X13))),X216) = c_Groups_Oone__class_Oone(X13) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__delta) ).
fof(fact_le__Suc__number__of,axiom,
! [X168,X20] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)))
<=> 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(X168))),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),X20)),c_Int_Onat))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__number__of) ).
fof(fact_less__Suc__number__of,axiom,
! [X168,X20] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)))
<=> 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(X168))),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),X20)),c_Int_Onat))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__number__of) ).
fof(fact_apsnd__apfst__commute,axiom,
! [X166,X1,X195,X2,X10,X13,X125] : hAPP(c_Product__Type_Oapsnd(X125,X13,X10,X2),hAPP(c_Product__Type_Oapfst(X195,X10,X125,X1),X166)) = hAPP(c_Product__Type_Oapfst(X195,X10,X13,X1),hAPP(c_Product__Type_Oapsnd(X125,X13,X195,X2),X166)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apsnd__apfst__commute) ).
fof(fact_apfst__def,axiom,
! [X2,X13,X125,X10] : c_Product__Type_Oapfst(X10,X125,X13,X2) = c_Product__Type_Omap__pair(X10,X125,X13,X13,X2,c_Fun_Oid(X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apfst__def) ).
fof(fact_lexord__append__leftD,axiom,
! [X177,X168,X165,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Oappend(X10),X16),X165)),hAPP(hAPP(c_List_Oappend(X10),X16),X168))),c_List_Olexord(X10,X177)))
=> ( ! [X116] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X116),X116)),X177))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X165),X168)),c_List_Olexord(X10,X177))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__append__leftD) ).
fof(fact_rel__pow__E2,axiom,
! [X196,X20,X73,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X73)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X20),X196)))
=> ( ( X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> X16 != X73 )
=> ~ ! [X90,X122] :
( X20 = hAPP(c_Nat_OSuc,X122)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X90)),X196))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X90),X73)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X122),X196))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__E2) ).
fof(fact_map__comp__Some__iff,axiom,
! [X168,X101,X277,X278,X125,X10,X13] :
( c_Map_Omap__comp(X13,X10,X125,X278,X277,X101) = hAPP(c_Option_Ooption_OSome(X10),X168)
<=> ? [X288] :
( hAPP(X277,X101) = hAPP(c_Option_Ooption_OSome(X13),X288)
& hAPP(X278,X288) = hAPP(c_Option_Ooption_OSome(X10),X168) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__Some__iff) ).
fof(fact_map__comp__def,axiom,
! [X101,X1,X2,X125,X10,X13] : c_Map_Omap__comp(X13,X10,X125,X2,X1,X101) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X10),X13,c_Option_Ooption_ONone(X10),X2),hAPP(X1,X101)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__def) ).
fof(fact_dvd_OatLeastLessThan__empty__iff,axiom,
! [X38,X39] :
( 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)))),X39,X38) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
<=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X39),X38))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X38),X39)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastLessThan__empty__iff) ).
fof(fact_dvd_OgreaterThanAtMost__empty__iff,axiom,
! [X162,X101] :
( 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)))),X101,X162) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
<=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X101),X162))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X162),X101)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OgreaterThanAtMost__empty__iff) ).
fof(fact_dvd_OatLeastLessThan__empty__iff2,axiom,
! [X38,X39] :
( 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)))),X39,X38)
<=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X39),X38))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X38),X39)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastLessThan__empty__iff2) ).
fof(fact_dvd_OgreaterThanAtMost__empty__iff2,axiom,
! [X162,X101] :
( 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)))),X101,X162)
<=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X101),X162))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X162),X101)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OgreaterThanAtMost__empty__iff2) ).
fof(fact_dvd_Ostrict__monoD,axiom,
! [X25,X16,X2,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X10,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),X16),X25))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25),X16)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(X2,X16)),hAPP(X2,X25))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Ostrict__monoD) ).
fof(fact_power__odd__eq,axiom,
! [X42,X84,X94] :
( class_Groups_Omonoid__mult(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),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)))),X42))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),hAPP(hAPP(c_Power_Opower__class_Opower(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42)),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,
! [X77,X54,X39,X19,X48] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(X48,X19,X39)),X54),X77))
=> ~ ! [X67] :
( X77 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X67),hAPP(c_Natural_Ogetlocs,X54))),X48),hAPP(hAPP(c_Natural_Ogetlocs,X67),c_Com_ORes))
=> ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X19)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X54),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X39,X54))),X67)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I7_J) ).
fof(fact_apsnd__compose,axiom,
! [X16,X1,X195,X2,X10,X13,X125] : hAPP(c_Product__Type_Oapsnd(X125,X13,X10,X2),hAPP(c_Product__Type_Oapsnd(X195,X125,X10,X1),X16)) = hAPP(c_Product__Type_Oapsnd(X195,X13,X10,hAPP(c_Fun_Ocomp(X125,X13,X195,X2),X1)),X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apsnd__compose) ).
fof(fact_apfst__compose,axiom,
! [X16,X1,X195,X2,X13,X10,X125] : hAPP(c_Product__Type_Oapfst(X125,X10,X13,X2),hAPP(c_Product__Type_Oapfst(X195,X125,X13,X1),X16)) = hAPP(c_Product__Type_Oapfst(X195,X10,X13,hAPP(c_Fun_Ocomp(X125,X10,X195,X2),X1)),X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apfst__compose) ).
fof(fact_sum__power2__eq__zero__iff,axiom,
! [X25,X16,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X16),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(X10),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(X10)
<=> ( X16 = c_Groups_Ozero__class_Ozero(X10)
& X25 = c_Groups_Ozero__class_Ozero(X10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__power2__eq__zero__iff) ).
fof(fact_evaln__elim__cases_I3_J,axiom,
! [X53,X20,X54,X18,X39,X78] :
( c_Natural_Oevaln(c_Com_Ocom_OLocal(X78,X39,X18),X54,X20,X53)
=> ~ ! [X67] :
( X53 = hAPP(hAPP(hAPP(c_Natural_Oupdate,X67),c_Com_Ovname_OLoc(X78)),hAPP(hAPP(c_Natural_Ogetlocs,X54),X78))
=> ~ c_Natural_Oevaln(X18,hAPP(hAPP(hAPP(c_Natural_Oupdate,X54),c_Com_Ovname_OLoc(X78)),hAPP(X39,X54)),X20,X67) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I3_J) ).
fof(fact_transpose__rectangle,axiom,
! [X20,X10,X290] :
( ( X290 = c_List_Olist_ONil(tc_List_Olist(X10))
=> X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
=> ( ! [X152] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X152),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),X290)))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X10)),X290),X152)) = X20 )
=> c_List_Otranspose(X10,X290) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X10)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X10)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X10),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X10)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X10)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X10),hAPP(hAPP(c_COMBB(tc_List_Olist(X10),tc_fun(tc_Nat_Onat,X10),tc_Nat_Onat),c_List_Onth(X10)),hAPP(c_List_Onth(tc_List_Olist(X10)),X290))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),X290)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__rectangle) ).
fof(fact_negDivAlg_Opinduct,axiom,
! [X19,X51,X192] :
( 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),X192),X51)))
=> ( ! [X116,X193] :
( 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),X116),X193)))
=> ( ( ~ ( 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),X116),X193)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X193),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
=> hBOOL(hAPP(hAPP(X19,X116),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)))),X193))) )
=> hBOOL(hAPP(hAPP(X19,X116),X193)) ) )
=> hBOOL(hAPP(hAPP(X19,X192),X51)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg_Opinduct) ).
fof(fact_setsum__delta_H,axiom,
! [X38,X39,X216,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X216))
=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X39),X216))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),hAPP(hAPP(c_COMBC(X10,X13,X13),hAPP(hAPP(c_COMBS(X10,X13,tc_fun(X13,X13)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X13,tc_fun(X13,X13)),X10),c_If(X13)),hAPP(c_fequal,X39))),X38)),c_Groups_Ozero__class_Ozero(X13))),X216) = hAPP(X38,X39) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X216))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),hAPP(hAPP(c_COMBC(X10,X13,X13),hAPP(hAPP(c_COMBS(X10,X13,tc_fun(X13,X13)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X13,tc_fun(X13,X13)),X10),c_If(X13)),hAPP(c_fequal,X39))),X38)),c_Groups_Ozero__class_Ozero(X13))),X216) = c_Groups_Ozero__class_Ozero(X13) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__delta_H) ).
fof(fact_setprod__delta_H,axiom,
! [X38,X39,X216,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X216))
=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X39),X216))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),hAPP(hAPP(c_COMBC(X10,X13,X13),hAPP(hAPP(c_COMBS(X10,X13,tc_fun(X13,X13)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X13,tc_fun(X13,X13)),X10),c_If(X13)),hAPP(c_fequal,X39))),X38)),c_Groups_Oone__class_Oone(X13))),X216) = hAPP(X38,X39) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X216))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),hAPP(hAPP(c_COMBC(X10,X13,X13),hAPP(hAPP(c_COMBS(X10,X13,tc_fun(X13,X13)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X13,tc_fun(X13,X13)),X10),c_If(X13)),hAPP(c_fequal,X39))),X38)),c_Groups_Oone__class_Oone(X13))),X216) = c_Groups_Oone__class_Oone(X13) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__delta_H) ).
fof(fact_posDivAlg_Opinduct,axiom,
! [X19,X51,X192] :
( 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),X192),X51)))
=> ( ! [X116,X193] :
( 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),X116),X193)))
=> ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X116),X193))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X193),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
=> hBOOL(hAPP(hAPP(X19,X116),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)))),X193))) )
=> hBOOL(hAPP(hAPP(X19,X116),X193)) ) )
=> hBOOL(hAPP(hAPP(X19,X192),X51)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg_Opinduct) ).
fof(fact_listrel__Cons2,axiom,
! [X177,X289,X25,X290,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X290),hAPP(hAPP(c_List_Olist_OCons(X10),X25),X289))),c_List_Olistrel(X10,X177)))
=> ~ ! [X3,X303] :
( X290 = hAPP(hAPP(c_List_Olist_OCons(X10),X3),X303)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X25)),X177))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X303),X289)),c_List_Olistrel(X10,X177))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__Cons2) ).
fof(fact_rel__pow__Suc__E2,axiom,
! [X196,X20,X73,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X73)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),hAPP(c_Nat_OSuc,X20)),X196)))
=> ~ ! [X90] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X90)),X196))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X90),X73)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X20),X196))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__Suc__E2) ).
fof(fact_Nitpick_Otimes__frac__def,axiom,
! [X143,X149,X94] : c_Nitpick_Otimes__frac(X94,X149,X143) = hAPP(hAPP(c_Nitpick_Ofrac(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X94),X149)),hAPP(c_Nitpick_Onum(X94),X143))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(X94),X149)),hAPP(c_Nitpick_Odenom(X94),X143))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Otimes__frac__def) ).
fof(fact_rel__pow__E,axiom,
! [X196,X20,X73,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X73)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X20),X196)))
=> ( ( X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> X16 != X73 )
=> ~ ! [X90,X122] :
( X20 = hAPP(c_Nat_OSuc,X122)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X90)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X122),X196)))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X90),X73)),X196)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__E) ).
fof(fact_rel__pow__Suc__E,axiom,
! [X196,X20,X73,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X73)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),hAPP(c_Nat_OSuc,X20)),X196)))
=> ~ ! [X90] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X90)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X20),X196)))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X90),X73)),X196)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__Suc__E) ).
fof(fact_negDivAlg_Opsimps,axiom,
! [X38,X39] :
( 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),X39),X38)))
=> ( ( ( 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),X39),X38)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X38),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
=> c_Divides_OnegDivAlg(X39,X38) = 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),X39),X38)) )
& ( ~ ( 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),X39),X38)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X38),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
=> c_Divides_OnegDivAlg(X39,X38) = hAPP(c_Divides_Oadjust(X38),c_Divides_OnegDivAlg(X39,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)))),X38))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg_Opsimps) ).
fof(fact_posDivAlg_Opsimps,axiom,
! [X38,X39] :
( 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),X39),X38)))
=> ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X39),X38))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X38),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
=> c_Divides_OposDivAlg(X39,X38) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X39) )
& ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X39),X38))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X38),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
=> c_Divides_OposDivAlg(X39,X38) = hAPP(c_Divides_Oadjust(X38),c_Divides_OposDivAlg(X39,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)))),X38))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg_Opsimps) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
! [X42,X93,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),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)))),X42))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X93),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),X42)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),X42))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J) ).
fof(fact_arith__series__int,axiom,
! [X20,X141,X39] : 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),X39)),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))),X141))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X20))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X39),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X39),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),X20),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X141)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arith__series__int) ).
fof(fact_le__number__of__Suc,axiom,
! [X20,X168] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)),hAPP(c_Nat_OSuc,X20)))
<=> 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(X168))),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)),X20)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__number__of__Suc) ).
fof(fact_less__number__of__Suc,axiom,
! [X20,X168] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)),hAPP(c_Nat_OSuc,X20)))
<=> 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(X168))),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)),X20)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__number__of__Suc) ).
fof(fact_of__nat__double,axiom,
! [X93,X94] :
( class_Rings_Osemiring__1(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X93))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),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)))),X93))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),hAPP(c_Int_Onat,X93))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),hAPP(c_Int_Onat,X93))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__double) ).
fof(fact_negDivAlg_Osimps,axiom,
! [X92,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),X84),X92)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X92),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
=> c_Divides_OnegDivAlg(X84,X92) = 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),X84),X92)) )
& ( ~ ( 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),X84),X92)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X92),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
=> c_Divides_OnegDivAlg(X84,X92) = hAPP(c_Divides_Oadjust(X92),c_Divides_OnegDivAlg(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)))),X92))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg_Osimps) ).
fof(fact_posDivAlg_Osimps,axiom,
! [X92,X84] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),X92))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X92),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
=> c_Divides_OposDivAlg(X84,X92) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84) )
& ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),X92))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X92),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
=> c_Divides_OposDivAlg(X84,X92) = hAPP(c_Divides_Oadjust(X92),c_Divides_OposDivAlg(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)))),X92))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg_Osimps) ).
fof(fact_power__minus1__odd,axiom,
! [X42,X94] :
( class_Rings_Oring__1(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),c_Groups_Oone__class_Oone(X94))),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)))),X42))) = hAPP(c_Groups_Ouminus__class_Ouminus(X94),c_Groups_Oone__class_Oone(X94)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__minus1__odd) ).
fof(fact_power__minus__even,axiom,
! [X42,X84,X94] :
( class_Rings_Oring__1(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X84)),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)))),X42)) = hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),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)))),X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__minus__even) ).
fof(fact_power__m1__odd,axiom,
! [X42,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),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)))),X42))) = hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OMin) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__m1__odd) ).
fof(fact_Suc3__eq__add__3,axiom,
! [X42] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X42))) = 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)))),X42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc3__eq__add__3) ).
fof(fact_ImageE,axiom,
! [X154,X177,X13,X38,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X38),hAPP(c_Relation_OImage(X13,X10,X177),X154)))
=> ~ ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X13,X10)),hAPP(hAPP(c_Product__Type_OPair(X13,X10),X3),X38)),X177))
=> ~ hBOOL(hAPP(hAPP(c_member(X13),X3),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ImageE) ).
fof(fact_nat__case__add__eq__if,axiom,
! [X20,X168,X2,X39,X10] : c_Nat_Onat_Onat__case(X10,X39,X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)),X20)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X10),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X168))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X10,X10),hAPP(hAPP(c_COMBC(tc_Int_Oint,X10,tc_fun(X10,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_fun(X10,X10)),tc_Int_Oint),c_If(X10)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(X10,X39,X2,X20))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,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)),X20)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__add__eq__if) ).
fof(fact_mod2__gr__0,axiom,
! [X102] :
( 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,X102,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,X102,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,X16,X2,X10,X13,X125] :
( hAPP(c_Product__Type_Oapsnd(X125,X13,X10,X2),X16) = hAPP(c_Product__Type_Oapsnd(X125,X13,X10,X1),X16)
<=> hAPP(X2,hAPP(c_Product__Type_Osnd(X10,X125),X16)) = hAPP(X1,hAPP(c_Product__Type_Osnd(X10,X125),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apsnd__eq__conv) ).
fof(fact_apfst__eq__conv,axiom,
! [X1,X16,X2,X13,X10,X125] :
( hAPP(c_Product__Type_Oapfst(X125,X10,X13,X2),X16) = hAPP(c_Product__Type_Oapfst(X125,X10,X13,X1),X16)
<=> hAPP(X2,hAPP(c_Product__Type_Ofst(X125,X13),X16)) = hAPP(X1,hAPP(c_Product__Type_Ofst(X125,X13),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apfst__eq__conv) ).
fof(fact_Id__def,axiom,
! [X10] : c_Relation_OId(X10) = hAPP(c_Set_OCollect(tc_prod(X10,X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X10,X10)),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBC(tc_prod(X10,X10),tc_fun(X10,tc_prod(X10,X10)),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_fun(X10,tc_prod(X10,X10)),tc_fun(X10,tc_HOL_Obool)),tc_prod(X10,X10)),c_COMBB(tc_prod(X10,X10),tc_HOL_Obool,X10)),c_fequal)),hAPP(hAPP(c_COMBS(X10,X10,tc_prod(X10,X10)),c_Product__Type_OPair(X10,X10)),c_COMBI(X10))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__def) ).
fof(fact_apsnd__apfst,axiom,
! [X16,X1,X195,X2,X10,X13,X125] : hAPP(c_Product__Type_Oapsnd(X125,X13,X10,X2),hAPP(c_Product__Type_Oapfst(X195,X10,X125,X1),X16)) = hAPP(hAPP(c_Product__Type_OPair(X10,X13),hAPP(X1,hAPP(c_Product__Type_Ofst(X195,X125),X16))),hAPP(X2,hAPP(c_Product__Type_Osnd(X195,X125),X16))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apsnd__apfst) ).
fof(fact_apfst__apsnd,axiom,
! [X16,X1,X195,X2,X13,X10,X125] : hAPP(c_Product__Type_Oapfst(X125,X10,X13,X2),hAPP(c_Product__Type_Oapsnd(X195,X13,X125,X1),X16)) = hAPP(hAPP(c_Product__Type_OPair(X10,X13),hAPP(X2,hAPP(c_Product__Type_Ofst(X125,X195),X16))),hAPP(X1,hAPP(c_Product__Type_Osnd(X125,X195),X16))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apfst__apsnd) ).
fof(fact_dvd_Ostrict__monoI,axiom,
! [X2,X10] :
( class_Orderings_Oorder(X10)
=> ( ! [X3,X90] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X90))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X90),X3)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(X2,X3)),hAPP(X2,X90))) )
=> c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X10,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,
! [X177,X10] :
( ( class_Fields_Olinordered__field__inverse__zero(X10)
& class_Int_Onumber__ring(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X177),hAPP(c_Int_Onumber__class_Onumber__of(X10),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X177)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_half__gt__zero__iff) ).
fof(fact_max__Suc__number__of,axiom,
! [X20,X168] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)),hAPP(c_Nat_OSuc,X20)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X168))),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,X20))),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)),X20)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__Suc__number__of) ).
fof(fact_zero__less__power2,axiom,
! [X39,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X39),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
<=> X39 != c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__power2) ).
fof(fact_min__Suc__number__of,axiom,
! [X20,X168] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)),hAPP(c_Nat_OSuc,X20)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X168))),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)),X20)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__Suc__number__of) ).
fof(fact_nat__rec__number__of,axiom,
! [X168,X2,X39,X10] : hAPP(c_Nat_Onat_Onat__rec(X10,X39,X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X10),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X168))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X10,X10),hAPP(hAPP(c_COMBC(tc_Int_Oint,X10,tc_fun(X10,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_fun(X10,X10)),tc_Int_Oint),c_If(X10)),c_Nat__Numeral_Oneg)),X39)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X10,X10),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X10,X10),tc_Int_Oint),X2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,tc_Int_Oint),c_Nat_Onat_Onat__rec(X10,X39,X2)),c_Int_Onat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__rec__number__of) ).
fof(fact_transpose__aux__filter__head,axiom,
! [X328,X10] : c_List_Oconcat(X10,hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_Olist__case(tc_List_Olist(X10),X10,c_List_Olist_ONil(X10),hAPP(hAPP(c_COMBB(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_List_Olist(X10)),X10),c_COMBK(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_COMBC(X10,tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_OCons(X10)),c_List_Olist_ONil(X10))))),X328)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),X10),c_List_Ohd(X10)),hAPP(c_List_Ofilter(tc_List_Olist(X10),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X10)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_List_Olist(X10),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X10)))),X328)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__aux__filter__head) ).
fof(fact_transpose__aux__filter__tail,axiom,
! [X328,X10] : c_List_Oconcat(tc_List_Olist(X10),hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_List_Olist(tc_List_Olist(X10))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X10)),X10,c_List_Olist_ONil(tc_List_Olist(X10)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X10),tc_List_Olist(tc_List_Olist(X10))),X10),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_List_Olist(tc_List_Olist(X10)),tc_List_Olist(tc_List_Olist(X10))),c_List_Olist_OCons(tc_List_Olist(X10))),c_List_Olist_ONil(tc_List_Olist(X10)))))),X328)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Otl(X10)),hAPP(c_List_Ofilter(tc_List_Olist(X10),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X10)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_List_Olist(X10),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X10)))),X328)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__aux__filter__tail) ).
fof(fact_rtrancl__Int__subset,axiom,
! [X177,X54,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Relation_OId(X10)),X54))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X10,X177)),X54)),X177)),X54))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X10,X177)),X54)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Int__subset) ).
fof(fact_listrel__Cons1,axiom,
! [X177,X290,X289,X25,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X25),X289)),X290)),c_List_Olistrel(X10,X177)))
=> ~ ! [X90,X304] :
( X290 = hAPP(hAPP(c_List_Olist_OCons(X10),X90),X304)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X25),X90)),X177))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X289),X304)),c_List_Olistrel(X10,X177))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__Cons1) ).
fof(fact_power__even__eq,axiom,
! [X42,X84,X94] :
( class_Groups_Omonoid__mult(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),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)))),X42)) = hAPP(hAPP(c_Power_Opower__class_Opower(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42)),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,
! [X154,X290,X10] : c_List_Osublist(X10,X290,X154) = hAPP(hAPP(c_List_Omap(tc_prod(X10,tc_Nat_Onat),X10),c_Product__Type_Ofst(X10,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X10,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X10,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(X10,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X10,tc_Nat_Onat))),X154)),hAPP(hAPP(c_List_Ozip(X10,tc_Nat_Onat),X290),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__def) ).
fof(fact_fold1Set_Oequations,axiom,
! [X50,X52,X51,X2,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X10,X2,hAPP(hAPP(c_Set_Oinsert(X10),X51),X52)),X50))
<=> ? [X116,X246] :
( hAPP(hAPP(c_Set_Oinsert(X10),X51),X52) = hAPP(hAPP(c_Set_Oinsert(X10),X116),X246)
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X10,X2,X116,X246),X50))
& ~ hBOOL(hAPP(hAPP(c_member(X10),X116),X246)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1Set_Oequations) ).
fof(fact_Nitpick_Ouminus__frac__def,axiom,
! [X149,X94] : c_Nitpick_Ouminus__frac(X94,X149) = c_Nitpick_OAbs__Frac(X94,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(X94),X149))),hAPP(c_Nitpick_Odenom(X94),X149))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Ouminus__frac__def) ).
fof(fact_snd__apsnd,axiom,
! [X16,X2,X125,X10,X13] : hAPP(c_Product__Type_Osnd(X13,X10),hAPP(c_Product__Type_Oapsnd(X125,X10,X13,X2),X16)) = hAPP(X2,hAPP(c_Product__Type_Osnd(X13,X125),X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__apsnd) ).
fof(fact_fst__apfst,axiom,
! [X16,X2,X125,X13,X10] : hAPP(c_Product__Type_Ofst(X10,X13),hAPP(c_Product__Type_Oapfst(X125,X10,X13,X2),X16)) = hAPP(X2,hAPP(c_Product__Type_Ofst(X125,X13),X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__apfst) ).
fof(fact_fst__apsnd,axiom,
! [X16,X2,X125,X13,X10] : hAPP(c_Product__Type_Ofst(X10,X13),hAPP(c_Product__Type_Oapsnd(X125,X13,X10,X2),X16)) = hAPP(c_Product__Type_Ofst(X10,X125),X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__apsnd) ).
fof(fact_snd__apfst,axiom,
! [X16,X2,X125,X10,X13] : hAPP(c_Product__Type_Osnd(X13,X10),hAPP(c_Product__Type_Oapfst(X125,X13,X10,X2),X16)) = hAPP(c_Product__Type_Osnd(X125,X10),X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__apfst) ).
fof(fact_small_H_Opinduct,axiom,
! [X19,X52,X51,X192] :
( 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)),X192),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X51),X52))))
=> ( ! [X247,X164,X152] :
( 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)),X247),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X164),X152))))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X164),X152))
=> ( hAPP(X247,X152) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
=> hBOOL(hAPP(hAPP(hAPP(X19,X247),X164),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X152),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) )
=> hBOOL(hAPP(hAPP(hAPP(X19,X247),X164),X152)) ) )
=> hBOOL(hAPP(hAPP(hAPP(X19,X192),X51),X52)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_small_H_Opinduct) ).
fof(fact_nat__case__number__of,axiom,
! [X168,X2,X39,X10] : c_Nat_Onat_Onat__case(X10,X39,X2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X10),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X168))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X10,X10),hAPP(hAPP(c_COMBC(tc_Int_Oint,X10,tc_fun(X10,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_fun(X10,X10)),tc_Int_Oint),c_If(X10)),c_Nat__Numeral_Oneg)),X39)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,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,
! [X168,X20] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X168))),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,X20))),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),X20)),c_Int_Onat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__number__of__Suc) ).
fof(fact_min__number__of__Suc,axiom,
! [X168,X20] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X168))),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),X20)),c_Int_Onat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__number__of__Suc) ).
fof(fact_Suc__n__div__2__gt__zero,axiom,
! [X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X42))
=> 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),X42),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,
! [X143,X94] :
( ( class_Fields_Olinordered__field__inverse__zero(X94)
& class_Int_Onumber__ring(X94) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X143))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X143),hAPP(c_Int_Onumber__class_Onumber__of(X94),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,
! [X42,X93,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),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)))),X42)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),X42)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
fof(fact_div__2__gt__zero,axiom,
! [X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X42))
=> 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),X42),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,
! [X84,X94] :
( class_Groups_Omonoid__mult(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),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(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X84)),X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power3__eq__cube) ).
fof(fact_zero__le__power2,axiom,
! [X84,X94] :
( class_Rings_Olinordered__idom(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),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,
! [X42,X94] :
( class_Rings_Oring__1(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),c_Groups_Oone__class_Oone(X94))),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)))),X42)) = c_Groups_Oone__class_Oone(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__minus1__even) ).
fof(fact_power__m1__even,axiom,
! [X42,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),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)))),X42)) = c_Groups_Oone__class_Oone(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__m1__even) ).
fof(fact_diff__nat__number__of,axiom,
! [X168,X174] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X174),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X174)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X174),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X174)) = 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),X168),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X174)))),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,
! [X73,X146] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X146))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X73)),hAPP(c_Int_Onat,X146)) = hAPP(c_Int_Onat,X73) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X146))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X73)),hAPP(c_Int_Onat,X146)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X73),X146)),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,
! [X39,X16,X154,X38,X10] :
( class_Groups_Oab__semigroup__mult(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X10,c_Groups_Otimes__class_Otimes(X10),X38,X154),X16))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X38),X154))
=> hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X10,c_Groups_Otimes__class_Otimes(X10),X39,hAPP(hAPP(c_Set_Oinsert(X10),X38),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))),X16)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph__permute__diff) ).
fof(fact_concat__map__singleton,axiom,
! [X290,X2,X13,X10] : c_List_Oconcat(X10,hAPP(hAPP(c_List_Omap(X13,tc_List_Olist(X10)),hAPP(hAPP(c_COMBC(X13,tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_COMBB(X10,tc_fun(tc_List_Olist(X10),tc_List_Olist(X10)),X13),c_List_Olist_OCons(X10)),X2)),c_List_Olist_ONil(X10))),X290)) = hAPP(hAPP(c_List_Omap(X13,X10),X2),X290),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__map__singleton) ).
fof(fact_Nitpick_Oless__eq__frac__def,axiom,
! [X177,X158,X10] :
( c_Nitpick_Oless__eq__frac(X10,X158,X177)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X10),c_Nitpick_Oplus__frac(X10,X158,c_Nitpick_Ouminus__frac(X10,X177)))),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,
! [X177,X158,X10] :
( c_Nitpick_Oless__frac(X10,X158,X177)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X10),c_Nitpick_Oplus__frac(X10,X158,c_Nitpick_Ouminus__frac(X10,X177)))),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,
! [X105,X93,X94] :
( class_Rings_Olinordered__semidom(X94)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),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(X94),X105),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(X94),c_Groups_Ozero__class_Ozero(X94)),X93))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X105))
=> X93 = X105 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__eq__imp__eq) ).
fof(fact_less__2__cases,axiom,
! [X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
=> ( X42 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X42 = 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,
! [X97] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X97))),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),X97),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,
! [X84,X94] :
( class_Rings_Olinordered__idom(X94)
=> hAPP(c_Groups_Oabs__class_Oabs(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),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(X94),X84),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,
! [X149,X94,X10] :
( ( class_Rings_Oinverse(X10)
& class_Rings_Oring__1(X10) )
=> c_Nitpick_Oof__frac(X94,X10,X149) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),hAPP(c_Int_Oring__1__class_Oof__int(X10),hAPP(c_Nitpick_Onum(X94),X149))),hAPP(c_Int_Oring__1__class_Oof__int(X10),hAPP(c_Nitpick_Odenom(X94),X149))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Oof__frac__def) ).
fof(fact_converseE,axiom,
! [X177,X276,X13,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),X276),hAPP(c_Relation_Oconverse(X13,X10),X177)))
=> ~ ! [X3,X90] :
( X276 = hAPP(hAPP(c_Product__Type_OPair(X10,X13),X90),X3)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X13,X10)),hAPP(hAPP(c_Product__Type_OPair(X13,X10),X3),X90)),X177)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converseE) ).
fof(fact_setsum__natinterval__difff,axiom,
! [X2,X20,X102,X10] :
( class_Groups_Oab__group__add(X10)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X10)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,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,X102,X20)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),hAPP(X2,X102)),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X10)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,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,X102,X20)) = c_Groups_Ozero__class_Ozero(X10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__natinterval__difff) ).
fof(fact_map__upd__upds__conv__if,axiom,
! [X25,X2,X290,X289,X13,X16,X10] :
( ( hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Otake(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13)),X289)),X290))))
=> c_Map_Omap__upds(X10,X13,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),X2),X16),hAPP(c_Option_Ooption_OSome(X13),X25)),X290,X289) = c_Map_Omap__upds(X10,X13,X2,X290,X289) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Otake(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13)),X289)),X290))))
=> c_Map_Omap__upds(X10,X13,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),X2),X16),hAPP(c_Option_Ooption_OSome(X13),X25)),X290,X289) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),c_Map_Omap__upds(X10,X13,X2,X290,X289)),X16),hAPP(c_Option_Ooption_OSome(X13),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upd__upds__conv__if) ).
fof(fact_fold__graph__insert__swap,axiom,
! [X73,X25,X154,X38,X10] :
( class_Groups_Oab__semigroup__mult(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X10,c_Groups_Otimes__class_Otimes(X10),X38,X154),X25))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X38),X154))
=> hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X10,c_Groups_Otimes__class_Otimes(X10),X73,hAPP(hAPP(c_Set_Oinsert(X10),X38),X154)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X73),X25))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph__insert__swap) ).
fof(fact_fold__graph_OinsertI,axiom,
! [X25,X73,X2,X13,X154,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X13,X2,X73,X154),X25))
=> hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X13,X2,X73,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)),hAPP(hAPP(X2,X16),X25))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_OinsertI) ).
fof(fact_map__comp__None__iff,axiom,
! [X101,X277,X278,X125,X10,X13] :
( c_Map_Omap__comp(X13,X10,X125,X278,X277,X101) = c_Option_Ooption_ONone(X10)
<=> ( hAPP(X277,X101) = c_Option_Ooption_ONone(X13)
| ? [X288] :
( hAPP(X277,X101) = hAPP(c_Option_Ooption_OSome(X13),X288)
& hAPP(X278,X288) = c_Option_Ooption_ONone(X10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__None__iff) ).
fof(fact_tranclD,axiom,
! [X196,X25,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),c_Transitive__Closure_Otrancl(X10,X196)))
=> ? [X159] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X159)),X196))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X159),X25)),c_Transitive__Closure_Ortrancl(X10,X196))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tranclD) ).
fof(fact_tranclD2,axiom,
! [X196,X25,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),c_Transitive__Closure_Otrancl(X10,X196)))
=> ? [X159] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X159)),c_Transitive__Closure_Ortrancl(X10,X196)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X159),X25)),X196)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tranclD2) ).
fof(fact_apfst__conv,axiom,
! [X25,X16,X2,X13,X10,X125] : hAPP(c_Product__Type_Oapfst(X125,X10,X13,X2),hAPP(hAPP(c_Product__Type_OPair(X125,X13),X16),X25)) = hAPP(hAPP(c_Product__Type_OPair(X10,X13),hAPP(X2,X16)),X25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apfst__conv) ).
fof(fact_apsnd__conv,axiom,
! [X25,X16,X2,X10,X13,X125] : hAPP(c_Product__Type_Oapsnd(X125,X13,X10,X2),hAPP(hAPP(c_Product__Type_OPair(X10,X125),X16),X25)) = hAPP(hAPP(c_Product__Type_OPair(X10,X13),X16),hAPP(X2,X25)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apsnd__conv) ).
fof(fact_bset_I10_J,axiom,
! [X53,X160,X197,X141] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X141),X197))
=> ! [X3] :
( ! [X227] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X227),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X197)))
=> ! [X249] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X249),X160))
=> X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X249),X227) ) )
=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X141),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X53)))
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X141),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X197)),X53))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I10_J) ).
fof(fact_aset_I10_J,axiom,
! [X53,X154,X197,X141] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X141),X197))
=> ! [X3] :
( ! [X227] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X227),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X197)))
=> ! [X249] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X249),X154))
=> X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X249),X227) ) )
=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X141),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X53)))
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X141),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X197)),X53))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I10_J) ).
fof(fact_map__upds__twist,axiom,
! [X313,X38,X102,X13,X312,X39,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),hAPP(c_List_Oset(X10),X312)))
=> c_Map_Omap__upds(X10,X13,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),X102),X39),hAPP(c_Option_Ooption_OSome(X13),X38)),X312,X313) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),c_Map_Omap__upds(X10,X13,X102,X312,X313)),X39),hAPP(c_Option_Ooption_OSome(X13),X38)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upds__twist) ).
fof(fact_evalc__elim__cases_I3_J,axiom,
! [X53,X54,X18,X39,X78] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(X78,X39,X18)),X54),X53))
=> ~ ! [X67] :
( X53 = hAPP(hAPP(hAPP(c_Natural_Oupdate,X67),c_Com_Ovname_OLoc(X78)),hAPP(hAPP(c_Natural_Ogetlocs,X54),X78))
=> ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X18),hAPP(hAPP(hAPP(c_Natural_Oupdate,X54),c_Com_Ovname_OLoc(X78)),hAPP(X39,X54))),X67)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I3_J) ).
fof(fact_transpose__max__length,axiom,
! [X290,X10] : c_List_Ofoldr(tc_List_Olist(X10),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X10)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X10))),c_List_Otranspose(X10,X290),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),hAPP(c_List_Ofilter(tc_List_Olist(X10),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X10)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_List_Olist(X10),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X10)))),X290)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__max__length) ).
fof(fact_zmod__number__of__Bit0,axiom,
! [X133,X144] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X133))) = 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),X144),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__number__of__Bit0) ).
fof(fact_power2__abs,axiom,
! [X84,X94] :
( class_Rings_Olinordered__idom(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),X84)),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(X94),X84),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,
! [X84,X94] :
( class_Rings_Oring__1(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X84)),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(X94),X84),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,
! [X97] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X97)),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,X97,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,
! [X19,X154,X225,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X225))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X225),X154))
=> ( hBOOL(hAPP(X19,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))
=> ( ! [X116,X251] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X251))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X116),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X116),X251))
=> ( hBOOL(hAPP(X19,X251))
=> hBOOL(hAPP(X19,hAPP(hAPP(c_Set_Oinsert(X10),X116),X251))) ) ) ) )
=> hBOOL(hAPP(X19,X225)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__subset__induct) ).
fof(fact_mult__2,axiom,
! [X104,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X104) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X104),X104) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__2) ).
fof(fact_nat__mult__2,axiom,
! [X104] : 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)))),X104) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X104),X104),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__2) ).
fof(fact_add__2__eq__Suc,axiom,
! [X42] : 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)))),X42) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__2__eq__Suc) ).
fof(fact_folding__image__simple_Oinsert,axiom,
! [X16,X154,X225,X1,X73,X2,X13,X10] :
( c_Finite__Set_Ofolding__image__simple(X10,X13,X2,X73,X1,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X13),X16),X154))
=> hAPP(X225,hAPP(hAPP(c_Set_Oinsert(X13),X16),X154)) = hAPP(hAPP(X2,hAPP(X1,X16)),hAPP(X225,X154)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oinsert) ).
fof(fact_RangeE,axiom,
! [X177,X13,X38,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X38),hAPP(c_Relation_ORange(X13,X10),X177)))
=> ~ ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X13,X10)),hAPP(hAPP(c_Product__Type_OPair(X13,X10),X3),X38)),X177)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeE) ).
fof(fact_trancl__trans,axiom,
! [X18,X177,X38,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),c_Transitive__Closure_Otrancl(X10,X177)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X38),X18)),c_Transitive__Closure_Otrancl(X10,X177)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X18)),c_Transitive__Closure_Otrancl(X10,X177))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__trans) ).
fof(fact_trancl__converseI,axiom,
! [X177,X25,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),hAPP(c_Relation_Oconverse(X10,X10),c_Transitive__Closure_Otrancl(X10,X177))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),c_Transitive__Closure_Otrancl(X10,hAPP(c_Relation_Oconverse(X10,X10),X177)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__converseI) ).
fof(fact_trancl__converseD,axiom,
! [X177,X25,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),c_Transitive__Closure_Otrancl(X10,hAPP(c_Relation_Oconverse(X10,X10),X177))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),hAPP(c_Relation_Oconverse(X10,X10),c_Transitive__Closure_Otrancl(X10,X177)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__converseD) ).
fof(fact_restrict__fun__upd,axiom,
! [X25,X102,X13,X197,X16,X10] :
( ( hBOOL(hAPP(hAPP(c_member(X10),X16),X197))
=> c_Map_Orestrict__map(X10,X13,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),X102),X16),X25),X197) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),c_Map_Orestrict__map(X10,X13,X102,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X197),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))),X16),X25) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X197))
=> c_Map_Orestrict__map(X10,X13,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),X102),X16),X25),X197) = c_Map_Orestrict__map(X10,X13,X102,X197) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__fun__upd) ).
fof(fact_fold1Set_Ointros,axiom,
! [X16,X154,X39,X2,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X10,X2,X39,X154),X16))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hBOOL(hAPP(c_Finite__Set_Ofold1Set(X10,X2,hAPP(hAPP(c_Set_Oinsert(X10),X39),X154)),X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1Set_Ointros) ).
fof(fact_power2__eq__1__iff,axiom,
! [X39,X10] :
( class_Rings_Oring__1__no__zero__divisors(X10)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X10),X39),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X10)
<=> ( X39 = c_Groups_Oone__class_Oone(X10)
| X39 = hAPP(c_Groups_Ouminus__class_Ouminus(X10),c_Groups_Oone__class_Oone(X10)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__eq__1__iff) ).
fof(fact_zero__eq__power2,axiom,
! [X39,X10] :
( class_Rings_Oring__1__no__zero__divisors(X10)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X10),X39),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X10)
<=> X39 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__eq__power2) ).
fof(fact_map__of__zip__upd,axiom,
! [X73,X25,X16,X299,X290,X13,X289,X10] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X289) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13)),X290)
=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X299) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13)),X290)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X13),X16),hAPP(c_List_Oset(X13),X290)))
=> ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X13,tc_Option_Ooption(X10)),c_Map_Omap__of(X13,X10,hAPP(hAPP(c_List_Ozip(X13,X10),X290),X289))),X16),hAPP(c_Option_Ooption_OSome(X10),X25)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X13,tc_Option_Ooption(X10)),c_Map_Omap__of(X13,X10,hAPP(hAPP(c_List_Ozip(X13,X10),X290),X299))),X16),hAPP(c_Option_Ooption_OSome(X10),X73))
=> c_Map_Omap__of(X13,X10,hAPP(hAPP(c_List_Ozip(X13,X10),X290),X289)) = c_Map_Omap__of(X13,X10,hAPP(hAPP(c_List_Ozip(X13,X10),X290),X299)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__zip__upd) ).
fof(fact_rotate__rev,axiom,
! [X297,X42,X94] : hAPP(c_List_Orotate(X94,X42),hAPP(c_List_Orev(X94),X297)) = hAPP(c_List_Orev(X94),hAPP(c_List_Orotate(X94,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X42,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)))),X297)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__rev) ).
fof(fact_rotate__def,axiom,
! [X20,X10] : c_List_Orotate(X10,X20) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X10),tc_List_Olist(X10)),X20),c_List_Orotate1(X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__def) ).
fof(fact_rtrancl__trancl__trancl,axiom,
! [X73,X177,X25,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),c_Transitive__Closure_Ortrancl(X10,X177)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X25),X73)),c_Transitive__Closure_Otrancl(X10,X177)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X73)),c_Transitive__Closure_Otrancl(X10,X177))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__trancl__trancl) ).
fof(fact_trancl__rtrancl__trancl,axiom,
! [X18,X177,X38,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),c_Transitive__Closure_Otrancl(X10,X177)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X38),X18)),c_Transitive__Closure_Ortrancl(X10,X177)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X18)),c_Transitive__Closure_Otrancl(X10,X177))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__rtrancl__trancl) ).
fof(fact_trancl__into__trancl2,axiom,
! [X18,X177,X38,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),X177))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X38),X18)),c_Transitive__Closure_Otrancl(X10,X177)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X18)),c_Transitive__Closure_Otrancl(X10,X177))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__into__trancl2) ).
fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
! [X18,X177,X38,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),c_Transitive__Closure_Otrancl(X10,X177)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X38),X18)),X177))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X18)),c_Transitive__Closure_Otrancl(X10,X177))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Transitive__Closure_Otrancl__into__trancl) ).
fof(fact_Collect__conv__if,axiom,
! [X10,X39,X19] :
( ( hBOOL(hAPP(X19,X39))
=> hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X39))),X19)) = hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) )
& ( ~ hBOOL(hAPP(X19,X39))
=> hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X39))),X19)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__conv__if) ).
fof(fact_foldr__map,axiom,
! [X39,X290,X2,X125,X1,X10,X13] : c_List_Ofoldr(X13,X10,X1,hAPP(hAPP(c_List_Omap(X125,X13),X2),X290),X39) = c_List_Ofoldr(X125,X10,hAPP(c_Fun_Ocomp(X13,tc_fun(X10,X10),X125,X1),X2),X290,X39),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldr__map) ).
fof(fact_trancl__subset__Sigma,axiom,
! [X154,X177,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X177),hAPP(hAPP(c_Product__Type_OSigma(X10,X10),X154),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X10),X154))))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X10,X177)),hAPP(hAPP(c_Product__Type_OSigma(X10,X10),X154),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X10),X154)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__subset__Sigma) ).
fof(fact_norm__frac_Opsimps,axiom,
! [X38,X39] :
( 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),X39),X38)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X38),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> c_Nitpick_Onorm__frac(X39,X38) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X39),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X38),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( ( ( X39 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X38 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
=> c_Nitpick_Onorm__frac(X39,X38) = 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)) )
& ( ~ ( X39 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X38 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
=> c_Nitpick_Onorm__frac(X39,X38) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X39),X38)),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),X39))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X38))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__frac_Opsimps) ).
fof(fact_foldr__append,axiom,
! [X39,X289,X290,X2,X10,X13] : c_List_Ofoldr(X13,X10,X2,hAPP(hAPP(c_List_Oappend(X13),X290),X289),X39) = c_List_Ofoldr(X13,X10,X2,X290,c_List_Ofoldr(X13,X10,X2,X289,X39)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldr__append) ).
fof(fact_psubset__insert__iff,axiom,
! [X160,X16,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),X160)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X16),X160))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X154),X160)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X160))
=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),X160)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__insert__iff) ).
fof(fact_lexord__irreflexive,axiom,
! [X25,X177,X10] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X3)),X177))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X25),X25)),c_List_Olexord(X10,X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__irreflexive) ).
fof(fact_diff__bin__simps_I8_J,axiom,
! [X121,X103] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X103)),c_Int_OBit1(X121)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(X103)),X121)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I8_J) ).
fof(fact_inj__on__insert,axiom,
! [X154,X39,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,hAPP(hAPP(c_Set_Oinsert(X10),X39),X154))
<=> ( c_Fun_Oinj__on(X10,X13,X2,X154)
& ~ hBOOL(hAPP(hAPP(c_member(X13),hAPP(X2,X39)),hAPP(c_Set_Oimage(X10,X13,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__insert) ).
fof(fact_apfst__id,axiom,
! [X13,X10] : c_Product__Type_Oapfst(X10,X10,X13,c_Fun_Oid(X10)) = c_Fun_Oid(tc_prod(X10,X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apfst__id) ).
fof(fact_apsnd__id,axiom,
! [X10,X13] : c_Product__Type_Oapsnd(X13,X13,X10,c_Fun_Oid(X13)) = c_Fun_Oid(tc_prod(X10,X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apsnd__id) ).
fof(fact_trancl__reflcl,axiom,
! [X177,X10] : c_Transitive__Closure_Otrancl(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X177),c_Relation_OId(X10))) = c_Transitive__Closure_Ortrancl(X10,X177),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__reflcl) ).
fof(fact_subset__insert__iff,axiom,
! [X160,X16,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),X160)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),X160)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insert__iff) ).
fof(fact_eq__special_I4_J,axiom,
! [X16,X10] :
( class_Int_Onumber__ring(X10)
=> ( hAPP(c_Int_Onumber__class_Onumber__of(X10),X16) = c_Groups_Oone__class_Oone(X10)
<=> c_Int_Oiszero(X10,hAPP(c_Int_Onumber__class_Onumber__of(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16),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,
! [X25,X10] :
( class_Int_Onumber__ring(X10)
=> ( c_Groups_Oone__class_Oone(X10) = hAPP(c_Int_Onumber__class_Onumber__of(X10),X25)
<=> c_Int_Oiszero(X10,hAPP(c_Int_Onumber__class_Onumber__of(X10),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),X25)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__special_I2_J) ).
fof(fact_small_H_Opsimps,axiom,
! [X113,X141,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),X141),X113))))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X141),X113))
=> c_Smallcheck_Osmall_H(X2,X141,X113) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X141),X113))
=> c_Smallcheck_Osmall_H(X2,X141,X113) = 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,X141,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X113),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(X2,X113)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_small_H_Opsimps) ).
fof(fact_norm__frac_Osimps,axiom,
! [X39,X38] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X38),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> c_Nitpick_Onorm__frac(X39,X38) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X39),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X38),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( ( ( X39 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X38 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
=> c_Nitpick_Onorm__frac(X39,X38) = 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)) )
& ( ~ ( X39 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X38 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
=> c_Nitpick_Onorm__frac(X39,X38) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X39),X38)),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),X39))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X38))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__frac_Osimps) ).
fof(fact_rtrancl__into__trancl2,axiom,
! [X18,X177,X38,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),X177))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X38),X18)),c_Transitive__Closure_Ortrancl(X10,X177)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X18)),c_Transitive__Closure_Otrancl(X10,X177))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__into__trancl2) ).
fof(fact_rtrancl__into__trancl1,axiom,
! [X18,X177,X38,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),c_Transitive__Closure_Ortrancl(X10,X177)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X38),X18)),X177))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X18)),c_Transitive__Closure_Otrancl(X10,X177))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__into__trancl1) ).
fof(fact_power2__eq__square__number__of,axiom,
! [X133,X10] :
( ( class_Groups_Omonoid__mult(X10)
& class_Int_Onumber(X10) )
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X133)),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(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X133)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X133)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__eq__square__number__of) ).
fof(fact_r__r__into__trancl,axiom,
! [X18,X196,X38,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),X196))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X38),X18)),X196))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X18)),c_Transitive__Closure_Otrancl(X10,X196))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__r__into__trancl) ).
fof(fact_DomainE,axiom,
! [X177,X13,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X39),hAPP(c_Relation_ODomain(X10,X13),X177)))
=> ~ ! [X90] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X39),X90)),X177)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainE) ).
fof(fact_add__self__div__2,axiom,
! [X97] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X97)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X97,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__self__div__2) ).
fof(fact_dvd_OatLeastatMost__subset__iff,axiom,
! [X141,X18,X38,X39] :
( 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),X39,X38)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X18,X141)))
<=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X39),X38))
| ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X18),X39))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X38),X141)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastatMost__subset__iff) ).
fof(fact_mult__2__right,axiom,
! [X104,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X104),hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X104),X104) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__2__right) ).
fof(fact_power2__eq__square,axiom,
! [X84,X94] :
( class_Groups_Omonoid__mult(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),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(X94),X84),X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__eq__square) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
! [X93,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X93),X93) = hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),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,
! [X39,X18,X38,X160,X154,X125,X13,X10] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_fun(X125,tc_HOL_Obool))),X154),X160),X38),X18))
=> ( ~ hBOOL(hAPP(hAPP(hAPP(X160,X39),X38),X18))
=> ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF2__E) ).
fof(fact_nat__mult__2__right,axiom,
! [X104] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X104),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),X104),X104),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__2__right) ).
fof(fact_add__2__eq__Suc_H,axiom,
! [X42] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),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,X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__2__eq__Suc_H) ).
fof(fact_one__power2,axiom,
! [X94] :
( class_Rings_Osemiring__1(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),c_Groups_Oone__class_Oone(X94)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__power2) ).
fof(fact_zero__power2,axiom,
! [X94] :
( class_Rings_Osemiring__1(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__power2) ).
fof(fact_trancl__mono,axiom,
! [X54,X177,X166,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X166),c_Transitive__Closure_Otrancl(X10,X177)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X177),X54))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X166),c_Transitive__Closure_Otrancl(X10,X54))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__mono) ).
fof(fact_not__sum__squares__lt__zero,axiom,
! [X105,X93,X94] :
( class_Rings_Olinordered__ring(X94)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X93),X93)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X105),X105))),c_Groups_Ozero__class_Ozero(X94))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).
fof(fact_trancl__subset__Field2,axiom,
! [X177,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X10,X177)),hAPP(hAPP(c_Product__Type_OSigma(X10,X10),hAPP(c_Relation_OField(X10),X177)),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X10),hAPP(c_Relation_OField(X10),X177))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__subset__Field2) ).
fof(fact_sup2E,axiom,
! [X25,X16,X160,X154,X13,X10] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_fun(X13,tc_HOL_Obool))),X154),X160),X16),X25))
=> ( ~ hBOOL(hAPP(hAPP(X154,X16),X25))
=> hBOOL(hAPP(hAPP(X160,X16),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2E) ).
fof(fact_rtrancl__eq__or__trancl,axiom,
! [X196,X25,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),c_Transitive__Closure_Ortrancl(X10,X196)))
<=> ( X16 = X25
| ( X16 != X25
& hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),c_Transitive__Closure_Otrancl(X10,X196))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__eq__or__trancl) ).
fof(fact_trancl__into__rtrancl,axiom,
! [X177,X38,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),c_Transitive__Closure_Otrancl(X10,X177)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),c_Transitive__Closure_Ortrancl(X10,X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__into__rtrancl) ).
fof(fact_inf2E,axiom,
! [X25,X16,X160,X154,X13,X10] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_fun(X13,tc_HOL_Obool))),X154),X160),X16),X25))
=> ~ ( hBOOL(hAPP(hAPP(X154,X16),X25))
=> ~ hBOOL(hAPP(hAPP(X160,X16),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2E) ).
fof(fact_rel__simps_I34_J,axiom,
! [X162,X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X101)),c_Int_OBit1(X162)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X101),X162)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I34_J) ).
fof(fact_less__eq__int__code_I16_J,axiom,
! [X175,X176] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X176)),c_Int_OBit1(X175)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X176),X175)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__int__code_I16_J) ).
fof(fact_rel__simps_I17_J,axiom,
! [X162,X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X101)),c_Int_OBit1(X162)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),X162)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I17_J) ).
fof(fact_less__int__code_I16_J,axiom,
! [X175,X176] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X176)),c_Int_OBit1(X175)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X176),X175)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__int__code_I16_J) ).
fof(fact_length__transpose,axiom,
! [X290,X10] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),c_List_Otranspose(X10,X290)) = c_List_Ofoldr(tc_List_Olist(X10),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X10)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X10))),X290,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__transpose) ).
fof(fact_trancl__power,axiom,
! [X196,X166,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X166),c_Transitive__Closure_Otrancl(X10,X196)))
<=> ? [X83] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X83))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X166),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X83),X196))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__power) ).
fof(fact_concat__append,axiom,
! [X298,X297,X94] : c_List_Oconcat(X94,hAPP(hAPP(c_List_Oappend(tc_List_Olist(X94)),X297),X298)) = hAPP(hAPP(c_List_Oappend(X94),c_List_Oconcat(X94,X297)),c_List_Oconcat(X94,X298)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__append) ).
fof(fact_distinct__list__update,axiom,
! [X113,X39,X290,X10] :
( hBOOL(hAPP(c_List_Odistinct(X10),X290))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),X290)),hAPP(hAPP(c_Set_Oinsert(X10),hAPP(hAPP(c_List_Onth(X10),X290),X113)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))))
=> hBOOL(hAPP(c_List_Odistinct(X10),hAPP(hAPP(c_List_Olist__update(X10,X290),X113),X39))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__list__update) ).
fof(fact_pigeonhole,axiom,
! [X154,X2,X13,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),hAPP(c_Set_Oimage(X13,X10,X2),X154))),hAPP(c_Finite__Set_Ocard(X13),X154)))
=> ~ c_Fun_Oinj__on(X13,X10,X2,X154) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pigeonhole) ).
fof(fact_rtranclD,axiom,
! [X196,X38,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),c_Transitive__Closure_Ortrancl(X10,X196)))
=> ( X39 = X38
| ( X39 != X38
& hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),c_Transitive__Closure_Otrancl(X10,X196))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtranclD) ).
fof(fact_trancl_Or__into__trancl,axiom,
! [X177,X38,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),X177))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),c_Transitive__Closure_Otrancl(X10,X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl_Or__into__trancl) ).
fof(fact_divide__le__eq__number__of,axiom,
! [X131,X18,X38,X10] :
( ( class_Fields_Olinordered__field__inverse__zero(X10)
& class_Int_Onumber(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),X18)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),X18))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),X18)),X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131))) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__le__eq__number__of) ).
fof(fact_divide__less__eq__number__of,axiom,
! [X131,X18,X38,X10] :
( ( class_Fields_Olinordered__field__inverse__zero(X10)
& class_Int_Onumber(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),X18)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),X18))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),X18)),X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131))) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__less__eq__number__of) ).
fof(fact_le__divide__eq__number__of,axiom,
! [X18,X38,X131,X10] :
( ( class_Fields_Olinordered__field__inverse__zero(X10)
& class_Int_Onumber(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),X18)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),X18)),X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),X18))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),c_Groups_Ozero__class_Ozero(X10))) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__divide__eq__number__of) ).
fof(fact_less__divide__eq__number__of,axiom,
! [X18,X38,X131,X10] :
( ( class_Fields_Olinordered__field__inverse__zero(X10)
& class_Int_Onumber(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),X18)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),X18)),X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),X18))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),c_Groups_Ozero__class_Ozero(X10))) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__divide__eq__number__of) ).
fof(fact_Collect__conv__if2,axiom,
! [X10,X39,X19] :
( ( hBOOL(hAPP(X19,X39))
=> hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(c_fequal,X39))),X19)) = hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) )
& ( ~ hBOOL(hAPP(X19,X39))
=> hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(c_fequal,X39))),X19)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__conv__if2) ).
fof(fact_rotate__drop__take,axiom,
! [X297,X42,X94] : hAPP(c_List_Orotate(X94,X42),X297) = hAPP(hAPP(c_List_Oappend(X94),hAPP(hAPP(c_List_Odrop(X94),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X42,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297))),X297)),hAPP(hAPP(c_List_Otake(X94),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X42,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297))),X297)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__drop__take) ).
fof(fact_in__set__zipE,axiom,
! [X289,X290,X25,X16,X13,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X16),X25)),hAPP(c_List_Oset(tc_prod(X10,X13)),hAPP(hAPP(c_List_Ozip(X10,X13),X290),X289))))
=> ~ ( hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
=> ~ hBOOL(hAPP(hAPP(c_member(X13),X25),hAPP(c_List_Oset(X13),X289))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__zipE) ).
fof(fact_map__add__upd__left,axiom,
! [X273,X274,X275,X13,X102,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X102),c_Map_Odom(X10,X13,X275)))
=> c_Map_Omap__add(X10,X13,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),X274),X102),hAPP(c_Option_Ooption_OSome(X13),X273)),X275) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),c_Map_Omap__add(X10,X13,X274,X275)),X102),hAPP(c_Option_Ooption_OSome(X13),X273)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__upd__left) ).
fof(fact_acyclic__insert,axiom,
! [X177,X16,X25,X10] :
( c_Wellfounded_Oacyclic(X10,hAPP(hAPP(c_Set_Oinsert(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X25),X16)),X177))
<=> ( c_Wellfounded_Oacyclic(X10,X177)
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),c_Transitive__Closure_Ortrancl(X10,X177))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__insert) ).
fof(fact_wf__insert,axiom,
! [X177,X16,X25,X10] :
( c_Wellfounded_Owf(X10,hAPP(hAPP(c_Set_Oinsert(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X25),X16)),X177))
<=> ( c_Wellfounded_Owf(X10,X177)
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),c_Transitive__Closure_Ortrancl(X10,X177))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__insert) ).
fof(fact_trancl__unfold,axiom,
! [X177,X10] : c_Transitive__Closure_Otrancl(X10,X177) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X177),hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),c_Transitive__Closure_Otrancl(X10,X177)),X177)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__unfold) ).
fof(fact_wf__eq__minimal,axiom,
! [X177,X10] :
( c_Wellfounded_Owf(X10,X177)
<=> ! [X271] :
( ? [X3] : hBOOL(hAPP(hAPP(c_member(X10),X3),X271))
=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X271))
& ! [X90] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X90),X3)),X177))
=> ~ hBOOL(hAPP(hAPP(c_member(X10),X90),X271)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__eq__minimal) ).
fof(fact_rel__simps_I33_J,axiom,
! [X162,X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X101)),c_Int_OBit0(X162)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),X162)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I33_J) ).
fof(fact_less__eq__int__code_I15_J,axiom,
! [X175,X176] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X176)),c_Int_OBit0(X175)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X176),X175)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__int__code_I15_J) ).
fof(fact_less__int__code_I15_J,axiom,
! [X175,X176] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X176)),c_Int_OBit0(X175)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X176),X175)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__int__code_I15_J) ).
fof(fact_rel__simps_I16_J,axiom,
! [X162,X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X101)),c_Int_OBit0(X162)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),X162)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I16_J) ).
fof(fact_fun__upd__None__restrict,axiom,
! [X102,X13,X197,X16,X10] :
( ( hBOOL(hAPP(hAPP(c_member(X10),X16),X197))
=> hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),c_Map_Orestrict__map(X10,X13,X102,X197)),X16),c_Option_Ooption_ONone(X13)) = c_Map_Orestrict__map(X10,X13,X102,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X197),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X197))
=> hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),c_Map_Orestrict__map(X10,X13,X102,X197)),X16),c_Option_Ooption_ONone(X13)) = c_Map_Orestrict__map(X10,X13,X102,X197) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__None__restrict) ).
fof(fact_Nitpick_Oint__lcm__def,axiom,
! [X105,X93] : c_Nitpick_Oint__lcm(X93,X105) = 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),X93)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X105)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Oint__lcm__def) ).
fof(fact_Nitpick_Onat__lcm__def,axiom,
! [X105,X93] : c_Nitpick_Onat__lcm(X93,X105) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X105)),c_Nitpick_Onat__gcd(X93,X105)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Onat__lcm__def) ).
fof(fact_foldr_Osimps_I2_J,axiom,
! [X39,X290,X16,X2,X10,X13] : c_List_Ofoldr(X13,X10,X2,hAPP(hAPP(c_List_Olist_OCons(X13),X16),X290),X39) = hAPP(hAPP(X2,X16),c_List_Ofoldr(X13,X10,X2,X290,X39)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldr_Osimps_I2_J) ).
fof(fact_wf__not__sym,axiom,
! [X16,X39,X177,X10] :
( c_Wellfounded_Owf(X10,X177)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X16)),X177))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X39)),X177)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__not__sym) ).
fof(fact_wf__asym,axiom,
! [X16,X39,X177,X10] :
( c_Wellfounded_Owf(X10,X177)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X16)),X177))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X39)),X177)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__asym) ).
fof(fact_divmod__nat__rel__def,axiom,
! [X199,X20,X102] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X102,X20),X199))
<=> ( X102 = 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),X199)),X20)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X199))
& ( X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X199) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X20 != 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)),X20))
=> ( 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),X199)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X199)),X20)) ) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X199)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X199)),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,
! [X39,X131,X38,X10] :
( ( class_Fields_Olinordered__field__inverse__zero(X10)
& class_Int_Onumber(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131))),X39))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131))),X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X39)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__le__eq__number__of1) ).
fof(fact_divide__less__eq__number__of1,axiom,
! [X39,X131,X38,X10] :
( ( class_Fields_Olinordered__field__inverse__zero(X10)
& class_Int_Onumber(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131))),X39))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131))),X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X39)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__less__eq__number__of1) ).
fof(fact_minus__Bit1,axiom,
! [X103] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(X103)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X103))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__Bit1) ).
fof(fact_evaln__WHILE__case,axiom,
! [X53,X20,X54,X18,X38] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X38,X18),X54,X20,X53)
=> ( ( X53 = X54
=> hBOOL(hAPP(X38,X54)) )
=> ~ ( hBOOL(hAPP(X38,X54))
=> ! [X67] :
( c_Natural_Oevaln(X18,X54,X20,X67)
=> ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X38,X18),X67,X20,X53) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__WHILE__case) ).
fof(fact_evaln_Oequations_I8_J,axiom,
! [X65,X72,X52,X50,X51] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X51,X50),X52,X72,X65)
<=> ( ( X65 = X52
& ~ hBOOL(hAPP(X51,X52)) )
| ( hBOOL(hAPP(X51,X52))
& ? [X67] :
( c_Natural_Oevaln(X50,X52,X72,X67)
& c_Natural_Oevaln(c_Com_Ocom_OWhile(X51,X50),X67,X72,X65) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I8_J) ).
fof(fact_evaln__elim__cases_I4_J,axiom,
! [X44,X42,X45,X62,X58] :
( c_Natural_Oevaln(c_Com_Ocom_OSemi(X58,X62),X45,X42,X44)
=> ~ ! [X67] :
( c_Natural_Oevaln(X58,X45,X42,X67)
=> ~ c_Natural_Oevaln(X62,X67,X42,X44) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I4_J) ).
fof(fact_less__eq,axiom,
! [X20,X102] :
( 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),X102),X20)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq) ).
fof(fact_quotientE,axiom,
! [X177,X154,X48,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X48),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X154),X177)))
=> ~ ! [X3] :
( X48 = hAPP(c_Relation_OImage(X10,X10,X177),hAPP(hAPP(c_Set_Oinsert(X10),X3),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))
=> ~ hBOOL(hAPP(hAPP(c_member(X10),X3),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotientE) ).
fof(fact_divmod__nat__if,axiom,
! [X102,X20] :
( ( ( X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X20)) )
=> c_Divides_Odivmod__nat(X102,X20) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X102) )
& ( ~ ( X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X20)) )
=> c_Divides_Odivmod__nat(X102,X20) = 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),X102),X20),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__if) ).
fof(fact_divmod__nat__def,axiom,
! [X20,X102] : c_Divides_Odivmod__nat(X102,X20) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X102,X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__def) ).
fof(fact_bin__less__0__simps_I4_J,axiom,
! [X131] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X131)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X131),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,
! [X323,X324,X325,X326,X10] :
( hAPP(hAPP(c_List_Oappend(X10),X326),X325) = hAPP(hAPP(c_List_Oappend(X10),X324),X323)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X326)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X324)))
=> ( X326 = hAPP(hAPP(c_List_Otake(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X326)),X324)
& X325 = hAPP(hAPP(c_List_Oappend(X10),hAPP(hAPP(c_List_Odrop(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X326)),X324)),X323) ) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X326)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X324)))
=> ( hAPP(hAPP(c_List_Otake(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X324)),X326) = X324
& hAPP(hAPP(c_List_Oappend(X10),hAPP(hAPP(c_List_Odrop(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X324)),X326)),X325) = X323 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__eq__append__conv__if) ).
fof(fact_rel__simps_I30_J,axiom,
! [X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X101)),c_Int_OMin))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X101),c_Int_OMin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I30_J) ).
fof(fact_rel__simps_I29_J,axiom,
! [X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X101)),c_Int_OPls))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),c_Int_OPls)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I29_J) ).
fof(fact_rel__simps_I12_J,axiom,
! [X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X101)),c_Int_OPls))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),c_Int_OPls)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I12_J) ).
fof(fact_rel__simps_I13_J,axiom,
! [X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X101)),c_Int_OMin))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),c_Int_OMin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I13_J) ).
fof(fact_neg__number__of__Bit1,axiom,
! [X131] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X131))))
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X131))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__number__of__Bit1) ).
fof(fact_le__special_I2_J,axiom,
! [X25,X10] :
( ( class_Int_Onumber__ring(X10)
& class_Rings_Olinordered__idom(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Oone__class_Oone(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X25)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__special_I2_J) ).
fof(fact_less__special_I2_J,axiom,
! [X25,X10] :
( ( class_Int_Onumber__ring(X10)
& class_Rings_Olinordered__idom(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Oone__class_Oone(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X25)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__special_I2_J) ).
fof(fact_le__divide__eq__number__of1,axiom,
! [X131,X38,X39,X10] :
( ( class_Fields_Olinordered__field__inverse__zero(X10)
& class_Int_Onumber(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131))))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131))),X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),c_Groups_Ozero__class_Ozero(X10))) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__divide__eq__number__of1) ).
fof(fact_less__divide__eq__number__of1,axiom,
! [X131,X38,X39,X10] :
( ( class_Fields_Olinordered__field__inverse__zero(X10)
& class_Int_Onumber(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131))))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131))),X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),c_Groups_Ozero__class_Ozero(X10))) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__divide__eq__number__of1) ).
fof(fact_sup2CI,axiom,
! [X13,X10,X154,X25,X16,X160] :
( ( ~ hBOOL(hAPP(hAPP(X160,X16),X25))
=> hBOOL(hAPP(hAPP(X154,X16),X25)) )
=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_fun(X13,tc_HOL_Obool))),X154),X160),X16),X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2CI) ).
fof(fact_not__acc__down,axiom,
! [X196,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),c_Wellfounded_Oacc(X10,X196)))
=> ~ ! [X159] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X159),X16)),X196))
=> hBOOL(hAPP(hAPP(c_member(X10),X159),c_Wellfounded_Oacc(X10,X196))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__acc__down) ).
fof(fact_flat__lub__def,axiom,
! [X38,X154,X10] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X38),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))
=> c_Partial__Function_Oflat__lub(X10,X38,X154) = X38 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X38),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))
=> c_Partial__Function_Oflat__lub(X10,X38,X154) = c_HOL_OThe(X10,hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X38),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_flat__lub__def) ).
fof(fact_evalc__WHILE__case,axiom,
! [X53,X54,X18,X38] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X38,X18)),X54),X53))
=> ( ( X53 = X54
=> hBOOL(hAPP(X38,X54)) )
=> ~ ( hBOOL(hAPP(X38,X54))
=> ! [X67] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X18),X54),X67))
=> ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X38,X18)),X67),X53)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__WHILE__case) ).
fof(fact_evalc_Oequations_I8_J,axiom,
! [X66,X52,X50,X51] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X51,X50)),X52),X66))
<=> ( ( X66 = X52
& ~ hBOOL(hAPP(X51,X52)) )
| ( hBOOL(hAPP(X51,X52))
& ? [X67] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X50),X52),X67))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X51,X50)),X67),X66)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I8_J) ).
fof(fact_not__Nil__listrel1,axiom,
! [X177,X290,X10] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_ONil(X10)),X290)),c_List_Olistrel1(X10,X177))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Nil__listrel1) ).
fof(fact_Nil__notin__lex,axiom,
! [X177,X289,X10] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_ONil(X10)),X289)),c_List_Olex(X10,X177))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nil__notin__lex) ).
fof(fact_fun__upd__image,axiom,
! [X25,X2,X13,X154,X16,X10] :
( ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Set_Oimage(X10,X13,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,X13),X2),X16),X25)),X154) = hAPP(hAPP(c_Set_Oinsert(X13),X25),hAPP(c_Set_Oimage(X10,X13,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Set_Oimage(X10,X13,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,X13),X2),X16),X25)),X154) = hAPP(c_Set_Oimage(X10,X13,X2),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__image) ).
fof(fact_not__listrel1__Nil,axiom,
! [X177,X290,X10] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X290),c_List_Olist_ONil(X10))),c_List_Olistrel1(X10,X177))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__listrel1__Nil) ).
fof(fact_lexord__Nil__right,axiom,
! [X177,X16,X10] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X16),c_List_Olist_ONil(X10))),c_List_Olexord(X10,X177))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__Nil__right) ).
fof(fact_Nil2__notin__lex,axiom,
! [X177,X290,X10] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X290),c_List_Olist_ONil(X10))),c_List_Olex(X10,X177))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nil2__notin__lex) ).
fof(fact_foldl__foldr1__lemma,axiom,
! [X290,X39,X10] :
( class_Groups_Omonoid__add(X10)
=> hAPP(c_List_Ofoldl(X10,X10,c_Groups_Oplus__class_Oplus(X10),X39),X290) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X39),c_List_Ofoldr(X10,X10,c_Groups_Oplus__class_Oplus(X10),X290,c_Groups_Ozero__class_Ozero(X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__foldr1__lemma) ).
fof(fact_pair__in__Id__conv,axiom,
! [X38,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),c_Relation_OId(X10)))
<=> X39 = X38 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__in__Id__conv) ).
fof(fact_map__of__eq__None__iff,axiom,
! [X16,X285,X10,X13] :
( hAPP(c_Map_Omap__of(X13,X10,X285),X16) = c_Option_Ooption_ONone(X10)
<=> ~ hBOOL(hAPP(hAPP(c_member(X13),X16),hAPP(c_Set_Oimage(tc_prod(X13,X10),X13,c_Product__Type_Ofst(X13,X10)),hAPP(c_List_Oset(tc_prod(X13,X10)),X285)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__eq__None__iff) ).
fof(fact_one__add__one__is__two,axiom,
! [X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),c_Groups_Oone__class_Oone(X94)),c_Groups_Oone__class_Oone(X94)) = hAPP(c_Int_Onumber__class_Onumber__of(X94),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,
! [X289,X2,X13,X290,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
=> hAPP(c_Map_Omap__upds(X10,X13,X2,X290,X289),X16) = hAPP(X2,X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upds__apply__nontin) ).
fof(fact_override__on__def,axiom,
! [X1,X2,X13,X154,X39,X10] :
( ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(c_Fun_Ooverride__on(X10,X13,X2,X1,X154),X39) = hAPP(X1,X39) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(c_Fun_Ooverride__on(X10,X13,X2,X1,X154),X39) = hAPP(X2,X39) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_override__on__def) ).
fof(fact_divmod__nat__step,axiom,
! [X97,X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X42))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),X97))
=> c_Divides_Odivmod__nat(X97,X42) = 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),X97),X42)),X42))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__step) ).
fof(fact_evalc__elim__cases_I4_J,axiom,
! [X44,X45,X62,X58] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X58,X62)),X45),X44))
=> ~ ! [X67] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X58),X45),X67))
=> ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X62),X67),X44)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I4_J) ).
fof(fact_foldl__foldr,axiom,
! [X290,X39,X2,X13,X10] : hAPP(c_List_Ofoldl(X10,X13,X2,X39),X290) = c_List_Ofoldr(X13,X10,hAPP(c_COMBC(X10,X13,X10),X2),hAPP(c_List_Orev(X13),X290),X39),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__foldr) ).
fof(fact_override__on__apply__notin,axiom,
! [X1,X2,X13,X154,X39,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(c_Fun_Ooverride__on(X10,X13,X2,X1,X154),X39) = hAPP(X2,X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_override__on__apply__notin) ).
fof(fact_comm__monoid__big_OF__eq,axiom,
! [X1,X154,X225,X73,X2,X13,X10] :
( c_Big__Operators_Ocomm__monoid__big(X10,X13,X2,X73,X225)
=> ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X154))
=> hAPP(hAPP(X225,X1),X154) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X10,X13,X2),X1),X73),X154) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X154))
=> hAPP(hAPP(X225,X1),X154) = X73 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__monoid__big_OF__eq) ).
fof(fact_in__measure,axiom,
! [X2,X25,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),hAPP(c_Wellfounded_Omeasure(X10),X2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X16)),hAPP(X2,X25))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__measure) ).
fof(fact_measure__def,axiom,
! [X10] : c_Wellfounded_Omeasure(X10) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X10),c_Wellfounded_Oless__than),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_measure__def) ).
fof(fact_SigmaE2,axiom,
! [X160,X154,X38,X39,X13,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X39),X38)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X154),X160)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> ~ hBOOL(hAPP(hAPP(c_member(X13),X38),hAPP(X160,X39))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaE2) ).
fof(fact_map__concat,axiom,
! [X290,X2,X10,X13] : hAPP(hAPP(c_List_Omap(X13,X10),X2),c_List_Oconcat(X13,X290)) = c_List_Oconcat(X10,hAPP(hAPP(c_List_Omap(tc_List_Olist(X13),tc_List_Olist(X10)),hAPP(c_List_Omap(X13,X10),X2)),X290)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__concat) ).
fof(fact_diff__bin__simps_I9_J,axiom,
! [X121,X103] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X103)),c_Int_OBit0(X121)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X103),X121)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I9_J) ).
fof(fact_add__Bit1__Bit0,axiom,
! [X121,X103] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X103)),c_Int_OBit0(X121)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X103),X121)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Bit1__Bit0) ).
fof(fact_insort__insert__insort__key,axiom,
! [X290,X13,X16,X2,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),hAPP(X2,X16)),hAPP(c_Set_Oimage(X13,X10,X2),hAPP(c_List_Oset(X13),X290))))
=> c_List_Olinorder__class_Oinsort__insert__key(X13,X10,X2,X16,X290) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X13,X10,X2),X16),X290) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__insert__insort__key) ).
fof(fact_total__on__diff__Id,axiom,
! [X177,X154,X10] :
( c_Relation_Ototal__on(X10,X154,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X177),c_Relation_OId(X10)))
<=> c_Relation_Ototal__on(X10,X154,X177) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__diff__Id) ).
fof(fact_Suc__diff__eq__diff__pred,axiom,
! [X97,X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),X42))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X97)),X42) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X42),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,
! [X121,X103] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(X103)),X121) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X103),X121))),X121),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Bit1) ).
fof(fact_number__of1,axiom,
! [X42] :
( 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),X42)))
=> ( 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(X42))))
& 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(X42)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of1) ).
fof(fact_add__Bit1__Bit1,axiom,
! [X121,X103] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X103)),c_Int_OBit1(X121)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X103),c_Int_Osucc(X121))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Bit1__Bit1) ).
fof(fact_less__eq__int__code_I14_J,axiom,
! [X175,X176] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X176)),c_Int_OBit1(X175)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X176),X175)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__int__code_I14_J) ).
fof(fact_rel__simps_I32_J,axiom,
! [X162,X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X101)),c_Int_OBit1(X162)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X101),X162)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I32_J) ).
fof(fact_rel__simps_I15_J,axiom,
! [X162,X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X101)),c_Int_OBit1(X162)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X101),X162)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I15_J) ).
fof(fact_less__int__code_I14_J,axiom,
! [X175,X176] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X176)),c_Int_OBit1(X175)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X176),X175)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__int__code_I14_J) ).
fof(fact_finite__trancl,axiom,
! [X177,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10,X10)),c_Transitive__Closure_Otrancl(X10,X177)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10,X10)),X177)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__trancl) ).
fof(fact_card__Diff__insert,axiom,
! [X160,X39,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X160))
=> hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),X160))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff__insert) ).
fof(fact_rev__concat,axiom,
! [X290,X10] : hAPP(c_List_Orev(X10),c_List_Oconcat(X10,X290)) = c_List_Oconcat(X10,hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Orev(X10)),hAPP(c_List_Orev(tc_List_Olist(X10)),X290))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__concat) ).
fof(fact_fold__image__insert,axiom,
! [X73,X1,X39,X154,X10,X13] :
( class_Groups_Oab__semigroup__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13,X10,c_Groups_Otimes__class_Otimes(X13)),X1),X73),hAPP(hAPP(c_Set_Oinsert(X10),X39),X154)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),hAPP(X1,X39)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13,X10,c_Groups_Otimes__class_Otimes(X13)),X1),X73),X154)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__insert) ).
fof(fact_filter__concat,axiom,
! [X290,X166,X10] : hAPP(c_List_Ofilter(X10,X166),c_List_Oconcat(X10,X290)) = c_List_Oconcat(X10,hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Ofilter(X10,X166)),X290)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__concat) ).
fof(fact_divide__le__eq,axiom,
! [X39,X18,X38,X10] :
( class_Fields_Olinordered__field__inverse__zero(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),X18)),X39))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X18))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X18)),X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X39)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__le__eq) ).
fof(fact_divide__less__eq,axiom,
! [X39,X18,X38,X10] :
( class_Fields_Olinordered__field__inverse__zero(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),X18)),X39))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X18))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X18)),X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X39)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__less__eq) ).
fof(fact_distinct__rotate,axiom,
! [X290,X20,X10] :
( hBOOL(hAPP(c_List_Odistinct(X10),hAPP(c_List_Orotate(X10,X20),X290)))
<=> hBOOL(hAPP(c_List_Odistinct(X10),X290)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__rotate) ).
fof(fact_Not__Domain__rtrancl,axiom,
! [X25,X196,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_Relation_ODomain(X10,X10),X196)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),c_Transitive__Closure_Ortrancl(X10,X196)))
<=> X16 = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Not__Domain__rtrancl) ).
fof(fact_add__Bit0__Bit1,axiom,
! [X121,X103] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X103)),c_Int_OBit1(X121)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X103),X121)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Bit0__Bit1) ).
fof(fact_comm__monoid__big_Oinfinite,axiom,
! [X1,X154,X225,X73,X2,X13,X10] :
( c_Big__Operators_Ocomm__monoid__big(X10,X13,X2,X73,X225)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X154))
=> hAPP(hAPP(X225,X1),X154) = X73 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__monoid__big_Oinfinite) ).
fof(fact_diff__special_I2_J,axiom,
! [X144,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),X144)),c_Groups_Oone__class_Oone(X94)) = hAPP(c_Int_Onumber__class_Onumber__of(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X144),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,
! [X290,X16,X2,X10,X13] :
( class_Orderings_Olinorder(X13)
=> ( hBOOL(hAPP(c_List_Odistinct(X10),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X13,X2),X16),X290)))
<=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
& hBOOL(hAPP(c_List_Odistinct(X10),X290)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__insort) ).
fof(fact_diff__special_I1_J,axiom,
! [X133,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),c_Groups_Oone__class_Oone(X94)),hAPP(c_Int_Onumber__class_Onumber__of(X94),X133)) = hAPP(c_Int_Onumber__class_Onumber__of(X94),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),X133))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__special_I1_J) ).
fof(fact_r__into__trancl_H,axiom,
! [X177,X166,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X166),X177))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X166),c_Transitive__Closure_Otrancl(X10,X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__into__trancl_H) ).
fof(fact_concat_Osimps_I2_J,axiom,
! [X297,X93,X94] : c_List_Oconcat(X94,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X94)),X93),X297)) = hAPP(hAPP(c_List_Oappend(X94),X93),c_List_Oconcat(X94,X297)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat_Osimps_I2_J) ).
fof(fact_add__special_I2_J,axiom,
! [X133,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),c_Groups_Oone__class_Oone(X94)),hAPP(c_Int_Onumber__class_Onumber__of(X94),X133)) = hAPP(c_Int_Onumber__class_Onumber__of(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X133)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__special_I2_J) ).
fof(fact_atLeastatMost__psubset__iff,axiom,
! [X141,X18,X38,X39,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X39,X38)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X18,X141)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),X38))
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X18),X39))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X38),X141))
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),X39))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X38),X141)) ) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X18),X141)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastatMost__psubset__iff) ).
fof(fact_insert__partition,axiom,
! [X225,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X16),X225))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(tc_fun(X10,tc_HOL_Obool)),X16),X225)))
=> ! [X227] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X227),hAPP(hAPP(c_Set_Oinsert(tc_fun(X10,tc_HOL_Obool)),X16),X225)))
=> ( X3 != X227
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X3),X227) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ) )
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X16),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X225)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__partition) ).
fof(fact_reflcl__trancl,axiom,
! [X177,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X10,X177)),c_Relation_OId(X10)) = c_Transitive__Closure_Ortrancl(X10,X177),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reflcl__trancl) ).
fof(fact_list__update__append,axiom,
! [X93,X298,X297,X94,X42] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)))
=> hAPP(hAPP(c_List_Olist__update(X94,hAPP(hAPP(c_List_Oappend(X94),X297),X298)),X42),X93) = hAPP(hAPP(c_List_Oappend(X94),hAPP(hAPP(c_List_Olist__update(X94,X297),X42),X93)),X298) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)))
=> hAPP(hAPP(c_List_Olist__update(X94,hAPP(hAPP(c_List_Oappend(X94),X297),X298)),X42),X93) = hAPP(hAPP(c_List_Oappend(X94),X297),hAPP(hAPP(c_List_Olist__update(X94,X298),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297))),X93)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__append) ).
fof(fact_le__divide__eq,axiom,
! [X18,X38,X39,X10] :
( class_Fields_Olinordered__field__inverse__zero(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),X18)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X18)),X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X18))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),c_Groups_Ozero__class_Ozero(X10))) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__divide__eq) ).
fof(fact_less__divide__eq,axiom,
! [X18,X38,X39,X10] :
( class_Fields_Olinordered__field__inverse__zero(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),X18)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X18)),X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X18))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),c_Groups_Ozero__class_Ozero(X10))) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__divide__eq) ).
fof(fact_mult__numeral__1,axiom,
! [X84,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OBit1(c_Int_OPls))),X84) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__numeral__1) ).
fof(fact_rotate__add,axiom,
! [X20,X102,X10] : c_List_Orotate(X10,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X20)) = hAPP(c_Fun_Ocomp(tc_List_Olist(X10),tc_List_Olist(X10),tc_List_Olist(X10),c_List_Orotate(X10,X102)),c_List_Orotate(X10,X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__add) ).
fof(fact_atLeastatMost__subset__iff,axiom,
! [X141,X18,X38,X39,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X39,X38)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X18,X141)))
<=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),X38))
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X18),X39))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X38),X141)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastatMost__subset__iff) ).
fof(fact_le__special_I4_J,axiom,
! [X16,X10] :
( ( class_Int_Onumber__ring(X10)
& class_Rings_Olinordered__idom(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X16)),c_Groups_Oone__class_Oone(X10)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X16),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,
! [X16,X10] :
( ( class_Int_Onumber__ring(X10)
& class_Rings_Olinordered__idom(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X16)),c_Groups_Oone__class_Oone(X10)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16),c_Int_OBit1(c_Int_OPls))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__special_I4_J) ).
fof(fact_IdE,axiom,
! [X166,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X166),c_Relation_OId(X10)))
=> ~ ! [X3] : X166 != hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IdE) ).
fof(fact_evalc_Oequations_I6_J,axiom,
! [X72,X52,X50,X66,X51] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X51,X66,X50)),X52),X72))
<=> ( ( hBOOL(hAPP(X51,X52))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X66),X52),X72)) )
| ( ~ hBOOL(hAPP(X51,X52))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X50),X52),X72)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I6_J) ).
fof(fact_evalc_Oequations_I5_J,axiom,
! [X72,X52,X66,X50,X51] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X51,X50,X66)),X52),X72))
<=> ( ( hBOOL(hAPP(X51,X52))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X50),X52),X72)) )
| ( ~ hBOOL(hAPP(X51,X52))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X66),X52),X72)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I5_J) ).
fof(fact_evalc__elim__cases_I5_J,axiom,
! [X53,X54,X74,X75,X38] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X38,X75,X74)),X54),X53))
=> ( ( hBOOL(hAPP(X38,X54))
=> ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X75),X54),X53)) )
=> ~ ( ~ hBOOL(hAPP(X38,X54))
=> ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X74),X54),X53)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I5_J) ).
fof(fact_diff__bin__simps_I4_J,axiom,
! [X121] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X121)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X121)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I4_J) ).
fof(fact_IdI,axiom,
! [X39,X10] : hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X39)),c_Relation_OId(X10))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IdI) ).
fof(fact_foldl__conv__concat,axiom,
! [X328,X290,X10] : hAPP(c_List_Ofoldl(tc_List_Olist(X10),tc_List_Olist(X10),c_List_Oappend(X10),X290),X328) = hAPP(hAPP(c_List_Oappend(X10),X290),c_List_Oconcat(X10,X328)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__conv__concat) ).
fof(fact_diff__bin__simps_I10_J,axiom,
! [X121,X103] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X103)),c_Int_OBit1(X121)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X103),X121)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I10_J) ).
fof(fact_insort__insert__insort,axiom,
! [X290,X16,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
=> c_List_Olinorder__class_Oinsort__insert__key(X10,X10,c_COMBI(X10),X16,X290) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X10,c_COMBI(X10)),X16),X290) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__insert__insort) ).
fof(fact_irrefl__def,axiom,
! [X177,X10] :
( c_Relation_Oirrefl(X10,X177)
<=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X3)),X177)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_irrefl__def) ).
fof(fact_wf__not__refl,axiom,
! [X39,X177,X10] :
( c_Wellfounded_Owf(X10,X177)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X39)),X177)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__not__refl) ).
fof(fact_wf__irrefl,axiom,
! [X39,X177,X10] :
( c_Wellfounded_Owf(X10,X177)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X39)),X177)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__irrefl) ).
fof(fact_rtrancl__unfold,axiom,
! [X177,X10] : c_Transitive__Closure_Ortrancl(X10,X177) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Relation_OId(X10)),hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),c_Transitive__Closure_Ortrancl(X10,X177)),X177)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__unfold) ).
fof(fact_INT__E,axiom,
! [X39,X160,X154,X13,X38,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X38),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X154),X160)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X38),hAPP(X160,X39)))
=> ~ hBOOL(hAPP(hAPP(c_member(X13),X39),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__E) ).
fof(fact_rel__simps_I22_J,axiom,
! [X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X101)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X101)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I22_J) ).
fof(fact_rel__simps_I5_J,axiom,
! [X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X101)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X101)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I5_J) ).
fof(fact_rel__simps_I26_J,axiom,
! [X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X101)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X101)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I26_J) ).
fof(fact_rel__simps_I9_J,axiom,
! [X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X101)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X101)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I9_J) ).
fof(fact_power__number__of__even__number__of,axiom,
! [X131,X168,X10] :
( class_Int_Onumber__ring(X10)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X168)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X131))) = hAPP(hAPP(c_HOL_OLet(X10,X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X168)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X131))),hAPP(hAPP(c_COMBS(X10,X10,X10),c_Groups_Otimes__class_Otimes(X10)),c_COMBI(X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__number__of__even__number__of) ).
fof(fact_inj__on__fun__updI,axiom,
! [X16,X25,X154,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,X154)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X13),X25),hAPP(c_Set_Oimage(X10,X13,X2),X154)))
=> c_Fun_Oinj__on(X10,X13,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,X13),X2),X16),X25),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__fun__updI) ).
fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
! [X16,X25,X18] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18),X25))
=> 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)),X18)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X16),X25)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16),X18)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),X18)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18),X25))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16),X25))
=> 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)),X18)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X16),X25)) = 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),X16),X25))
=> 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)),X18)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X16),X25)) = 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,
! [X290,X10] :
( class_Groups_Omonoid__add(X10)
=> hAPP(c_List_Ofoldl(X10,X10,c_Groups_Oplus__class_Oplus(X10),c_Groups_Ozero__class_Ozero(X10)),X290) = c_List_Ofoldr(X10,X10,c_Groups_Oplus__class_Oplus(X10),X290,c_Groups_Ozero__class_Ozero(X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__foldr1) ).
fof(fact_nth__map__upt,axiom,
! [X2,X10,X102,X20,X113] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X113),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20),X102)))
=> hAPP(hAPP(c_List_Onth(X10),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X10),X2),c_List_Oupt(X102,X20))),X113) = hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X113)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__map__upt) ).
fof(fact_rotate__rotate,axiom,
! [X297,X42,X97,X94] : hAPP(c_List_Orotate(X94,X97),hAPP(c_List_Orotate(X94,X42),X297)) = hAPP(c_List_Orotate(X94,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X42)),X297),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__rotate) ).
fof(fact_foldr__conv__foldl,axiom,
! [X39,X290,X10] :
( class_Groups_Oab__semigroup__add(X10)
=> c_List_Ofoldr(X10,X10,c_Groups_Oplus__class_Oplus(X10),X290,X39) = hAPP(c_List_Ofoldl(X10,X10,c_Groups_Oplus__class_Oplus(X10),X39),X290) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldr__conv__foldl) ).
fof(fact_map__of__zip__map,axiom,
! [X2,X13,X290,X16,X10] :
( ( hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
=> hAPP(c_Map_Omap__of(X10,X13,hAPP(hAPP(c_List_Ozip(X10,X13),X290),hAPP(hAPP(c_List_Omap(X10,X13),X2),X290))),X16) = hAPP(c_Option_Ooption_OSome(X13),hAPP(X2,X16)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
=> hAPP(c_Map_Omap__of(X10,X13,hAPP(hAPP(c_List_Ozip(X10,X13),X290),hAPP(hAPP(c_List_Omap(X10,X13),X2),X290))),X16) = c_Option_Ooption_ONone(X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__zip__map) ).
fof(fact_rotate__conv__mod,axiom,
! [X297,X42,X94] : hAPP(c_List_Orotate(X94,X42),X297) = hAPP(c_List_Orotate(X94,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X42,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297))),X297),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__conv__mod) ).
fof(fact_image__map__upd,axiom,
! [X25,X102,X13,X154,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Set_Oimage(X10,tc_Option_Ooption(X13),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),X102),X16),hAPP(c_Option_Ooption_OSome(X13),X25))),X154) = hAPP(c_Set_Oimage(X10,tc_Option_Ooption(X13),X102),X154) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__map__upd) ).
fof(fact_pred__Bit0,axiom,
! [X103] : c_Int_Opred(c_Int_OBit0(X103)) = c_Int_OBit1(c_Int_Opred(X103)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__Bit0) ).
fof(fact_setprod__diff1,axiom,
! [X39,X2,X154,X10,X13] :
( class_Fields_Ofield(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hAPP(X2,X39) != c_Groups_Ozero__class_Ozero(X13)
=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),X154)),hAPP(X2,X39)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),X154) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__diff1) ).
fof(fact_refl__reflcl,axiom,
! [X177,X10] : c_Relation_Orefl__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X177),c_Relation_OId(X10))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__reflcl) ).
fof(fact_setsum__diff1,axiom,
! [X2,X39,X154,X10,X13] :
( class_Groups_Oab__group__add(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X13),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),X154)),hAPP(X2,X39)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),X154) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff1) ).
fof(fact_set__concat,axiom,
! [X290,X10] : hAPP(c_List_Oset(X10),c_List_Oconcat(X10,X290)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X10),tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X10)),X290)),c_List_Oset(X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__concat) ).
fof(fact_length__concat,axiom,
! [X328,X10] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_List_Oconcat(X10,X328)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X10))),X328)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__concat) ).
fof(fact_INF1__E,axiom,
! [X39,X38,X160,X154,X13,X10] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X154),X160),X38))
=> ( ~ hBOOL(hAPP(hAPP(X160,X39),X38))
=> ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF1__E) ).
fof(fact_foldr__max__sorted,axiom,
! [X25,X290,X10] :
( class_Orderings_Olinorder(X10)
=> ( c_List_Olinorder__class_Osorted(X10,hAPP(c_List_Orev(X10),X290))
=> ( ( X290 = c_List_Olist_ONil(X10)
=> c_List_Ofoldr(X10,X10,c_Orderings_Oord__class_Omax(X10),X290,X25) = X25 )
& ( X290 != c_List_Olist_ONil(X10)
=> c_List_Ofoldr(X10,X10,c_Orderings_Oord__class_Omax(X10),X290,X25) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_List_Onth(X10),X290),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X25) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldr__max__sorted) ).
fof(fact_length__filter__less,axiom,
! [X19,X290,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
=> ( ~ hBOOL(hAPP(X19,X16))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),hAPP(c_List_Ofilter(X10,X19),X290))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__filter__less) ).
fof(fact_rtrancl__reflcl,axiom,
! [X196,X10] : c_Transitive__Closure_Ortrancl(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X196),c_Relation_OId(X10))) = c_Transitive__Closure_Ortrancl(X10,X196),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__reflcl) ).
fof(fact_rtrancl__r__diff__Id,axiom,
! [X177,X10] : c_Transitive__Closure_Ortrancl(X10,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X177),c_Relation_OId(X10))) = c_Transitive__Closure_Ortrancl(X10,X177),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__r__diff__Id) ).
fof(fact_irrefl__diff__Id,axiom,
! [X177,X10] : c_Relation_Oirrefl(X10,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X177),c_Relation_OId(X10))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_irrefl__diff__Id) ).
fof(fact_divmod__int__relI,axiom,
! [X143,X149,X92,X84] :
( X84 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X92),X149)),X143)
=> ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X143))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X143),X92)) ) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X92),X143))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X143),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(X84,X92),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X149),X143))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__relI) ).
fof(fact_diff__bin__simps_I5_J,axiom,
! [X121] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X121)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X121)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I5_J) ).
fof(fact_setsum__diff1__nat,axiom,
! [X2,X154,X39,X10] :
( ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),X154)),hAPP(X2,X39)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff1__nat) ).
fof(fact_wf__converse__trancl,axiom,
! [X177,X10] :
( c_Wellfounded_Owf(X10,hAPP(c_Relation_Oconverse(X10,X10),X177))
=> c_Wellfounded_Owf(X10,hAPP(c_Relation_Oconverse(X10,X10),c_Transitive__Closure_Otrancl(X10,X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__converse__trancl) ).
fof(fact_small_H_Osimps,axiom,
! [X2,X113,X141] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X141),X113))
=> c_Smallcheck_Osmall_H(X2,X141,X113) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X141),X113))
=> c_Smallcheck_Osmall_H(X2,X141,X113) = 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,X141,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X113),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(X2,X113)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_small_H_Osimps) ).
fof(fact_concat__eq__Nil__conv,axiom,
! [X328,X10] :
( c_List_Oconcat(X10,X328) = c_List_Olist_ONil(X10)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X3),hAPP(c_List_Oset(tc_List_Olist(X10)),X328)))
=> X3 = c_List_Olist_ONil(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__eq__Nil__conv) ).
fof(fact_Nil__eq__concat__conv,axiom,
! [X328,X10] :
( c_List_Olist_ONil(X10) = c_List_Oconcat(X10,X328)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X3),hAPP(c_List_Oset(tc_List_Olist(X10)),X328)))
=> X3 = c_List_Olist_ONil(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nil__eq__concat__conv) ).
fof(fact_upt__add__eq__append,axiom,
! [X103,X119,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X120),X119))
=> c_List_Oupt(X120,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X119),X103)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X120,X119)),c_List_Oupt(X119,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X119),X103))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__add__eq__append) ).
fof(fact_setsum__cl__ivl__Suc,axiom,
! [X2,X102,X20,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)),X102))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X102,hAPP(c_Nat_OSuc,X20))) = c_Groups_Ozero__class_Ozero(X10) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)),X102))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X102,hAPP(c_Nat_OSuc,X20))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X102,X20))),hAPP(X2,hAPP(c_Nat_OSuc,X20))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__cl__ivl__Suc) ).
fof(fact_UnE,axiom,
! [X160,X154,X18,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X18),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X18),X154))
=> hBOOL(hAPP(hAPP(c_member(X10),X18),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnE) ).
fof(fact_folding_Oinsert,axiom,
! [X16,X154,X225,X2,X13,X10] :
( c_Finite__Set_Ofolding(X10,X13,X2,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(X225,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(c_Fun_Ocomp(X13,X13,X13,hAPP(X225,X154)),hAPP(X2,X16)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Oinsert) ).
fof(fact_succ__Bit1,axiom,
! [X103] : c_Int_Osucc(c_Int_OBit1(X103)) = c_Int_OBit0(c_Int_Osucc(X103)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_succ__Bit1) ).
fof(fact_evaln__elim__cases_I6_J,axiom,
! [X59,X42,X45,X87] :
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X87),X45,X42,X59)
=> ~ ! [X83] :
( X42 = hAPP(c_Nat_OSuc,X83)
=> ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X87)),X45,X83,X59) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I6_J) ).
fof(fact_power__number__of__even,axiom,
! [X131,X73,X10] :
( class_Int_Onumber__ring(X10)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),X73),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X131))) = hAPP(hAPP(c_HOL_OLet(X10,X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X73),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X131))),hAPP(hAPP(c_COMBS(X10,X10,X10),c_Groups_Otimes__class_Otimes(X10)),c_COMBI(X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__number__of__even) ).
fof(fact_Diff__iff,axiom,
! [X160,X154,X18,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X18),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160)))
<=> ( hBOOL(hAPP(hAPP(c_member(X10),X18),X154))
& ~ hBOOL(hAPP(hAPP(c_member(X10),X18),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__iff) ).
fof(fact_DiffD2,axiom,
! [X160,X154,X18,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X18),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160)))
=> ~ hBOOL(hAPP(hAPP(c_member(X10),X18),X160)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffD2) ).
fof(fact_card__Suc__eq,axiom,
! [X101,X154,X10] :
( hAPP(c_Finite__Set_Ocard(X10),X154) = hAPP(c_Nat_OSuc,X101)
<=> ? [X193,X231] :
( X154 = hAPP(hAPP(c_Set_Oinsert(X10),X193),X231)
& ~ hBOOL(hAPP(hAPP(c_member(X10),X193),X231))
& hAPP(c_Finite__Set_Ocard(X10),X231) = X101
& ( X101 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> X231 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Suc__eq) ).
fof(fact_take__upt,axiom,
! [X42,X97,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X120),X97)),X42))
=> hAPP(hAPP(c_List_Otake(tc_Nat_Onat),X97),c_List_Oupt(X120,X42)) = c_List_Oupt(X120,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X120),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__upt) ).
fof(fact_rotate__map,axiom,
! [X290,X2,X13,X20,X10] : hAPP(c_List_Orotate(X10,X20),hAPP(hAPP(c_List_Omap(X13,X10),X2),X290)) = hAPP(hAPP(c_List_Omap(X13,X10),X2),hAPP(c_List_Orotate(X13,X20),X290)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__map) ).
fof(fact_trancl__converse,axiom,
! [X177,X10] : c_Transitive__Closure_Otrancl(X10,hAPP(c_Relation_Oconverse(X10,X10),X177)) = hAPP(c_Relation_Oconverse(X10,X10),c_Transitive__Closure_Otrancl(X10,X177)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__converse) ).
fof(fact_insort__key_Osimps_I2_J,axiom,
! [X289,X13,X25,X16,X2,X10] :
( class_Orderings_Olinorder(X10)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(X2,X16)),hAPP(X2,X25)))
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X13,X10,X2),X16),hAPP(hAPP(c_List_Olist_OCons(X13),X25),X289)) = hAPP(hAPP(c_List_Olist_OCons(X13),X16),hAPP(hAPP(c_List_Olist_OCons(X13),X25),X289)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(X2,X16)),hAPP(X2,X25)))
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X13,X10,X2),X16),hAPP(hAPP(c_List_Olist_OCons(X13),X25),X289)) = hAPP(hAPP(c_List_Olist_OCons(X13),X25),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X13,X10,X2),X16),X289)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__key_Osimps_I2_J) ).
fof(fact_upto__rec__number__of,axiom,
! [X42,X97] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X97)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X42)))
=> c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X97),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X42)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X97)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X97)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X42))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X97)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X42)))
=> c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X97),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X42)) = c_List_Olist_ONil(tc_Int_Oint) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upto__rec__number__of) ).
fof(fact_subset__insert,axiom,
! [X160,X154,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),X160)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insert) ).
fof(fact_IntE,axiom,
! [X160,X154,X18,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X18),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(X10),X18),X154))
=> ~ hBOOL(hAPP(hAPP(c_member(X10),X18),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntE) ).
fof(fact_upto_Opsimps,axiom,
! [X163,X113] :
( 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),X113),X163)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X113),X163))
=> c_List_Oupto(X113,X163) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X113),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X113),c_Groups_Oone__class_Oone(tc_Int_Oint)),X163)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X113),X163))
=> c_List_Oupto(X113,X163) = 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,
! [X73,X16,X154,X2,X13,X10] :
( c_Finite__Set_Ofun__left__comm(X10,X13,X2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(hAPP(c_Finite__Set_Ofold(X10,X13,X2),X73),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(X2,X16),hAPP(hAPP(c_Finite__Set_Ofold(X10,X13,X2),X73),X154)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__insert) ).
fof(fact_evalc_OIfFalse,axiom,
! [X76,X77,X75,X54,X38] :
( ~ hBOOL(hAPP(X38,X54))
=> ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X75),X54),X77))
=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X38,X76,X75)),X54),X77)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OIfFalse) ).
fof(fact_map__of__zip__is__None,axiom,
! [X16,X289,X13,X290,X10] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13)),X289)
=> ( hAPP(c_Map_Omap__of(X10,X13,hAPP(hAPP(c_List_Ozip(X10,X13),X290),X289)),X16) = c_Option_Ooption_ONone(X13)
<=> ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__zip__is__None) ).
fof(fact_map__fun__upd,axiom,
! [X168,X2,X13,X290,X25,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X25),hAPP(c_List_Oset(X10),X290)))
=> hAPP(hAPP(c_List_Omap(X10,X13),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,X13),X2),X25),X168)),X290) = hAPP(hAPP(c_List_Omap(X10,X13),X2),X290) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__fun__upd) ).
fof(fact_notin__set__sublistI,axiom,
! [X241,X290,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
=> ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),c_List_Osublist(X10,X290,X241)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_notin__set__sublistI) ).
fof(fact_notin__set__remove1,axiom,
! [X25,X290,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
=> ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),c_List_Oremove1(X10,X25,X290)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_notin__set__remove1) ).
fof(fact_nth__upt,axiom,
! [X119,X103,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X120),X103)),X119))
=> hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(X120,X119)),X103) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X120),X103) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__upt) ).
fof(fact_zpower__number__of__even,axiom,
! [X131,X73] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X73),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X131))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X73),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X131))),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,X10,X13] :
( class_Orderings_Oord(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,X13)),X2),X1))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X13)),X2),X1))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X13)),X1),X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__fun__def) ).
fof(fact_pick_Osimps,axiom,
! [X297,X93,X94,X120] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X120),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X94),X93)))
=> hAPP(c_Random_Opick(X94,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X94)),X93),X297)),X120) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X94),X93) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X120),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X94),X93)))
=> hAPP(c_Random_Opick(X94,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X94)),X93),X297)),X120) = hAPP(c_Random_Opick(X94,X297),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X120),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X94),X93))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pick_Osimps) ).
fof(fact_UnionE,axiom,
! [X198,X154,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X154),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X198)))
=> ~ ! [X270] :
( hBOOL(hAPP(hAPP(c_member(X10),X154),X270))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X270),X198)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnionE) ).
fof(fact_less__eq__int__code_I13_J,axiom,
! [X175,X176] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X176)),c_Int_OBit0(X175)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X176),X175)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__int__code_I13_J) ).
fof(fact_rel__simps_I31_J,axiom,
! [X162,X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X101)),c_Int_OBit0(X162)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X101),X162)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I31_J) ).
fof(fact_less__int__code_I13_J,axiom,
! [X175,X176] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X176)),c_Int_OBit0(X175)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X176),X175)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__int__code_I13_J) ).
fof(fact_rel__simps_I14_J,axiom,
! [X162,X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X101)),c_Int_OBit0(X162)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),X162)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I14_J) ).
fof(fact_card__Diff__singleton__if,axiom,
! [X16,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X154)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(X10),X154) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff__singleton__if) ).
fof(fact_add__special_I3_J,axiom,
! [X144,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),X144)),c_Groups_Oone__class_Oone(X94)) = hAPP(c_Int_Onumber__class_Onumber__of(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X144),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,
! [X131,X168,X10] :
( ( class_Int_Onumber(X10)
& class_Orderings_Olinorder(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X168)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)))
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X168))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__number__of__eq__not__less) ).
fof(fact_bot2E,axiom,
! [X25,X16,X13,X10] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X10,tc_fun(X13,tc_HOL_Obool))),X16),X25)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot2E) ).
fof(fact_evaln_Oequations_I5_J,axiom,
! [X66,X72,X52,X65,X50,X51] :
( c_Natural_Oevaln(c_Com_Ocom_OCond(X51,X50,X65),X52,X72,X66)
<=> ( ( hBOOL(hAPP(X51,X52))
& c_Natural_Oevaln(X50,X52,X72,X66) )
| ( ~ hBOOL(hAPP(X51,X52))
& c_Natural_Oevaln(X65,X52,X72,X66) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I5_J) ).
fof(fact_evaln_Oequations_I6_J,axiom,
! [X66,X72,X52,X50,X65,X51] :
( c_Natural_Oevaln(c_Com_Ocom_OCond(X51,X65,X50),X52,X72,X66)
<=> ( ( hBOOL(hAPP(X51,X52))
& c_Natural_Oevaln(X65,X52,X72,X66) )
| ( ~ hBOOL(hAPP(X51,X52))
& c_Natural_Oevaln(X50,X52,X72,X66) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I6_J) ).
fof(fact_evaln__elim__cases_I5_J,axiom,
! [X53,X20,X54,X74,X75,X38] :
( c_Natural_Oevaln(c_Com_Ocom_OCond(X38,X75,X74),X54,X20,X53)
=> ( ( hBOOL(hAPP(X38,X54))
=> ~ c_Natural_Oevaln(X75,X54,X20,X53) )
=> ~ ( ~ hBOOL(hAPP(X38,X54))
=> ~ c_Natural_Oevaln(X74,X54,X20,X53) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I5_J) ).
fof(fact_divmod__int__rel__mod__eq,axiom,
! [X105,X155,X156,X126] :
( X126 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X156),X155)),X105)
=> ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X156))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X105))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X105),X156)) ) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X156))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X156),X105))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X105),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
=> ( X156 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X126,X156) = X105 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__mod__eq) ).
fof(fact_foldr_Osimps_I1_J,axiom,
! [X39,X2,X10,X13] : c_List_Ofoldr(X13,X10,X2,c_List_Olist_ONil(X13),X39) = X39,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldr_Osimps_I1_J) ).
fof(fact_divmod__int__rel__div__eq,axiom,
! [X157,X105,X156,X126] :
( X126 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X156),X105)),X157)
=> ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X156))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X157))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X157),X156)) ) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X156))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X156),X157))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X157),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
=> ( X156 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X126),X156) = X105 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__div__eq) ).
fof(fact_rotate__Suc,axiom,
! [X297,X42,X94] : hAPP(c_List_Orotate(X94,hAPP(c_Nat_OSuc,X42)),X297) = hAPP(c_List_Orotate1(X94),hAPP(c_List_Orotate(X94,X42),X297)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__Suc) ).
fof(fact_fun__left__comm_Ofold__insert2,axiom,
! [X73,X16,X154,X2,X13,X10] :
( c_Finite__Set_Ofun__left__comm(X10,X13,X2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(hAPP(c_Finite__Set_Ofold(X10,X13,X2),X73),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X13,X2),hAPP(hAPP(X2,X16),X73)),X154) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__insert2) ).
fof(fact_upt__eq__Cons__conv,axiom,
! [X290,X16,X163,X113] :
( c_List_Oupt(X113,X163) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X16),X290)
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X113),X163))
& X113 = X16
& c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X113),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X163) = X290 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__eq__Cons__conv) ).
fof(fact_setsum__op__ivl__Suc,axiom,
! [X2,X102,X20,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X102))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X102),hAPP(c_Nat_OSuc,X20))) = c_Groups_Ozero__class_Ozero(X10) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X102))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X102),hAPP(c_Nat_OSuc,X20))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X102),X20))),hAPP(X2,X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__op__ivl__Suc) ).
fof(fact_sup1E,axiom,
! [X16,X160,X154,X10] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160),X16))
=> ( ~ hBOOL(hAPP(X154,X16))
=> hBOOL(hAPP(X160,X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1E) ).
fof(fact_pred__Bit1,axiom,
! [X103] : c_Int_Opred(c_Int_OBit1(X103)) = c_Int_OBit0(X103),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__Bit1) ).
fof(fact_nat__number__of__add__left,axiom,
! [X103,X170,X144] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)),X103)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)),X103) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X170)))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)),X103)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),X103) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X170)))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)),X103)) = 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),X144),X170))),X103) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__add__left) ).
fof(fact_trancl__empty,axiom,
! [X10] : c_Transitive__Closure_Otrancl(X10,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__empty) ).
fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
! [X20,X102,X2,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X102,X20))) = hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X10),X2),c_List_Oupt(X102,X20))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__set__upt__conv__listsum__nat) ).
fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
! [X20,X102,X2,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X10),X2),c_List_Oupt(X102,X20))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X102,X20))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_interv__listsum__conv__setsum__set__nat) ).
fof(fact_inf1E,axiom,
! [X16,X160,X154,X10] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160),X16))
=> ~ ( hBOOL(hAPP(X154,X16))
=> ~ hBOOL(hAPP(X160,X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1E) ).
fof(fact_rotate1__rotate__swap,axiom,
! [X297,X42,X94] : hAPP(c_List_Orotate1(X94),hAPP(c_List_Orotate(X94,X42),X297)) = hAPP(c_List_Orotate(X94,X42),hAPP(c_List_Orotate1(X94),X297)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate1__rotate__swap) ).
fof(fact_number__of__Bit1,axiom,
! [X133,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OBit1(X133)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),c_Groups_Oone__class_Oone(X94)),hAPP(c_Int_Onumber__class_Onumber__of(X94),X133))),hAPP(c_Int_Onumber__class_Onumber__of(X94),X133)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__Bit1) ).
fof(fact_DiffI,axiom,
! [X160,X154,X18,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X18),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X18),X160))
=> hBOOL(hAPP(hAPP(c_member(X10),X18),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffI) ).
fof(fact_code__numeral_Orecs_I2_J,axiom,
! [X181,X37,X12,X10] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X10,X12,X37,c_Code__Numeral_OSuc__code__numeral(X181)) = hAPP(hAPP(X37,X181),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X10,X12,X37,X181)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Orecs_I2_J) ).
fof(fact_Suc__code__numeral__def,axiom,
! [X103] : c_Code__Numeral_OSuc__code__numeral(X103) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X103))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__code__numeral__def) ).
fof(fact_card__def,axiom,
! [X154,X10] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(c_Finite__Set_Ocard(X10),X154) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X10,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X10),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X154) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(c_Finite__Set_Ocard(X10),X154) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__def) ).
fof(fact_Id__O__R,axiom,
! [X196,X13,X10] : hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X13),c_Relation_OId(X10)),X196) = X196,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__O__R) ).
fof(fact_divide__numeral__1,axiom,
! [X84,X94] :
( ( class_Fields_Ofield(X94)
& class_Int_Onumber__ring(X94) )
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X84),hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OBit1(c_Int_OPls))) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__numeral__1) ).
fof(fact_divide__Numeral1,axiom,
! [X93,X94] :
( ( class_Fields_Ofield(X94)
& class_Int_Onumber__ring(X94) )
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X93),hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OBit1(c_Int_OPls))) = X93 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__Numeral1) ).
fof(fact_le__supE,axiom,
! [X93,X92,X84,X94] :
( class_Lattices_Osemilattice__sup(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X84),X92)),X93))
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X93))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X92),X93)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__supE) ).
fof(fact_min__max_Ole__supE,axiom,
! [X93,X92,X84,X94] :
( class_Orderings_Olinorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X84),X92)),X93))
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X93))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X92),X93)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__supE) ).
fof(fact_mult__numeral__1__right,axiom,
! [X84,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OBit1(c_Int_OPls))) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__numeral__1__right) ).
fof(fact_hd__rotate__conv__nth,axiom,
! [X42,X94,X297] :
( X297 != c_List_Olist_ONil(X94)
=> hAPP(c_List_Ohd(X94),hAPP(c_List_Orotate(X94,X42),X297)) = hAPP(hAPP(c_List_Onth(X94),X297),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X42,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__rotate__conv__nth) ).
fof(fact_nat__number__of__mult__left,axiom,
! [X103,X170,X144] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X144),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)),X103)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X144),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)),X103)) = 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),X144),X170))),X103) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__mult__left) ).
fof(fact_rotate__length01,axiom,
! [X42,X297,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
=> hAPP(c_List_Orotate(X94,X42),X297) = X297 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__length01) ).
fof(fact_Int__insert__left,axiom,
! [X160,X198,X39,X10] :
( ( hBOOL(hAPP(hAPP(c_member(X10),X39),X198))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X39),X160)),X198) = hAPP(hAPP(c_Set_Oinsert(X10),X39),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X160),X198)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X198))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X39),X160)),X198) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X160),X198) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__left) ).
fof(fact_UnCI,axiom,
! [X154,X160,X18,X10] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X10),X18),X160))
=> hBOOL(hAPP(hAPP(c_member(X10),X18),X154)) )
=> hBOOL(hAPP(hAPP(c_member(X10),X18),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnCI) ).
fof(fact_map__add__dom__app__simps_I2_J,axiom,
! [X281,X282,X13,X102,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X102),c_Map_Odom(X10,X13,X282)))
=> hAPP(c_Map_Omap__add(X10,X13,X282,X281),X102) = hAPP(X281,X102) ),
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,
! [X282,X281,X13,X102,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X102),c_Map_Odom(X10,X13,X281)))
=> hAPP(c_Map_Omap__add(X10,X13,X282,X281),X102) = hAPP(X282,X102) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__dom__app__simps_I3_J) ).
fof(fact_not__square__less__zero,axiom,
! [X84,X94] :
( class_Rings_Olinordered__ring(X94)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X84)),c_Groups_Ozero__class_Ozero(X94))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__square__less__zero) ).
fof(fact_bin__less__0__simps_I3_J,axiom,
! [X131] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X131)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X131),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,
! [X133,X144] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X144))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X133))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__number__of__Bit0) ).
fof(fact_add__leE,axiom,
! [X42,X103,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X103)),X42))
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),X42))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X103),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leE) ).
fof(fact_rel__simps_I27_J,axiom,
! [X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X101)),c_Int_OPls))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X101),c_Int_OPls)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I27_J) ).
fof(fact_rel__simps_I28_J,axiom,
! [X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X101)),c_Int_OMin))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X101),c_Int_OMin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I28_J) ).
fof(fact_rel__simps_I11_J,axiom,
! [X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X101)),c_Int_OMin))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X101),c_Int_OMin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I11_J) ).
fof(fact_rel__simps_I10_J,axiom,
! [X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X101)),c_Int_OPls))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),c_Int_OPls)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I10_J) ).
fof(fact_neg__number__of__Bit0,axiom,
! [X131] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X131))))
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X131))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__number__of__Bit0) ).
fof(fact_Image__Id,axiom,
! [X154,X10] : hAPP(c_Relation_OImage(X10,X10,c_Relation_OId(X10)),X154) = X154,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Id) ).
fof(fact_insert__Diff__if,axiom,
! [X154,X160,X16,X10] :
( ( hBOOL(hAPP(hAPP(c_member(X10),X16),X160))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)),X160) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X160))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)),X160) = hAPP(hAPP(c_Set_Oinsert(X10),X16),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Diff__if) ).
fof(fact_map__comp__empty_I2_J,axiom,
! [X16,X102,X125,X10,X13] : c_Map_Omap__comp(X13,X10,X125,hAPP(c_COMBK(tc_Option_Ooption(X10),X13),c_Option_Ooption_ONone(X10)),X102,X16) = c_Option_Ooption_ONone(X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__empty_I2_J) ).
fof(fact_map__comp__empty_I1_J,axiom,
! [X16,X102,X125,X10,X13] : c_Map_Omap__comp(X13,X10,X125,X102,hAPP(c_COMBK(tc_Option_Ooption(X13),X125),c_Option_Ooption_ONone(X13)),X16) = c_Option_Ooption_ONone(X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__empty_I1_J) ).
fof(fact_le__iff__pred__less,axiom,
! [X162,X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X101),X162))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X101)),X162)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__pred__less) ).
fof(fact_diff__bin__simps_I6_J,axiom,
! [X121] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X121)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X121)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I6_J) ).
fof(fact_evaln_OIfFalse,axiom,
! [X76,X77,X20,X75,X54,X38] :
( ~ hBOOL(hAPP(X38,X54))
=> ( c_Natural_Oevaln(X75,X54,X20,X77)
=> c_Natural_Oevaln(c_Com_Ocom_OCond(X38,X76,X75),X54,X20,X77) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OIfFalse) ).
fof(fact_div__if,axiom,
! [X97,X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X42))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X97),X42) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X97),X42) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42)),X42)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__if) ).
fof(fact_div__geq,axiom,
! [X97,X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X42))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X97),X42) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42)),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__geq) ).
fof(fact_not__zle__0__negative,axiom,
! [X42] : ~ 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,X42))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__zle__0__negative) ).
fof(fact_rtrancl__reflcl__absorb,axiom,
! [X196,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X10,X196)),c_Relation_OId(X10)) = c_Transitive__Closure_Ortrancl(X10,X196),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__reflcl__absorb) ).
fof(fact_upt__Suc__append,axiom,
! [X119,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X120),X119))
=> c_List_Oupt(X120,hAPP(c_Nat_OSuc,X119)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X120,X119)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X119),c_List_Olist_ONil(tc_Nat_Onat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__Suc__append) ).
fof(fact_Int__insert__right,axiom,
! [X160,X154,X39,X10] :
( ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),X160)) = hAPP(hAPP(c_Set_Oinsert(X10),X39),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__right) ).
fof(fact_setsum_OF__eq,axiom,
! [X1,X154,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1),X154) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13,X10,c_Groups_Oplus__class_Oplus(X13)),X1),c_Groups_Ozero__class_Ozero(X13)),X154) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1),X154) = c_Groups_Ozero__class_Ozero(X13) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_OF__eq) ).
fof(fact_setprod_OF__eq,axiom,
! [X1,X154,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),X154) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13,X10,c_Groups_Otimes__class_Otimes(X13)),X1),c_Groups_Oone__class_Oone(X13)),X154) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),X154) = c_Groups_Oone__class_Oone(X13) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_OF__eq) ).
fof(fact_nth__append,axiom,
! [X298,X297,X94,X42] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)))
=> hAPP(hAPP(c_List_Onth(X94),hAPP(hAPP(c_List_Oappend(X94),X297),X298)),X42) = hAPP(hAPP(c_List_Onth(X94),X297),X42) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)))
=> hAPP(hAPP(c_List_Onth(X94),hAPP(hAPP(c_List_Oappend(X94),X297),X298)),X42) = hAPP(hAPP(c_List_Onth(X94),X298),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__append) ).
fof(fact_Compl__iff,axiom,
! [X154,X18,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X18),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X154)))
<=> ~ hBOOL(hAPP(hAPP(c_member(X10),X18),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__iff) ).
fof(fact_ComplD,axiom,
! [X154,X18,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X18),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X154)))
=> ~ hBOOL(hAPP(hAPP(c_member(X10),X18),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ComplD) ).
fof(fact_ComplE,axiom,
! [X154,X18,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X18),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X154)))
=> ~ hBOOL(hAPP(hAPP(c_member(X10),X18),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ComplE) ).
fof(fact_nat__number__of__Bit0,axiom,
! [X131] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X131)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X131)),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,
! [X144,X80,X10] :
( ( class_Int_Onumber(X10)
& class_Orderings_Oord(X10) )
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X80)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X144)))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X80)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X144)) = hAPP(c_Int_Onumber__class_Onumber__of(X10),X144) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X80)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X144)))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X80)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X144)) = hAPP(c_Int_Onumber__class_Onumber__of(X10),X80) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__number__of) ).
fof(fact_min__number__of,axiom,
! [X144,X80,X10] :
( ( class_Int_Onumber(X10)
& class_Orderings_Oord(X10) )
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X80)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X144)))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X80)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X144)) = hAPP(c_Int_Onumber__class_Onumber__of(X10),X80) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X80)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X144)))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X80)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X144)) = hAPP(c_Int_Onumber__class_Onumber__of(X10),X144) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__number__of) ).
fof(fact_not__add__less1,axiom,
! [X119,X120] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X120),X119)),X120)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less1) ).
fof(fact_not__add__less2,axiom,
! [X120,X119] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X119),X120)),X120)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less2) ).
fof(fact_remove1__append,axiom,
! [X289,X290,X16,X10] :
( ( hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
=> c_List_Oremove1(X10,X16,hAPP(hAPP(c_List_Oappend(X10),X290),X289)) = hAPP(hAPP(c_List_Oappend(X10),c_List_Oremove1(X10,X16,X290)),X289) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
=> c_List_Oremove1(X10,X16,hAPP(hAPP(c_List_Oappend(X10),X290),X289)) = hAPP(hAPP(c_List_Oappend(X10),X290),c_List_Oremove1(X10,X16,X289)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1__append) ).
fof(fact_neg__number__of__pred__iff__0,axiom,
! [X168] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X168))))
<=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168) = 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,
! [X16,X2,X10] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X10,X2,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__fold1SetE) ).
fof(fact_rel__simps_I51_J,axiom,
! [X162,X101] :
( c_Int_OBit1(X101) = c_Int_OBit1(X162)
<=> X101 = X162 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I51_J) ).
fof(fact_restrict__map__def,axiom,
! [X102,X13,X154,X16,X10] :
( ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Map_Orestrict__map(X10,X13,X102,X154),X16) = hAPP(X102,X16) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Map_Orestrict__map(X10,X13,X102,X154),X16) = c_Option_Ooption_ONone(X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__map__def) ).
fof(fact_nat__diff__split__asm,axiom,
! [X38,X39,X19] :
( hBOOL(hAPP(X19,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X39),X38)))
<=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X39),X38))
& ~ hBOOL(hAPP(X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X164] :
( X39 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X38),X164)
& ~ hBOOL(hAPP(X19,X164)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).
fof(fact_distinct_Osimps_I2_J,axiom,
! [X290,X16,X10] :
( hBOOL(hAPP(c_List_Odistinct(X10),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290)))
<=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
& hBOOL(hAPP(c_List_Odistinct(X10),X290)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct_Osimps_I2_J) ).
fof(fact_finite__map__freshness,axiom,
! [X2,X13,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Map_Odom(X10,X13,X2)))
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))))
=> ? [X3] : hAPP(X2,X3) = c_Option_Ooption_ONone(X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__map__freshness) ).
fof(fact_length__rotate,axiom,
! [X297,X42,X94] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),hAPP(c_List_Orotate(X94,X42),X297)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__rotate) ).
fof(fact_Diff__insert__absorb,axiom,
! [X154,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = X154 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__insert__absorb) ).
fof(fact_setsum__insert,axiom,
! [X2,X39,X225,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X225))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X225))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),hAPP(hAPP(c_Set_Oinsert(X10),X39),X225)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(X2,X39)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),X225)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__insert) ).
fof(fact_setsum_Oinsert,axiom,
! [X1,X16,X154,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(X1,X16)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1),X154)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oinsert) ).
fof(fact_setprod_Oinsert,axiom,
! [X1,X16,X154,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),hAPP(X1,X16)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),X154)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Oinsert) ).
fof(fact_setprod__insert,axiom,
! [X2,X39,X154,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),hAPP(hAPP(c_Set_Oinsert(X10),X39),X154)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),hAPP(X2,X39)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),X154)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__insert) ).
fof(fact_drop__upt,axiom,
! [X119,X120,X97] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),X97),c_List_Oupt(X120,X119)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X120),X97),X119),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__upt) ).
fof(fact_filter__empty__conv,axiom,
! [X290,X19,X10] :
( hAPP(c_List_Ofilter(X10,X19),X290) = c_List_Olist_ONil(X10)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X290)))
=> ~ hBOOL(hAPP(X19,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__empty__conv) ).
fof(fact_not__int__zless__negative,axiom,
! [X97,X42] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X42)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X97)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__int__zless__negative) ).
fof(fact_set__rotate,axiom,
! [X290,X20,X10] : hAPP(c_List_Oset(X10),hAPP(c_List_Orotate(X10,X20),X290)) = hAPP(c_List_Oset(X10),X290),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rotate) ).
fof(fact_sup1CI,axiom,
! [X10,X154,X16,X160] :
( ( ~ hBOOL(hAPP(X160,X16))
=> hBOOL(hAPP(X154,X16)) )
=> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1CI) ).
fof(fact_partition__P,axiom,
! [X329,X330,X290,X19,X10] :
( c_List_Opartition(X10,X19,X290) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X330),X329)
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X330)))
=> hBOOL(hAPP(X19,X3)) )
& ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X329)))
=> ~ hBOOL(hAPP(X19,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition__P) ).
fof(fact_trancl__domain,axiom,
! [X177,X10] : hAPP(c_Relation_ODomain(X10,X10),c_Transitive__Closure_Otrancl(X10,X177)) = hAPP(c_Relation_ODomain(X10,X10),X177),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__domain) ).
fof(fact_trancl__range,axiom,
! [X177,X10] : hAPP(c_Relation_ORange(X10,X10),c_Transitive__Closure_Otrancl(X10,X177)) = hAPP(c_Relation_ORange(X10,X10),X177),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__range) ).
fof(fact_le__nat__number__of,axiom,
! [X174,X168] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X174)))
<=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X168),X174))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X168),c_Int_OPls)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__nat__number__of) ).
fof(fact_dvd_Oless__trans,axiom,
! [X104,X105,X93] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X93),X105))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X105),X93)) )
=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X105),X104))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X104),X105)) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X93),X104))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X104),X93)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__trans) ).
fof(fact_diff__bin__simps_I7_J,axiom,
! [X121,X103] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X103)),c_Int_OBit0(X121)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X103),X121)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I7_J) ).
fof(fact_add__Bit0__Bit0,axiom,
! [X121,X103] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X103)),c_Int_OBit0(X121)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X103),X121)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Bit0__Bit0) ).
fof(fact_folding__one_Oeq__fold_H,axiom,
! [X16,X154,X225,X2,X10] :
( c_Finite__Set_Ofolding__one(X10,X2,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(X225,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,X2),X16),X154) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oeq__fold_H) ).
fof(fact_Abs__Integ__cases,axiom,
! [X16] :
~ ! [X90] :
( X16 = hAPP(c_Int_OAbs__Integ,X90)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X90),c_Int_OInteg)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Abs__Integ__cases) ).
fof(fact_upt__conv__Cons,axiom,
! [X119,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),X119))
=> c_List_Oupt(X120,X119) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X120),c_List_Oupt(hAPP(c_Nat_OSuc,X120),X119)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__conv__Cons) ).
fof(fact_map__comp__simps_I2_J,axiom,
! [X278,X13,X125,X287,X10,X101,X277] :
( hAPP(X277,X101) = hAPP(c_Option_Ooption_OSome(X10),X287)
=> c_Map_Omap__comp(X10,X125,X13,X278,X277,X101) = hAPP(X278,X287) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__simps_I2_J) ).
fof(fact_filter__insort__triv,axiom,
! [X290,X2,X10,X16,X19,X13] :
( class_Orderings_Olinorder(X13)
=> ( ~ hBOOL(hAPP(X19,X16))
=> hAPP(c_List_Ofilter(X10,X19),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X13,X2),X16),X290)) = hAPP(c_List_Ofilter(X10,X19),X290) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__insort__triv) ).
fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omin(X10)),X16),X154) ) ) ),
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,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omax(X10)),X16),X154) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oeq__fold_H) ).
fof(fact_nat__dvd__iff,axiom,
! [X102,X73] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X73)),X102))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X73),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X102))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73))
=> X102 = 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,
! [X154,X10] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X154),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__psubset__empty) ).
fof(fact_restrict__out,axiom,
! [X102,X13,X154,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Map_Orestrict__map(X10,X13,X102,X154),X16) = c_Option_Ooption_ONone(X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__out) ).
fof(fact_fold1__eq__fold,axiom,
! [X39,X154,X10] :
( class_Groups_Oab__semigroup__mult(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),hAPP(hAPP(c_Set_Oinsert(X10),X39),X154)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Groups_Otimes__class_Otimes(X10)),X39),X154) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__eq__fold) ).
fof(fact_number__of__Bit0,axiom,
! [X133,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OBit0(X133)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(c_Int_Onumber__class_Onumber__of(X94),X133))),hAPP(c_Int_Onumber__class_Onumber__of(X94),X133)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__Bit0) ).
fof(fact_map__nth,axiom,
! [X290,X10] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X10),hAPP(c_List_Onth(X10),X290)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290))) = X290,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__nth) ).
fof(fact_le__infE,axiom,
! [X92,X84,X93,X94] :
( class_Lattices_Osemilattice__inf(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X84),X92)))
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X84))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X92)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infE) ).
fof(fact_min__max_Ole__infE,axiom,
! [X92,X84,X93,X94] :
( class_Orderings_Olinorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X84),X92)))
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X84))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X92)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__infE) ).
fof(fact_length__remove1,axiom,
! [X290,X16,X10] :
( ( hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_List_Oremove1(X10,X16,X290)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_List_Oremove1(X10,X16,X290)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__remove1) ).
fof(fact_Int__insert__left__if0,axiom,
! [X160,X198,X39,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X198))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X39),X160)),X198) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X160),X198) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__left__if0) ).
fof(fact_nat__of__aux__code,axiom,
! [X42,X120] :
( ( X120 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> c_Code__Numeral_Onat__of__aux(X120,X42) = X42 )
& ( X120 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> c_Code__Numeral_Onat__of__aux(X120,X42) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X120),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of__aux__code) ).
fof(fact_nat__of__aux__def,axiom,
! [X42,X120] : c_Code__Numeral_Onat__of__aux(X120,X42) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X120)),X42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of__aux__def) ).
fof(fact_wf__trancl,axiom,
! [X177,X10] :
( c_Wellfounded_Owf(X10,X177)
=> c_Wellfounded_Owf(X10,c_Transitive__Closure_Otrancl(X10,X177)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__trancl) ).
fof(fact_R__O__Id,axiom,
! [X196,X13,X10] : hAPP(hAPP(c_Relation_Orel__comp(X10,X13,X13),X196),c_Relation_OId(X13)) = X196,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_R__O__Id) ).
fof(fact_map__comp__simps_I1_J,axiom,
! [X278,X13,X125,X10,X101,X277] :
( hAPP(X277,X101) = c_Option_Ooption_ONone(X10)
=> c_Map_Omap__comp(X10,X125,X13,X278,X277,X101) = c_Option_Ooption_ONone(X125) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__simps_I1_J) ).
fof(fact_trancl__unfold__right,axiom,
! [X177,X10] : c_Transitive__Closure_Otrancl(X10,X177) = hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),c_Transitive__Closure_Ortrancl(X10,X177)),X177),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__unfold__right) ).
fof(fact_trancl__rtrancl__absorb,axiom,
! [X196,X10] : c_Transitive__Closure_Ortrancl(X10,c_Transitive__Closure_Otrancl(X10,X196)) = c_Transitive__Closure_Ortrancl(X10,X196),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__rtrancl__absorb) ).
fof(fact_concat_Osimps_I1_J,axiom,
! [X94] : c_List_Oconcat(X94,c_List_Olist_ONil(tc_List_Olist(X94))) = c_List_Olist_ONil(X94),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat_Osimps_I1_J) ).
fof(fact_dvd_OatLeastatMost__empty__iff,axiom,
! [X38,X39] :
( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X39,X38) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
<=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X39),X38)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastatMost__empty__iff) ).
fof(fact_dvd_OatLeastatMost__empty__iff2,axiom,
! [X38,X39] :
( 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),X39,X38)
<=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X39),X38)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastatMost__empty__iff2) ).
fof(fact_Min_Oeq__fold_H,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> c_Big__Operators_Olinorder__class_OMin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omin(X10)),X16),X154) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oeq__fold_H) ).
fof(fact_Max_Oeq__fold_H,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> c_Big__Operators_Olinorder__class_OMax(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omax(X10)),X16),X154) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oeq__fold_H) ).
fof(fact_Inf__fin_Oeq__fold_H,axiom,
! [X16,X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__inf__class_Oinf(X10)),X16),X154) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oeq__fold_H) ).
fof(fact_Sup__fin_Oeq__fold_H,axiom,
! [X16,X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__sup__class_Osup(X10)),X16),X154) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oeq__fold_H) ).
fof(fact_eq__nat__number__of,axiom,
! [X174,X168] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X174)
<=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X168)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X174)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X168)))
=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X174)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X168) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X174)))
=> X168 = X174 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__nat__number__of) ).
fof(fact_abs__number__of,axiom,
! [X93,X94] :
( ( class_Int_Onumber__ring(X94)
& class_Rings_Olinordered__idom(X94) )
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),X93)),c_Groups_Ozero__class_Ozero(X94)))
=> hAPP(c_Groups_Oabs__class_Oabs(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),X93)) = hAPP(c_Groups_Ouminus__class_Ouminus(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),X93)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),X93)),c_Groups_Ozero__class_Ozero(X94)))
=> hAPP(c_Groups_Oabs__class_Oabs(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),X93)) = hAPP(c_Int_Onumber__class_Onumber__of(X94),X93) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__number__of) ).
fof(fact_converse__Id,axiom,
! [X10] : hAPP(c_Relation_Oconverse(X10,X10),c_Relation_OId(X10)) = c_Relation_OId(X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__Id) ).
fof(fact_mod__nat__number__of,axiom,
! [X170,X144] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X170)))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X170)))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X170))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__nat__number__of) ).
fof(fact_min__max_OInf__fin_Oinsert,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X16),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X154)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oinsert) ).
fof(fact_min__max_OSup__fin_Oinsert,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X16),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X154)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oinsert) ).
fof(fact_mult__Bit0,axiom,
! [X121,X103] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(X103)),X121) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X103),X121)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Bit0) ).
fof(fact_dvd_Ole__less__trans,axiom,
! [X104,X105,X93] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X93),X105))
=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X105),X104))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X104),X105)) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X93),X104))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X104),X93)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Ole__less__trans) ).
fof(fact_dvd_Oless__le__trans,axiom,
! [X104,X105,X93] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X93),X105))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X105),X93)) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X105),X104))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X93),X104))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X104),X93)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__le__trans) ).
fof(fact_power__nat__number__of__number__of,axiom,
! [X133,X144] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X133)) = 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),X133)) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X133)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X133))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__nat__number__of__number__of) ).
fof(fact_div__nat__number__of,axiom,
! [X170,X144] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X170))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__nat__number__of) ).
fof(fact_fold1__insert,axiom,
! [X16,X154,X10] :
( class_Groups_Oab__semigroup__mult(X10)
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X16),hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),X154)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__insert) ).
fof(fact_dvd_OatLeastatMost__empty,axiom,
! [X39,X38] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X38),X39))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X39),X38)) )
=> c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X39,X38) = 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,
! [X97,X144] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X144))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X97)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X144))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__number__of) ).
fof(fact_ex__least__nat__less,axiom,
! [X20,X19] :
( ~ hBOOL(hAPP(X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(X19,X20))
=> ? [X124] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X124),X20))
& ! [X152] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X152),X124))
=> ~ hBOOL(hAPP(X19,X152)) )
& hBOOL(hAPP(X19,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X124),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,
! [X102,X20] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X20,X102) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X20),hAPP(c_Nat_OSuc,X102))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanAtMost__upt) ).
fof(fact_rel__simps_I21_J,axiom,
! [X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X101)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X101)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I21_J) ).
fof(fact_rel__simps_I4_J,axiom,
! [X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X101)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X101)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I4_J) ).
fof(fact_rel__simps_I25_J,axiom,
! [X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X101)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X101)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I25_J) ).
fof(fact_rel__simps_I8_J,axiom,
! [X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X101)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X101)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I8_J) ).
fof(fact_Int__insert__right__if0,axiom,
! [X160,X154,X39,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__right__if0) ).
fof(fact_rotate__id,axiom,
! [X297,X94,X42] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X42,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_List_Orotate(X94,X42),X297) = X297 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__id) ).
fof(fact_rotate__is__Nil__conv,axiom,
! [X290,X20,X10] :
( hAPP(c_List_Orotate(X10,X20),X290) = c_List_Olist_ONil(X10)
<=> X290 = c_List_Olist_ONil(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__is__Nil__conv) ).
fof(fact_simp__from__to,axiom,
! [X113,X163] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X163),X113))
=> c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X113,X163) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X163),X113))
=> c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X113,X163) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),X113),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X113),c_Groups_Oone__class_Oone(tc_Int_Oint)),X163)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_simp__from__to) ).
fof(fact_double__number__of__Bit0,axiom,
! [X133,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),c_Groups_Oone__class_Oone(X94)),c_Groups_Oone__class_Oone(X94))),hAPP(c_Int_Onumber__class_Onumber__of(X94),X133)) = hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OBit0(X133)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__number__of__Bit0) ).
fof(fact_insertCI,axiom,
! [X38,X160,X39,X10] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X160))
=> X39 = X38 )
=> hBOOL(hAPP(hAPP(c_member(X10),X39),hAPP(hAPP(c_Set_Oinsert(X10),X38),X160))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertCI) ).
fof(fact_Bit1__def,axiom,
! [X103] : c_Int_OBit1(X103) = 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)),X103)),X103),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit1__def) ).
fof(fact_internal__split__conv,axiom,
! [X38,X39,X18,X10,X125,X13] : hAPP(hAPP(c_Product__Type_Ointernal__split(X13,X125,X10),X18),hAPP(hAPP(c_Product__Type_OPair(X13,X125),X39),X38)) = hAPP(hAPP(X18,X39),X38),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_internal__split__conv) ).
fof(fact_internal__split__def,axiom,
! [X125,X13,X10] : c_Product__Type_Ointernal__split(X10,X13,X125) = c_Product__Type_Oprod_Oprod__case(X10,X13,X125),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_internal__split__def) ).
fof(fact_ComplI,axiom,
! [X154,X18,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X18),X154))
=> hBOOL(hAPP(hAPP(c_member(X10),X18),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X154))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ComplI) ).
fof(fact_vimage__const,axiom,
! [X13,X154,X18,X10] :
( ( hBOOL(hAPP(hAPP(c_member(X10),X18),X154))
=> hAPP(c_Set_Ovimage(X13,X10,hAPP(c_COMBK(X10,X13),X18)),X154) = c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X18),X154))
=> hAPP(c_Set_Ovimage(X13,X10,hAPP(c_COMBK(X10,X13),X18)),X154) = c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__const) ).
fof(fact_folding__one_Oinsert,axiom,
! [X16,X154,X225,X2,X10] :
( c_Finite__Set_Ofolding__one(X10,X2,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(X225,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(X2,X16),hAPP(X225,X154)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oinsert) ).
fof(fact_zdvd__not__zless,axiom,
! [X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X97))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X97),X42))
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X42),X97)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__not__zless) ).
fof(fact_nat__dvd__not__less,axiom,
! [X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X97))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42))
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X42),X97)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__dvd__not__less) ).
fof(fact_map__Suc__upt,axiom,
! [X20,X102] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(X102,X20)) = c_List_Oupt(hAPP(c_Nat_OSuc,X102),hAPP(c_Nat_OSuc,X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__Suc__upt) ).
fof(fact_divmod__int__def,axiom,
! [X92,X84] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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)),X92))
=> c_Divides_Odivmod__int(X84,X92) = c_Divides_OposDivAlg(X84,X92) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X92))
=> ( ( X84 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odivmod__int(X84,X92) = 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)) )
& ( X84 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odivmod__int(X84,X92) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X84),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X92))) ) ) ) ) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X92))
=> c_Divides_Odivmod__int(X84,X92) = c_Divides_OnegDivAlg(X84,X92) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X92))
=> c_Divides_Odivmod__int(X84,X92) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X84),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X92))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__def) ).
fof(fact_refl__Id,axiom,
! [X10] : c_Relation_Orefl__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),c_Relation_OId(X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__Id) ).
fof(fact_numeral__1__eq__1,axiom,
! [X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_numeral__1__eq__1) ).
fof(fact_semiring__norm_I110_J,axiom,
! [X94] :
( class_Int_Onumber__ring(X94)
=> c_Groups_Oone__class_Oone(X94) = hAPP(c_Int_Onumber__class_Onumber__of(X94),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,
! [X20,X102] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)),X102)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
fof(fact_abs__not__less__zero,axiom,
! [X84,X94] :
( class_Groups_Oordered__ab__group__add__abs(X94)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),X84)),c_Groups_Ozero__class_Ozero(X94))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__not__less__zero) ).
fof(fact_of__nat__less__0__iff,axiom,
! [X97,X94] :
( class_Rings_Olinordered__semidom(X94)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),X97)),c_Groups_Ozero__class_Ozero(X94))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__less__0__iff) ).
fof(fact_iszero__number__of__Bit0,axiom,
! [X131,X10] :
( ( class_Int_Onumber__ring(X10)
& class_Int_Oring__char__0(X10) )
=> ( c_Int_Oiszero(X10,hAPP(c_Int_Onumber__class_Onumber__of(X10),c_Int_OBit0(X131)))
<=> c_Int_Oiszero(X10,hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iszero__number__of__Bit0) ).
fof(fact_add__nat__number__of,axiom,
! [X170,X144] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X144),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X144),c_Int_OPls))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X170),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X170),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X144),X170)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nat__number__of) ).
fof(fact_power__nat__number__of,axiom,
! [X42,X144] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),X42) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X42) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),X42) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__nat__number__of) ).
fof(fact_diff__bin__simps_I3_J,axiom,
! [X121] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X121)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X121)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I3_J) ).
fof(fact_minus__shift__def,axiom,
! [X143,X121,X103] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X103),X121))
=> c_Random_Ominus__shift(X143,X103,X121) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X143),X103)),X121) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X103),X121))
=> c_Random_Ominus__shift(X143,X103,X121) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X103),X121) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__shift__def) ).
fof(fact_split__zmod,axiom,
! [X101,X20,X19] :
( hBOOL(hAPP(X19,c_Divides_Odiv__class_Omod(tc_Int_Oint,X20,X101)))
<=> ( ( X101 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(X19,X20)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X101))
=> ! [X152,X123] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X123))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X123),X101))
& X20 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X101),X152)),X123) )
=> hBOOL(hAPP(X19,X123)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ! [X152,X123] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),X123))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X123),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& X20 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X101),X152)),X123) )
=> hBOOL(hAPP(X19,X123)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__zmod) ).
fof(fact_upto_Osimps,axiom,
! [X119,X120] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X120),X119))
=> c_List_Oupto(X120,X119) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X120),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X120),c_Groups_Oone__class_Oone(tc_Int_Oint)),X119)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X120),X119))
=> c_List_Oupto(X120,X119) = c_List_Olist_ONil(tc_Int_Oint) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upto_Osimps) ).
fof(fact_rel__simps_I49_J,axiom,
! [X121,X103] : c_Int_OBit0(X103) != c_Int_OBit1(X121),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I49_J) ).
fof(fact_rel__simps_I50_J,axiom,
! [X121,X103] : c_Int_OBit1(X103) != c_Int_OBit0(X121),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I50_J) ).
fof(fact_divmod__nat__div__mod,axiom,
! [X42,X97] : c_Divides_Odivmod__nat(X97,X42) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X97),X42)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X97,X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__div__mod) ).
fof(fact_code__numeral_Osimps_I5_J,axiom,
! [X181,X37,X12,X10] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X10,X12,X37,c_Code__Numeral_OSuc__code__numeral(X181)) = hAPP(X37,X181),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Osimps_I5_J) ).
fof(fact_greaterThanLessThan__upt,axiom,
! [X102,X20] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X20,X102) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X20),X102)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanLessThan__upt) ).
fof(fact_of__int__of__nat,axiom,
! [X103,X94] :
( class_Rings_Oring__1(X94)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X103),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Int_Oring__1__class_Oof__int(X94),X103) = hAPP(c_Groups_Ouminus__class_Ouminus(X94),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X103)))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X103),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Int_Oring__1__class_Oof__int(X94),X103) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),hAPP(c_Int_Onat,X103)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__of__nat) ).
fof(fact_WTs__elim__cases_I5_J,axiom,
! [X74,X75,X38] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X38,X75,X74)))
=> ~ ( hBOOL(hAPP(c_Com_OWT,X75))
=> ~ hBOOL(hAPP(c_Com_OWT,X74)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WTs__elim__cases_I5_J) ).
fof(fact_Domain__Id,axiom,
! [X10] : hAPP(c_Relation_ODomain(X10,X10),c_Relation_OId(X10)) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Id) ).
fof(fact_Range__Id,axiom,
! [X10] : hAPP(c_Relation_ORange(X10,X10),c_Relation_OId(X10)) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Id) ).
fof(fact_Min_Oinsert,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X16),c_Big__Operators_Olinorder__class_OMin(X10,X154)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oinsert) ).
fof(fact_Max_Oinsert,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X16),c_Big__Operators_Olinorder__class_OMax(X10,X154)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oinsert) ).
fof(fact_Inf__fin_Oinsert,axiom,
! [X16,X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X16),c_Big__Operators_Olattice__class_OInf__fin(X10,X154)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oinsert) ).
fof(fact_Sup__fin_Oinsert,axiom,
! [X16,X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X16),c_Big__Operators_Olattice__class_OSup__fin(X10,X154)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oinsert) ).
fof(fact_rtrancl__trancl__absorb,axiom,
! [X196,X10] : c_Transitive__Closure_Otrancl(X10,c_Transitive__Closure_Ortrancl(X10,X196)) = c_Transitive__Closure_Ortrancl(X10,X196),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__trancl__absorb) ).
fof(fact_sublist__singleton,axiom,
! [X16,X10,X154] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X154))
=> c_List_Osublist(X10,hAPP(hAPP(c_List_Olist_OCons(X10),X16),c_List_Olist_ONil(X10)),X154) = hAPP(hAPP(c_List_Olist_OCons(X10),X16),c_List_Olist_ONil(X10)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X154))
=> c_List_Osublist(X10,hAPP(hAPP(c_List_Olist_OCons(X10),X16),c_List_Olist_ONil(X10)),X154) = c_List_Olist_ONil(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__singleton) ).
fof(fact_one__mod__nat__number__of,axiom,
! [X170] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X170)))
=> 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),X170)) = 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),X170)))
=> 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),X170)) = 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),X170))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__mod__nat__number__of) ).
fof(fact_single__valued__Id,axiom,
! [X10] : c_Relation_Osingle__valued(X10,X10,c_Relation_OId(X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__Id) ).
fof(fact_less__le__not__le,axiom,
! [X25,X16,X10] :
( class_Orderings_Opreorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X16),X25))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X25))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X25),X16)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(fact_card_Oinsert,axiom,
! [X16,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X10),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oinsert) ).
fof(fact_split__zdiv,axiom,
! [X101,X20,X19] :
( hBOOL(hAPP(X19,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20),X101)))
<=> ( ( X101 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(X19,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)),X101))
=> ! [X152] :
( ? [X123] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X123))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X123),X101))
& X20 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X101),X152)),X123) )
=> hBOOL(hAPP(X19,X152)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ! [X152] :
( ? [X123] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),X123))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X123),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& X20 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X101),X152)),X123) )
=> hBOOL(hAPP(X19,X152)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__zdiv) ).
fof(fact_insert__ident,axiom,
! [X160,X154,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X160))
=> ( hAPP(hAPP(c_Set_Oinsert(X10),X16),X154) = hAPP(hAPP(c_Set_Oinsert(X10),X16),X160)
<=> X154 = X160 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__ident) ).
fof(fact_card__insert__if,axiom,
! [X16,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(c_Finite__Set_Ocard(X10),X154) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X10),X154)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__if) ).
fof(fact_last__upt,axiom,
! [X119,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),X119))
=> c_List_Olast(tc_Nat_Onat,c_List_Oupt(X120,X119)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X119),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,
! [X42] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X42)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = X42,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__code__numeral__minus__one) ).
fof(fact_not__less__eq,axiom,
! [X20,X102] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X20))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),hAPP(c_Nat_OSuc,X102))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq) ).
fof(fact_distinct__upt,axiom,
! [X119,X120] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X120,X119))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__upt) ).
fof(fact_relpow_Osimps_I1_J,axiom,
! [X196,X10] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X196) = c_Relation_OId(X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_relpow_Osimps_I1_J) ).
fof(fact_int__less__0__conv,axiom,
! [X103] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X103)),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,
! [X162] :
( c_Int_OMin = c_Int_OBit1(X162)
<=> c_Int_OMin = X162 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I43_J) ).
fof(fact_rel__simps_I47_J,axiom,
! [X101] :
( c_Int_OBit1(X101) = c_Int_OMin
<=> X101 = c_Int_OMin ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I47_J) ).
fof(fact_rel__simps_I46_J,axiom,
! [X103] : c_Int_OBit1(X103) != c_Int_OPls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I46_J) ).
fof(fact_rel__simps_I39_J,axiom,
! [X121] : c_Int_OPls != c_Int_OBit1(X121),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I39_J) ).
fof(fact_of__nat__number__of__lemma,axiom,
! [X144,X94] :
( class_Int_Onumber__ring(X94)
=> ( ( 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),X144)))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)) = hAPP(c_Int_Onumber__class_Onumber__of(X94),X144) )
& ( ~ 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),X144)))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)) = c_Groups_Ozero__class_Ozero(X94) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__number__of__lemma) ).
fof(fact_card__insert__disjoint,axiom,
! [X16,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X10),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__disjoint) ).
fof(fact_linorder__antisym__conv2,axiom,
! [X25,X16,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X25))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X16),X25))
<=> X16 = X25 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
fof(fact_infinite__UNIV__listI,axiom,
! [X10] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X10)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X10),tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_infinite__UNIV__listI) ).
fof(fact_evalc_OWhileFalse,axiom,
! [X18,X54,X38] :
( ~ hBOOL(hAPP(X38,X54))
=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X38,X18)),X54),X54)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OWhileFalse) ).
fof(fact_order__less__asym_H,axiom,
! [X92,X84,X94] :
( class_Orderings_Opreorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),X92))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X92),X84)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
fof(fact_order__less__imp__not__less,axiom,
! [X105,X93,X94] :
( class_Orderings_Opreorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X105))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X105),X93)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
fof(fact_order__less__not__sym,axiom,
! [X105,X93,X94] :
( class_Orderings_Opreorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X105))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X105),X93)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
fof(fact_order__less__asym,axiom,
! [X105,X93,X94] :
( class_Orderings_Opreorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X105))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X105),X93)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym) ).
fof(fact_linorder__not__le,axiom,
! [X25,X16,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X25))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X25),X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__le) ).
fof(fact_leD,axiom,
! [X93,X105,X94] :
( class_Orderings_Olinorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X105),X93))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X105)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leD) ).
fof(fact_linorder__not__less,axiom,
! [X25,X16,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X16),X25))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X25),X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__less) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [X25,X16,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X16),X25))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X25),X16))
| X16 = X25 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(fact_xt1_I9_J,axiom,
! [X84,X92,X94] :
( class_Orderings_Oorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X92),X84))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),X92)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
fof(fact_mult__nat__number__of,axiom,
! [X170,X144] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X144),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X144),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X144),X170)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nat__number__of) ).
fof(fact_hd__upt,axiom,
! [X119,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),X119))
=> hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(X120,X119)) = X120 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__upt) ).
fof(fact_empty__iff,axiom,
! [X18,X10] : ~ hBOOL(hAPP(hAPP(c_member(X10),X18),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__iff) ).
fof(fact_emptyE,axiom,
! [X39,X10] : ~ hBOOL(hAPP(hAPP(c_member(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_emptyE) ).
fof(fact_le__SucE,axiom,
! [X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),hAPP(c_Nat_OSuc,X42)))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),X42))
=> X97 = hAPP(c_Nat_OSuc,X42) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucE) ).
fof(fact_atLeastAtMost__upt,axiom,
! [X102,X20] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X20,X102) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X20,hAPP(c_Nat_OSuc,X102))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMost__upt) ).
fof(fact_atLeastLessThanSuc,axiom,
! [X20,X102] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20))
=> hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X102),hAPP(c_Nat_OSuc,X20)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X20),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X102),X20)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20))
=> hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X102),hAPP(c_Nat_OSuc,X20)) = 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,
! [X290,X10,X16,X19] :
( ( hBOOL(hAPP(X19,X16))
=> hAPP(c_List_Ofilter(X10,X19),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290)) = hAPP(hAPP(c_List_Olist_OCons(X10),X16),hAPP(c_List_Ofilter(X10,X19),X290)) )
& ( ~ hBOOL(hAPP(X19,X16))
=> hAPP(c_List_Ofilter(X10,X19),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290)) = hAPP(c_List_Ofilter(X10,X19),X290) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter_Osimps_I2_J) ).
fof(fact_not__less__less__Suc__eq,axiom,
! [X102,X20] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X102))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),hAPP(c_Nat_OSuc,X102)))
<=> X20 = X102 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
fof(fact_less__antisym,axiom,
! [X97,X42] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),X97))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_OSuc,X97)))
=> X97 = X42 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__antisym) ).
fof(fact_less__SucE,axiom,
! [X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),hAPP(c_Nat_OSuc,X42)))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42))
=> X97 = X42 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucE) ).
fof(fact_divmod__nat__rel__divmod__nat,axiom,
! [X42,X97] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X97,X42),c_Divides_Odivmod__nat(X97,X42))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__divmod__nat) ).
fof(fact_code__numeral_Osize_I4_J,axiom,
! [X179] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X179)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),X179)),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,
! [X20] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X20) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atMost__upto) ).
fof(fact_number__of__pred,axiom,
! [X133,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_Opred(X133)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),c_Groups_Oone__class_Oone(X94))),hAPP(c_Int_Onumber__class_Onumber__of(X94),X133)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__pred) ).
fof(fact_evaln_OWhileFalse,axiom,
! [X20,X18,X54,X38] :
( ~ hBOOL(hAPP(X38,X54))
=> c_Natural_Oevaln(c_Com_Ocom_OWhile(X38,X18),X54,X20,X54) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OWhileFalse) ).
fof(fact_atLeastatMost__empty__iff2,axiom,
! [X38,X39,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(X10,X39,X38)
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),X38)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastatMost__empty__iff2) ).
fof(fact_greaterThanAtMost__empty__iff2,axiom,
! [X162,X101,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X101,X162)
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X101),X162)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanAtMost__empty__iff2) ).
fof(fact_atLeastatMost__empty__iff,axiom,
! [X38,X39,X10] :
( class_Orderings_Oorder(X10)
=> ( c_SetInterval_Oord__class_OatLeastAtMost(X10,X39,X38) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),X38)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastatMost__empty__iff) ).
fof(fact_greaterThanAtMost__empty__iff,axiom,
! [X162,X101,X10] :
( class_Orderings_Oorder(X10)
=> ( c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X101,X162) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X101),X162)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanAtMost__empty__iff) ).
fof(fact_dvd_Ole__less,axiom,
! [X25,X16] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X16),X25))
<=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X16),X25))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25),X16)) )
| X16 = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Ole__less) ).
fof(fact_dvd_Oless__le,axiom,
! [X25,X16] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X16),X25))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25),X16)) )
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X16),X25))
& X16 != X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__le) ).
fof(fact_dvd_Oneq__le__trans,axiom,
! [X92,X84] :
( X84 != X92
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X84),X92))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X84),X92))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X92),X84)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oneq__le__trans) ).
fof(fact_dvd_Ole__imp__less__or__eq,axiom,
! [X105,X93] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X93),X105))
=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X93),X105))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X105),X93)) )
| X93 = X105 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Ole__imp__less__or__eq) ).
fof(fact_dvd_Ole__neq__trans,axiom,
! [X92,X84] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X84),X92))
=> ( X84 != X92
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X84),X92))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X92),X84)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Ole__neq__trans) ).
fof(fact_divmod__nat__base,axiom,
! [X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42))
=> c_Divides_Odivmod__nat(X97,X42) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X97) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__base) ).
fof(fact_equalityE,axiom,
! [X10,X160,X154] :
( X154 = X160
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityE) ).
fof(fact_Suc__n__not__le__n,axiom,
! [X42] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X42)),X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
fof(fact_z3div__def,axiom,
! [X103,X121] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X121))
=> c_SMT_Oz3div(X103,X121) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X103),X121) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X121))
=> c_SMT_Oz3div(X103,X121) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X103),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X121))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_z3div__def) ).
fof(fact_mod__if,axiom,
! [X42,X97] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X97,X42) = X97 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X97,X42) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42),X42) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__if) ).
fof(fact_mod__geq,axiom,
! [X42,X97] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X97,X42) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42),X42) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__geq) ).
fof(fact_linorder__antisym__conv1,axiom,
! [X25,X16,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X16),X25))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X25))
<=> X16 = X25 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
fof(fact_atLeastLessThan__empty__iff,axiom,
! [X38,X39,X10] :
( class_Orderings_Oorder(X10)
=> ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X39),X38) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),X38)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__empty__iff) ).
fof(fact_atLeastLessThan__empty__iff2,axiom,
! [X38,X39,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X39),X38)
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),X38)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__empty__iff2) ).
fof(fact_code__numeral_Oinject,axiom,
! [X180,X181] :
( c_Code__Numeral_OSuc__code__numeral(X181) = c_Code__Numeral_OSuc__code__numeral(X180)
<=> X181 = X180 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Oinject) ).
fof(fact_code__numeral_Osize_I2_J,axiom,
! [X179] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(X179)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X179)),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,
! [X103] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(X103)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X103)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__Bit0) ).
fof(fact_all__not__in__conv,axiom,
! [X154,X10] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
<=> X154 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__not__in__conv) ).
fof(fact_remove1__idem,axiom,
! [X290,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
=> c_List_Oremove1(X10,X16,X290) = X290 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1__idem) ).
fof(fact_length__upt,axiom,
! [X119,X120] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(X120,X119)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X119),X120),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__upt) ).
fof(fact_sgn__if,axiom,
! [X93,X94] :
( class_Groups_Osgn__if(X94)
=> ( ( X93 = c_Groups_Ozero__class_Ozero(X94)
=> c_Groups_Osgn__class_Osgn(X94,X93) = c_Groups_Ozero__class_Ozero(X94) )
& ( X93 != c_Groups_Ozero__class_Ozero(X94)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X93))
=> c_Groups_Osgn__class_Osgn(X94,X93) = c_Groups_Oone__class_Oone(X94) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X93))
=> c_Groups_Osgn__class_Osgn(X94,X93) = hAPP(c_Groups_Ouminus__class_Ouminus(X94),c_Groups_Oone__class_Oone(X94)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__if) ).
fof(fact_upt__eq__Nil__conv,axiom,
! [X163,X113] :
( c_List_Oupt(X113,X163) = c_List_Olist_ONil(tc_Nat_Onat)
<=> ( X163 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X163),X113)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__eq__Nil__conv) ).
fof(fact_upt__conv__Nil,axiom,
! [X120,X119] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X119),X120))
=> c_List_Oupt(X120,X119) = c_List_Olist_ONil(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__conv__Nil) ).
fof(fact_z3mod__def,axiom,
! [X103,X121] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X121))
=> c_SMT_Oz3mod(X103,X121) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X103,X121) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X121))
=> c_SMT_Oz3mod(X103,X121) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X103,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X121)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_z3mod__def) ).
fof(fact_abs__if,axiom,
! [X84,X94] :
( class_Groups_Oabs__if(X94)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),c_Groups_Ozero__class_Ozero(X94)))
=> hAPP(c_Groups_Oabs__class_Oabs(X94),X84) = hAPP(c_Groups_Ouminus__class_Ouminus(X94),X84) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),c_Groups_Ozero__class_Ozero(X94)))
=> hAPP(c_Groups_Oabs__class_Oabs(X94),X84) = X84 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__if) ).
fof(fact_not__one__le__zero,axiom,
! [X94] :
( class_Rings_Olinordered__semidom(X94)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Oone__class_Oone(X94)),c_Groups_Ozero__class_Ozero(X94))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
fof(fact_not__one__less__zero,axiom,
! [X94] :
( class_Rings_Olinordered__semidom(X94)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Oone__class_Oone(X94)),c_Groups_Ozero__class_Ozero(X94))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
fof(fact_add__diff__inverse,axiom,
! [X42,X97] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42)) = X97 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__inverse) ).
fof(fact_atLeast__upt,axiom,
! [X20] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X20) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__upt) ).
fof(fact_linorder__neqE,axiom,
! [X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> ( X93 != X105
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X105))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X105),X93)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE) ).
fof(fact_linorder__antisym__conv3,axiom,
! [X16,X25,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X25),X16))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X16),X25))
<=> X16 = X25 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
fof(fact_linorder__cases,axiom,
! [X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X105))
=> ( X93 != X105
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X105),X93)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__cases) ).
fof(fact_linorder__neqE__linordered__idom,axiom,
! [X105,X93,X94] :
( class_Rings_Olinordered__idom(X94)
=> ( X93 != X105
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X105))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X105),X93)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
fof(fact_linorder__le__cases,axiom,
! [X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X105))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X105),X93)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
fof(fact_leI,axiom,
! [X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X105))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X105),X93)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leI) ).
fof(fact_not__leE,axiom,
! [X93,X105,X94] :
( class_Orderings_Olinorder(X94)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X105),X93))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X105)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__leE) ).
fof(fact_set__upt,axiom,
! [X163,X113] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X113,X163)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X113),X163),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__upt) ).
fof(fact_atLeastLessThan__upt,axiom,
! [X163,X113] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X113),X163) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X113,X163)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__upt) ).
fof(fact_succ__pred,axiom,
! [X93] : c_Int_Osucc(c_Int_Opred(X93)) = X93,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_succ__pred) ).
fof(fact_number__of__succ,axiom,
! [X103,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_Osucc(X103)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),c_Groups_Oone__class_Oone(X94)),hAPP(c_Int_Onumber__class_Onumber__of(X94),X103)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__succ) ).
fof(fact_equals0D,axiom,
! [X39,X10,X154] :
( X154 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equals0D) ).
fof(fact_not__neg__eq__ge__0,axiom,
! [X16] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X16))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__neg__eq__ge__0) ).
fof(fact_nat__eq__iff,axiom,
! [X102,X131] :
( hAPP(c_Int_Onat,X131) = X102
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X131))
=> X131 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X102) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X131))
=> X102 = 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,
! [X131,X102] :
( X102 = hAPP(c_Int_Onat,X131)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X131))
=> X131 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X102) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X131))
=> X102 = 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,
! [X104] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X104))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X104)) = X104 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X104))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X104)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__nat__eq) ).
fof(fact_tsub__def,axiom,
! [X93,X105] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X105),X93))
=> c_Nat__Transfer_Otsub(X93,X105) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X93),X105) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X105),X93))
=> c_Nat__Transfer_Otsub(X93,X105) = 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,
! [X144,X94] :
( class_Int_Onumber__ring(X94)
=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)) = c_Groups_Ozero__class_Ozero(X94) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)) = hAPP(c_Int_Onumber__class_Onumber__of(X94),X144) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__number__of__eq) ).
fof(fact_mod__nat__def,axiom,
! [X42,X97] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X97,X42) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X97,X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__nat__def) ).
fof(fact_remove1__filter__not,axiom,
! [X290,X10,X16,X19] :
( ~ hBOOL(hAPP(X19,X16))
=> c_List_Oremove1(X10,X16,hAPP(c_List_Ofilter(X10,X19),X290)) = hAPP(c_List_Ofilter(X10,X19),X290) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1__filter__not) ).
fof(fact_div__nat__def,axiom,
! [X42,X97] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X97),X42) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X97,X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__nat__def) ).
fof(fact_int__nat__number__of,axiom,
! [X144] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__nat__number__of) ).
fof(fact_zabs__def,axiom,
! [X120] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X120),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X120) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X120) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X120),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X120) = X120 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zabs__def) ).
fof(fact_linorder__neqE__nat,axiom,
! [X105,X93] :
( X93 != X105
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X93),X105))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X105),X93)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
fof(fact_divmod__nat__eq,axiom,
! [X185,X42,X97] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X97,X42),X185))
=> c_Divides_Odivmod__nat(X97,X42) = X185 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__eq) ).
fof(fact_zsgn__def,axiom,
! [X120] :
( ( X120 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Groups_Osgn__class_Osgn(tc_Int_Oint,X120) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( X120 != 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)),X120))
=> c_Groups_Osgn__class_Osgn(tc_Int_Oint,X120) = 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)),X120))
=> c_Groups_Osgn__class_Osgn(tc_Int_Oint,X120) = 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,
! [X119,X120] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X120,X119)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__upt) ).
fof(fact_wf__measure,axiom,
! [X2,X10] : c_Wellfounded_Owf(X10,hAPP(c_Wellfounded_Omeasure(X10),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__measure) ).
fof(fact_order__less__irrefl,axiom,
! [X93,X94] :
( class_Orderings_Opreorder(X94)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X93)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
fof(fact_beyond__def,axiom,
! [X121,X103] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X103),X121))
=> c_Quickcheck_Obeyond(X103,X121) = X121 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X103),X121))
=> c_Quickcheck_Obeyond(X103,X121) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_beyond__def) ).
fof(fact_rotate0,axiom,
! [X10] : c_List_Orotate(X10,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate0) ).
fof(fact_less__nat__zero__code,axiom,
! [X42] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),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,
! [X42] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less0) ).
fof(fact_less__zeroE,axiom,
! [X42] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),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,
! [X62,X58] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X58,X62)))
=> ~ ( hBOOL(hAPP(c_Com_OWT,X58))
=> ~ hBOOL(hAPP(c_Com_OWT,X62)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WTs__elim__cases_I4_J) ).
fof(fact_divmod__nat__zero,axiom,
! [X97] : c_Divides_Odivmod__nat(X97,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)),X97),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__zero) ).
fof(fact_less__irrefl__nat,axiom,
! [X42] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
fof(fact_less__not__refl,axiom,
! [X42] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).
fof(fact_rel__simps_I48_J,axiom,
! [X162,X101] :
( c_Int_OBit0(X101) = c_Int_OBit0(X162)
<=> X101 = X162 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I48_J) ).
fof(fact_setsum__infinite,axiom,
! [X2,X154,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),X154) = c_Groups_Ozero__class_Ozero(X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__infinite) ).
fof(fact_setsum_Oinfinite,axiom,
! [X1,X154,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1),X154) = c_Groups_Ozero__class_Ozero(X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oinfinite) ).
fof(fact_setprod_Oinfinite,axiom,
! [X1,X154,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),X154) = c_Groups_Oone__class_Oone(X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Oinfinite) ).
fof(fact_setprod__infinite,axiom,
! [X2,X154,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),X154) = c_Groups_Oone__class_Oone(X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__infinite) ).
fof(fact_not__neg__int,axiom,
! [X42] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X42))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__neg__int) ).
fof(fact_code__numeral_Osimps_I3_J,axiom,
! [X183] : c_Code__Numeral_OSuc__code__numeral(X183) != 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,
! [X182] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(X182),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Osimps_I2_J) ).
fof(help_c__fimplies__3,axiom,
! [X17,X19] :
( ~ hBOOL(hAPP(hAPP(c_fimplies,X19),X17))
| ~ hBOOL(X19)
| hBOOL(X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fimplies__3) ).
fof(fact_card__eq__0__iff,axiom,
! [X154,X10] :
( hAPP(c_Finite__Set_Ocard(X10),X154) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X154 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__eq__0__iff) ).
fof(help_c__fdisj__3,axiom,
! [X17,X19] :
( ~ hBOOL(hAPP(hAPP(c_fdisj,X19),X17))
| hBOOL(X19)
| hBOOL(X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fdisj__3) ).
fof(help_c__fconj__2,axiom,
! [X17,X19] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X19),X17))
| hBOOL(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__2) ).
fof(help_c__fconj__3,axiom,
! [X17,X19] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X19),X17))
| hBOOL(X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__3) ).
fof(fact_empty__Collect__eq,axiom,
! [X19,X10] :
( c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X10),X19)
<=> ! [X3] : ~ hBOOL(hAPP(X19,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__Collect__eq) ).
fof(fact_Collect__empty__eq,axiom,
! [X19,X10] :
( hAPP(c_Set_OCollect(X10),X19) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X19,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
fof(help_c__fequal__1,axiom,
! [X25,X16] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X16),X25))
| X16 = X25 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__1) ).
fof(fact_nat__of__code,axiom,
! [X120] : hAPP(c_Code__Numeral_Onat__of,X120) = c_Code__Numeral_Onat__of__aux(X120,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of__code) ).
fof(fact_succ__def,axiom,
! [X103] : c_Int_Osucc(X103) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X103),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_succ__def) ).
fof(fact_pred__def,axiom,
! [X103] : c_Int_Opred(X103) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X103),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__def) ).
fof(fact_upt__0,axiom,
! [X120] : c_List_Oupt(X120,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,
! [X17,X19] :
( ~ hBOOL(X19)
| ~ hBOOL(X17)
| hBOOL(hAPP(hAPP(c_fconj,X19),X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__1) ).
fof(fact_add__Min,axiom,
! [X103] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X103) = c_Int_Opred(X103),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Min) ).
fof(fact_nonzero__number__of__Min,axiom,
! [X94] :
( class_Int_Onumber__ring(X94)
=> ~ c_Int_Oiszero(X94,hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OMin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__number__of__Min) ).
fof(help_c__fdisj__1,axiom,
! [X17,X19] :
( ~ hBOOL(X19)
| hBOOL(hAPP(hAPP(c_fdisj,X19),X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fdisj__1) ).
fof(help_c__fdisj__2,axiom,
! [X19,X17] :
( ~ hBOOL(X17)
| hBOOL(hAPP(hAPP(c_fdisj,X19),X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fdisj__2) ).
fof(help_c__fimplies__2,axiom,
! [X19,X17] :
( ~ hBOOL(X17)
| hBOOL(hAPP(hAPP(c_fimplies,X19),X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fimplies__2) ).
fof(fact_is__none__code_I2_J,axiom,
! [X93,X10] : ~ c_Option_Ois__none(X10,hAPP(c_Option_Ooption_OSome(X10),X93)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_is__none__code_I2_J) ).
fof(fact_return__list__def,axiom,
! [X162] : c_List_Oreturn__list(X162) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),X162),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_return__list__def) ).
fof(fact_rel__simps_I38_J,axiom,
! [X162] :
( c_Int_OPls = c_Int_OBit0(X162)
<=> c_Int_OPls = X162 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I38_J) ).
fof(fact_rel__simps_I44_J,axiom,
! [X101] :
( c_Int_OBit0(X101) = c_Int_OPls
<=> X101 = c_Int_OPls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I44_J) ).
fof(fact_rel__simps_I45_J,axiom,
! [X103] : c_Int_OBit0(X103) != c_Int_OMin,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I45_J) ).
fof(fact_rel__simps_I42_J,axiom,
! [X121] : c_Int_OMin != c_Int_OBit0(X121),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I42_J) ).
fof(fact_not__neg__nat,axiom,
! [X104] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X104))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X104)) = X104 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__neg__nat) ).
fof(fact_card__infinite,axiom,
! [X154,X10] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(c_Finite__Set_Ocard(X10),X154) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__infinite) ).
fof(help_c__fNot__1,axiom,
! [X19] :
( ~ hBOOL(hAPP(c_fNot,X19))
| ~ hBOOL(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(fact_not__iszero__1,axiom,
! [X94] :
( class_Rings_Osemiring__1(X94)
=> ~ c_Int_Oiszero(X94,c_Groups_Oone__class_Oone(X94)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__iszero__1) ).
fof(help_c__fNot__2,axiom,
! [X19] :
( ~ ~ hBOOL(X19)
| hBOOL(hAPP(c_fNot,X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__2) ).
fof(fact_UN__equiv__class__type2,axiom,
! [X160,X243,X244,X2,X125,X233,X234,X13,X235,X236,X10] :
( c_Equiv__Relations_Oequiv(X10,X236,X235)
=> ( c_Equiv__Relations_Oequiv(X13,X234,X233)
=> ( c_Equiv__Relations_Ocongruent2(X10,X13,tc_fun(X125,tc_HOL_Obool),X235,X233,X2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X244),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X236),X235)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X13,tc_HOL_Obool)),X243),hAPP(hAPP(c_Equiv__Relations_Oquotient(X13),X234),X233)))
=> ( ! [X147] :
( hBOOL(hAPP(hAPP(c_member(X10),X147),X236))
=> ! [X245] :
( hBOOL(hAPP(hAPP(c_member(X13),X245),X234))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X125,tc_HOL_Obool)),hAPP(hAPP(X2,X147),X245)),X160)) ) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X125,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X125,tc_HOL_Obool)),X244),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_fun(X125,tc_HOL_Obool)),tc_fun(X125,tc_HOL_Obool),X10),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X125,tc_HOL_Obool)),X243)),X2))),X160)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__equiv__class__type2) ).
fof(fact_com_Orecs_I5_J,axiom,
! [X55,X56,X29,X31,X32,X33,X34,X35,X36,X37,X12,X10] : c_Com_Ocom_Ocom__rec(X10,X12,X37,X36,X35,X34,X33,X32,X31,c_Com_Ocom_OCond(X29,X56,X55)) = hAPP(hAPP(hAPP(hAPP(hAPP(X34,X29),X56),X55),c_Com_Ocom_Ocom__rec(X10,X12,X37,X36,X35,X34,X33,X32,X31,X56)),c_Com_Ocom_Ocom__rec(X10,X12,X37,X36,X35,X34,X33,X32,X31,X55)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I5_J) ).
fof(fact_com_Orecs_I4_J,axiom,
! [X55,X56,X31,X32,X33,X34,X35,X36,X37,X12,X10] : c_Com_Ocom_Ocom__rec(X10,X12,X37,X36,X35,X34,X33,X32,X31,c_Com_Ocom_OSemi(X56,X55)) = hAPP(hAPP(hAPP(hAPP(X35,X56),X55),c_Com_Ocom_Ocom__rec(X10,X12,X37,X36,X35,X34,X33,X32,X31,X56)),c_Com_Ocom_Ocom__rec(X10,X12,X37,X36,X35,X34,X33,X32,X31,X55)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I4_J) ).
fof(fact_setsum__mult__setsum__if__inj,axiom,
! [X160,X154,X1,X2,X13,X10,X125] :
( class_Rings_Osemiring__0(X125)
=> ( c_Fun_Oinj__on(tc_prod(X10,X13),X125,hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,X125),hAPP(hAPP(c_COMBC(X10,tc_fun(X13,X125),tc_fun(X13,X125)),hAPP(hAPP(c_COMBB(tc_fun(X125,X125),tc_fun(tc_fun(X13,X125),tc_fun(X13,X125)),X10),c_COMBB(X125,X125,X13)),hAPP(hAPP(c_COMBB(X125,tc_fun(X125,X125),X10),c_Groups_Otimes__class_Otimes(X125)),X2))),X1)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X154),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),X160)))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X125),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X125),X2),X154)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X125),X1),X160)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X125,X125),c_Fun_Oid(X125)),hAPP(c_Set_OCollect(X125),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X125),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X13,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool),X125),hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X13))),hAPP(hAPP(c_COMBC(X125,tc_fun(X10,tc_fun(X13,tc_HOL_Obool)),tc_fun(X10,tc_fun(X13,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool))),tc_fun(tc_fun(X10,tc_fun(X13,tc_HOL_Obool)),tc_fun(X10,tc_fun(X13,tc_HOL_Obool))),X125),c_COMBS(X10,tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X13,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X10,tc_fun(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool))),X125),hAPP(c_COMBB(tc_fun(X13,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_COMBS(X13,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X13,tc_HOL_Obool)),tc_fun(X10,tc_fun(X13,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X125),hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X13),c_fconj))),hAPP(hAPP(c_COMBC(X125,tc_fun(X10,tc_fun(X13,X125)),tc_fun(X10,tc_fun(X13,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X13,X125),tc_fun(X13,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_fun(X13,X125)),tc_fun(X10,tc_fun(X13,tc_HOL_Obool))),X125),c_COMBB(tc_fun(X13,X125),tc_fun(X13,tc_HOL_Obool),X10)),hAPP(hAPP(c_COMBB(tc_fun(X125,tc_HOL_Obool),tc_fun(tc_fun(X13,X125),tc_fun(X13,tc_HOL_Obool)),X125),c_COMBB(X125,tc_HOL_Obool,X13)),c_fequal))),hAPP(hAPP(c_COMBC(X10,tc_fun(X13,X125),tc_fun(X13,X125)),hAPP(hAPP(c_COMBB(tc_fun(X125,X125),tc_fun(tc_fun(X13,X125),tc_fun(X13,X125)),X10),c_COMBB(X125,X125,X13)),hAPP(hAPP(c_COMBB(X125,tc_fun(X125,X125),X10),c_Groups_Otimes__class_Otimes(X125)),X2))),X1)))))),hAPP(hAPP(c_COMBC(X10,tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X13)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X154)))),hAPP(hAPP(c_COMBC(X13,tc_fun(X13,tc_HOL_Obool),tc_HOL_Obool),c_member(X13)),X160))))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__mult__setsum__if__inj) ).
fof(fact_rel__comp__def,axiom,
! [X54,X177,X13,X125,X10] : hAPP(hAPP(c_Relation_Orel__comp(X10,X125,X13),X177),X54) = hAPP(c_Set_OCollect(tc_prod(X10,X13)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_fun(X125,tc_HOL_Obool)),tc_fun(X13,tc_HOL_Obool),X10),hAPP(c_COMBB(tc_fun(X125,tc_HOL_Obool),tc_HOL_Obool,X13),c_HOL_OEx(X125))),hAPP(hAPP(c_COMBC(X10,tc_fun(X13,tc_fun(X125,tc_HOL_Obool)),tc_fun(X13,tc_fun(X125,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X125,tc_HOL_Obool),tc_fun(X125,tc_HOL_Obool)),tc_fun(tc_fun(X13,tc_fun(X125,tc_HOL_Obool)),tc_fun(X13,tc_fun(X125,tc_HOL_Obool))),X10),c_COMBB(tc_fun(X125,tc_HOL_Obool),tc_fun(X125,tc_HOL_Obool),X13)),hAPP(hAPP(c_COMBB(tc_fun(X125,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X125,tc_HOL_Obool),tc_fun(X125,tc_HOL_Obool)),X10),c_COMBS(X125,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X125,tc_HOL_Obool),tc_fun(X125,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X125),c_fconj)),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X125),tc_HOL_Obool),tc_fun(X125,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X125,tc_fun(tc_fun(tc_prod(X10,X125),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X125),tc_HOL_Obool),tc_fun(X125,tc_HOL_Obool)),X10),c_COMBC(X125,tc_fun(tc_prod(X10,X125),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X125,tc_prod(X10,X125)),tc_fun(X125,tc_fun(tc_fun(tc_prod(X10,X125),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X125),tc_fun(tc_fun(tc_prod(X10,X125),tc_HOL_Obool),tc_HOL_Obool),X125),c_member(tc_prod(X10,X125)))),c_Product__Type_OPair(X10,X125)))),X177))))),hAPP(hAPP(c_COMBC(X13,tc_fun(tc_prod(X125,X13),tc_HOL_Obool),tc_fun(X125,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X125,tc_fun(tc_fun(tc_prod(X125,X13),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X125,X13),tc_HOL_Obool),tc_fun(X125,tc_HOL_Obool)),X13),c_COMBC(X125,tc_fun(tc_prod(X125,X13),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X125,tc_prod(X125,X13)),tc_fun(X125,tc_fun(tc_fun(tc_prod(X125,X13),tc_HOL_Obool),tc_HOL_Obool)),X13),hAPP(c_COMBB(tc_prod(X125,X13),tc_fun(tc_fun(tc_prod(X125,X13),tc_HOL_Obool),tc_HOL_Obool),X125),c_member(tc_prod(X125,X13)))),hAPP(c_COMBC(X125,X13,tc_prod(X125,X13)),c_Product__Type_OPair(X125,X13))))),X54))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__def) ).
fof(fact_min__max_Osup__Inf2__distrib,axiom,
! [X160,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( X160 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X154)),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X160)) = c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool),X10),hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X10))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),tc_fun(tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),X10),c_COMBS(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X10,tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),X10),hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X10),hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_fun(X10,X10)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_fun(X10,X10)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),X10),c_COMBB(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool),X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(X10,tc_HOL_Obool,X10)),c_fequal))),c_Orderings_Oord__class_Omax(X10)))))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X154)))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X160))))))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__Inf2__distrib) ).
fof(fact_min__max_Oinf__Sup2__distrib,axiom,
! [X160,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( X160 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X154)),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X160)) = c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool),X10),hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X10))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),tc_fun(tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),X10),c_COMBS(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X10,tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),X10),hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X10),hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_fun(X10,X10)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_fun(X10,X10)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),X10),c_COMBB(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool),X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(X10,tc_HOL_Obool,X10)),c_fequal))),c_Orderings_Oord__class_Omin(X10)))))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X154)))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X160))))))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__Sup2__distrib) ).
fof(fact_inf__Sup2__distrib,axiom,
! [X160,X154,X10] :
( class_Lattices_Odistrib__lattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( X160 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),c_Big__Operators_Olattice__class_OSup__fin(X10,X154)),c_Big__Operators_Olattice__class_OSup__fin(X10,X160)) = c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool),X10),hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X10))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),tc_fun(tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),X10),c_COMBS(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X10,tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),X10),hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X10),hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_fun(X10,X10)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_fun(X10,X10)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),X10),c_COMBB(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool),X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(X10,tc_HOL_Obool,X10)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(X10)))))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X154)))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X160))))))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Sup2__distrib) ).
fof(fact_sup__Inf2__distrib,axiom,
! [X160,X154,X10] :
( class_Lattices_Odistrib__lattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( X160 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),c_Big__Operators_Olattice__class_OInf__fin(X10,X154)),c_Big__Operators_Olattice__class_OInf__fin(X10,X160)) = c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool),X10),hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X10))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),tc_fun(tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),X10),c_COMBS(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X10,tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),X10),hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X10),hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_fun(X10,X10)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_fun(X10,X10)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),X10),c_COMBB(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool),X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(X10,tc_HOL_Obool,X10)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(X10)))))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X154)))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X160))))))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Inf2__distrib) ).
fof(fact_com_Orecs_I3_J,axiom,
! [X8,X29,X79,X31,X32,X33,X34,X35,X36,X37,X12,X10] : c_Com_Ocom_Ocom__rec(X10,X12,X37,X36,X35,X34,X33,X32,X31,c_Com_Ocom_OLocal(X79,X29,X8)) = hAPP(hAPP(hAPP(hAPP(X36,X79),X29),X8),c_Com_Ocom_Ocom__rec(X10,X12,X37,X36,X35,X34,X33,X32,X31,X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I3_J) ).
fof(fact_com_Orecs_I6_J,axiom,
! [X8,X29,X31,X32,X33,X34,X35,X36,X37,X12,X10] : c_Com_Ocom_Ocom__rec(X10,X12,X37,X36,X35,X34,X33,X32,X31,c_Com_Ocom_OWhile(X29,X8)) = hAPP(hAPP(hAPP(X33,X29),X8),c_Com_Ocom_Ocom__rec(X10,X12,X37,X36,X35,X34,X33,X32,X31,X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I6_J) ).
fof(fact_set__Cons__def,axiom,
! [X219,X154,X10] : c_List_Oset__Cons(X10,X154,X219) = hAPP(c_Set_OCollect(tc_List_Olist(X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(X10)),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool),tc_List_Olist(X10)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(tc_List_Olist(X10)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(X10,tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),tc_fun(X10,tc_fun(tc_List_Olist(X10),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_HOL_Obool))),tc_fun(tc_fun(X10,tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),tc_fun(X10,tc_fun(tc_List_Olist(X10),tc_HOL_Obool))),tc_List_Olist(X10)),c_COMBS(X10,tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_List_Olist(X10),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X10,tc_fun(tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_HOL_Obool))),tc_List_Olist(X10)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X10),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),X10),c_COMBS(tc_List_Olist(X10),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),tc_fun(X10,tc_fun(tc_List_Olist(X10),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(X10)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X10)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(X10,tc_fun(tc_List_Olist(X10),tc_List_Olist(X10))),tc_fun(X10,tc_fun(tc_List_Olist(X10),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(X10),tc_List_Olist(X10)),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_fun(tc_List_Olist(X10),tc_List_Olist(X10))),tc_fun(X10,tc_fun(tc_List_Olist(X10),tc_HOL_Obool))),tc_List_Olist(X10)),c_COMBB(tc_fun(tc_List_Olist(X10),tc_List_Olist(X10)),tc_fun(tc_List_Olist(X10),tc_HOL_Obool),X10)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X10),tc_List_Olist(X10)),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),tc_List_Olist(X10)),c_COMBB(tc_List_Olist(X10),tc_HOL_Obool,tc_List_Olist(X10))),c_fequal))),c_List_Olist_OCons(X10)))))),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),X10),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X10))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X154)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X10))),X219)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__Cons__def) ).
fof(fact_hoare__derivs_OCall,axiom,
! [X39,X48,X209,X17,X49,X19,X210,X10] :
( c_Hoare__Mirabelle_Ohoare__derivs(X10,X210,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X10)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X10),X19),hAPP(c_Com_Ocom_OBODY,X49)),hAPP(hAPP(c_COMBC(X10,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)),X10),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X17)),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,X209)))),X48)),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(X10),tc_HOL_Obool))))
=> c_Hoare__Mirabelle_Ohoare__derivs(X10,X210,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X10)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X10),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),X10),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,X209)))),hAPP(hAPP(c_COMBC(X10,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)),X10),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X19)),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))),X39)))),c_Com_Ocom_OCall(X48,X49,X39)),X17)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X10),tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_OCall) ).
fof(fact_image__INT,axiom,
! [X163,X160,X154,X125,X198,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,X198)
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X125),X3),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(X160,X3)),X198)) )
=> ( hBOOL(hAPP(hAPP(c_member(X125),X163),X154))
=> hAPP(c_Set_Oimage(X10,X13,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X125,tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X125,tc_fun(X13,tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool),X125),c_Set_Oimage(X10,X13,X2)),X160)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__INT) ).
fof(fact_com_Orecs_I8_J,axiom,
! [X29,X15,X30,X31,X32,X33,X34,X35,X36,X37,X12,X10] : c_Com_Ocom_Ocom__rec(X10,X12,X37,X36,X35,X34,X33,X32,X31,c_Com_Ocom_OCall(X30,X15,X29)) = hAPP(hAPP(hAPP(X31,X30),X15),X29),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I8_J) ).
fof(fact_com_Osimps_I66_J,axiom,
! [X8,X29,X79,X31,X32,X33,X34,X35,X36,X37,X12,X10] : c_Com_Ocom_Ocom__case(X10,X12,X37,X36,X35,X34,X33,X32,X31,c_Com_Ocom_OLocal(X79,X29,X8)) = hAPP(hAPP(hAPP(X36,X79),X29),X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I66_J) ).
fof(fact_com_Osimps_I68_J,axiom,
! [X55,X56,X29,X31,X32,X33,X34,X35,X36,X37,X12,X10] : c_Com_Ocom_Ocom__case(X10,X12,X37,X36,X35,X34,X33,X32,X31,c_Com_Ocom_OCond(X29,X56,X55)) = hAPP(hAPP(hAPP(X34,X29),X56),X55),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I68_J) ).
fof(fact_com_Osimps_I71_J,axiom,
! [X29,X15,X30,X31,X32,X33,X34,X35,X36,X37,X12,X10] : c_Com_Ocom_Ocom__case(X10,X12,X37,X36,X35,X34,X33,X32,X31,c_Com_Ocom_OCall(X30,X15,X29)) = hAPP(hAPP(hAPP(X31,X30),X15),X29),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I71_J) ).
fof(fact_com_Orecs_I2_J,axiom,
! [X29,X30,X31,X32,X33,X34,X35,X36,X37,X12,X10] : c_Com_Ocom_Ocom__rec(X10,X12,X37,X36,X35,X34,X33,X32,X31,c_Com_Ocom_OAss(X30,X29)) = hAPP(hAPP(X37,X30),X29),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I2_J) ).
fof(fact_com_Osimps_I69_J,axiom,
! [X8,X29,X31,X32,X33,X34,X35,X36,X37,X12,X10] : c_Com_Ocom_Ocom__case(X10,X12,X37,X36,X35,X34,X33,X32,X31,c_Com_Ocom_OWhile(X29,X8)) = hAPP(hAPP(X33,X29),X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I69_J) ).
fof(fact_com_Osimps_I67_J,axiom,
! [X55,X56,X31,X32,X33,X34,X35,X36,X37,X12,X10] : c_Com_Ocom_Ocom__case(X10,X12,X37,X36,X35,X34,X33,X32,X31,c_Com_Ocom_OSemi(X56,X55)) = hAPP(hAPP(X35,X56),X55),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I67_J) ).
fof(fact_com_Osimps_I65_J,axiom,
! [X29,X30,X31,X32,X33,X34,X35,X36,X37,X12,X10] : c_Com_Ocom_Ocom__case(X10,X12,X37,X36,X35,X34,X33,X32,X31,c_Com_Ocom_OAss(X30,X29)) = hAPP(hAPP(X37,X30),X29),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I65_J) ).
fof(fact_com_Orecs_I7_J,axiom,
! [X15,X31,X32,X33,X34,X35,X36,X37,X12,X10] : c_Com_Ocom_Ocom__rec(X10,X12,X37,X36,X35,X34,X33,X32,X31,hAPP(c_Com_Ocom_OBODY,X15)) = hAPP(X32,X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I7_J) ).
fof(fact_com_Osimps_I70_J,axiom,
! [X15,X31,X32,X33,X34,X35,X36,X37,X12,X10] : c_Com_Ocom_Ocom__case(X10,X12,X37,X36,X35,X34,X33,X32,X31,hAPP(c_Com_Ocom_OBODY,X15)) = hAPP(X32,X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I70_J) ).
fof(fact_com_Orecs_I1_J,axiom,
! [X31,X32,X33,X34,X35,X36,X37,X12,X10] : c_Com_Ocom_Ocom__rec(X10,X12,X37,X36,X35,X34,X33,X32,X31,c_Com_Ocom_OSKIP) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I1_J) ).
fof(fact_com_Osimps_I64_J,axiom,
! [X31,X32,X33,X34,X35,X36,X37,X12,X10] : c_Com_Ocom_Ocom__case(X10,X12,X37,X36,X35,X34,X33,X32,X31,c_Com_Ocom_OSKIP) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I64_J) ).
fof(fact_inf__Int__eq2,axiom,
! [X25,X16,X216,X196,X13,X10] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_fun(X13,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_COMBC(X13,tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_prod(X10,X13)),tc_fun(X13,tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X13),tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool),X13),c_member(tc_prod(X10,X13)))),c_Product__Type_OPair(X10,X13)))),X196)),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_COMBC(X13,tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_prod(X10,X13)),tc_fun(X13,tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X13),tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool),X13),c_member(tc_prod(X10,X13)))),c_Product__Type_OPair(X10,X13)))),X216)),X16),X25))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X16),X25)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),X196),X216))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Int__eq2) ).
fof(fact_sup__Un__eq2,axiom,
! [X25,X16,X216,X196,X13,X10] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_fun(X13,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_COMBC(X13,tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_prod(X10,X13)),tc_fun(X13,tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X13),tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool),X13),c_member(tc_prod(X10,X13)))),c_Product__Type_OPair(X10,X13)))),X196)),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_COMBC(X13,tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_prod(X10,X13)),tc_fun(X13,tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X13),tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool),X13),c_member(tc_prod(X10,X13)))),c_Product__Type_OPair(X10,X13)))),X216)),X16),X25))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X16),X25)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),X196),X216))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Un__eq2) ).
fof(fact_lenlex__conv,axiom,
! [X177,X10] : c_List_Olenlex(X10,X177) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X10),tc_List_Olist(X10),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X10),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),tc_List_Olist(X10)),c_COMBS(tc_List_Olist(X10),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X10)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X10)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_Nat_Onat),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X10),tc_Nat_Onat),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),tc_List_Olist(X10)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X10))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X10)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X10))))),c_Nat_Osize__class_Osize(tc_List_Olist(X10)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X10),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),tc_List_Olist(X10)),c_COMBS(tc_List_Olist(X10),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X10)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X10)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_Nat_Onat),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X10),tc_Nat_Onat),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),tc_List_Olist(X10)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X10))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X10)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X10))))),c_Nat_Osize__class_Osize(tc_List_Olist(X10)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X10),tc_fun(tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),tc_List_Olist(X10)),c_COMBC(tc_List_Olist(X10),tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X10),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),tc_fun(tc_List_Olist(X10),tc_fun(tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(X10)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X10)),c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))))),c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10))))),c_List_Olex(X10,X177)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lenlex__conv) ).
fof(fact_INF__INT__eq2,axiom,
! [X25,X16,X177,X125,X13,X10] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_fun(X125,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X13,X125),tc_HOL_Obool),tc_fun(X13,tc_fun(X125,tc_HOL_Obool)),X10),hAPP(c_COMBC(X13,tc_fun(tc_prod(X13,X125),tc_HOL_Obool),tc_fun(X125,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X125,tc_fun(tc_fun(tc_prod(X13,X125),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X13,X125),tc_HOL_Obool),tc_fun(X125,tc_HOL_Obool)),X13),c_COMBC(X125,tc_fun(tc_prod(X13,X125),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X125,tc_prod(X13,X125)),tc_fun(X125,tc_fun(tc_fun(tc_prod(X13,X125),tc_HOL_Obool),tc_HOL_Obool)),X13),hAPP(c_COMBB(tc_prod(X13,X125),tc_fun(tc_fun(tc_prod(X13,X125),tc_HOL_Obool),tc_HOL_Obool),X125),c_member(tc_prod(X13,X125)))),c_Product__Type_OPair(X13,X125))))),X177)),X16),X25))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X13,X125)),hAPP(hAPP(c_Product__Type_OPair(X13,X125),X16),X25)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(tc_prod(X13,X125),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__INT__eq2) ).
fof(fact_SUP__UN__eq2,axiom,
! [X25,X16,X177,X125,X13,X10] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_fun(X125,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X13,X125),tc_HOL_Obool),tc_fun(X13,tc_fun(X125,tc_HOL_Obool)),X10),hAPP(c_COMBC(X13,tc_fun(tc_prod(X13,X125),tc_HOL_Obool),tc_fun(X125,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X125,tc_fun(tc_fun(tc_prod(X13,X125),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X13,X125),tc_HOL_Obool),tc_fun(X125,tc_HOL_Obool)),X13),c_COMBC(X125,tc_fun(tc_prod(X13,X125),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X125,tc_prod(X13,X125)),tc_fun(X125,tc_fun(tc_fun(tc_prod(X13,X125),tc_HOL_Obool),tc_HOL_Obool)),X13),hAPP(c_COMBB(tc_prod(X13,X125),tc_fun(tc_fun(tc_prod(X13,X125),tc_HOL_Obool),tc_HOL_Obool),X125),c_member(tc_prod(X13,X125)))),c_Product__Type_OPair(X13,X125))))),X177)),X16),X25))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X13,X125)),hAPP(hAPP(c_Product__Type_OPair(X13,X125),X16),X25)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(tc_prod(X13,X125),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__UN__eq2) ).
fof(fact_UN__equiv__class__inject,axiom,
! [X78,X48,X2,X13,X177,X154,X10] :
( c_Equiv__Relations_Oequiv(X10,X154,X177)
=> ( c_Equiv__Relations_Ocongruent(X10,tc_fun(X13,tc_HOL_Obool),X177,X2)
=> ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X48),X2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X78),X2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X48),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X154),X177)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X78),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X154),X177)))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> ! [X90] :
( hBOOL(hAPP(hAPP(c_member(X10),X90),X154))
=> ( hAPP(X2,X3) = hAPP(X2,X90)
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X90)),X177)) ) ) )
=> X48 = X78 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__equiv__class__inject) ).
fof(fact_hoare__derivs_OBody,axiom,
! [X221,X17,X19,X210,X10] :
( c_Hoare__Mirabelle_Ohoare__derivs(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X10),tc_HOL_Obool)),X210),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X10),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X10,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X10)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X10,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X10))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X10,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X10))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X10)),X19)),c_Com_Ocom_OBODY)),X17)),X221)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X10),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X10,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X10)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X10,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X10))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X10,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X10))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X10)),X19)),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))),X17)),X221))
=> c_Hoare__Mirabelle_Ohoare__derivs(X10,X210,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X10),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X10,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X10)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X10,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X10))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X10,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X10))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X10)),X19)),c_Com_Ocom_OBODY)),X17)),X221)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_OBody) ).
fof(fact_finite__image__set,axiom,
! [X2,X13,X19,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Set_OCollect(X10),X19)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X13),hAPP(c_Set_OCollect(X13),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X13),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBC(X13,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X13),c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X13),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj)),hAPP(hAPP(c_COMBC(X13,tc_fun(X10,X13),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(tc_fun(X10,X13),tc_fun(X10,tc_HOL_Obool)),X13),c_COMBB(X13,tc_HOL_Obool,X10)),c_fequal)),X2)))),X19))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__image__set) ).
fof(fact_setsum__reindex__cong,axiom,
! [X204,X1,X160,X154,X2,X13,X10,X125] :
( class_Groups_Ocomm__monoid__add(X125)
=> ( c_Fun_Oinj__on(X10,X13,X2,X154)
=> ( X160 = hAPP(c_Set_Oimage(X10,X13,X2),X154)
=> ( ! [X116] :
( hBOOL(hAPP(hAPP(c_member(X10),X116),X154))
=> hAPP(X1,X116) = hAPP(X204,hAPP(X2,X116)) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X125),X204),X160) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X125),X1),X154) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__reindex__cong) ).
fof(fact_hoare__derivs_OLocal,axiom,
! [X39,X209,X48,X17,X18,X19,X210,X10] :
( c_Hoare__Mirabelle_Ohoare__derivs(X10,X210,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X10)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X10),X19),X18),hAPP(hAPP(c_COMBC(X10,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)),X10),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X17)),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(X48))),hAPP(hAPP(c_Natural_Ogetlocs,X209),X48))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X10),tc_HOL_Obool))))
=> c_Hoare__Mirabelle_Ohoare__derivs(X10,X210,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X10)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X10),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),X10),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,X209)))),hAPP(hAPP(c_COMBC(X10,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)),X10),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X19)),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(X48))),X39)))),c_Com_Ocom_OLocal(X48,X39,X18)),X17)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X10),tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_OLocal) ).
fof(fact_strong__setprod__reindex__cong,axiom,
! [X204,X1,X160,X154,X2,X13,X10,X125] :
( class_Groups_Ocomm__monoid__mult(X125)
=> ( c_Fun_Oinj__on(X10,X13,X2,X154)
=> ( X160 = hAPP(c_Set_Oimage(X10,X13,X2),X154)
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> hAPP(X1,X3) = hAPP(hAPP(c_Fun_Ocomp(X13,X125,X10,X204),X2),X3) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X13,X125),X204),X160) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X125),X1),X154) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_strong__setprod__reindex__cong) ).
fof(fact_setsum__ivl__cong,axiom,
! [X1,X2,X141,X38,X18,X39,X10,X13] :
( ( class_Groups_Ocomm__monoid__add(X13)
& class_Orderings_Oord(X10) )
=> ( X39 = X18
=> ( X38 = X141
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X18),X3))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X3),X141))
=> hAPP(X2,X3) = hAPP(X1,X3) ) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X39),X38)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X18),X141)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__ivl__cong) ).
fof(fact_minus__int__def,axiom,
! [X73] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X73) = 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,X73)),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,
! [X125,X2,X17,X166,X10,X13,X19] :
( hBOOL(hAPP(hAPP(X19,hAPP(c_Product__Type_Osnd(X13,X10),X166)),hAPP(c_Product__Type_Ofst(X13,X10),X166)))
=> ( ! [X3,X90] :
( hBOOL(hAPP(hAPP(X19,X90),X3))
=> hBOOL(hAPP(X17,hAPP(hAPP(X2,X3),X90))) )
=> hBOOL(hAPP(X17,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X13,X10,X125),X2),X166))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_exE__realizer) ).
fof(fact_rp__inv__image__def,axiom,
! [X13,X10] : c_FunDef_Orp__inv__image(X10,X13) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_fun(X13,X10),tc_prod(tc_fun(tc_prod(X13,X13),tc_HOL_Obool),tc_fun(tc_prod(X13,X13),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_fun(X13,X10),tc_fun(tc_prod(X13,X13),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_fun(X13,X10),tc_prod(tc_fun(tc_prod(X13,X13),tc_HOL_Obool),tc_fun(tc_prod(X13,X13),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(X13,X10),tc_fun(tc_prod(X13,X13),tc_HOL_Obool)),tc_fun(tc_fun(X13,X10),tc_prod(tc_fun(tc_prod(X13,X13),tc_HOL_Obool),tc_fun(tc_prod(X13,X13),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_fun(X13,X10),tc_fun(tc_prod(X13,X13),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_fun(X13,X10),tc_prod(tc_fun(tc_prod(X13,X13),tc_HOL_Obool),tc_fun(tc_prod(X13,X13),tc_HOL_Obool))))),tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(X13,X10),tc_fun(tc_prod(X13,X13),tc_HOL_Obool)),tc_fun(tc_fun(X13,X10),tc_prod(tc_fun(tc_prod(X13,X13),tc_HOL_Obool),tc_fun(tc_prod(X13,X13),tc_HOL_Obool))),tc_fun(tc_prod(X10,X10),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X13,X10),tc_fun(tc_fun(tc_prod(X13,X13),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X13,X13),tc_HOL_Obool),tc_fun(tc_prod(X13,X13),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(X13,X10),tc_fun(tc_prod(X13,X13),tc_HOL_Obool)),tc_fun(tc_fun(X13,X10),tc_prod(tc_fun(tc_prod(X13,X13),tc_HOL_Obool),tc_fun(tc_prod(X13,X13),tc_HOL_Obool)))),tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_COMBS(tc_fun(X13,X10),tc_fun(tc_prod(X13,X13),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X13,X13),tc_HOL_Obool),tc_fun(tc_prod(X13,X13),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X13,X10),tc_fun(tc_prod(X13,X13),tc_HOL_Obool)),tc_fun(tc_fun(X13,X10),tc_fun(tc_fun(tc_prod(X13,X13),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X13,X13),tc_HOL_Obool),tc_fun(tc_prod(X13,X13),tc_HOL_Obool)))),tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(X13,X13),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X13,X13),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X13,X13),tc_HOL_Obool),tc_fun(tc_prod(X13,X13),tc_HOL_Obool))),tc_fun(X13,X10)),c_Product__Type_OPair(tc_fun(tc_prod(X13,X13),tc_HOL_Obool),tc_fun(tc_prod(X13,X13),tc_HOL_Obool)))),c_Relation_Oinv__image(X10,X13))))),c_Relation_Oinv__image(X10,X13))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rp__inv__image__def) ).
fof(fact_inv__image__def,axiom,
! [X2,X177,X10,X13] : hAPP(hAPP(c_Relation_Oinv__image(X13,X10),X177),X2) = hAPP(c_Set_OCollect(tc_prod(X10,X10)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X10,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X13,X13),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_fun(tc_prod(X13,X13),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X13,X13),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBC(X10,tc_fun(tc_prod(X13,X13),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_prod(X13,X13)),tc_fun(X10,tc_fun(tc_fun(tc_prod(X13,X13),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X13,X13),tc_fun(tc_fun(tc_prod(X13,X13),tc_HOL_Obool),tc_HOL_Obool),X10),c_member(tc_prod(X13,X13)))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,X13),tc_fun(X10,tc_prod(X13,X13))),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_prod(X13,X13)),tc_fun(tc_fun(X10,X13),tc_fun(X10,tc_prod(X13,X13))),X10),c_COMBB(X13,tc_prod(X13,X13),X10)),hAPP(hAPP(c_COMBB(X13,tc_fun(X13,tc_prod(X13,X13)),X10),c_Product__Type_OPair(X13,X13)),X2))),X2)))),X177))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__image__def) ).
fof(fact_set__zip,axiom,
! [X289,X290,X13,X10] : hAPP(c_List_Oset(tc_prod(X10,X13)),hAPP(hAPP(c_List_Ozip(X10,X13),X290),X289)) = hAPP(c_Set_OCollect(tc_prod(X10,X13)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X10,X13)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X10,X13),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(X10,X13)),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(X10,X13)),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(X10,X13),tc_fun(tc_Nat_Onat,tc_prod(X10,X13)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(X10,X13)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X10,X13)),c_COMBB(tc_prod(X10,X13),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X13,tc_prod(X10,X13)),hAPP(hAPP(c_COMBB(X10,tc_fun(X13,tc_prod(X10,X13)),tc_Nat_Onat),c_Product__Type_OPair(X10,X13)),hAPP(c_List_Onth(X10),X290))),hAPP(c_List_Onth(X13),X289)))))),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(X10)),X290)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13)),X289)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__zip) ).
fof(fact_pred__subset__eq2,axiom,
! [X216,X196,X13,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_fun(X13,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_COMBC(X13,tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_prod(X10,X13)),tc_fun(X13,tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X13),tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool),X13),c_member(tc_prod(X10,X13)))),c_Product__Type_OPair(X10,X13)))),X196)),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_COMBC(X13,tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_prod(X10,X13)),tc_fun(X13,tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X13),tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool),X13),c_member(tc_prod(X10,X13)))),c_Product__Type_OPair(X10,X13)))),X216)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),X196),X216)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq2) ).
fof(fact_Pow__Compl,axiom,
! [X154,X10] : hAPP(c_Set_OPow(X10),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X154)) = hAPP(c_Set_OCollect(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X10,tc_HOL_Obool)),c_HOL_OEx(tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),c_COMBS(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X10,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X10,tc_HOL_Obool)),hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X154)),c_Set_OPow(X10))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__Compl) ).
fof(fact_map__upds__fold__map__upd,axiom,
! [X320,X294,X102,X13,X10] : c_Map_Omap__upds(X10,X13,X102,X294,X320) = hAPP(c_List_Ofoldl(tc_fun(X10,tc_Option_Ooption(X13)),tc_prod(X10,X13),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X13,tc_fun(X10,tc_Option_Ooption(X13)))),tc_fun(tc_prod(X10,X13),tc_fun(X10,tc_Option_Ooption(X13))),tc_fun(X10,tc_Option_Ooption(X13))),c_Product__Type_Oprod_Oprod__case(X10,X13,tc_fun(X10,tc_Option_Ooption(X13)))),hAPP(hAPP(c_COMBC(tc_fun(X10,tc_Option_Ooption(X13)),tc_fun(X13,tc_Option_Ooption(X13)),tc_fun(X10,tc_fun(X13,tc_fun(X10,tc_Option_Ooption(X13))))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_fun(X13,tc_Option_Ooption(X13)),tc_fun(X13,tc_fun(X10,tc_Option_Ooption(X13))))),tc_fun(tc_fun(X13,tc_Option_Ooption(X13)),tc_fun(X10,tc_fun(X13,tc_fun(X10,tc_Option_Ooption(X13))))),tc_fun(X10,tc_Option_Ooption(X13))),c_COMBC(X10,tc_fun(X13,tc_Option_Ooption(X13)),tc_fun(X13,tc_fun(X10,tc_Option_Ooption(X13))))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_Option_Ooption(X13),tc_fun(X10,tc_Option_Ooption(X13)))),tc_fun(X10,tc_fun(tc_fun(X13,tc_Option_Ooption(X13)),tc_fun(X13,tc_fun(X10,tc_Option_Ooption(X13))))),tc_fun(X10,tc_Option_Ooption(X13))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X13),tc_fun(X10,tc_Option_Ooption(X13))),tc_fun(tc_fun(X13,tc_Option_Ooption(X13)),tc_fun(X13,tc_fun(X10,tc_Option_Ooption(X13)))),X10),c_COMBB(tc_Option_Ooption(X13),tc_fun(X10,tc_Option_Ooption(X13)),X13))),c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13))))),c_Option_Ooption_OSome(X13))),X102),hAPP(hAPP(c_List_Ozip(X10,X13),X294),X320)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upds__fold__map__upd) ).
fof(fact_UN__equiv__class__type,axiom,
! [X160,X48,X2,X13,X177,X154,X10] :
( c_Equiv__Relations_Oequiv(X10,X154,X177)
=> ( c_Equiv__Relations_Ocongruent(X10,tc_fun(X13,tc_HOL_Obool),X177,X2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X48),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X154),X177)))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X13,tc_HOL_Obool)),hAPP(X2,X3)),X160)) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X48),X2)),X160)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__equiv__class__type) ).
fof(fact_INF2__iff,axiom,
! [X18,X38,X160,X154,X125,X13,X10] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_fun(X125,tc_HOL_Obool))),X154),X160),X38),X18))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> hBOOL(hAPP(hAPP(hAPP(X160,X3),X38),X18)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF2__iff) ).
fof(fact_min__max_Osup__Inf1__distrib,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X16),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X154)) = c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(X10,tc_HOL_Obool,X10)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(X10),X16))))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X154))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__Inf1__distrib) ).
fof(fact_min__max_Oinf__Sup1__distrib,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X16),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X154)) = c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(X10,tc_HOL_Obool,X10)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(X10),X16))))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X154))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__Sup1__distrib) ).
fof(fact_inf__Sup1__distrib,axiom,
! [X16,X154,X10] :
( class_Lattices_Odistrib__lattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X16),c_Big__Operators_Olattice__class_OSup__fin(X10,X154)) = c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(X10,tc_HOL_Obool,X10)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X16))))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X154))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Sup1__distrib) ).
fof(fact_sup__Inf1__distrib,axiom,
! [X16,X154,X10] :
( class_Lattices_Odistrib__lattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X16),c_Big__Operators_Olattice__class_OInf__fin(X10,X154)) = c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(X10,tc_HOL_Obool,X10)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X16))))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X154))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Inf1__distrib) ).
fof(fact_add__Min__commute,axiom,
! [X101,X226,X10] :
( class_Groups_Olinordered__ab__semigroup__add(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X226))
=> ( X226 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X101),c_Big__Operators_Olinorder__class_OMin(X10,X226)) = c_Big__Operators_Olinorder__class_OMin(X10,hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(X10,tc_HOL_Obool,X10)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X10),X101))))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X226))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Min__commute) ).
fof(fact_add__Max__commute,axiom,
! [X101,X226,X10] :
( class_Groups_Olinordered__ab__semigroup__add(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X226))
=> ( X226 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X101),c_Big__Operators_Olinorder__class_OMax(X10,X226)) = c_Big__Operators_Olinorder__class_OMax(X10,hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(X10,tc_HOL_Obool,X10)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X10),X101))))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X226))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Max__commute) ).
fof(fact_anamorph_Osimps,axiom,
! [X16,X2,X10,X13,X101] :
( ( X101 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_Lazy__Sequence_Oanamorph(X13,X10,X2,X101),X16) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),X13),c_List_Olist_ONil(X10)),X16) )
& ( X101 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_Lazy__Sequence_Oanamorph(X13,X10,X2,X101),X16) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(X10),X13),tc_prod(X10,X13),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),X13),c_List_Olist_ONil(X10)),X16),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,tc_prod(tc_List_Olist(X10),X13)),hAPP(hAPP(c_COMBC(X10,tc_fun(X13,tc_prod(tc_List_Olist(X10),X13)),tc_fun(X13,tc_prod(tc_List_Olist(X10),X13))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(X10),X13),tc_prod(tc_List_Olist(X10),X13)),tc_fun(tc_fun(X13,tc_prod(tc_List_Olist(X10),X13)),tc_fun(X13,tc_prod(tc_List_Olist(X10),X13))),X10),c_COMBB(tc_prod(tc_List_Olist(X10),X13),tc_prod(tc_List_Olist(X10),X13),X13)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X10),tc_fun(X13,tc_prod(tc_List_Olist(X10),X13))),tc_fun(tc_prod(tc_List_Olist(X10),X13),tc_prod(tc_List_Olist(X10),X13)),X10),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X10),X13,tc_prod(tc_List_Olist(X10),X13))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X10),tc_List_Olist(X10)),tc_fun(tc_List_Olist(X10),tc_fun(X13,tc_prod(tc_List_Olist(X10),X13))),X10),hAPP(c_COMBB(tc_List_Olist(X10),tc_fun(X13,tc_prod(tc_List_Olist(X10),X13)),tc_List_Olist(X10)),c_Product__Type_OPair(tc_List_Olist(X10),X13))),c_List_Olist_OCons(X10))))),c_Lazy__Sequence_Oanamorph(X13,X10,X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X101),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(X2,X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_anamorph_Osimps) ).
fof(fact_listrel__iff__zip,axiom,
! [X177,X289,X290,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X290),X289)),c_List_Olistrel(X10,X177)))
<=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X289)
& ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X3),hAPP(c_List_Oset(tc_prod(X10,X10)),hAPP(hAPP(c_List_Ozip(X10,X10),X290),X289))))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X10,X10,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_prod(X10,X10)),tc_fun(X10,tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X10),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool),X10),c_member(tc_prod(X10,X10)))),c_Product__Type_OPair(X10,X10)))),X177)),X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__iff__zip) ).
fof(fact_DomainP__Domain__eq,axiom,
! [X16,X177,X13,X10] :
( hBOOL(hAPP(c_Predicate_ODomainP(X10,X13,hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_COMBC(X13,tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_prod(X10,X13)),tc_fun(X13,tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X13),tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool),X13),c_member(tc_prod(X10,X13)))),c_Product__Type_OPair(X10,X13)))),X177)),X16))
<=> hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_Relation_ODomain(X10,X13),X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainP__Domain__eq) ).
fof(fact_RangeP__Range__eq,axiom,
! [X16,X177,X13,X10] :
( hBOOL(hAPP(c_Predicate_ORangeP(X10,X13,hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_COMBC(X13,tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_prod(X10,X13)),tc_fun(X13,tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X13),tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool),X13),c_member(tc_prod(X10,X13)))),c_Product__Type_OPair(X10,X13)))),X177)),X16))
<=> hBOOL(hAPP(hAPP(c_member(X13),X16),hAPP(c_Relation_ORange(X10,X13),X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeP__Range__eq) ).
fof(fact_accp__acc__eq,axiom,
! [X16,X177,X10] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X10,hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_prod(X10,X10)),tc_fun(X10,tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X10),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool),X10),c_member(tc_prod(X10,X10)))),c_Product__Type_OPair(X10,X10)))),X177)),X16))
<=> hBOOL(hAPP(hAPP(c_member(X10),X16),c_Wellfounded_Oacc(X10,X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__acc__eq) ).
fof(fact_fold__graph_H_Oequations_I2_J,axiom,
! [X66,X51,X52,X72,X50,X13,X10] :
( c_Nitpick_Ofold__graph_H(X10,X13,X50,X72,X52,hAPP(hAPP(X50,X51),X66))
<=> ( ( X52 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
& hAPP(hAPP(X50,X51),X66) = X72 )
| ? [X3,X90] :
( hAPP(hAPP(X50,X51),X66) = hAPP(hAPP(X50,X3),X90)
& hBOOL(hAPP(hAPP(c_member(X10),X3),X52))
& c_Nitpick_Ofold__graph_H(X10,X13,X50,X72,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X52),hAPP(hAPP(c_Set_Oinsert(X10),X3),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),X90) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_H_Oequations_I2_J) ).
fof(fact_SUP2__iff,axiom,
! [X18,X38,X160,X154,X125,X13,X10] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_fun(X125,tc_HOL_Obool))),X154),X160),X38),X18))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
& hBOOL(hAPP(hAPP(hAPP(X160,X3),X38),X18)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP2__iff) ).
fof(fact_partition_Osimps_I2_J,axiom,
! [X290,X16,X19,X10] : c_List_Opartition(X10,X19,hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X10),tc_List_Olist(X10),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_COMBS(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),tc_fun(tc_List_Olist(X10),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X10),tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)))),tc_fun(tc_fun(tc_List_Olist(X10),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),tc_fun(tc_List_Olist(X10),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)))),tc_List_Olist(X10)),c_COMBS(tc_List_Olist(X10),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X10),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),tc_fun(tc_List_Olist(X10),tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)))),tc_List_Olist(X10)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),tc_List_Olist(X10)),hAPP(c_If(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(X19,X16)))),hAPP(hAPP(c_COMBB(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),tc_List_Olist(X10)),c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(c_List_Olist_OCons(X10),X16))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_List_Olist(X10)),tc_fun(tc_List_Olist(X10),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X10),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),tc_fun(tc_fun(tc_List_Olist(X10),tc_List_Olist(X10)),tc_fun(tc_List_Olist(X10),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)))),tc_List_Olist(X10)),c_COMBB(tc_List_Olist(X10),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_List_Olist(X10))),c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)))),hAPP(c_List_Olist_OCons(X10),X16)))),c_List_Opartition(X10,X19,X290)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition_Osimps_I2_J) ).
fof(fact_Ass,axiom,
! [X39,X48,X19,X210,X10] : c_Hoare__Mirabelle_Ohoare__derivs(X10,X210,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X10)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X10),hAPP(hAPP(c_COMBC(X10,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)),X10),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X19)),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),X48)),X39))),c_Com_Ocom_OAss(X48,X39)),X19)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X10),tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ass) ).
fof(fact_hoare__derivs_Oequations_I8_J,axiom,
! [X72,X50,X52,X51,X10] : c_Hoare__Mirabelle_Ohoare__derivs(X10,X51,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X10)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X10),hAPP(hAPP(c_COMBC(X10,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)),X10),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X52)),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),X50)),X72))),c_Com_Ocom_OAss(X50,X72)),X52)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X10),tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_Oequations_I8_J) ).
fof(fact_lexn_Osimps_I2_J,axiom,
! [X20,X177,X10] : hAPP(c_List_Olexn(X10,X177),hAPP(c_Nat_OSuc,X20)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(X10,tc_List_Olist(X10)),tc_prod(X10,tc_List_Olist(X10))),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),c_Product__Type_Omap__pair(tc_prod(X10,tc_List_Olist(X10)),tc_List_Olist(X10),tc_prod(X10,tc_List_Olist(X10)),tc_List_Olist(X10),hAPP(c_Product__Type_Oprod_Oprod__case(X10,tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_OCons(X10)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_OCons(X10)))),c_Wellfounded_Olex__prod(X10,tc_List_Olist(X10),X177,hAPP(c_List_Olexn(X10,X177),X20)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X10),tc_List_Olist(X10),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),tc_List_Olist(X10)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X10))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X10)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X10)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X10)))),hAPP(c_Nat_OSuc,X20))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X10)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X10)))),hAPP(c_Nat_OSuc,X20)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexn_Osimps_I2_J) ).
fof(fact_set__sublist,axiom,
! [X241,X290,X10] : hAPP(c_List_Oset(X10),c_List_Osublist(X10,X290,X241)) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X10,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)),X10),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)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_Nat_Onat,X10),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X10),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X10),c_COMBB(X10,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X10),X290))))),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(X10)),X290)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X241))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__sublist) ).
fof(fact_pred__comp__rel__comp__eq,axiom,
! [X25,X16,X54,X177,X125,X13,X10] :
( c_Predicate_Opred__comp(X10,X13,X125,hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_COMBC(X13,tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_prod(X10,X13)),tc_fun(X13,tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X13),tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool),X13),c_member(tc_prod(X10,X13)))),c_Product__Type_OPair(X10,X13)))),X177),hAPP(hAPP(c_COMBC(X13,tc_fun(tc_prod(X13,X125),tc_HOL_Obool),tc_fun(X125,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X125,tc_fun(tc_fun(tc_prod(X13,X125),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X13,X125),tc_HOL_Obool),tc_fun(X125,tc_HOL_Obool)),X13),c_COMBC(X125,tc_fun(tc_prod(X13,X125),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X125,tc_prod(X13,X125)),tc_fun(X125,tc_fun(tc_fun(tc_prod(X13,X125),tc_HOL_Obool),tc_HOL_Obool)),X13),hAPP(c_COMBB(tc_prod(X13,X125),tc_fun(tc_fun(tc_prod(X13,X125),tc_HOL_Obool),tc_HOL_Obool),X125),c_member(tc_prod(X13,X125)))),c_Product__Type_OPair(X13,X125)))),X54),X16,X25)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X125)),hAPP(hAPP(c_Product__Type_OPair(X10,X125),X16),X25)),hAPP(hAPP(c_Relation_Orel__comp(X10,X13,X125),X177),X54))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__comp__rel__comp__eq) ).
fof(fact_setsum__multicount__gen,axiom,
! [X101,X196,X53,X13,X54,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X54))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X53))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X13),X3),X53))
=> hAPP(c_Finite__Set_Ocard(X10),hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X54))),hAPP(hAPP(c_COMBC(X10,X13,tc_HOL_Obool),X196),X3)))) = hAPP(X101,X3) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_Nat_Onat,X10),c_Finite__Set_Ocard(X13)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool),X10),c_Set_OCollect(X13)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool),X10),hAPP(c_COMBS(X13,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X13),c_fconj),hAPP(hAPP(c_COMBC(X13,tc_fun(X13,tc_HOL_Obool),tc_HOL_Obool),c_member(X13)),X53)))),X196)))),X54) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,tc_Nat_Onat),X101),X53) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__multicount__gen) ).
fof(fact_set__conv__nth,axiom,
! [X290,X10] : hAPP(c_List_Oset(X10),X290) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X10,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)),X10),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)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_Nat_Onat,X10),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X10),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X10),c_COMBB(X10,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X10),X290))))),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(X10)),X290))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__conv__nth) ).
fof(fact_Sigma__def,axiom,
! [X160,X154,X13,X10] : hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X154),X160) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBS(X10,tc_fun(X13,tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(tc_fun(X13,tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),X10),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(tc_prod(X10,X13),tc_HOL_Obool))),X160)),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(X13,tc_fun(tc_prod(X10,X13),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(tc_prod(X10,X13),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(X13,tc_fun(tc_prod(X10,X13),tc_HOL_Obool))),X10),c_COMBC(X13,tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(tc_prod(X10,X13),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_prod(X10,X13)),tc_fun(X13,tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(tc_prod(X10,X13),tc_HOL_Obool))),X10),hAPP(c_COMBB(tc_prod(X10,X13),tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),X13),c_Set_Oinsert(tc_prod(X10,X13)))),c_Product__Type_OPair(X10,X13)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X13),tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__def) ).
fof(fact_setsum__multicount,axiom,
! [X101,X196,X232,X13,X216,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X216))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X232))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X13),X3),X232))
=> hAPP(c_Finite__Set_Ocard(X10),hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X216))),hAPP(hAPP(c_COMBC(X10,X13,tc_HOL_Obool),X196),X3)))) = X101 )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_Nat_Onat,X10),c_Finite__Set_Ocard(X13)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool),X10),c_Set_OCollect(X13)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool),X10),hAPP(c_COMBS(X13,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X13),c_fconj),hAPP(hAPP(c_COMBC(X13,tc_fun(X13,tc_HOL_Obool),tc_HOL_Obool),c_member(X13)),X232)))),X196)))),X216) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X101),hAPP(c_Finite__Set_Ocard(X13),X232)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__multicount) ).
fof(fact_setsum__setsum__restrict,axiom,
! [X196,X2,X232,X13,X216,X10,X125] :
( class_Groups_Ocomm__monoid__add(X125)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X216))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X232))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X125),hAPP(hAPP(c_COMBS(X10,tc_fun(X13,tc_HOL_Obool),X125),hAPP(hAPP(c_COMBB(tc_fun(X13,X125),tc_fun(tc_fun(X13,tc_HOL_Obool),X125),X10),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X125)),X2)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool),X10),c_Set_OCollect(X13)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool),X10),hAPP(c_COMBS(X13,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X13),c_fconj),hAPP(hAPP(c_COMBC(X13,tc_fun(X13,tc_HOL_Obool),tc_HOL_Obool),c_member(X13)),X232)))),X196)))),X216) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X125),hAPP(hAPP(c_COMBS(X13,tc_fun(X10,tc_HOL_Obool),X125),hAPP(hAPP(c_COMBB(tc_fun(X10,X125),tc_fun(tc_fun(X10,tc_HOL_Obool),X125),X13),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X125)),hAPP(c_COMBC(X10,X13,X125),X2))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X13),c_Set_OCollect(X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X13),hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X216)))),hAPP(c_COMBC(X10,X13,tc_HOL_Obool),X196))))),X232) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__setsum__restrict) ).
fof(fact_sequence__trans,axiom,
! [X101,X113,X177,X2,X10] :
( ! [X152] : hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),hAPP(X2,hAPP(c_Nat_OSuc,X152))),hAPP(X2,X152))),c_Transitive__Closure_Ortrancl(X10,X177)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X113),X101))),hAPP(X2,X113))),c_Transitive__Closure_Ortrancl(X10,X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sequence__trans) ).
fof(fact_divmod__int__rel__def,axiom,
! [X38,X39] : c_Divides_Odivmod__int__rel(X39,X38) = 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,X39))),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),X38)))))),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)),X38))),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)),X38))))),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)),X38)))),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),X38))),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,
! [X160,X1,X125,X154,X2,X13,X10] :
( class_Rings_Osemiring__0(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X10),X2),X154)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X125,X10),X1),X160)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X10),hAPP(hAPP(c_COMBC(X13,tc_fun(X125,tc_HOL_Obool),X10),hAPP(hAPP(c_COMBB(tc_fun(X125,X10),tc_fun(tc_fun(X125,tc_HOL_Obool),X10),X13),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X125,X10)),hAPP(hAPP(c_COMBC(X13,tc_fun(X125,X10),tc_fun(X125,X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,X10),tc_fun(tc_fun(X125,X10),tc_fun(X125,X10)),X13),c_COMBB(X10,X10,X125)),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X13),c_Groups_Otimes__class_Otimes(X10)),X2))),X1))),X160)),X154) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__product) ).
fof(fact_fold__image__Sigma,axiom,
! [X1,X160,X13,X154,X10,X125] :
( class_Groups_Ocomm__monoid__mult(X125)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X13),hAPP(X160,X3))) )
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X125,X10,c_Groups_Otimes__class_Otimes(X125)),hAPP(hAPP(c_COMBS(X10,tc_fun(X13,tc_HOL_Obool),X125),hAPP(hAPP(c_COMBC(X10,X125,tc_fun(tc_fun(X13,tc_HOL_Obool),X125)),hAPP(hAPP(c_COMBB(tc_fun(X13,X125),tc_fun(X125,tc_fun(tc_fun(X13,tc_HOL_Obool),X125)),X10),c_Finite__Set_Ofold__image(X125,X13,c_Groups_Otimes__class_Otimes(X125))),X1)),c_Groups_Oone__class_Oone(X125))),X160)),c_Groups_Oone__class_Oone(X125)),X154) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X125,tc_prod(X10,X13),c_Groups_Otimes__class_Otimes(X125)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,X125),X1)),c_Groups_Oone__class_Oone(X125)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X154),X160)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__Sigma) ).
fof(fact_finite__lists__length__le,axiom,
! [X20,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X10)),hAPP(c_Set_OCollect(tc_List_Olist(X10)),hAPP(hAPP(c_COMBS(tc_List_Olist(X10),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X10)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X10)),c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool))),c_List_Oset(X10))),X154))),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X10)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X10)))),X20))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__lists__length__le) ).
fof(fact_finite__lists__length__eq,axiom,
! [X20,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X10)),hAPP(c_Set_OCollect(tc_List_Olist(X10)),hAPP(hAPP(c_COMBS(tc_List_Olist(X10),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X10)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X10)),c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool))),c_List_Oset(X10))),X154))),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X10)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X10)))),X20))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__lists__length__eq) ).
fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
! [X160,X154,X225,X1,X73,X2,X13,X10] :
( c_Finite__Set_Ofolding__image__simple(X10,X13,X2,X73,X1,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X160))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X13),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13,tc_HOL_Obool)),X154),X160)))
=> hAPP(X1,X3) = X73 )
=> hAPP(X225,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(X2,hAPP(X225,X154)),hAPP(X225,X160)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Ounion__inter__neutral) ).
fof(fact_nat__def,axiom,
! [X73] : hAPP(c_Int_Onat,X73) = 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,X73)),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,
! [X66,X72,X52,X50,X51,X65] :
( c_Natural_Oevaln(c_Com_Ocom_OCall(X65,X51,X50),X52,X72,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X66),hAPP(c_Natural_Ogetlocs,X52))),X65),hAPP(hAPP(c_Natural_Ogetlocs,X66),c_Com_ORes)))
<=> ? [X67] :
( hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X66),hAPP(c_Natural_Ogetlocs,X52))),X65),hAPP(hAPP(c_Natural_Ogetlocs,X66),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X67),hAPP(c_Natural_Ogetlocs,X52))),X65),hAPP(hAPP(c_Natural_Ogetlocs,X67),c_Com_ORes))
& c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X51),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X52),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X50,X52)),X72,X67) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I10_J) ).
fof(fact_nat__intermed__int__val,axiom,
! [X101,X2,X20,X102] :
( ! [X152] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X152))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X152),X20)) )
=> 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),X152),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,X152)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X20))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,X102)),X101))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X101),hAPP(X2,X20)))
=> ? [X152] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X152))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X152),X20))
& hAPP(X2,X152) = X101 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__intermed__int__val) ).
fof(fact_Sigma__mono,axiom,
! [X197,X160,X13,X198,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X198))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool)),hAPP(X160,X3)),hAPP(X197,X3))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X154),X160)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X198),X197))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__mono) ).
fof(fact_setprod__dvd__setprod__subset2,axiom,
! [X1,X2,X154,X160,X10,X13] :
( class_Rings_Ocomm__semiring__1(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X13),hAPP(X2,X3)),hAPP(X1,X3))) )
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X13),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),X154)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),X160))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__dvd__setprod__subset2) ).
fof(fact_mem__splitI2,axiom,
! [X18,X73,X125,X13,X10,X166] :
( ! [X116,X193] :
( X166 = hAPP(hAPP(c_Product__Type_OPair(X10,X13),X116),X193)
=> hBOOL(hAPP(hAPP(c_member(X125),X73),hAPP(hAPP(X18,X116),X193))) )
=> hBOOL(hAPP(hAPP(c_member(X125),X73),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,tc_fun(X125,tc_HOL_Obool)),X18),X166))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__splitI2) ).
fof(fact_converse__def,axiom,
! [X177,X10,X13] : hAPP(c_Relation_Oconverse(X13,X10),X177) = hAPP(c_Set_OCollect(tc_prod(X10,X13)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X13,X10),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_fun(tc_fun(tc_prod(X13,X10),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X13,X10),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_COMBC(X13,tc_fun(tc_prod(X13,X10),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_prod(X13,X10)),tc_fun(X13,tc_fun(tc_fun(tc_prod(X13,X10),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X13,X10),tc_fun(tc_fun(tc_prod(X13,X10),tc_HOL_Obool),tc_HOL_Obool),X13),c_member(tc_prod(X13,X10)))),hAPP(c_COMBC(X13,X10,tc_prod(X13,X10)),c_Product__Type_OPair(X13,X10))))),X177))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__def) ).
fof(fact_card__less__Suc,axiom,
! [X113,X230] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X230))
=> 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)),X230))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X113))))) = 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)),X230))),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,X113))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__less__Suc) ).
fof(fact_setsum__image__gen,axiom,
! [X2,X125,X1,X216,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X216))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1),X216) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X125,X13),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),X13,X125),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X125),c_Set_OCollect(X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X125),hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X216)))),hAPP(c_COMBC(X10,X125,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X125,tc_fun(X125,tc_HOL_Obool),X10),c_fequal),X2)))))),hAPP(c_Set_Oimage(X10,X125,X2),X216)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__image__gen) ).
fof(fact_refl__on__def_H,axiom,
! [X177,X154,X10] :
( c_Relation_Orefl__on(X10,X154,X177)
<=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X3),X177))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X10,X10,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X154)))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X154))),X3)) )
& ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X3)),X177)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__def_H) ).
fof(fact_zip__Cons,axiom,
! [X289,X25,X290,X13,X10] : hAPP(hAPP(c_List_Ozip(X10,X13),X290),hAPP(hAPP(c_List_Olist_OCons(X13),X25),X289)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X10,X13)),X10,c_List_Olist_ONil(tc_prod(X10,X13)),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_List_Olist(X10),tc_List_Olist(tc_prod(X10,X13))),tc_fun(tc_List_Olist(X10),tc_List_Olist(tc_prod(X10,X13)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X10,X13)),tc_List_Olist(tc_prod(X10,X13))),tc_fun(tc_fun(tc_List_Olist(X10),tc_List_Olist(tc_prod(X10,X13))),tc_fun(tc_List_Olist(X10),tc_List_Olist(tc_prod(X10,X13)))),X10),c_COMBB(tc_List_Olist(tc_prod(X10,X13)),tc_List_Olist(tc_prod(X10,X13)),tc_List_Olist(X10))),hAPP(hAPP(c_COMBB(tc_prod(X10,X13),tc_fun(tc_List_Olist(tc_prod(X10,X13)),tc_List_Olist(tc_prod(X10,X13))),X10),c_List_Olist_OCons(tc_prod(X10,X13))),hAPP(hAPP(c_COMBC(X10,X13,tc_prod(X10,X13)),c_Product__Type_OPair(X10,X13)),X25)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_List_Olist(X13),tc_List_Olist(tc_prod(X10,X13))),c_List_Ozip(X10,X13)),X289))),X290),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__Cons) ).
fof(fact_max__extp__max__ext__eq,axiom,
! [X220,X16,X196,X10] :
( c_Wellfounded_Omax__extp(X10,hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_prod(X10,X10)),tc_fun(X10,tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X10),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool),X10),c_member(tc_prod(X10,X10)))),c_Product__Type_OPair(X10,X10)))),X196),X16,X220)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X16),X220)),c_Wellfounded_Omax__ext(X10,X196))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__extp__max__ext__eq) ).
fof(fact_listrelp__listrel__eq,axiom,
! [X220,X16,X177,X10] :
( c_List_Olistrelp(X10,hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_prod(X10,X10)),tc_fun(X10,tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X10),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool),X10),c_member(tc_prod(X10,X10)))),c_Product__Type_OPair(X10,X10)))),X177),X16,X220)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X16),X220)),c_List_Olistrel(X10,X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrelp__listrel__eq) ).
fof(fact_UN__Times__distrib,axiom,
! [X225,X258,X160,X154,X13,X10,X195,X125] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(X125,X195),tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X125,X195),X154),hAPP(c_COMBK(tc_fun(X195,tc_HOL_Obool),X125),X160))),hAPP(c_Product__Type_Oprod_Oprod__case(X125,X195,tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X125,tc_fun(X195,tc_fun(X10,tc_fun(X13,tc_HOL_Obool))),tc_fun(X195,tc_fun(tc_prod(X10,X13),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_fun(X13,tc_HOL_Obool)),tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),tc_fun(tc_fun(X195,tc_fun(X10,tc_fun(X13,tc_HOL_Obool))),tc_fun(X195,tc_fun(tc_prod(X10,X13),tc_HOL_Obool))),X125),c_COMBB(tc_fun(X10,tc_fun(X13,tc_HOL_Obool)),tc_fun(tc_prod(X10,X13),tc_HOL_Obool),X195)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_fun(X13,tc_HOL_Obool)),tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),X125),c_Product__Type_OSigma(X10,X13)),X258))),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X10,tc_fun(X13,tc_HOL_Obool)),X195),c_COMBK(tc_fun(X13,tc_HOL_Obool),X10)),X225)))) = hAPP(hAPP(c_Product__Type_OSigma(X10,X13),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X125,tc_fun(X10,tc_HOL_Obool)),X154),X258)),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X195,tc_fun(X13,tc_HOL_Obool)),X160),X225))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__Times__distrib) ).
fof(fact_equivp__equiv,axiom,
! [X154,X10] :
( c_Equiv__Relations_Oequiv(X10,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X154)
<=> c_Equiv__Relations_Oequivp(X10,hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_prod(X10,X10)),tc_fun(X10,tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X10),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool),X10),c_member(tc_prod(X10,X10)))),c_Product__Type_OPair(X10,X10)))),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivp__equiv) ).
fof(fact_wfP__wf__eq,axiom,
! [X177,X10] :
( c_Wellfounded_OwfP(X10,hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_prod(X10,X10)),tc_fun(X10,tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X10),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool),X10),c_member(tc_prod(X10,X10)))),c_Product__Type_OPair(X10,X10)))),X177))
<=> c_Wellfounded_Owf(X10,X177) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__wf__eq) ).
fof(fact_pred__equals__eq2,axiom,
! [X216,X196,X13,X10] :
( hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_COMBC(X13,tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_prod(X10,X13)),tc_fun(X13,tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X13),tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool),X13),c_member(tc_prod(X10,X13)))),c_Product__Type_OPair(X10,X13)))),X196) = hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_COMBC(X13,tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_prod(X10,X13)),tc_fun(X13,tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X13),tc_fun(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_HOL_Obool),X13),c_member(tc_prod(X10,X13)))),c_Product__Type_OPair(X10,X13)))),X216)
<=> X196 = X216 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq2) ).
fof(fact_map__zip__map2,axiom,
! [X289,X1,X195,X290,X2,X10,X125,X13] : hAPP(hAPP(c_List_Omap(tc_prod(X13,X125),X10),X2),hAPP(hAPP(c_List_Ozip(X13,X125),X290),hAPP(hAPP(c_List_Omap(X195,X125),X1),X289))) = hAPP(hAPP(c_List_Omap(tc_prod(X13,X195),X10),hAPP(c_Product__Type_Oprod_Oprod__case(X13,X195,X10),hAPP(hAPP(c_COMBB(tc_fun(X195,tc_prod(X13,X125)),tc_fun(X195,X10),X13),hAPP(c_COMBB(tc_prod(X13,X125),X10,X195),X2)),hAPP(hAPP(c_COMBC(X13,tc_fun(X195,X125),tc_fun(X195,tc_prod(X13,X125))),hAPP(hAPP(c_COMBB(tc_fun(X125,tc_prod(X13,X125)),tc_fun(tc_fun(X195,X125),tc_fun(X195,tc_prod(X13,X125))),X13),c_COMBB(X125,tc_prod(X13,X125),X195)),c_Product__Type_OPair(X13,X125))),X1)))),hAPP(hAPP(c_List_Ozip(X13,X195),X290),X289)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__zip__map2) ).
fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
! [X39,X25,X154,X73,X2,X13,X10] :
( c_Finite__Set_Ofun__left__comm(X10,X13,X2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X13,X2,X73,X154),X25))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> ? [X265] :
( X25 = hAPP(hAPP(X2,X39),X265)
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X13,X2,X73,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),X265)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__insertE__aux) ).
fof(fact_map__of__map,axiom,
! [X290,X2,X125,X13,X10] : c_Map_Omap__of(X10,X13,hAPP(hAPP(c_List_Omap(tc_prod(X10,X125),tc_prod(X10,X13)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X125,tc_prod(X10,X13)),hAPP(hAPP(c_COMBC(X10,tc_fun(X125,X13),tc_fun(X125,tc_prod(X10,X13))),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_prod(X10,X13)),tc_fun(tc_fun(X125,X13),tc_fun(X125,tc_prod(X10,X13))),X10),c_COMBB(X13,tc_prod(X10,X13),X125)),c_Product__Type_OPair(X10,X13))),X2))),X290)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(X125),tc_Option_Ooption(X13),X10,hAPP(c_Option_Omap(X125,X13),X2)),c_Map_Omap__of(X10,X125,X290)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__map) ).
fof(fact_zip__Cons1,axiom,
! [X289,X290,X16,X13,X10] : hAPP(hAPP(c_List_Ozip(X10,X13),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290)),X289) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X10,X13)),X13,c_List_Olist_ONil(tc_prod(X10,X13)),hAPP(hAPP(c_COMBC(X13,tc_fun(tc_List_Olist(X13),tc_List_Olist(tc_prod(X10,X13))),tc_fun(tc_List_Olist(X13),tc_List_Olist(tc_prod(X10,X13)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X10,X13)),tc_List_Olist(tc_prod(X10,X13))),tc_fun(tc_fun(tc_List_Olist(X13),tc_List_Olist(tc_prod(X10,X13))),tc_fun(tc_List_Olist(X13),tc_List_Olist(tc_prod(X10,X13)))),X13),c_COMBB(tc_List_Olist(tc_prod(X10,X13)),tc_List_Olist(tc_prod(X10,X13)),tc_List_Olist(X13))),hAPP(hAPP(c_COMBB(tc_prod(X10,X13),tc_fun(tc_List_Olist(tc_prod(X10,X13)),tc_List_Olist(tc_prod(X10,X13))),X13),c_List_Olist_OCons(tc_prod(X10,X13))),hAPP(c_Product__Type_OPair(X10,X13),X16)))),hAPP(c_List_Ozip(X10,X13),X290))),X289),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__Cons1) ).
fof(fact_wf__if__measure,axiom,
! [X10,X1,X2,X19] :
( ! [X3] :
( hBOOL(hAPP(X19,X3))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,hAPP(X1,X3))),hAPP(X2,X3))) )
=> c_Wellfounded_Owf(X10,hAPP(c_Set_OCollect(tc_prod(X10,X10)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X10,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X10),hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),X19))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(X10,tc_HOL_Obool,X10)),c_fequal)),X1))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__if__measure) ).
fof(fact_max__ext__compat,axiom,
! [X216,X196,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X196),X216)),X196))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Wellfounded_Omax__ext(X10,X196)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(X10,X216)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(X10,X196))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext__compat) ).
fof(fact_min__ext__compat,axiom,
! [X216,X196,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X196),X216)),X196))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Wellfounded_Omin__ext(X10,X196)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(X10,X216)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(X10,X196))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__ext__compat) ).
fof(fact_hoare__derivs_OIf,axiom,
! [X141,X17,X18,X38,X19,X210,X10] :
( c_Hoare__Mirabelle_Ohoare__derivs(X10,X210,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X10)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X10),c_Hoare__Mirabelle_Opeek__and(X10,X19,X38)),X18),X17)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X10),tc_HOL_Obool))))
=> ( c_Hoare__Mirabelle_Ohoare__derivs(X10,X210,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X10)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X10),c_Hoare__Mirabelle_Opeek__and(X10,X19,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X38))),X141),X17)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X10),tc_HOL_Obool))))
=> c_Hoare__Mirabelle_Ohoare__derivs(X10,X210,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X10)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X10),X19),c_Com_Ocom_OCond(X38,X18,X141)),X17)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X10),tc_HOL_Obool)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_OIf) ).
fof(fact_setsum__restrict__set_H,axiom,
! [X160,X2,X154,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X154))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X160)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),hAPP(hAPP(c_COMBC(X10,X13,X13),hAPP(hAPP(c_COMBS(X10,X13,tc_fun(X13,X13)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X13,tc_fun(X13,X13)),X10),c_If(X13)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X160))),X2)),c_Groups_Ozero__class_Ozero(X13))),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__restrict__set_H) ).
fof(fact_zip__map__map,axiom,
! [X289,X1,X195,X290,X2,X125,X13,X10] : hAPP(hAPP(c_List_Ozip(X10,X13),hAPP(hAPP(c_List_Omap(X125,X10),X2),X290)),hAPP(hAPP(c_List_Omap(X195,X13),X1),X289)) = hAPP(hAPP(c_List_Omap(tc_prod(X125,X195),tc_prod(X10,X13)),hAPP(c_Product__Type_Oprod_Oprod__case(X125,X195,tc_prod(X10,X13)),hAPP(hAPP(c_COMBC(X125,tc_fun(X195,X13),tc_fun(X195,tc_prod(X10,X13))),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_prod(X10,X13)),tc_fun(tc_fun(X195,X13),tc_fun(X195,tc_prod(X10,X13))),X125),c_COMBB(X13,tc_prod(X10,X13),X195)),hAPP(hAPP(c_COMBB(X10,tc_fun(X13,tc_prod(X10,X13)),X125),c_Product__Type_OPair(X10,X13)),X2))),X1))),hAPP(hAPP(c_List_Ozip(X125,X195),X290),X289)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__map__map) ).
fof(fact_finite__psubset__def,axiom,
! [X10] : c_Wellfounded_Ofinite__psubset(X10) = hAPP(c_Set_OCollect(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),c_COMBS(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool))))),c_Finite__Set_Ofinite(X10)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__psubset__def) ).
fof(fact_map__pair__imageI,axiom,
! [X1,X2,X195,X125,X196,X38,X39,X13,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X39),X38)),X196))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X125,X195)),hAPP(hAPP(c_Product__Type_OPair(X125,X195),hAPP(X2,X39)),hAPP(X1,X38))),hAPP(c_Set_Oimage(tc_prod(X10,X13),tc_prod(X125,X195),c_Product__Type_Omap__pair(X10,X125,X13,X195,X2,X1)),X196))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__imageI) ).
fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
! [X201,X202,X203,X2,X196,X10,X13] : c_New__Random__Sequence_Oneg__decr__bind(X13,X10,X196,X2,X203,X202,X201) = c_New__DSequence_Oneg__decr__bind(X13,X10,hAPP(hAPP(hAPP(X196,X203),X202),X201),hAPP(hAPP(c_COMBC(X13,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(X10)))),hAPP(hAPP(c_COMBC(X13,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(X10))))),hAPP(hAPP(c_COMBC(X13,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(X10)))))),X2),X203)),X202)),X201)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__Random__Sequence_Oneg__decr__bind__def) ).
fof(fact_INTER__def,axiom,
! [X160,X154,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X154),X160) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OAll(X13)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool),X10),hAPP(c_COMBS(X13,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X13),c_fimplies),hAPP(hAPP(c_COMBC(X13,tc_fun(X13,tc_HOL_Obool),tc_HOL_Obool),c_member(X13)),X154)))),hAPP(hAPP(c_COMBC(X10,tc_fun(X13,tc_fun(X10,tc_HOL_Obool)),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X13,tc_fun(X10,tc_HOL_Obool)),tc_fun(X13,tc_HOL_Obool)),X10),c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X13)),c_member(X10))),X160)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INTER__def) ).
fof(fact_congruent__def,axiom,
! [X2,X177,X13,X10] :
( c_Equiv__Relations_Ocongruent(X10,X13,X177,X2)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X3),X177))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X10,X10,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,X13),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(tc_fun(X10,X13),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(X13,tc_HOL_Obool,X10)),hAPP(hAPP(c_COMBB(X13,tc_fun(X13,tc_HOL_Obool),X10),c_fequal),X2))),X2)),X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_congruent__def) ).
fof(fact_finite__Collect__bounded__ex,axiom,
! [X17,X13,X19,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Set_OCollect(X10),X19)))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),hAPP(c_Set_OCollect(X13),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X13),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X13),hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),X19))),X17)))))
<=> ! [X90] :
( hBOOL(hAPP(X19,X90))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X13),hAPP(c_Set_OCollect(X13),hAPP(hAPP(c_COMBC(X13,X10,tc_HOL_Obool),X17),X90)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__bounded__ex) ).
fof(fact_setsum__Sigma,axiom,
! [X2,X160,X13,X154,X10,X125] :
( class_Groups_Ocomm__monoid__add(X125)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X13),hAPP(X160,X3))) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X125),hAPP(hAPP(c_COMBS(X10,tc_fun(X13,tc_HOL_Obool),X125),hAPP(hAPP(c_COMBB(tc_fun(X13,X125),tc_fun(tc_fun(X13,tc_HOL_Obool),X125),X10),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X125)),X2)),X160)),X154) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X10,X13),X125),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,X125),X2)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X154),X160)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Sigma) ).
fof(fact_setprod__Sigma,axiom,
! [X2,X160,X13,X154,X10,X125] :
( class_Groups_Ocomm__monoid__mult(X125)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X13),hAPP(X160,X3))) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X125),hAPP(hAPP(c_COMBS(X10,tc_fun(X13,tc_HOL_Obool),X125),hAPP(hAPP(c_COMBB(tc_fun(X13,X125),tc_fun(tc_fun(X13,tc_HOL_Obool),X125),X10),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X13,X125)),X2)),X160)),X154) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X10,X13),X125),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,X125),X2)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X154),X160)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__Sigma) ).
fof(fact_setsum__restrict__set,axiom,
! [X160,X2,X154,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),hAPP(hAPP(c_COMBC(X10,X13,X13),hAPP(hAPP(c_COMBS(X10,X13,tc_fun(X13,X13)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X13,tc_fun(X13,X13)),X10),c_If(X13)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X160))),X2)),c_Groups_Ozero__class_Ozero(X13))),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__restrict__set) ).
fof(fact_UN__finite2__subset,axiom,
! [X160,X101,X154,X10] :
( ! [X83] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X83)),X154)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,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),X83),X101))),X160)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X154)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X160))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__finite2__subset) ).
fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
! [X201,X202,X203,X2,X196,X10,X13] : c_New__Random__Sequence_Opos__decr__bind(X13,X10,X196,X2,X203,X202,X201) = c_New__DSequence_Opos__decr__bind(X13,X10,hAPP(hAPP(hAPP(X196,X203),X202),X201),hAPP(hAPP(c_COMBC(X13,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X10))),hAPP(hAPP(c_COMBC(X13,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(X10)))),hAPP(hAPP(c_COMBC(X13,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(X10))))),X2),X203)),X202)),X201)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__Random__Sequence_Opos__decr__bind__def) ).
fof(fact_image__split__eq__Sigma,axiom,
! [X154,X1,X2,X13,X10,X125] : hAPP(c_Set_Oimage(X125,tc_prod(X10,X13),hAPP(hAPP(c_COMBS(X125,X13,tc_prod(X10,X13)),hAPP(hAPP(c_COMBB(X10,tc_fun(X13,tc_prod(X10,X13)),X125),c_Product__Type_OPair(X10,X13)),X2)),X1)),X154) = hAPP(hAPP(c_Product__Type_OSigma(X10,X13),hAPP(c_Set_Oimage(X125,X10,X2),X154)),hAPP(hAPP(c_COMBB(tc_fun(X125,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool),X10),c_Set_Oimage(X125,X13,X1)),hAPP(hAPP(c_COMBC(X10,tc_fun(X125,tc_HOL_Obool),tc_fun(X125,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X125,tc_HOL_Obool),tc_fun(tc_fun(X125,tc_HOL_Obool),tc_fun(X125,tc_HOL_Obool)),X10),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X125,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X125,tc_HOL_Obool),X10),c_Set_Ovimage(X125,X10,X2)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Set_Oinsert(X10)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))),X154))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__split__eq__Sigma) ).
fof(fact_Sup__Inf,axiom,
! [X154,X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> c_Complete__Lattice_OSup__class_OSup(X10,X154) = c_Complete__Lattice_OInf__class_OInf(X10,hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OAll(X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X10),hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fimplies),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X154)))),hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X10)))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__Inf) ).
fof(fact_setsum__nonneg__leq__bound,axiom,
! [X113,X160,X2,X54,X10,X13] :
( class_Groups_Oordered__ab__group__add(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X54))
=> ( ! [X152] :
( hBOOL(hAPP(hAPP(c_member(X10),X152),X54))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13),c_Groups_Ozero__class_Ozero(X13)),hAPP(X2,X152))) )
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),X54) = X160
=> ( hBOOL(hAPP(hAPP(c_member(X10),X113),X54))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13),hAPP(X2,X113)),X160)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__nonneg__leq__bound) ).
fof(fact_Inf__Sup,axiom,
! [X154,X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> c_Complete__Lattice_OInf__class_OInf(X10,X154) = c_Complete__Lattice_OSup__class_OSup(X10,hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OAll(X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X10),hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fimplies),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X154)))),c_Orderings_Oord__class_Oless__eq(X10))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__Sup) ).
fof(fact_Int__UN__distrib2,axiom,
! [X160,X242,X125,X154,X241,X13,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X241),X154)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X125,tc_fun(X10,tc_HOL_Obool)),X242),X160)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X241),hAPP(hAPP(c_COMBB(tc_fun(X125,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool),X13),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X125,tc_fun(X10,tc_HOL_Obool)),X242)),hAPP(hAPP(c_COMBC(X13,tc_fun(X125,tc_fun(X10,tc_HOL_Obool)),tc_fun(X125,tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),tc_fun(tc_fun(X125,tc_fun(X10,tc_HOL_Obool)),tc_fun(X125,tc_fun(X10,tc_HOL_Obool))),X13),c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X125)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X13),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool))),X154))),X160))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__UN__distrib2) ).
fof(fact_Un__INT__distrib2,axiom,
! [X160,X242,X125,X154,X241,X13,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X241),X154)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X125,tc_fun(X10,tc_HOL_Obool)),X242),X160)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X241),hAPP(hAPP(c_COMBB(tc_fun(X125,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool),X13),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X125,tc_fun(X10,tc_HOL_Obool)),X242)),hAPP(hAPP(c_COMBC(X13,tc_fun(X125,tc_fun(X10,tc_HOL_Obool)),tc_fun(X125,tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),tc_fun(tc_fun(X125,tc_fun(X10,tc_HOL_Obool)),tc_fun(X125,tc_fun(X10,tc_HOL_Obool))),X13),c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X125)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X13),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool))),X154))),X160))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__INT__distrib2) ).
fof(fact_neg__bind__def,axiom,
! [X201,X202,X203,X2,X196,X10,X13] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(X13,X10,X196,X2),X203),X202),X201) = c_New__DSequence_Oneg__bind(X13,X10,hAPP(hAPP(hAPP(X196,X203),X202),X201),hAPP(hAPP(c_COMBC(X13,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(X10)))),hAPP(hAPP(c_COMBC(X13,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(X10))))),hAPP(hAPP(c_COMBC(X13,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(X10)))))),X2),X203)),X202)),X201)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__bind__def) ).
fof(fact_Inter__eq,axiom,
! [X154,X10] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X154) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OAll(tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),X10),hAPP(c_COMBS(tc_fun(X10,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(X10,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X10,tc_HOL_Obool))),X154)))),c_member(X10)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__eq) ).
fof(fact_rtrancl__Un__separator__converseE,axiom,
! [X17,X19,X38,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),c_Transitive__Closure_Ortrancl(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X19),X17))))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X38)),c_Transitive__Closure_Ortrancl(X10,X19)))
=> ! [X90] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X90),X3)),X17))
=> X90 = X3 ) )
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),c_Transitive__Closure_Ortrancl(X10,X19))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__separator__converseE) ).
fof(fact_rtrancl__Un__separatorE,axiom,
! [X17,X19,X38,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),c_Transitive__Closure_Ortrancl(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X19),X17))))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X3)),c_Transitive__Closure_Ortrancl(X10,X19)))
=> ! [X90] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X90)),X17))
=> X3 = X90 ) )
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),c_Transitive__Closure_Ortrancl(X10,X19))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__separatorE) ).
fof(fact_zip__map2,axiom,
! [X289,X2,X125,X290,X13,X10] : hAPP(hAPP(c_List_Ozip(X10,X13),X290),hAPP(hAPP(c_List_Omap(X125,X13),X2),X289)) = hAPP(hAPP(c_List_Omap(tc_prod(X10,X125),tc_prod(X10,X13)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X125,tc_prod(X10,X13)),hAPP(hAPP(c_COMBC(X10,tc_fun(X125,X13),tc_fun(X125,tc_prod(X10,X13))),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_prod(X10,X13)),tc_fun(tc_fun(X125,X13),tc_fun(X125,tc_prod(X10,X13))),X10),c_COMBB(X13,tc_prod(X10,X13),X125)),c_Product__Type_OPair(X10,X13))),X2))),hAPP(hAPP(c_List_Ozip(X10,X125),X290),X289)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__map2) ).
fof(fact_nat0__intermed__int__val,axiom,
! [X101,X2,X20] :
( ! [X152] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X152),X20))
=> 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),X152),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,X152)))),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))),X101))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X101),hAPP(X2,X20)))
=> ? [X152] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X152),X20))
& hAPP(X2,X152) = X101 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat0__intermed__int__val) ).
fof(fact_int__val__lemma,axiom,
! [X101,X2,X20] :
( ! [X152] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X152),X20))
=> 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),X152),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,X152)))),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))),X101))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X101),hAPP(X2,X20)))
=> ? [X152] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X152),X20))
& hAPP(X2,X152) = X101 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__val__lemma) ).
fof(fact_small__prod__def,axiom,
! [X141,X2,X10,X13] :
( ( class_Smallcheck_Osmall(X13)
& class_Smallcheck_Osmall(X10) )
=> hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(X10,X13)),X2),X141) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(X10),hAPP(hAPP(c_COMBC(X10,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(X13,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))),X10),c_Smallcheck_Osmall__class_Osmall(X13)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_prod(X10,X13)),tc_fun(X13,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),X10),hAPP(c_COMBB(tc_prod(X10,X13),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),X13),X2)),c_Product__Type_OPair(X10,X13)))),X141)),X141) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_small__prod__def) ).
fof(fact_inj__vimage__singleton,axiom,
! [X39,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X10,X13,X2),hAPP(hAPP(c_Set_Oinsert(X13),X39),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X10),c_HOL_OThe(X10,hAPP(hAPP(c_COMBC(X10,X13,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X13,tc_fun(X13,tc_HOL_Obool),X10),c_fequal),X2)),X39))),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__vimage__singleton) ).
fof(fact_pos__bind__def,axiom,
! [X201,X202,X203,X2,X196,X10,X13] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(X13,X10,X196,X2),X203),X202),X201) = c_New__DSequence_Opos__bind(X13,X10,hAPP(hAPP(hAPP(X196,X203),X202),X201),hAPP(hAPP(c_COMBC(X13,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X10))),hAPP(hAPP(c_COMBC(X13,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(X10)))),hAPP(hAPP(c_COMBC(X13,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(X10))))),X2),X203)),X202)),X201)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__bind__def) ).
fof(fact_evalc_Oequations_I10_J,axiom,
! [X72,X52,X50,X51,X66] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(X66,X51,X50)),X52),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X72),hAPP(c_Natural_Ogetlocs,X52))),X66),hAPP(hAPP(c_Natural_Ogetlocs,X72),c_Com_ORes))))
<=> ? [X67] :
( hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X72),hAPP(c_Natural_Ogetlocs,X52))),X66),hAPP(hAPP(c_Natural_Ogetlocs,X72),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X67),hAPP(c_Natural_Ogetlocs,X52))),X66),hAPP(hAPP(c_Natural_Ogetlocs,X67),c_Com_ORes))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X51)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X52),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X50,X52))),X67)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I10_J) ).
fof(fact_Nitpick_Oprod__def,axiom,
! [X160,X154,X13,X10] : c_Nitpick_Oprod(X10,X13,X154,X160) = hAPP(c_Set_OCollect(tc_prod(X10,X13)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X10,tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X13)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X154)))),hAPP(hAPP(c_COMBC(X13,tc_fun(X13,tc_HOL_Obool),tc_HOL_Obool),c_member(X13)),X160)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Oprod__def) ).
fof(fact_dvd_Ostrict__mono__mono,axiom,
! [X2,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X10,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,X10,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,
! [X259,X113,X204,X205,X194,X1,X2,X13,X195,X10,X125] : hAPP(c_Product__Type_Omap__pair(X125,X10,X195,X13,X2,X1),hAPP(c_Product__Type_Omap__pair(X194,X125,X205,X195,X204,X113),X259)) = hAPP(c_Product__Type_Omap__pair(X194,X10,X205,X13,hAPP(c_Fun_Ocomp(X125,X10,X194,X2),X204),hAPP(c_Fun_Ocomp(X195,X13,X205,X1),X113)),X259),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair_Ocompositionality) ).
fof(fact_le,axiom,
! [X168,X165,X25,X16] :
( 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),X16),X25)),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),X165),X168)),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),X16),X168)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X165),X25))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le) ).
fof(fact_less,axiom,
! [X168,X165,X25,X16] :
( 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),X16),X25)),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),X165),X168)),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),X16),X168)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X165),X25))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less) ).
fof(fact_setsum__reindex__nonzero,axiom,
! [X13,X204,X2,X216,X10,X125] :
( class_Groups_Ocomm__monoid__add(X125)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X216))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X216))
=> ! [X90] :
( hBOOL(hAPP(hAPP(c_member(X10),X90),X216))
=> ( X3 != X90
=> ( hAPP(X2,X3) = hAPP(X2,X90)
=> hAPP(X204,hAPP(X2,X3)) = c_Groups_Ozero__class_Ozero(X125) ) ) ) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X125),X204),hAPP(c_Set_Oimage(X10,X13,X2),X216)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X125),hAPP(c_Fun_Ocomp(X13,X125,X10,X204),X2)),X216) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__reindex__nonzero) ).
fof(fact_if__image__distrib,axiom,
! [X216,X1,X2,X19,X10,X13] : hAPP(c_Set_Oimage(X13,X10,hAPP(hAPP(c_COMBS(X13,X10,X10),hAPP(hAPP(c_COMBS(X13,X10,tc_fun(X10,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_fun(X10,X10)),X13),c_If(X10)),X19)),X2)),X1)),X216) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X13,X10,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13,tc_HOL_Obool)),X216),hAPP(c_Set_OCollect(X13),X19)))),hAPP(c_Set_Oimage(X13,X10,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13,tc_HOL_Obool)),X216),hAPP(c_Set_OCollect(X13),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X13),c_fNot),X19))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_if__image__distrib) ).
fof(fact_mult,axiom,
! [X168,X165,X25,X16] : 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),X16),X25)),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),X165),X168)),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),X16),X165)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X168))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16),X168)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X165)))),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,
! [X65,X66,X52,X51,X72,X50] :
( c_Natural_Oevaln(c_Com_Ocom_OLocal(X50,X72,X51),X52,X66,hAPP(hAPP(hAPP(c_Natural_Oupdate,X65),c_Com_Ovname_OLoc(X50)),hAPP(hAPP(c_Natural_Ogetlocs,X52),X50)))
<=> ? [X67] :
( hAPP(hAPP(hAPP(c_Natural_Oupdate,X65),c_Com_Ovname_OLoc(X50)),hAPP(hAPP(c_Natural_Ogetlocs,X52),X50)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,X67),c_Com_Ovname_OLoc(X50)),hAPP(hAPP(c_Natural_Ogetlocs,X52),X50))
& c_Natural_Oevaln(X51,hAPP(hAPP(hAPP(c_Natural_Oupdate,X52),c_Com_Ovname_OLoc(X50)),hAPP(X72,X52)),X66,X67) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I3_J) ).
fof(fact_fold__image__cong,axiom,
! [X73,X204,X1,X154,X10,X13] :
( class_Groups_Oab__semigroup__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> hAPP(X1,X3) = hAPP(X204,X3) )
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13,X10,c_Groups_Otimes__class_Otimes(X13)),X1),X73),X154) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13,X10,c_Groups_Otimes__class_Otimes(X13)),X204),X73),X154) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__cong) ).
fof(fact_pred__comp_Oequations,axiom,
! [X50,X51,X54,X177,X125,X13,X10] :
( c_Predicate_Opred__comp(X10,X13,X125,X177,X54,X51,X50)
<=> ? [X193] :
( hBOOL(hAPP(hAPP(X177,X51),X193))
& hBOOL(hAPP(hAPP(X54,X193),X50)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__comp_Oequations) ).
fof(fact_wf__map__pair__image,axiom,
! [X2,X13,X177,X10] :
( c_Wellfounded_Owf(X10,X177)
=> ( c_Fun_Oinj__on(X10,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> c_Wellfounded_Owf(X13,hAPP(c_Set_Oimage(tc_prod(X10,X10),tc_prod(X13,X13),c_Product__Type_Omap__pair(X10,X13,X10,X13,X2,X2)),X177)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__map__pair__image) ).
fof(fact_inj__on__INTER,axiom,
! [X154,X2,X125,X13,X10,X241] :
( X241 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( ! [X152] :
( hBOOL(hAPP(hAPP(c_member(X10),X152),X241))
=> c_Fun_Oinj__on(X13,X125,X2,hAPP(X154,X152)) )
=> c_Fun_Oinj__on(X13,X125,X2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X241),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__INTER) ).
fof(fact_listsum__mono,axiom,
! [X1,X2,X290,X10,X13] :
( ( class_Groups_Omonoid__add(X13)
& class_Groups_Oordered__ab__semigroup__add(X13) )
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X290)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13),hAPP(X2,X3)),hAPP(X1,X3))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13),hAPP(c_List_Omonoid__add__class_Olistsum(X13),hAPP(hAPP(c_List_Omap(X10,X13),X2),X290))),hAPP(c_List_Omonoid__add__class_Olistsum(X13),hAPP(hAPP(c_List_Omap(X10,X13),X1),X290)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__mono) ).
fof(fact_setsum__strict__mono,axiom,
! [X1,X2,X154,X10,X13] :
( ( class_Groups_Ocomm__monoid__add(X13)
& class_Groups_Oordered__cancel__ab__semigroup__add(X13) )
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),hAPP(X2,X3)),hAPP(X1,X3))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),X154)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1),X154))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__strict__mono) ).
fof(fact_setsum__cases,axiom,
! [X1,X2,X19,X154,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),hAPP(hAPP(c_COMBS(X10,X13,X13),hAPP(hAPP(c_COMBS(X10,X13,tc_fun(X13,X13)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X13,tc_fun(X13,X13)),X10),c_If(X13)),X19)),X2)),X1)),X154) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(c_Set_OCollect(X10),X19)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_OCollect(X10),X19))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__cases) ).
fof(fact_folding__one__idem_Ohom__commute,axiom,
! [X226,X204,X225,X2,X10] :
( c_Finite__Set_Ofolding__one__idem(X10,X2,X225)
=> ( ! [X3,X90] : hAPP(X204,hAPP(hAPP(X2,X3),X90)) = hAPP(hAPP(X2,hAPP(X204,X3)),hAPP(X204,X90))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X226))
=> ( X226 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(X204,hAPP(X225,X226)) = hAPP(X225,hAPP(c_Set_Oimage(X10,X10,X204),X226)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Ohom__commute) ).
fof(fact_map__pair_Ocomp,axiom,
! [X113,X204,X1,X2,X13,X10,X195,X125,X205,X194] : hAPP(c_Fun_Ocomp(tc_prod(X194,X205),tc_prod(X125,X195),tc_prod(X10,X13),c_Product__Type_Omap__pair(X194,X125,X205,X195,X2,X1)),c_Product__Type_Omap__pair(X10,X194,X13,X205,X204,X113)) = c_Product__Type_Omap__pair(X10,X125,X13,X195,hAPP(c_Fun_Ocomp(X194,X125,X10,X2),X204),hAPP(c_Fun_Ocomp(X205,X195,X13,X1),X113)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair_Ocomp) ).
fof(fact_map__pair__compose,axiom,
! [X206,X207,X205,X37,X12,X194,X195,X13,X125,X10] : c_Product__Type_Omap__pair(X10,X125,X13,X195,hAPP(c_Fun_Ocomp(X194,X125,X10,X12),X37),hAPP(c_Fun_Ocomp(X205,X195,X13,X207),X206)) = hAPP(c_Fun_Ocomp(tc_prod(X194,X205),tc_prod(X125,X195),tc_prod(X10,X13),c_Product__Type_Omap__pair(X194,X125,X205,X195,X12,X207)),c_Product__Type_Omap__pair(X10,X194,X13,X205,X37,X206)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__compose) ).
fof(fact_listrel__iff__nth,axiom,
! [X177,X289,X290,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X290),X289)),c_List_Olistrel(X10,X177)))
<=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X289)
& ! [X83] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X83),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),hAPP(hAPP(c_List_Onth(X10),X290),X83)),hAPP(hAPP(c_List_Onth(X10),X289),X83))),X177)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__iff__nth) ).
fof(fact_rel__pow__Suc__D2,axiom,
! [X196,X20,X73,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X73)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),hAPP(c_Nat_OSuc,X20)),X196)))
=> ? [X90] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X90)),X196))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X90),X73)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X20),X196))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__Suc__D2) ).
fof(fact_quotient__def,axiom,
! [X177,X154,X10] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X154),X177) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),X10),c_Set_Oinsert(tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X10),c_Relation_OImage(X10,X10,X177)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Set_Oinsert(X10)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X10,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,
! [X154,X177,X13,X38,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X38),hAPP(c_Relation_OImage(X13,X10,X177),X154)))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X13),X3),X154))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X13,X10)),hAPP(hAPP(c_Product__Type_OPair(X13,X10),X3),X38)),X177)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__iff) ).
fof(fact_set__map__of__compr,axiom,
! [X290,X13,X10] :
( hBOOL(hAPP(c_List_Odistinct(X10),hAPP(hAPP(c_List_Omap(tc_prod(X10,X13),X10),c_Product__Type_Ofst(X10,X13)),X290)))
=> hAPP(c_List_Oset(tc_prod(X10,X13)),X290) = hAPP(c_Set_OCollect(tc_prod(X10,X13)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X10,tc_fun(X13,tc_Option_Ooption(X13)),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X13),tc_HOL_Obool),tc_fun(tc_fun(X13,tc_Option_Ooption(X13)),tc_fun(X13,tc_HOL_Obool)),X10),c_COMBB(tc_Option_Ooption(X13),tc_HOL_Obool,X13)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X13),tc_fun(tc_Option_Ooption(X13),tc_HOL_Obool),X10),c_fequal),c_Map_Omap__of(X10,X13,X290)))),c_Option_Ooption_OSome(X13)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__map__of__compr) ).
fof(fact_folding__one_Oclosed,axiom,
! [X154,X225,X2,X10] :
( c_Finite__Set_Ofolding__one(X10,X2,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( ! [X3,X90] : hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(X2,X3),X90)),hAPP(hAPP(c_Set_Oinsert(X10),X3),hAPP(hAPP(c_Set_Oinsert(X10),X90),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(X10),hAPP(X225,X154)),X154)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oclosed) ).
fof(fact_quotient__diff1,axiom,
! [X39,X154,X177,X10] :
( c_Fun_Oinj__on(X10,tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),X10),c_Equiv__Relations_Oquotient(X10)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Set_Oinsert(X10)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),X177),X154)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),X177) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X154),X177)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),X177)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__diff1) ).
fof(fact_Collect__ball__eq,axiom,
! [X19,X154,X13,X10] : hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OAll(X13)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool),X10),hAPP(c_COMBS(X13,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X13),c_fimplies),hAPP(hAPP(c_COMBC(X13,tc_fun(X13,tc_HOL_Obool),tc_HOL_Obool),c_member(X13)),X154)))),X19))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X13),c_Set_OCollect(X10)),hAPP(c_COMBC(X10,X13,tc_HOL_Obool),X19))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__ball__eq) ).
fof(fact_sublist__append,axiom,
! [X154,X319,X162,X10] : c_List_Osublist(X10,hAPP(hAPP(c_List_Oappend(X10),X162),X319),X154) = hAPP(hAPP(c_List_Oappend(X10),c_List_Osublist(X10,X162,X154)),c_List_Osublist(X10,X319,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(X10)),X162)))),X154)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__append) ).
fof(fact_map__filter__map__filter,axiom,
! [X290,X19,X2,X10,X13] : hAPP(hAPP(c_List_Omap(X13,X10),X2),hAPP(c_List_Ofilter(X13,X19),X290)) = c_List_Omap__filter(X13,X10,hAPP(hAPP(c_COMBC(X13,tc_Option_Ooption(X10),tc_Option_Ooption(X10)),hAPP(hAPP(c_COMBS(X13,tc_Option_Ooption(X10),tc_fun(tc_Option_Ooption(X10),tc_Option_Ooption(X10))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X10),tc_fun(tc_Option_Ooption(X10),tc_Option_Ooption(X10))),X13),c_If(tc_Option_Ooption(X10))),X19)),hAPP(hAPP(c_COMBB(X10,tc_Option_Ooption(X10),X13),c_Option_Ooption_OSome(X10)),X2))),c_Option_Ooption_ONone(X10)),X290),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__filter__map__filter) ).
fof(fact_card__quotient__disjoint,axiom,
! [X177,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( c_Fun_Oinj__on(X10,tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),X10),c_Equiv__Relations_Oquotient(X10)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Set_Oinsert(X10)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),X177),X154)
=> hAPP(c_Finite__Set_Ocard(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X154),X177)) = hAPP(c_Finite__Set_Ocard(X10),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__quotient__disjoint) ).
fof(fact_dom__if,axiom,
! [X1,X2,X19,X13,X10] : c_Map_Odom(X10,X13,hAPP(hAPP(c_COMBS(X10,tc_Option_Ooption(X13),tc_Option_Ooption(X13)),hAPP(hAPP(c_COMBS(X10,tc_Option_Ooption(X13),tc_fun(tc_Option_Ooption(X13),tc_Option_Ooption(X13))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X13),tc_fun(tc_Option_Ooption(X13),tc_Option_Ooption(X13))),X10),c_If(tc_Option_Ooption(X13))),X19)),X2)),X1)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_Map_Odom(X10,X13,X2)),hAPP(c_Set_OCollect(X10),X19))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_Map_Odom(X10,X13,X1)),hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10),c_fNot),X19)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__if) ).
fof(fact_map__filter__def,axiom,
! [X290,X2,X10,X13] : c_List_Omap__filter(X13,X10,X2,X290) = hAPP(hAPP(c_List_Omap(X13,X10),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X10),X10,X13,c_Option_Othe(X10)),X2)),hAPP(c_List_Ofilter(X13,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X13),c_fNot),hAPP(hAPP(c_COMBC(X13,tc_Option_Ooption(X10),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X10),tc_fun(tc_Option_Ooption(X10),tc_HOL_Obool),X13),c_fequal),X2)),c_Option_Ooption_ONone(X10)))),X290)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__filter__def) ).
fof(fact_arith__series__general,axiom,
! [X20,X141,X39,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),c_Groups_Oone__class_Oone(X10)),c_Groups_Oone__class_Oone(X10))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),hAPP(hAPP(c_COMBB(X10,X10,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(X10),X39)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(X10)),c_Nat_Osemiring__1__class_Oof__nat(X10))),X141))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X20))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),X20)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X39),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X39),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X141)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arith__series__general) ).
fof(fact_dvd_OatLeastLessThan__empty,axiom,
! [X39,X38] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X38),X39))
=> 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)))),X39,X38) = 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,
! [X101,X162] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X162),X101))
=> 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)))),X101,X162) = 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,
! [X101,X162] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X162),X101))
=> 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)))),X101,X162) = 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,
! [X19,X10] :
( c_FunDef_Oreduction__pair(X10,X19)
<=> ( c_Wellfounded_Owf(X10,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X19))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X19)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X19))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X19))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reduction__pair__def) ).
fof(fact_UN__subset__iff,axiom,
! [X160,X154,X241,X13,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X241),X154)),X160))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X13),X3),X241))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(X154,X3)),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__subset__iff) ).
fof(fact_setsum__bounded,axiom,
! [X250,X2,X154,X10,X13] :
( ( class_Groups_Oordered__ab__semigroup__add(X13)
& class_Rings_Osemiring__1(X13) )
=> ( ! [X152] :
( hBOOL(hAPP(hAPP(c_member(X10),X152),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13),hAPP(X2,X152)),X250)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),X154)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X13),hAPP(c_Finite__Set_Ocard(X10),X154))),X250))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__bounded) ).
fof(fact_map__pair__def,axiom,
! [X1,X2,X195,X13,X125,X10] : c_Product__Type_Omap__pair(X10,X125,X13,X195,X2,X1) = hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,tc_prod(X125,X195)),hAPP(hAPP(c_COMBC(X10,tc_fun(X13,X195),tc_fun(X13,tc_prod(X125,X195))),hAPP(hAPP(c_COMBB(tc_fun(X195,tc_prod(X125,X195)),tc_fun(tc_fun(X13,X195),tc_fun(X13,tc_prod(X125,X195))),X10),c_COMBB(X195,tc_prod(X125,X195),X13)),hAPP(hAPP(c_COMBB(X125,tc_fun(X195,tc_prod(X125,X195)),X10),c_Product__Type_OPair(X125,X195)),X2))),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__def) ).
fof(fact_decr__lemma,axiom,
! [X104,X93,X112] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X112))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X93),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),X93),X104))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X112))),X104)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_decr__lemma) ).
fof(fact_SUP__le__iff,axiom,
! [X165,X230,X154,X13,X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,X10),X154),X230)),X165))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X13),X3),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(X230,X3)),X165)) ) ) ),
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,
! [X177,X25,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X16),X25)),c_List_Olexord(X10,X177)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X16)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X25)))
& hAPP(hAPP(c_List_Otake(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X16)),X25) = X16 )
| ? [X152] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X152),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X16)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X25))))
& hAPP(hAPP(c_List_Otake(X10),X152),X16) = hAPP(hAPP(c_List_Otake(X10),X152),X25)
& hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),hAPP(hAPP(c_List_Onth(X10),X16),X152)),hAPP(hAPP(c_List_Onth(X10),X25),X152))),X177)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__take__index__conv) ).
fof(fact_pred__comp_Ointros,axiom,
! [X125,X13,X10,X18,X54,X38,X39,X177] :
( hBOOL(hAPP(hAPP(X177,X39),X38))
=> ( hBOOL(hAPP(hAPP(X54,X38),X18))
=> c_Predicate_Opred__comp(X10,X13,X125,X177,X54,X39,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__comp_Ointros) ).
fof(fact_SetCompr__Sigma__eq,axiom,
! [X17,X19,X13,X10] : hAPP(c_Set_OCollect(tc_prod(X10,X13)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X10,tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X13)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),X19))),X17))) = hAPP(hAPP(c_Product__Type_OSigma(X10,X13),hAPP(c_Set_OCollect(X10),X19)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool),X10),c_Set_OCollect(X13)),X17)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SetCompr__Sigma__eq) ).
fof(fact_card__less,axiom,
! [X113,X230] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X230))
=> 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)),X230))),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,X113))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__less) ).
fof(fact_Eps__split__eq,axiom,
! [X25,X16,X13,X10] : c_Hilbert__Choice_OEps(tc_prod(X10,X13),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X10,tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X13)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(c_fequal,X16)))),hAPP(c_fequal,X25)))) = hAPP(hAPP(c_Product__Type_OPair(X10,X13),X16),X25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Eps__split__eq) ).
fof(fact_The__split__eq,axiom,
! [X25,X16,X13,X10] : c_HOL_OThe(tc_prod(X10,X13),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X10,tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X13)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(c_fequal,X16)))),hAPP(c_fequal,X25)))) = hAPP(hAPP(c_Product__Type_OPair(X10,X13),X16),X25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_The__split__eq) ).
fof(fact_setsum__commute,axiom,
! [X154,X160,X2,X125,X13,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X10),hAPP(hAPP(c_COMBC(X13,tc_fun(X125,tc_HOL_Obool),X10),hAPP(hAPP(c_COMBB(tc_fun(X125,X10),tc_fun(tc_fun(X125,tc_HOL_Obool),X10),X13),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X125,X10)),X2)),X160)),X154) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X125,X10),hAPP(hAPP(c_COMBC(X125,tc_fun(X13,tc_HOL_Obool),X10),hAPP(hAPP(c_COMBB(tc_fun(X13,X10),tc_fun(tc_fun(X13,tc_HOL_Obool),X10),X125),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X10)),hAPP(c_COMBC(X13,X125,X10),X2))),X154)),X160) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__commute) ).
fof(fact_Collect__split,axiom,
! [X17,X19,X13,X10] : hAPP(c_Set_OCollect(tc_prod(X10,X13)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X10,tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X13)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),X19))),X17))) = hAPP(hAPP(c_Product__Type_OSigma(X10,X13),hAPP(c_Set_OCollect(X10),X19)),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),hAPP(c_Set_OCollect(X13),X17))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__split) ).
fof(fact_image__eq__fold__image,axiom,
! [X2,X13,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(c_Set_Oimage(X10,X13,X2),X154) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(X13,tc_HOL_Obool),X10,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X10,tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X13,tc_fun(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_Set_Oinsert(X13)),X2)),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool))),X154) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__eq__fold__image) ).
fof(fact_card__Diff2__less,axiom,
! [X25,X16,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X25),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X10),X25),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X10),X154))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff2__less) ).
fof(fact_Id__on__def_H,axiom,
! [X154,X10] : c_Relation_OId__on(X10,X154) = hAPP(c_Product__Type_Oprod_Oprod__case(X10,X10,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(X10,tc_HOL_Obool)),X10),c_COMBC(X10,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj)),c_fequal))),X154)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__def_H) ).
fof(fact_int__ge__less__than__def,axiom,
! [X141] : c_Int_Oint__ge__less__than(X141) = 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),X141)))),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,
! [X204,X1,X2,X205,X194,X13,X195,X125,X10] : hAPP(hAPP(c_Product__Type_Oscomp(X10,X125,X195,X13),hAPP(hAPP(c_Product__Type_Oscomp(X10,X194,X205,tc_prod(X125,X195)),X2),X1)),X204) = hAPP(hAPP(c_Product__Type_Oscomp(X10,X194,X205,X13),X2),hAPP(hAPP(c_COMBC(X194,tc_fun(X125,tc_fun(X195,X13)),tc_fun(X205,X13)),hAPP(hAPP(c_COMBB(tc_fun(X205,tc_prod(X125,X195)),tc_fun(tc_fun(X125,tc_fun(X195,X13)),tc_fun(X205,X13)),X194),c_Product__Type_Oscomp(X205,X125,X195,X13)),X1)),X204)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_scomp__scomp) ).
fof(fact_wmax__insertI,axiom,
! [X219,X16,X218,X25] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X25),X218))
=> ( 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)),X16),X25)),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)),X219),X218)),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)),X16),X219)),X218)),c_FunDef_Omax__weak)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wmax__insertI) ).
fof(fact_smax__insertI,axiom,
! [X48,X16,X78,X25] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X25),X78))
=> ( 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)),X16),X25)),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)),X48),X78)),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)),X16),X48)),X78)),c_FunDef_Omax__strict)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smax__insertI) ).
fof(fact_sorted__map__same,axiom,
! [X290,X1,X2,X13,X10] :
( class_Orderings_Olinorder(X10)
=> c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Omap(X13,X10),X2),hAPP(c_List_Ofilter(X13,hAPP(hAPP(c_COMBC(X13,X10,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,tc_HOL_Obool),X13),c_fequal),X2)),hAPP(X1,X290))),X290))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__map__same) ).
fof(fact_Loop,axiom,
! [X18,X38,X19,X210,X10] :
( c_Hoare__Mirabelle_Ohoare__derivs(X10,X210,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X10)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X10),c_Hoare__Mirabelle_Opeek__and(X10,X19,X38)),X18),X19)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X10),tc_HOL_Obool))))
=> c_Hoare__Mirabelle_Ohoare__derivs(X10,X210,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X10)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X10),X19),c_Com_Ocom_OWhile(X38,X18)),c_Hoare__Mirabelle_Opeek__and(X10,X19,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X38)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X10),tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Loop) ).
fof(fact_max__ext_Osimps,axiom,
! [X196,X52,X51,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X51),X52)),c_Wellfounded_Omax__ext(X10,X196)))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X51))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X52))
& X52 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
& ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X51))
=> ? [X227] :
( hBOOL(hAPP(hAPP(c_member(X10),X227),X52))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X227)),X196)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext_Osimps) ).
fof(fact_wf__union__merge,axiom,
! [X216,X196,X10] :
( c_Wellfounded_Owf(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X196),X216))
<=> c_Wellfounded_Owf(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X196),X196)),hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X216),X196))),X216)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__union__merge) ).
fof(fact_map__pair__surj__on,axiom,
! [X260,X160,X1,X125,X195,X223,X154,X2,X10,X13] :
( hAPP(c_Set_Oimage(X13,X10,X2),X154) = X223
=> ( hAPP(c_Set_Oimage(X195,X125,X1),X160) = X260
=> hAPP(c_Set_Oimage(tc_prod(X13,X195),tc_prod(X10,X125),c_Product__Type_Omap__pair(X13,X10,X195,X125,X2,X1)),hAPP(hAPP(c_Product__Type_OSigma(X13,X195),X154),hAPP(c_COMBK(tc_fun(X195,tc_HOL_Obool),X13),X160))) = hAPP(hAPP(c_Product__Type_OSigma(X10,X125),X223),hAPP(c_COMBK(tc_fun(X125,tc_HOL_Obool),X10),X260)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__surj__on) ).
fof(fact_wmin__insertI,axiom,
! [X218,X25,X219,X16] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X16),X219))
=> ( 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)),X16),X25)),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)),X219),X218)),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)),X219),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X25),X218))),c_FunDef_Omin__weak)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wmin__insertI) ).
fof(fact_smin__insertI,axiom,
! [X218,X25,X219,X16] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X16),X219))
=> ( 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)),X16),X25)),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)),X219),X218)),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)),X219),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X25),X218))),c_FunDef_Omin__strict)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smin__insertI) ).
fof(fact_insert__fold1SetE,axiom,
! [X16,X48,X39,X2,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X10,X2,hAPP(hAPP(c_Set_Oinsert(X10),X39),X48)),X16))
=> ~ ! [X116,X246] :
( hAPP(hAPP(c_Set_Oinsert(X10),X39),X48) = hAPP(hAPP(c_Set_Oinsert(X10),X116),X246)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X10,X2,X116,X246),X16))
=> hBOOL(hAPP(hAPP(c_member(X10),X116),X246)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__fold1SetE) ).
fof(fact_listrel1__iff__update,axiom,
! [X177,X289,X290,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X290),X289)),c_List_Olistrel1(X10,X177)))
<=> ? [X90,X83] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),hAPP(hAPP(c_List_Onth(X10),X290),X83)),X90)),X177))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X83),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290)))
& X289 = hAPP(hAPP(c_List_Olist__update(X10,X290),X83),X90) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1__iff__update) ).
fof(fact_map__pair__surj,axiom,
! [X1,X125,X195,X2,X10,X13] :
( hAPP(c_Set_Oimage(X13,X10,X2),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))
=> ( hAPP(c_Set_Oimage(X195,X125,X1),c_Orderings_Otop__class_Otop(tc_fun(X195,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X125,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(tc_prod(X13,X195),tc_prod(X10,X125),c_Product__Type_Omap__pair(X13,X10,X195,X125,X2,X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X13,X195),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X10,X125),tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__surj) ).
fof(fact_minus__fold__remove,axiom,
! [X160,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X160),X154) = hAPP(hAPP(c_Finite__Set_Ofold(X10,tc_fun(X10,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),hAPP(c_COMBC(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Set_Oinsert(X10)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),X160),X154) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__fold__remove) ).
fof(fact_map__of__mapk__SomeI,axiom,
! [X16,X101,X53,X125,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> ( hAPP(c_Map_Omap__of(X10,X125,X53),X101) = hAPP(c_Option_Ooption_OSome(X125),X16)
=> hAPP(c_Map_Omap__of(X13,X125,hAPP(hAPP(c_List_Omap(tc_prod(X10,X125),tc_prod(X13,X125)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X125,tc_prod(X13,X125)),hAPP(hAPP(c_COMBB(X13,tc_fun(X125,tc_prod(X13,X125)),X10),c_Product__Type_OPair(X13,X125)),X2))),X53)),hAPP(X2,X101)) = hAPP(c_Option_Ooption_OSome(X125),X16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__mapk__SomeI) ).
fof(fact_fst__map__pair,axiom,
! [X16,X1,X2,X195,X125,X13,X10] : hAPP(c_Product__Type_Ofst(X10,X13),hAPP(c_Product__Type_Omap__pair(X125,X10,X195,X13,X2,X1),X16)) = hAPP(X2,hAPP(c_Product__Type_Ofst(X125,X195),X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__map__pair) ).
fof(fact_snd__prod__fun,axiom,
! [X16,X1,X2,X195,X125,X10,X13] : hAPP(c_Product__Type_Osnd(X13,X10),hAPP(c_Product__Type_Omap__pair(X125,X13,X195,X10,X2,X1),X16)) = hAPP(X1,hAPP(c_Product__Type_Osnd(X125,X195),X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__prod__fun) ).
fof(fact_lexord__linear,axiom,
! [X25,X16,X177,X10] :
( ! [X116,X193] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X116),X193)),X177))
| X116 = X193
| hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X193),X116)),X177)) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X16),X25)),c_List_Olexord(X10,X177)))
| X16 = X25
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X25),X16)),c_List_Olexord(X10,X177))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__linear) ).
fof(fact_add,axiom,
! [X168,X165,X25,X16] : 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),X16),X25)),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),X165),X168)),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),X16),X165)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X168))),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,
! [X154,X10] : c_Relation_OId__on(X10,X154) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(X10,X10),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X10),c_Set_Oinsert(tc_prod(X10,X10))),hAPP(hAPP(c_COMBS(X10,X10,tc_prod(X10,X10)),c_Product__Type_OPair(X10,X10)),c_COMBI(X10)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__def) ).
fof(fact_map__zip__map,axiom,
! [X289,X290,X1,X195,X2,X10,X125,X13] : hAPP(hAPP(c_List_Omap(tc_prod(X13,X125),X10),X2),hAPP(hAPP(c_List_Ozip(X13,X125),hAPP(hAPP(c_List_Omap(X195,X13),X1),X290)),X289)) = hAPP(hAPP(c_List_Omap(tc_prod(X195,X125),X10),hAPP(c_Product__Type_Oprod_Oprod__case(X195,X125,X10),hAPP(hAPP(c_COMBB(tc_fun(X125,tc_prod(X13,X125)),tc_fun(X125,X10),X195),hAPP(c_COMBB(tc_prod(X13,X125),X10,X125),X2)),hAPP(hAPP(c_COMBB(X13,tc_fun(X125,tc_prod(X13,X125)),X195),c_Product__Type_OPair(X13,X125)),X1)))),hAPP(hAPP(c_List_Ozip(X195,X125),X290),X289)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__zip__map) ).
fof(fact_sublist__Cons,axiom,
! [X154,X162,X16,X10] : c_List_Osublist(X10,hAPP(hAPP(c_List_Olist_OCons(X10),X16),X162),X154) = hAPP(hAPP(c_List_Oappend(X10),hAPP(hAPP(hAPP(c_If(tc_List_Olist(X10)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X154)),hAPP(hAPP(c_List_Olist_OCons(X10),X16),c_List_Olist_ONil(X10))),c_List_Olist_ONil(X10))),c_List_Osublist(X10,X162,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)),X154)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__Cons) ).
fof(fact_dom__override__on,axiom,
! [X154,X1,X2,X13,X10] : c_Map_Odom(X10,X13,c_Fun_Ooverride__on(X10,tc_Option_Ooption(X13),X2,X1,X154)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),c_Map_Odom(X10,X13,X2)),hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),c_Map_Odom(X10,X13,X1)))))),hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),c_Map_Odom(X10,X13,X1))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__override__on) ).
fof(fact_nth__nth__transpose__sorted,axiom,
! [X163,X113,X290,X10] :
( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X10))),X290)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X113),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),c_List_Otranspose(X10,X290))))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X163),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),hAPP(c_List_Ofilter(tc_List_Olist(X10),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X10)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X113)),c_Nat_Osize__class_Osize(tc_List_Olist(X10)))),X290))))
=> hAPP(hAPP(c_List_Onth(X10),hAPP(hAPP(c_List_Onth(tc_List_Olist(X10)),c_List_Otranspose(X10,X290)),X113)),X163) = hAPP(hAPP(c_List_Onth(X10),hAPP(hAPP(c_List_Onth(tc_List_Olist(X10)),X290),X163)),X113) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__nth__transpose__sorted) ).
fof(fact_INF__less__iff,axiom,
! [X39,X2,X154,X13,X10] :
( ( class_Complete__Lattice_Ocomplete__lattice(X10)
& class_Orderings_Olinorder(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,X10),X154),X2)),X39))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X13),X3),X154))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(X2,X3)),X39)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__less__iff) ).
fof(fact_ball__UN,axiom,
! [X19,X160,X154,X13,X10] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X154),X160)))
=> hBOOL(hAPP(X19,X3)) )
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X13),X3),X154))
=> ! [X227] :
( hBOOL(hAPP(hAPP(c_member(X10),X227),hAPP(X160,X3)))
=> hBOOL(hAPP(X19,X227)) ) ) ),
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,
! [X197,X198,X196,X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X154),X160)),c_Wellfounded_Omax__ext(X10,X196)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X198),X197)),c_Wellfounded_Omax__ext(X10,X196)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X198)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X160),X197))),c_Wellfounded_Omax__ext(X10,X196))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext__additive) ).
fof(fact_SigmaE,axiom,
! [X160,X154,X18,X13,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),X18),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X154),X160)))
=> ~ ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> ! [X90] :
( hBOOL(hAPP(hAPP(c_member(X13),X90),hAPP(X160,X3)))
=> X18 != hAPP(hAPP(c_Product__Type_OPair(X10,X13),X3),X90) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaE) ).
fof(fact_foldl__map,axiom,
! [X290,X2,X125,X39,X1,X13,X10] : hAPP(c_List_Ofoldl(X10,X13,X1,X39),hAPP(hAPP(c_List_Omap(X125,X13),X2),X290)) = hAPP(c_List_Ofoldl(X10,X125,hAPP(hAPP(c_COMBC(X10,tc_fun(X125,X13),tc_fun(X125,X10)),hAPP(hAPP(c_COMBB(tc_fun(X13,X10),tc_fun(tc_fun(X125,X13),tc_fun(X125,X10)),X10),c_COMBB(X13,X10,X125)),X1)),X2),X39),X290),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__map) ).
fof(fact_rel__comp__UNION__distrib2,axiom,
! [X54,X177,X241,X195,X13,X125,X10] : hAPP(hAPP(c_Relation_Orel__comp(X10,X125,X13),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X195,tc_fun(tc_prod(X10,X125),tc_HOL_Obool)),X241),X177)),X54) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X195,tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),X241),hAPP(hAPP(c_COMBC(X195,tc_fun(tc_prod(X125,X13),tc_HOL_Obool),tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X10,X125),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X125,X13),tc_HOL_Obool),tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),X195),c_Relation_Orel__comp(X10,X125,X13)),X177)),X54)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__UNION__distrib2) ).
fof(fact_finite__Collect__disjI,axiom,
! [X17,X19,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fdisj),X19)),X17))))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Set_OCollect(X10),X19)))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Set_OCollect(X10),X17))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__disjI) ).
fof(fact_UN__equiv__class2,axiom,
! [X52,X51,X2,X125,X233,X234,X13,X235,X236,X10] :
( c_Equiv__Relations_Oequiv(X10,X236,X235)
=> ( c_Equiv__Relations_Oequiv(X13,X234,X233)
=> ( c_Equiv__Relations_Ocongruent2(X10,X13,tc_fun(X125,tc_HOL_Obool),X235,X233,X2)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X51),X236))
=> ( hBOOL(hAPP(hAPP(c_member(X13),X52),X234))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X125,tc_HOL_Obool)),hAPP(c_Relation_OImage(X10,X10,X235),hAPP(hAPP(c_Set_Oinsert(X10),X51),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_fun(X125,tc_HOL_Obool)),tc_fun(X125,tc_HOL_Obool),X10),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X125,tc_HOL_Obool)),hAPP(c_Relation_OImage(X13,X13,X233),hAPP(hAPP(c_Set_Oinsert(X13),X52),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool)))))),X2)) = hAPP(hAPP(X2,X51),X52) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__equiv__class2) ).
fof(fact_length__sublist,axiom,
! [X241,X290,X10] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_List_Osublist(X10,X290,X241)) = 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(X10)),X290)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X241)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__sublist) ).
fof(fact_length__filter__conv__card,axiom,
! [X290,X166,X10] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),hAPP(c_List_Ofilter(X10,X166),X290)) = 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(X10)),X290)))),hAPP(hAPP(c_COMBB(X10,tc_HOL_Obool,tc_Nat_Onat),X166),hAPP(c_List_Onth(X10),X290))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__filter__conv__card) ).
fof(fact_fold__image__distrib,axiom,
! [X204,X1,X154,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13,X10,c_Groups_Otimes__class_Otimes(X13)),hAPP(hAPP(c_COMBS(X10,X13,X13),hAPP(hAPP(c_COMBB(X13,tc_fun(X13,X13),X10),c_Groups_Otimes__class_Otimes(X13)),X1)),X204)),c_Groups_Oone__class_Oone(X13)),X154) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13,X10,c_Groups_Otimes__class_Otimes(X13)),X1),c_Groups_Oone__class_Oone(X13)),X154)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13,X10,c_Groups_Otimes__class_Otimes(X13)),X204),c_Groups_Oone__class_Oone(X13)),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__distrib) ).
fof(fact_snoc__listrel1__snoc__iff,axiom,
! [X177,X25,X289,X16,X290,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Oappend(X10),X290),hAPP(hAPP(c_List_Olist_OCons(X10),X16),c_List_Olist_ONil(X10)))),hAPP(hAPP(c_List_Oappend(X10),X289),hAPP(hAPP(c_List_Olist_OCons(X10),X25),c_List_Olist_ONil(X10))))),c_List_Olistrel1(X10,X177)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X290),X289)),c_List_Olistrel1(X10,X177)))
& X16 = X25 )
| ( X290 = X289
& hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),X177)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snoc__listrel1__snoc__iff) ).
fof(fact_UN__finite2__eq,axiom,
! [X160,X101,X154,X10] :
( ! [X83] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X83)),X154) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,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),X83),X101))),X160)
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X154) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X160) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__finite2__eq) ).
fof(fact_max__ext_Ointros,axiom,
! [X196,X78,X48,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X48))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X78))
=> ( X78 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X48))
=> ? [X227] :
( hBOOL(hAPP(hAPP(c_member(X10),X227),X78))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X227)),X196)) ) )
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X48),X78)),c_Wellfounded_Omax__ext(X10,X196))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext_Ointros) ).
fof(fact_ran__def,axiom,
! [X102,X10,X13] : c_Map_Oran(X13,X10,X102) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X13)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X10),tc_fun(X13,tc_HOL_Obool),X10),hAPP(c_COMBC(X13,tc_Option_Ooption(X10),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X10),tc_fun(tc_Option_Ooption(X10),tc_HOL_Obool),X13),c_fequal),X102))),c_Option_Ooption_OSome(X10)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ran__def) ).
fof(fact_wf__no__infinite__down__chainE,axiom,
! [X2,X177,X10] :
( c_Wellfounded_Owf(X10,X177)
=> ~ ! [X124] : hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),hAPP(X2,hAPP(c_Nat_OSuc,X124))),hAPP(X2,X124))),X177)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__no__infinite__down__chainE) ).
fof(fact_wf__iff__no__infinite__down__chain,axiom,
! [X177,X10] :
( c_Wellfounded_Owf(X10,X177)
<=> ~ ? [X247] :
! [X152] : hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),hAPP(X247,hAPP(c_Nat_OSuc,X152))),hAPP(X247,X152))),X177)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__iff__no__infinite__down__chain) ).
fof(fact_congruent2__implies__congruent__UN,axiom,
! [X39,X2,X125,X233,X234,X13,X235,X236,X10] :
( c_Equiv__Relations_Oequiv(X10,X236,X235)
=> ( c_Equiv__Relations_Oequiv(X13,X234,X233)
=> ( c_Equiv__Relations_Ocongruent2(X10,X13,tc_fun(X125,tc_HOL_Obool),X235,X233,X2)
=> ( hBOOL(hAPP(hAPP(c_member(X13),X39),X234))
=> c_Equiv__Relations_Ocongruent(X10,tc_fun(X125,tc_HOL_Obool),X235,hAPP(hAPP(c_COMBB(tc_fun(X13,tc_fun(X125,tc_HOL_Obool)),tc_fun(X125,tc_HOL_Obool),X10),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X125,tc_HOL_Obool)),hAPP(c_Relation_OImage(X13,X13,X233),hAPP(hAPP(c_Set_Oinsert(X13),X39),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool)))))),X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_congruent2__implies__congruent__UN) ).
fof(fact_Diff1__fold__graph,axiom,
! [X25,X16,X154,X73,X2,X13,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X13,X2,X73,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),X25))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X13,X2,X73,X154),hAPP(hAPP(X2,X16),X25))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff1__fold__graph) ).
fof(fact_setsum__mono3,axiom,
! [X2,X154,X160,X10,X13] :
( ( class_Groups_Ocomm__monoid__add(X13)
& class_Groups_Oordered__ab__semigroup__add(X13) )
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X160),X154)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13),c_Groups_Ozero__class_Ozero(X13)),hAPP(X2,X3))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),X154)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),X160))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__mono3) ).
fof(fact_setsum__mono2,axiom,
! [X2,X154,X160,X10,X13] :
( class_Groups_Oordered__comm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> ( ! [X193] :
( hBOOL(hAPP(hAPP(c_member(X10),X193),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X160),X154)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13),c_Groups_Ozero__class_Ozero(X13)),hAPP(X2,X193))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),X154)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),X160))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__mono2) ).
fof(fact_INF__INT__eq,axiom,
! [X16,X177,X13,X10] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool),X10),hAPP(c_COMBC(X13,tc_fun(X13,tc_HOL_Obool),tc_HOL_Obool),c_member(X13))),X177)),X16))
<=> hBOOL(hAPP(hAPP(c_member(X13),X16),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__INT__eq) ).
fof(fact_SUP__UN__eq,axiom,
! [X16,X177,X13,X10] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool),X10),hAPP(c_COMBC(X13,tc_fun(X13,tc_HOL_Obool),tc_HOL_Obool),c_member(X13))),X177)),X16))
<=> hBOOL(hAPP(hAPP(c_member(X13),X16),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__UN__eq) ).
fof(fact_le__add__iff1,axiom,
! [X141,X38,X18,X161,X39,X10] :
( class_Rings_Oordered__ring(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X161)),X18)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X38),X161)),X141)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X39),X38)),X161)),X18)),X141)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__iff1) ).
fof(fact_less__add__iff1,axiom,
! [X141,X38,X18,X161,X39,X10] :
( class_Rings_Oordered__ring(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X161)),X18)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X38),X161)),X141)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X39),X38)),X161)),X18)),X141)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__iff1) ).
fof(fact_fold__graph_H_Ointros_I2_J,axiom,
! [X25,X73,X2,X13,X154,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( c_Nitpick_Ofold__graph_H(X10,X13,X2,X73,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),X25)
=> c_Nitpick_Ofold__graph_H(X10,X13,X2,X73,X154,hAPP(hAPP(X2,X16),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_H_Ointros_I2_J) ).
fof(fact_INT__subset__iff,axiom,
! [X154,X241,X13,X160,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X241),X154)))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X13),X3),X241))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),hAPP(X154,X3))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__subset__iff) ).
fof(fact_zminus1__lemma,axiom,
! [X177,X158,X38,X39] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X39,X38),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X158),X177)))
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X39),X38),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X177),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X158)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X158)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X177),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),X38),X177))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus1__lemma) ).
fof(fact_INT__iff,axiom,
! [X160,X154,X13,X38,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X38),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X154),X160)))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X13),X3),X154))
=> hBOOL(hAPP(hAPP(c_member(X10),X38),hAPP(X160,X3))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__iff) ).
fof(fact_vimage__Times,axiom,
! [X160,X154,X2,X125,X13,X10] : hAPP(c_Set_Ovimage(X10,tc_prod(X13,X125),X2),hAPP(hAPP(c_Product__Type_OSigma(X13,X125),X154),hAPP(c_COMBK(tc_fun(X125,tc_HOL_Obool),X13),X160))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X10,X13,hAPP(c_Fun_Ocomp(tc_prod(X13,X125),X13,X10,c_Product__Type_Ofst(X13,X125)),X2)),X154)),hAPP(c_Set_Ovimage(X10,X125,hAPP(c_Fun_Ocomp(tc_prod(X13,X125),X125,X10,c_Product__Type_Osnd(X13,X125)),X2)),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Times) ).
fof(fact_in__lex__prod,axiom,
! [X54,X177,X118,X96,X38,X39,X13,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X10,X13),tc_prod(X10,X13))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X10,X13),tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X39),X38)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X96),X118))),c_Wellfounded_Olex__prod(X10,X13,X177,X54)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X96)),X177))
| ( X39 = X96
& hBOOL(hAPP(hAPP(c_member(tc_prod(X13,X13)),hAPP(hAPP(c_Product__Type_OPair(X13,X13),X38),X118)),X54)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__lex__prod) ).
fof(fact_INF1__iff,axiom,
! [X38,X160,X154,X13,X10] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X154),X160),X38))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> hBOOL(hAPP(hAPP(X160,X3),X38)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF1__iff) ).
fof(fact_finite__M__bounded__by__nat,axiom,
! [X113,X19] : 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),X19)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X113))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__M__bounded__by__nat) ).
fof(fact_incr__lemma,axiom,
! [X93,X104,X112] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X112))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X104),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X93),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),X93),X104))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X112)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_incr__lemma) ).
fof(fact_le__INF__iff,axiom,
! [X230,X154,X13,X165,X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X165),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,X10),X154),X230)))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X13),X3),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X165),hAPP(X230,X3))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__INF__iff) ).
fof(fact_setsum__nonneg__0,axiom,
! [X113,X2,X54,X10,X13] :
( class_Groups_Oordered__ab__group__add(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X54))
=> ( ! [X152] :
( hBOOL(hAPP(hAPP(c_member(X10),X152),X54))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13),c_Groups_Ozero__class_Ozero(X13)),hAPP(X2,X152))) )
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),X54) = c_Groups_Ozero__class_Ozero(X13)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X113),X54))
=> hAPP(X2,X113) = c_Groups_Ozero__class_Ozero(X13) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__nonneg__0) ).
fof(fact_the__inv__into__def,axiom,
! [X16,X2,X154,X13,X10] : hAPP(c_Fun_Othe__inv__into(X10,X13,X154,X2),X16) = c_HOL_OThe(X10,hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X154))),hAPP(hAPP(c_COMBC(X10,X13,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X13,tc_fun(X13,tc_HOL_Obool),X10),c_fequal),X2)),X16))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__def) ).
fof(fact_listrel1E,axiom,
! [X177,X289,X290,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X290),X289)),c_List_Olistrel1(X10,X177)))
=> ~ ! [X3,X90] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X90)),X177))
=> ! [X318,X322] :
( X290 = hAPP(hAPP(c_List_Oappend(X10),X318),hAPP(hAPP(c_List_Olist_OCons(X10),X3),X322))
=> X289 != hAPP(hAPP(c_List_Oappend(X10),X318),hAPP(hAPP(c_List_Olist_OCons(X10),X90),X322)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1E) ).
fof(fact_setsum__Plus,axiom,
! [X2,X160,X13,X154,X10,X125] :
( class_Groups_Ocomm__monoid__add(X125)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X160))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_sum(X10,X13),X125),X2),c_Sum__Type_OPlus(X10,X13,X154,X160)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X125),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X125),hAPP(c_Fun_Ocomp(tc_sum(X10,X13),X125,X10,X2),c_Sum__Type_OInl(X10,X13))),X154)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X125),hAPP(c_Fun_Ocomp(tc_sum(X10,X13),X125,X13,X2),c_Sum__Type_OInr(X13,X10))),X160)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Plus) ).
fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
! [X25,X16,X154,X73,X2,X13,X10] :
( c_Finite__Set_Ofun__left__comm(X10,X13,X2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X13,X2,X73,X154),X16))
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X13,X2,X73,X154),X25))
=> X25 = X16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__determ) ).
fof(fact_listsum__subtractf,axiom,
! [X290,X1,X2,X13,X10] :
( class_Groups_Oab__group__add(X10)
=> hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(X13,X10),hAPP(hAPP(c_COMBS(X13,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X13),c_Groups_Ominus__class_Ominus(X10)),X2)),X1)),X290)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(X13,X10),X2),X290))),hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(X13,X10),X1),X290))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__subtractf) ).
fof(fact_listsum__addf,axiom,
! [X290,X1,X2,X13,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(X13,X10),hAPP(hAPP(c_COMBS(X13,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X13),c_Groups_Oplus__class_Oplus(X10)),X2)),X1)),X290)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(X13,X10),X2),X290))),hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(X13,X10),X1),X290))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__addf) ).
fof(fact_UN__Pow__subset,axiom,
! [X160,X154,X13,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),X13),c_Set_OPow(X10)),X160))),hAPP(c_Set_OPow(X10),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X154),X160)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__Pow__subset) ).
fof(fact_nat__le__add__iff1,axiom,
! [X20,X102,X165,X113,X163] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X163),X113))
=> ( 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),X113),X165)),X102)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X163),X165)),X20)))
<=> 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),X113),X163)),X165)),X102)),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__add__iff1) ).
fof(fact_nat__less__add__iff1,axiom,
! [X20,X102,X165,X113,X163] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X163),X113))
=> ( 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),X113),X165)),X102)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X163),X165)),X20)))
<=> 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),X113),X163)),X165)),X102)),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__add__iff1) ).
fof(fact_listsum__mult__const,axiom,
! [X290,X18,X2,X13,X10] :
( class_Rings_Osemiring__0(X10)
=> hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(X13,X10),hAPP(hAPP(c_COMBC(X13,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X13),c_Groups_Otimes__class_Otimes(X10)),X2)),X18)),X290)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(X13,X10),X2),X290))),X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__mult__const) ).
fof(fact_int__ge__less__than2__def,axiom,
! [X141] : c_Int_Oint__ge__less__than2(X141) = 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),X141)))),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,X232,X216,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X216))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X232))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X216),X232)))
=> hAPP(X2,X3) = c_Groups_Oone__class_Oone(X13) )
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13,X10,c_Groups_Otimes__class_Otimes(X13)),X2),c_Groups_Oone__class_Oone(X13)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X216),X232)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13,X10,c_Groups_Otimes__class_Otimes(X13)),X2),c_Groups_Oone__class_Oone(X13)),X216)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13,X10,c_Groups_Otimes__class_Otimes(X13)),X2),c_Groups_Oone__class_Oone(X13)),X232)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__Un__one) ).
fof(fact_inf__Int__eq,axiom,
! [X16,X216,X196,X10] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X196)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X216)),X16))
<=> hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X196),X216))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Int__eq) ).
fof(fact_sup__Un__eq,axiom,
! [X16,X216,X196,X10] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X196)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X216)),X16))
<=> hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X196),X216))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Un__eq) ).
fof(fact_insert__Collect,axiom,
! [X19,X39,X10] : hAPP(hAPP(c_Set_Oinsert(X10),X39),hAPP(c_Set_OCollect(X10),X19)) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10),c_fNot),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X39)))),X19)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Collect) ).
fof(fact_equiv__class__nondisjoint,axiom,
! [X38,X39,X16,X177,X154,X10] :
( c_Equiv__Relations_Oequiv(X10,X154,X177)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_OImage(X10,X10,X177),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X10,X10,X177),hAPP(hAPP(c_Set_Oinsert(X10),X38),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),X177)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__class__nondisjoint) ).
fof(fact_divmod__nat__rel__add1__eq,axiom,
! [X186,X187,X92,X188,X189,X81,X84] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X84,X81),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X189),X188)))
=> ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X92,X81),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X187),X186)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X81))
=> hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X84),X92),X81),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),X189),X187)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X188),X186)),X81))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X188),X186),X81)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__add1__eq) ).
fof(fact_Random__Sequence_Omap__def,axiom,
! [X19,X2,X10,X13] : c_Random__Sequence_Omap(X13,X10,X2,X19) = c_Random__Sequence_Obind(X13,X10,X19,hAPP(c_Fun_Ocomp(X10,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(X10)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),X13,c_Random__Sequence_Osingle(X10)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Random__Sequence_Omap__def) ).
fof(fact_setprod__Un,axiom,
! [X2,X160,X154,X10,X13] :
( class_Fields_Ofield(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)))
=> hAPP(X2,X3) != c_Groups_Ozero__class_Ozero(X13) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),X154)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),X160))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__Un) ).
fof(fact_zadd1__lemma,axiom,
! [X186,X187,X92,X188,X189,X81,X84] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X84,X81),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X189),X188)))
=> ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X92,X81),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X187),X186)))
=> ( X81 != 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),X84),X92),X81),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),X189),X187)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X188),X186)),X81))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X188),X186),X81)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd1__lemma) ).
fof(fact_setsum__cartesian__product,axiom,
! [X154,X160,X2,X125,X13,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X10),hAPP(hAPP(c_COMBC(X13,tc_fun(X125,tc_HOL_Obool),X10),hAPP(hAPP(c_COMBB(tc_fun(X125,X10),tc_fun(tc_fun(X125,tc_HOL_Obool),X10),X13),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X125,X10)),X2)),X160)),X154) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X13,X125),X10),hAPP(c_Product__Type_Oprod_Oprod__case(X13,X125,X10),X2)),hAPP(hAPP(c_Product__Type_OSigma(X13,X125),X154),hAPP(c_COMBK(tc_fun(X125,tc_HOL_Obool),X13),X160))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__cartesian__product) ).
fof(fact_setprod__cartesian__product,axiom,
! [X154,X160,X2,X125,X13,X10] :
( class_Groups_Ocomm__monoid__mult(X10)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X13,X10),hAPP(hAPP(c_COMBC(X13,tc_fun(X125,tc_HOL_Obool),X10),hAPP(hAPP(c_COMBB(tc_fun(X125,X10),tc_fun(tc_fun(X125,tc_HOL_Obool),X10),X13),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X125,X10)),X2)),X160)),X154) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X13,X125),X10),hAPP(c_Product__Type_Oprod_Oprod__case(X13,X125,X10),X2)),hAPP(hAPP(c_Product__Type_OSigma(X13,X125),X154),hAPP(c_COMBK(tc_fun(X125,tc_HOL_Obool),X13),X160))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__cartesian__product) ).
fof(fact_map__pair__inj__on,axiom,
! [X160,X1,X195,X125,X154,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,X154)
=> ( c_Fun_Oinj__on(X125,X195,X1,X160)
=> c_Fun_Oinj__on(tc_prod(X10,X125),tc_prod(X13,X195),c_Product__Type_Omap__pair(X10,X13,X125,X195,X2,X1),hAPP(hAPP(c_Product__Type_OSigma(X10,X125),X154),hAPP(c_COMBK(tc_fun(X125,tc_HOL_Obool),X10),X160))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__inj__on) ).
fof(fact_divmod__nat__rel__mult1__eq,axiom,
! [X84,X143,X149,X81,X92] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X92,X81),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X149),X143)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X81))
=> hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X84),X92),X81),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),X84),X149)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X84),X143)),X81))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X84),X143),X81)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__mult1__eq) ).
fof(fact_lift__Suc__mono__less__iff,axiom,
! [X102,X20,X2,X10] :
( class_Orderings_Oorder(X10)
=> ( ! [X83] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(X2,X83)),hAPP(X2,hAPP(c_Nat_OSuc,X83))))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(X2,X20)),hAPP(X2,X102)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X102)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lift__Suc__mono__less__iff) ).
fof(fact_lift__Suc__mono__less,axiom,
! [X132,X20,X2,X10] :
( class_Orderings_Oorder(X10)
=> ( ! [X83] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(X2,X83)),hAPP(X2,hAPP(c_Nat_OSuc,X83))))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X132))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(X2,X20)),hAPP(X2,X132))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lift__Suc__mono__less) ).
fof(fact_ran__restrictD,axiom,
! [X154,X102,X13,X25,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X25),c_Map_Oran(X13,X10,c_Map_Orestrict__map(X13,X10,X102,X154))))
=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X13),X3),X154))
& hAPP(X102,X3) = hAPP(c_Option_Ooption_OSome(X10),X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ran__restrictD) ).
fof(fact_zmult1__lemma,axiom,
! [X84,X143,X149,X81,X92] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X92,X81),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X149),X143)))
=> ( X81 != 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),X84),X92),X81),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),X84),X149)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),X143)),X81))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),X143),X81)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult1__lemma) ).
fof(fact_Ex__inj__on__UNION__Sigma,axiom,
! [X154,X241,X13,X10] :
? [X247] :
( c_Fun_Oinj__on(X10,tc_prod(X13,X10),X247,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X241),X154))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X13,X10),tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,tc_prod(X13,X10),X247),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X241),X154))),hAPP(hAPP(c_Product__Type_OSigma(X13,X10),X241),X154))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ex__inj__on__UNION__Sigma) ).
fof(fact_sublist__shift__lemma__Suc,axiom,
! [X332,X290,X19,X10] : hAPP(hAPP(c_List_Omap(tc_prod(X10,tc_Nat_Onat),X10),c_Product__Type_Ofst(X10,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X10,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X10,tc_Nat_Onat)),X19),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(X10,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(X10,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(X10,tc_Nat_Onat),X290),X332))) = hAPP(hAPP(c_List_Omap(tc_prod(X10,tc_Nat_Onat),X10),c_Product__Type_Ofst(X10,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X10,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X10,tc_Nat_Onat)),X19),c_Product__Type_Osnd(X10,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(X10,tc_Nat_Onat),X290),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),X332)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__shift__lemma__Suc) ).
fof(fact_fst__comp__map__pair,axiom,
! [X1,X2,X13,X10,X195,X125] : hAPP(c_Fun_Ocomp(tc_prod(X125,X195),X125,tc_prod(X10,X13),c_Product__Type_Ofst(X125,X195)),c_Product__Type_Omap__pair(X10,X125,X13,X195,X2,X1)) = hAPP(c_Fun_Ocomp(X10,X125,tc_prod(X10,X13),X2),c_Product__Type_Ofst(X10,X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__comp__map__pair) ).
fof(fact_snd__comp__map__pair,axiom,
! [X1,X2,X13,X10,X125,X195] : hAPP(c_Fun_Ocomp(tc_prod(X195,X125),X125,tc_prod(X10,X13),c_Product__Type_Osnd(X195,X125)),c_Product__Type_Omap__pair(X10,X195,X13,X125,X2,X1)) = hAPP(c_Fun_Ocomp(X13,X125,tc_prod(X10,X13),X1),c_Product__Type_Osnd(X10,X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__comp__map__pair) ).
fof(fact_INT__extend__simps_I9_J,axiom,
! [X198,X160,X125,X154,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBC(X13,tc_fun(X125,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X125,tc_HOL_Obool),tc_fun(tc_fun(X125,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),X13),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X125,tc_fun(X10,tc_HOL_Obool))),X160)),X198)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X125,tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X125,tc_HOL_Obool)),X154),X160)),X198),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I9_J) ).
fof(fact_UN__extend__simps_I9_J,axiom,
! [X198,X160,X125,X154,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBC(X13,tc_fun(X125,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X125,tc_HOL_Obool),tc_fun(tc_fun(X125,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),X13),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X125,tc_fun(X10,tc_HOL_Obool))),X160)),X198)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X125,tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X125,tc_HOL_Obool)),X154),X160)),X198),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I9_J) ).
fof(fact_INT__simps_I9_J,axiom,
! [X198,X160,X154,X125,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X125,tc_fun(X13,tc_HOL_Obool)),X154),X160)),X198) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X125,tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBC(X125,tc_fun(X13,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(tc_fun(X13,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),X125),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool))),X160)),X198)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I9_J) ).
fof(fact_UN__simps_I9_J,axiom,
! [X198,X160,X154,X125,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X125,tc_fun(X13,tc_HOL_Obool)),X154),X160)),X198) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X125,tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBC(X125,tc_fun(X13,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(tc_fun(X13,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),X125),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool))),X160)),X198)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I9_J) ).
fof(fact_UN__UN__flatten,axiom,
! [X198,X160,X154,X125,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X125,tc_fun(X13,tc_HOL_Obool)),X154),X160)),X198) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X125,tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBC(X125,tc_fun(X13,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(tc_fun(X13,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),X125),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool))),X160)),X198)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__UN__flatten) ).
fof(fact_congruent2D,axiom,
! [X237,X238,X239,X240,X2,X233,X235,X125,X13,X10] :
( c_Equiv__Relations_Ocongruent2(X10,X13,X125,X235,X233,X2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X240),X239)),X235))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X13,X13)),hAPP(hAPP(c_Product__Type_OPair(X13,X13),X238),X237)),X233))
=> hAPP(hAPP(X2,X240),X238) = hAPP(hAPP(X2,X239),X237) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_congruent2D) ).
fof(fact_Int__Collect__mono,axiom,
! [X17,X19,X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> ( hBOOL(hAPP(X19,X3))
=> hBOOL(hAPP(X17,X3)) ) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(c_Set_OCollect(X10),X19))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X160),hAPP(c_Set_OCollect(X10),X17)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Collect__mono) ).
fof(fact_map__upds__append1,axiom,
! [X16,X102,X289,X13,X290,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13)),X289)))
=> c_Map_Omap__upds(X10,X13,X102,hAPP(hAPP(c_List_Oappend(X10),X290),hAPP(hAPP(c_List_Olist_OCons(X10),X16),c_List_Olist_ONil(X10))),X289) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),c_Map_Omap__upds(X10,X13,X102,X290,X289)),X16),hAPP(c_Option_Ooption_OSome(X13),hAPP(hAPP(c_List_Onth(X13),X289),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upds__append1) ).
fof(fact_UN__finite__subset,axiom,
! [X198,X154,X10] :
( ! [X83] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X83)),X154)),X198))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X154)),X198)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__finite__subset) ).
fof(fact_set__diff__eq,axiom,
! [X160,X154,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X154))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10),c_fNot),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X160)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__diff__eq) ).
fof(fact_finite__Collect__conjI,axiom,
! [X17,X19,X10] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Set_OCollect(X10),X19)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Set_OCollect(X10),X17))) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),X19)),X17)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__conjI) ).
fof(fact_evalc_Oequations_I3_J,axiom,
! [X66,X52,X51,X72,X50] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(X50,X72,X51)),X52),hAPP(hAPP(hAPP(c_Natural_Oupdate,X66),c_Com_Ovname_OLoc(X50)),hAPP(hAPP(c_Natural_Ogetlocs,X52),X50))))
<=> ? [X67] :
( hAPP(hAPP(hAPP(c_Natural_Oupdate,X66),c_Com_Ovname_OLoc(X50)),hAPP(hAPP(c_Natural_Ogetlocs,X52),X50)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,X67),c_Com_Ovname_OLoc(X50)),hAPP(hAPP(c_Natural_Ogetlocs,X52),X50))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X51),hAPP(hAPP(hAPP(c_Natural_Oupdate,X52),c_Com_Ovname_OLoc(X50)),hAPP(X72,X52))),X67)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I3_J) ).
fof(fact_UN__UN__finite__eq,axiom,
! [X154,X10] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,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(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X154)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X154),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__UN__finite__eq) ).
fof(fact_map__pair__simp,axiom,
! [X38,X39,X1,X2,X13,X195,X10,X125] : hAPP(c_Product__Type_Omap__pair(X125,X10,X195,X13,X2,X1),hAPP(hAPP(c_Product__Type_OPair(X125,X195),X39),X38)) = hAPP(hAPP(c_Product__Type_OPair(X10,X13),hAPP(X2,X39)),hAPP(X1,X38)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__simp) ).
fof(fact_map__pair__ident,axiom,
! [X73,X13,X10] : hAPP(c_Product__Type_Omap__pair(X10,X10,X13,X13,c_COMBI(X10),c_COMBI(X13)),X73) = X73,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__ident) ).
fof(fact_aset_I9_J,axiom,
! [X53,X154,X197,X141] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X141),X197))
=> ! [X3] :
( ! [X227] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X227),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X197)))
=> ! [X249] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X249),X154))
=> X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X249),X227) ) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X141),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X53)))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X141),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X197)),X53))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I9_J) ).
fof(fact_bset_I9_J,axiom,
! [X53,X160,X197,X141] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X141),X197))
=> ! [X3] :
( ! [X227] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X227),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X197)))
=> ! [X249] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X249),X160))
=> X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X249),X227) ) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X141),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X53)))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X141),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X197)),X53))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I9_J) ).
fof(fact_folding__image__simple_Ounion__inter,axiom,
! [X160,X154,X225,X1,X73,X2,X13,X10] :
( c_Finite__Set_Ofolding__image__simple(X10,X13,X2,X73,X1,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X160))
=> hAPP(hAPP(X2,hAPP(X225,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13,tc_HOL_Obool)),X154),X160))),hAPP(X225,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13,tc_HOL_Obool)),X154),X160))) = hAPP(hAPP(X2,hAPP(X225,X154)),hAPP(X225,X160)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Ounion__inter) ).
fof(fact_setsum__Un__zero,axiom,
! [X2,X232,X216,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X216))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X232))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X216),X232)))
=> hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X13) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X216),X232)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),X216)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),X232)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Un__zero) ).
fof(fact_setsum_Ounion__inter__neutral,axiom,
! [X1,X160,X154,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)))
=> hAPP(X1,X3) = c_Groups_Ozero__class_Ozero(X13) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1),X154)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1),X160)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Ounion__inter__neutral) ).
fof(fact_setprod__Un__one,axiom,
! [X2,X232,X216,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X216))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X232))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X216),X232)))
=> hAPP(X2,X3) = c_Groups_Oone__class_Oone(X13) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X216),X232)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),X216)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),X232)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__Un__one) ).
fof(fact_setprod_Ounion__inter__neutral,axiom,
! [X1,X160,X154,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)))
=> hAPP(X1,X3) = c_Groups_Oone__class_Oone(X13) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),X154)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),X160)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Ounion__inter__neutral) ).
fof(fact_Image__singleton,axiom,
! [X39,X177,X10,X13] : hAPP(c_Relation_OImage(X13,X10,X177),hAPP(hAPP(c_Set_Oinsert(X13),X39),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X13,X10),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X13,X10),tc_fun(tc_fun(tc_prod(X13,X10),tc_HOL_Obool),tc_HOL_Obool),X10),c_member(tc_prod(X13,X10))),hAPP(c_Product__Type_OPair(X13,X10),X39))),X177)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__singleton) ).
fof(fact_folding__image__simple_Oremove,axiom,
! [X16,X154,X225,X1,X73,X2,X13,X10] :
( c_Finite__Set_Ofolding__image__simple(X10,X13,X2,X73,X1,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X13),X16),X154))
=> hAPP(X225,X154) = hAPP(hAPP(X2,hAPP(X1,X16)),hAPP(X225,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X13),X16),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool)))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oremove) ).
fof(fact_subset__image__iff,axiom,
! [X154,X2,X13,X160,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),hAPP(c_Set_Oimage(X13,X10,X2),X154)))
<=> ? [X222] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool)),X222),X154))
& X160 = hAPP(c_Set_Oimage(X13,X10,X2),X222) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__image__iff) ).
fof(fact_UN__iff,axiom,
! [X160,X154,X13,X38,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X38),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X154),X160)))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X13),X3),X154))
& hBOOL(hAPP(hAPP(c_member(X10),X38),hAPP(X160,X3))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__iff) ).
fof(fact_folding__image__simple_Oinsert__remove,axiom,
! [X16,X154,X225,X1,X73,X2,X13,X10] :
( c_Finite__Set_Ofolding__image__simple(X10,X13,X2,X73,X1,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X154))
=> hAPP(X225,hAPP(hAPP(c_Set_Oinsert(X13),X16),X154)) = hAPP(hAPP(X2,hAPP(X1,X16)),hAPP(X225,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X13),X16),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool)))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oinsert__remove) ).
fof(fact_the__inv__into__comp,axiom,
! [X16,X154,X1,X125,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,hAPP(c_Set_Oimage(X125,X10,X1),X154))
=> ( c_Fun_Oinj__on(X125,X10,X1,X154)
=> ( hBOOL(hAPP(hAPP(c_member(X13),X16),hAPP(c_Set_Oimage(X10,X13,X2),hAPP(c_Set_Oimage(X125,X10,X1),X154))))
=> hAPP(c_Fun_Othe__inv__into(X125,X13,X154,hAPP(c_Fun_Ocomp(X10,X13,X125,X2),X1)),X16) = hAPP(hAPP(c_Fun_Ocomp(X10,X125,X13,c_Fun_Othe__inv__into(X125,X10,X154,X1)),c_Fun_Othe__inv__into(X10,X13,hAPP(c_Set_Oimage(X125,X10,X1),X154),X2)),X16) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__comp) ).
fof(fact_setsum__mono__zero__left,axiom,
! [X2,X216,X232,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X232))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X216),X232))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X232),X216)))
=> hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X13) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),X216) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),X232) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__mono__zero__left) ).
fof(fact_setsum__mono__zero__right,axiom,
! [X2,X216,X232,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X232))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X216),X232))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X232),X216)))
=> hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X13) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),X232) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),X216) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__mono__zero__right) ).
fof(fact_setprod__mono__one__left,axiom,
! [X2,X216,X232,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X232))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X216),X232))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X232),X216)))
=> hAPP(X2,X3) = c_Groups_Oone__class_Oone(X13) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),X216) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),X232) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__mono__one__left) ).
fof(fact_setprod__mono__one__right,axiom,
! [X2,X216,X232,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X232))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X216),X232))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X232),X216)))
=> hAPP(X2,X3) = c_Groups_Oone__class_Oone(X13) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),X232) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),X216) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__mono__one__right) ).
fof(fact_SUP1__iff,axiom,
! [X38,X160,X154,X13,X10] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X154),X160),X38))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
& hBOOL(hAPP(hAPP(X160,X3),X38)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP1__iff) ).
fof(fact_rtrancl__imp__UN__rel__pow,axiom,
! [X196,X166,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X166),c_Transitive__Closure_Ortrancl(X10,X196)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X166),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X10,X10),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(X10,X10),tc_HOL_Obool),tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool)),X196)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__imp__UN__rel__pow) ).
fof(fact_Int__Inter__image,axiom,
! [X160,X154,X198,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBS(X13,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X13),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool))),X154)),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),hAPP(c_Set_Oimage(X13,tc_fun(X10,tc_HOL_Obool),X154),X198))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),hAPP(c_Set_Oimage(X13,tc_fun(X10,tc_HOL_Obool),X160),X198))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Inter__image) ).
fof(fact_Un__Union__image,axiom,
! [X160,X154,X198,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBS(X13,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X13),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool))),X154)),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),hAPP(c_Set_Oimage(X13,tc_fun(X10,tc_HOL_Obool),X154),X198))),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),hAPP(c_Set_Oimage(X13,tc_fun(X10,tc_HOL_Obool),X160),X198))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Union__image) ).
fof(fact_lexord__append__left__rightI,axiom,
! [X25,X16,X165,X177,X38,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),X177))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Oappend(X10),X165),hAPP(hAPP(c_List_Olist_OCons(X10),X39),X16))),hAPP(hAPP(c_List_Oappend(X10),X165),hAPP(hAPP(c_List_Olist_OCons(X10),X38),X25)))),c_List_Olexord(X10,X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__append__left__rightI) ).
fof(fact_intrel__iff,axiom,
! [X168,X165,X25,X16] :
( 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),X16),X25)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X165),X168))),c_Int_Ointrel))
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16),X168) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X165),X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_intrel__iff) ).
fof(fact_same__fstI,axiom,
! [X10,X196,X25,X217,X13,X16,X19] :
( hBOOL(hAPP(X19,X16))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X13,X13)),hAPP(hAPP(c_Product__Type_OPair(X13,X13),X217),X25)),hAPP(X196,X16)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X10,X13),tc_prod(X10,X13))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X10,X13),tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X16),X217)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X16),X25))),c_Recdef_Osame__fst(X10,X13,X19,X196))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_same__fstI) ).
fof(fact_less__SUP__iff,axiom,
! [X2,X154,X13,X39,X10] :
( ( class_Complete__Lattice_Ocomplete__lattice(X10)
& class_Orderings_Olinorder(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,X10),X154),X2)))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X13),X3),X154))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),hAPP(X2,X3))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SUP__iff) ).
fof(fact_split__twice,axiom,
! [X166,X1,X194,X195,X2,X10,X125,X13] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X13,X125,X10),X2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X195,X194,tc_prod(X13,X125)),X1),X166)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X195,X194,X10),hAPP(hAPP(c_COMBB(tc_fun(X194,tc_prod(X13,X125)),tc_fun(X194,X10),X195),hAPP(c_COMBB(tc_prod(X13,X125),X10,X194),hAPP(c_Product__Type_Oprod_Oprod__case(X13,X125,X10),X2))),X1)),X166),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__twice) ).
fof(fact_list__size__pointwise,axiom,
! [X1,X2,X290,X10] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X290)))
=> 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(X10,X2,X290)),c_List_Olist_Olist__size(X10,X1,X290))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__size__pointwise) ).
fof(fact_inj__graph,axiom,
! [X13,X10] : c_Fun_Oinj__on(tc_fun(X10,X13),tc_fun(tc_prod(X10,X13),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(X10,X13)),c_Set_OCollect(tc_prod(X10,X13))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X13,tc_HOL_Obool)),tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(X10,X13)),c_Product__Type_Oprod_Oprod__case(X10,X13,tc_HOL_Obool)),hAPP(c_COMBB(X13,tc_fun(X13,tc_HOL_Obool),X10),hAPP(c_COMBC(X13,X13,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X10,X13),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,
! [X52,X51,X196,X10] :
( c_Wellfounded_Omax__extp(X10,X196,X51,X52)
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X51))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X52))
& X52 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
& ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X51))
=> ? [X227] :
( hBOOL(hAPP(hAPP(c_member(X10),X227),X52))
& hBOOL(hAPP(hAPP(X196,X3),X227)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__extp_Oequations) ).
fof(fact_Int__def,axiom,
! [X160,X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X154))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X160))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__def) ).
fof(fact_Un__def,axiom,
! [X160,X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fdisj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X154))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X160))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__def) ).
fof(fact_folding__image__simple_Ounion__disjoint,axiom,
! [X160,X154,X225,X1,X73,X2,X13,X10] :
( c_Finite__Set_Ofolding__image__simple(X10,X13,X2,X73,X1,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X160))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13,tc_HOL_Obool)),X154),X160) = c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool))
=> hAPP(X225,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(X2,hAPP(X225,X154)),hAPP(X225,X160)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Ounion__disjoint) ).
fof(fact_fun__upd__restrict__conv,axiom,
! [X25,X102,X13,X197,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X16),X197))
=> hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),c_Map_Orestrict__map(X10,X13,X102,X197)),X16),X25) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),c_Map_Orestrict__map(X10,X13,X102,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X197),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))),X16),X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__restrict__conv) ).
fof(fact_le__add__iff2,axiom,
! [X141,X38,X18,X161,X39,X10] :
( class_Rings_Oordered__ring(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X161)),X18)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X38),X161)),X141)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X18),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X38),X39)),X161)),X141))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__iff2) ).
fof(fact_less__add__iff2,axiom,
! [X141,X38,X18,X161,X39,X10] :
( class_Rings_Oordered__ring(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X161)),X18)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X38),X161)),X141)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X38),X39)),X161)),X141))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__iff2) ).
fof(fact_Image__INT__subset,axiom,
! [X160,X154,X125,X177,X13,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_OImage(X13,X10,X177),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X125,tc_fun(X13,tc_HOL_Obool)),X154),X160))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X125,tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X125),c_Relation_OImage(X13,X10,X177)),X160)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__INT__subset) ).
fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
! [X160,X154,X225,X1,X73,X2,X13,X10] :
( c_Finite__Set_Ofolding__image__simple__idem(X10,X13,X2,X73,X1,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X154))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool)),X160),X154))
=> hAPP(hAPP(X2,hAPP(X225,X160)),hAPP(X225,X154)) = hAPP(X225,X154) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Osubset__idem) ).
fof(fact_le__fun__def,axiom,
! [X1,X2,X10,X13] :
( class_Orderings_Oord(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X13)),X2),X1))
<=> ! [X3] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13),hAPP(X2,X3)),hAPP(X1,X3))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__fun__def) ).
fof(fact_fun__upd__restrict,axiom,
! [X25,X16,X197,X102,X13,X10] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),c_Map_Orestrict__map(X10,X13,X102,X197)),X16),X25) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),c_Map_Orestrict__map(X10,X13,X102,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X197),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))),X16),X25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__restrict) ).
fof(fact_folding__image__simple_Oeq__fold__g,axiom,
! [X154,X225,X1,X73,X2,X13,X10] :
( c_Finite__Set_Ofolding__image__simple(X10,X13,X2,X73,X1,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X154))
=> hAPP(X225,X154) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X10,X13,X2),X1),X73),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oeq__fold__g) ).
fof(fact_map__eq__conv,axiom,
! [X1,X290,X2,X10,X13] :
( hAPP(hAPP(c_List_Omap(X13,X10),X2),X290) = hAPP(hAPP(c_List_Omap(X13,X10),X1),X290)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X13),X3),hAPP(c_List_Oset(X13),X290)))
=> 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,
! [X160,X154,X225,X1,X73,X2,X13,X10] :
( c_Finite__Set_Ofolding__image__simple__idem(X10,X13,X2,X73,X1,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X160))
=> hAPP(X225,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(X2,hAPP(X225,X154)),hAPP(X225,X160)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Ounion__idem) ).
fof(fact_congruent2__implies__congruent,axiom,
! [X39,X2,X233,X125,X13,X235,X154,X10] :
( c_Equiv__Relations_Oequiv(X10,X154,X235)
=> ( c_Equiv__Relations_Ocongruent2(X10,X13,X125,X235,X233,X2)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> c_Equiv__Relations_Ocongruent(X13,X125,X233,hAPP(X2,X39)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_congruent2__implies__congruent) ).
fof(fact_append__eq__append__conv2,axiom,
! [X211,X299,X289,X290,X10] :
( hAPP(hAPP(c_List_Oappend(X10),X290),X289) = hAPP(hAPP(c_List_Oappend(X10),X299),X211)
<=> ? [X318] :
( ( X290 = hAPP(hAPP(c_List_Oappend(X10),X299),X318)
& hAPP(hAPP(c_List_Oappend(X10),X318),X289) = X211 )
| ( hAPP(hAPP(c_List_Oappend(X10),X290),X318) = X299
& X289 = hAPP(hAPP(c_List_Oappend(X10),X318),X211) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__eq__append__conv2) ).
fof(fact_inj__on__iff__card__le,axiom,
! [X160,X13,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X160))
=> ( ? [X247] :
( c_Fun_Oinj__on(X10,X13,X247,X154)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X13,X247),X154)),X160)) )
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X154)),hAPP(c_Finite__Set_Ocard(X13),X160))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__card__le) ).
fof(fact_folding__image__simple__idem_Oin__idem,axiom,
! [X16,X154,X225,X1,X73,X2,X13,X10] :
( c_Finite__Set_Ofolding__image__simple__idem(X10,X13,X2,X73,X1,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X13),X16),X154))
=> hAPP(hAPP(X2,hAPP(X1,X16)),hAPP(X225,X154)) = hAPP(X225,X154) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oin__idem) ).
fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
! [X16,X154,X225,X1,X73,X2,X13,X10] :
( c_Finite__Set_Ofolding__image__simple__idem(X10,X13,X2,X73,X1,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X154))
=> hAPP(X225,hAPP(hAPP(c_Set_Oinsert(X13),X16),X154)) = hAPP(hAPP(X2,hAPP(X1,X16)),hAPP(X225,X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oinsert__idem) ).
fof(fact_INT__Int__distrib,axiom,
! [X160,X154,X241,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X241),hAPP(hAPP(c_COMBS(X13,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X13),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool))),X154)),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X241),X154)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X241),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__Int__distrib) ).
fof(fact_UN__Un__distrib,axiom,
! [X160,X154,X241,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X241),hAPP(hAPP(c_COMBS(X13,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X13),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool))),X154)),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X241),X154)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X241),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__Un__distrib) ).
fof(fact_folding__image__simple_Oempty,axiom,
! [X225,X1,X73,X2,X13,X10] :
( c_Finite__Set_Ofolding__image__simple(X10,X13,X2,X73,X1,X225)
=> hAPP(X225,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool))) = X73 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oempty) ).
fof(fact_folding__image__simple__idem_Oidem,axiom,
! [X16,X225,X1,X73,X2,X13,X10] :
( c_Finite__Set_Ofolding__image__simple__idem(X10,X13,X2,X73,X1,X225)
=> hAPP(hAPP(X2,X16),X16) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).
fof(fact_smax__emptyI,axiom,
! [X78] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X78))
=> ( X78 != 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))),X78)),c_FunDef_Omax__strict)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smax__emptyI) ).
fof(fact_set__filter,axiom,
! [X290,X19,X10] : hAPP(c_List_Oset(X10),hAPP(c_List_Ofilter(X10,X19),X290)) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),hAPP(c_List_Oset(X10),X290)))),X19)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__filter) ).
fof(fact_sum__diff__distrib,axiom,
! [X20,X19,X17] :
( ! [X3] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X17,X3)),hAPP(X19,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),X19),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X20))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X17),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X20))) = 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)),X19)),X17)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__diff__distrib) ).
fof(fact_inj__on__iff__surj,axiom,
! [X223,X13,X10,X154] :
( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( ? [X247] :
( c_Fun_Oinj__on(X10,X13,X247,X154)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X13,X247),X154)),X223)) )
<=> ? [X248] : hAPP(c_Set_Oimage(X13,X10,X248),X223) = X154 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__surj) ).
fof(fact_Range__iff,axiom,
! [X177,X13,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X39),hAPP(c_Relation_ORange(X13,X10),X177)))
<=> ? [X90] : hBOOL(hAPP(hAPP(c_member(tc_prod(X13,X10)),hAPP(hAPP(c_Product__Type_OPair(X13,X10),X90),X39)),X177)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__iff) ).
fof(fact_wmax__emptyI,axiom,
! [X48] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X48))
=> 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))),X48)),c_FunDef_Omax__weak)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wmax__emptyI) ).
fof(fact_INT__simps_I1_J,axiom,
! [X160,X154,X13,X10,X198] :
( ( X198 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBC(X10,tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13,tc_HOL_Obool))),X154)),X160)) = c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)) )
& ( X198 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBC(X10,tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13,tc_HOL_Obool))),X154)),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X198),X154)),X160) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I1_J) ).
fof(fact_INT__simps_I3_J,axiom,
! [X160,X154,X13,X10,X198] :
( ( X198 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBC(X10,tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_Groups_Ominus__class_Ominus(tc_fun(X13,tc_HOL_Obool))),X154)),X160)) = c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)) )
& ( X198 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBC(X10,tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_Groups_Ominus__class_Ominus(tc_fun(X13,tc_HOL_Obool))),X154)),X160)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X198),X154)),X160) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I3_J) ).
fof(fact_UN__simps_I2_J,axiom,
! [X160,X154,X13,X10,X198] :
( ( X198 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBC(X10,tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13,tc_HOL_Obool))),X154)),X160)) = c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool)) )
& ( X198 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBC(X10,tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13,tc_HOL_Obool))),X154)),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X198),X154)),X160) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I2_J) ).
fof(fact_INT__extend__simps_I1_J,axiom,
! [X160,X154,X13,X10,X198] :
( ( X198 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X198),X154)),X160) = X160 )
& ( X198 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X198),X154)),X160) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBC(X10,tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13,tc_HOL_Obool))),X154)),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I1_J) ).
fof(fact_UN__extend__simps_I2_J,axiom,
! [X160,X154,X13,X10,X198] :
( ( X198 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X198),X154)),X160) = X160 )
& ( X198 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X198),X154)),X160) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBC(X10,tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13,tc_HOL_Obool))),X154)),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I2_J) ).
fof(fact_INT__extend__simps_I3_J,axiom,
! [X160,X154,X13,X10,X198] :
( ( X198 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X198),X154)),X160) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))),X160) )
& ( X198 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X198),X154)),X160) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBC(X10,tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_Groups_Ominus__class_Ominus(tc_fun(X13,tc_HOL_Obool))),X154)),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I3_J) ).
fof(fact_INT__simps_I6_J,axiom,
! [X160,X154,X198,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBC(X13,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X13),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool))),X154)),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X198),X154)),X160),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I6_J) ).
fof(fact_UN__simps_I4_J,axiom,
! [X160,X154,X198,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBC(X13,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X13),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool))),X154)),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X198),X154)),X160),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I4_J) ).
fof(fact_UN__simps_I6_J,axiom,
! [X160,X154,X198,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBC(X13,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X13),c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool))),X154)),X160)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X198),X154)),X160),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I6_J) ).
fof(fact_UN__extend__simps_I4_J,axiom,
! [X160,X154,X198,X13,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X198),X154)),X160) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBC(X13,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X13),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool))),X154)),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I4_J) ).
fof(fact_INT__extend__simps_I6_J,axiom,
! [X160,X154,X198,X13,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X198),X154)),X160) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBC(X13,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X13),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool))),X154)),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I6_J) ).
fof(fact_UN__extend__simps_I6_J,axiom,
! [X160,X154,X198,X13,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X198),X154)),X160) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBC(X13,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X13),c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool))),X154)),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I6_J) ).
fof(fact_rel__comp__subset__Sigma,axiom,
! [X198,X54,X125,X160,X154,X177,X13,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),X177),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X154),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),X160))))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X13,X125),tc_HOL_Obool)),X54),hAPP(hAPP(c_Product__Type_OSigma(X13,X125),X160),hAPP(c_COMBK(tc_fun(X125,tc_HOL_Obool),X13),X198))))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X125),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X10,X13,X125),X177),X54)),hAPP(hAPP(c_Product__Type_OSigma(X10,X125),X154),hAPP(c_COMBK(tc_fun(X125,tc_HOL_Obool),X10),X198)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__subset__Sigma) ).
fof(fact_Cons__listrel1__Cons,axiom,
! [X177,X289,X25,X290,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290)),hAPP(hAPP(c_List_Olist_OCons(X10),X25),X289))),c_List_Olistrel1(X10,X177)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),X177))
& X290 = X289 )
| ( X16 = X25
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X290),X289)),c_List_Olistrel1(X10,X177))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__listrel1__Cons) ).
fof(fact_lexord__cons__cons,axiom,
! [X177,X25,X38,X16,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X39),X16)),hAPP(hAPP(c_List_Olist_OCons(X10),X38),X25))),c_List_Olexord(X10,X177)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),X177))
| ( X39 = X38
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X16),X25)),c_List_Olexord(X10,X177))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__cons__cons) ).
fof(fact_Cons__in__lex,axiom,
! [X177,X289,X25,X290,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290)),hAPP(hAPP(c_List_Olist_OCons(X10),X25),X289))),c_List_Olex(X10,X177)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),X177))
& hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X289) )
| ( X16 = X25
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X290),X289)),c_List_Olex(X10,X177))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__in__lex) ).
fof(fact_Sigma__Int__distrib2,axiom,
! [X160,X154,X241,X13,X10] : hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X241),hAPP(hAPP(c_COMBS(X10,tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13,tc_HOL_Obool))),X154)),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X241),X154)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X241),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Int__distrib2) ).
fof(fact_Sigma__Un__distrib2,axiom,
! [X160,X154,X241,X13,X10] : hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X241),hAPP(hAPP(c_COMBS(X10,tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13,tc_HOL_Obool))),X154)),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X241),X154)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X241),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Un__distrib2) ).
fof(fact_Sigma__Diff__distrib2,axiom,
! [X160,X154,X241,X13,X10] : hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X241),hAPP(hAPP(c_COMBS(X10,tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X10),c_Groups_Ominus__class_Ominus(tc_fun(X13,tc_HOL_Obool))),X154)),X160)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X241),X154)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X241),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Diff__distrib2) ).
fof(fact_abs__diff__triangle__ineq,axiom,
! [X112,X81,X92,X84,X94] :
( class_Groups_Oordered__ab__group__add__abs(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X81),X112)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X84),X81))),hAPP(c_Groups_Oabs__class_Oabs(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X92),X112))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__diff__triangle__ineq) ).
fof(fact_nat__le__add__iff2,axiom,
! [X20,X102,X165,X163,X113] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X113),X163))
=> ( 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),X113),X165)),X102)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X163),X165)),X20)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),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),X163),X113)),X165)),X20))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__add__iff2) ).
fof(fact_nat__less__add__iff2,axiom,
! [X20,X102,X165,X163,X113] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X113),X163))
=> ( 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),X113),X165)),X102)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X163),X165)),X20)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),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),X163),X113)),X165)),X20))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__add__iff2) ).
fof(fact_folding__image_Odistrib,axiom,
! [X204,X1,X154,X225,X73,X2,X13,X10] :
( c_Finite__Set_Ofolding__image(X10,X13,X2,X73,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X154))
=> hAPP(hAPP(X225,hAPP(hAPP(c_COMBS(X13,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X13),X2),X1)),X204)),X154) = hAPP(hAPP(X2,hAPP(hAPP(X225,X1),X154)),hAPP(hAPP(X225,X204),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image_Odistrib) ).
fof(fact_fold__image__Un__Int,axiom,
! [X1,X160,X154,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13,X10,c_Groups_Otimes__class_Otimes(X13)),X1),c_Groups_Oone__class_Oone(X13)),X154)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13,X10,c_Groups_Otimes__class_Otimes(X13)),X1),c_Groups_Oone__class_Oone(X13)),X160)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13,X10,c_Groups_Otimes__class_Otimes(X13)),X1),c_Groups_Oone__class_Oone(X13)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13,X10,c_Groups_Otimes__class_Otimes(X13)),X1),c_Groups_Oone__class_Oone(X13)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__Un__Int) ).
fof(fact_arith__series__nat,axiom,
! [X20,X141,X39] : 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),X39)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),X141))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X20))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X39),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X39),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X141)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arith__series__nat) ).
fof(fact_Un__Int__crazy,axiom,
! [X198,X160,X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X160),X198))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X198),X154)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X160),X198))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X198),X154)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__crazy) ).
fof(fact_evalc_OCall,axiom,
! [X48,X77,X39,X85,X49] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X49)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X85),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X39,X85))),X77))
=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(X48,X49,X39)),X85),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X77),hAPP(c_Natural_Ogetlocs,X85))),X48),hAPP(hAPP(c_Natural_Ogetlocs,X77),c_Com_ORes)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OCall) ).
fof(fact_rtrancl__listrel1__ConsI2,axiom,
! [X289,X290,X177,X25,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),c_Transitive__Closure_Ortrancl(X10,X177)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X290),X289)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X10),c_List_Olistrel1(X10,X177))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290)),hAPP(hAPP(c_List_Olist_OCons(X10),X25),X289))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X10),c_List_Olistrel1(X10,X177)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__listrel1__ConsI2) ).
fof(fact_image__diff__subset,axiom,
! [X160,X154,X2,X13,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X13,X10,X2),X154)),hAPP(c_Set_Oimage(X13,X10,X2),X160))),hAPP(c_Set_Oimage(X13,X10,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13,tc_HOL_Obool)),X154),X160)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__diff__subset) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
! [X19] : hAPP(c_Set_OCollect(tc_Nat_Onat),X19) = 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),X19),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,
! [X177,X10] : c_List_Olenlex(X10,X177) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(X10)),tc_List_Olist(X10)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(X10),c_Wellfounded_Oless__than,c_List_Olex(X10,X177))),hAPP(hAPP(c_COMBS(tc_List_Olist(X10),tc_List_Olist(X10),tc_prod(tc_Nat_Onat,tc_List_Olist(X10))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(X10),tc_prod(tc_Nat_Onat,tc_List_Olist(X10))),tc_List_Olist(X10)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(X10))),c_Nat_Osize__class_Osize(tc_List_Olist(X10)))),c_COMBI(tc_List_Olist(X10)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lenlex__def) ).
fof(fact_refl__onI,axiom,
! [X154,X177,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X177),hAPP(hAPP(c_Product__Type_OSigma(X10,X10),X154),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X10),X154))))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X3)),X177)) )
=> c_Relation_Orefl__on(X10,X154,X177) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onI) ).
fof(fact_refl__on__def,axiom,
! [X177,X154,X10] :
( c_Relation_Orefl__on(X10,X154,X177)
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X177),hAPP(hAPP(c_Product__Type_OSigma(X10,X10),X154),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X10),X154))))
& ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X3)),X177)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__def) ).
fof(fact_map__of__map__keys,axiom,
! [X102,X13,X290,X10] :
( hAPP(c_List_Oset(X10),X290) = c_Map_Odom(X10,X13,X102)
=> c_Map_Omap__of(X10,X13,hAPP(hAPP(c_List_Omap(X10,tc_prod(X10,X13)),hAPP(hAPP(c_COMBS(X10,X13,tc_prod(X10,X13)),c_Product__Type_OPair(X10,X13)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X13),X13,X10),c_Option_Othe(X13)),X102))),X290)) = X102 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__map__keys) ).
fof(fact_insert__compr__raw,axiom,
! [X160,X39,X10] : hAPP(hAPP(c_Set_Oinsert(X10),X39),X160) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fdisj),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X39))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X160))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__compr__raw) ).
fof(fact_insert__compr,axiom,
! [X160,X39,X10] : hAPP(hAPP(c_Set_Oinsert(X10),X39),X160) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fdisj),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X39))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X160))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__compr) ).
fof(fact_listrel_OCons,axiom,
! [X289,X290,X177,X25,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),X177))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X290),X289)),c_List_Olistrel(X10,X177)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290)),hAPP(hAPP(c_List_Olist_OCons(X10),X25),X289))),c_List_Olistrel(X10,X177))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel_OCons) ).
fof(fact_dom__def,axiom,
! [X102,X13,X10] : c_Map_Odom(X10,X13,X102) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10),c_fNot),hAPP(hAPP(c_COMBC(X10,tc_Option_Ooption(X13),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X13),tc_fun(tc_Option_Ooption(X13),tc_HOL_Obool),X10),c_fequal),X102)),c_Option_Ooption_ONone(X13)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__def) ).
fof(fact_smin__emptyI,axiom,
! [X48] :
( X48 != 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)),X48),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,
! [X25,X16] : 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),X16),X25)),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),X25),X16)),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,
! [X48] : 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)),X48),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,
! [X25,X154,X73,X2,X13,X10] :
( c_Finite__Set_Ofun__left__comm(X10,X13,X2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X13,X2,X73,X154),X25))
=> hAPP(hAPP(c_Finite__Set_Ofold(X10,X13,X2),X73),X154) = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__equality) ).
fof(fact_empty__fold__graphE,axiom,
! [X16,X73,X2,X13,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X13,X2,X73,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),X16))
=> X16 = X73 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__fold__graphE) ).
fof(fact_subset__equiv__class,axiom,
! [X39,X38,X177,X154,X10] :
( c_Equiv__Relations_Oequiv(X10,X154,X177)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_OImage(X10,X10,X177),hAPP(hAPP(c_Set_Oinsert(X10),X38),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X10,X10,X177),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X38),X154))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),X177)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__equiv__class) ).
fof(fact_ord_OatLeastLessThan__iff,axiom,
! [X165,X162,X229,X228,X113,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X113),c_SetInterval_Oord_OatLeastLessThan(X10,X228,X229,X162,X165)))
<=> ( hBOOL(hAPP(hAPP(X228,X162),X113))
& hBOOL(hAPP(hAPP(X229,X113),X165)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OatLeastLessThan__iff) ).
fof(fact_ord_OgreaterThanAtMost__iff,axiom,
! [X165,X162,X229,X228,X113,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X113),c_SetInterval_Oord_OgreaterThanAtMost(X10,X228,X229,X162,X165)))
<=> ( hBOOL(hAPP(hAPP(X229,X162),X113))
& hBOOL(hAPP(hAPP(X228,X113),X165)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OgreaterThanAtMost__iff) ).
fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
! [X1,X2,X160,X154,X10] :
( ( class_Groups_Ocomm__monoid__add(X10)
& class_Groups_Ocomm__monoid__mult(X10) )
=> ( X154 = X160
=> ( c_Nat__Transfer_Onat__set(X160)
=> ( ! [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,X10),X2),X154) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X10),X1),X160) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod__cong_I1_J) ).
fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
! [X1,X2,X160,X154,X10] :
( ( class_Groups_Ocomm__monoid__add(X10)
& class_Groups_Ocomm__monoid__mult(X10) )
=> ( X154 = X160
=> ( c_Nat__Transfer_Onat__set(X160)
=> ( ! [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,X10),X2),X154) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X10),X1),X160) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod__cong_I2_J) ).
fof(fact_select__weigth__drop__zero,axiom,
! [X290,X10] : c_Random_Oselect__weight(X10,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X10),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X10,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X10)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X290)) = c_Random_Oselect__weight(X10,X290),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_select__weigth__drop__zero) ).
fof(fact_pick__drop__zero,axiom,
! [X290,X10] : c_Random_Opick(X10,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X10),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X10,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X10)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X290)) = c_Random_Opick(X10,X290),
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,
! [X162,X2,X13,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X10)),hAPP(c_Set_Oimage(X13,tc_Option_Ooption(X10),X2),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X10)),hAPP(c_Set_Oimage(X13,tc_Option_Ooption(X10),c_Map_Omap__add(X13,X10,X2,c_Map_Omap__of(X13,X10,X162))),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__range__map__of__map__add) ).
fof(fact_Domain__Int__subset,axiom,
! [X160,X154,X13,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X10,X13),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),X154),X160))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X10,X13),X154)),hAPP(c_Relation_ODomain(X10,X13),X160)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Int__subset) ).
fof(fact_Range__Int__subset,axiom,
! [X160,X154,X13,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_ORange(X13,X10),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X13,X10),tc_HOL_Obool)),X154),X160))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_ORange(X13,X10),X154)),hAPP(c_Relation_ORange(X13,X10),X160)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Int__subset) ).
fof(fact_setsum_Odistrib,axiom,
! [X204,X1,X154,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),hAPP(hAPP(c_COMBS(X10,X13,X13),hAPP(hAPP(c_COMBB(X13,tc_fun(X13,X13),X10),c_Groups_Oplus__class_Oplus(X13)),X1)),X204)),X154) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1),X154)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X204),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Odistrib) ).
fof(fact_setprod__dividef,axiom,
! [X1,X2,X154,X10,X13] :
( class_Fields_Ofield__inverse__zero(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),hAPP(hAPP(c_COMBS(X10,X13,X13),hAPP(hAPP(c_COMBB(X13,tc_fun(X13,X13),X10),c_Rings_Oinverse__class_Odivide(X13)),X2)),X1)),X154) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),X154)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__dividef) ).
fof(fact_setprod_Odistrib,axiom,
! [X204,X1,X154,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),hAPP(hAPP(c_COMBS(X10,X13,X13),hAPP(hAPP(c_COMBB(X13,tc_fun(X13,X13),X10),c_Groups_Otimes__class_Otimes(X13)),X1)),X204)),X154) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),X154)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X204),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Odistrib) ).
fof(fact_fold__graph__imp__finite,axiom,
! [X16,X154,X73,X2,X13,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X13,X2,X73,X154),X16))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph__imp__finite) ).
fof(fact_rotate1__def,axiom,
! [X290,X10] : hAPP(c_List_Orotate1(X10),X290) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(X10),X10,c_List_Olist_ONil(X10),hAPP(hAPP(c_COMBB(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_List_Olist(X10)),X10),hAPP(c_COMBC(tc_List_Olist(X10),tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Oappend(X10))),hAPP(hAPP(c_COMBC(X10,tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_OCons(X10)),c_List_Olist_ONil(X10)))),X290),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate1__def) ).
fof(fact_setsum__subtractf,axiom,
! [X154,X1,X2,X13,X10] :
( class_Groups_Oab__group__add(X10)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X10),hAPP(hAPP(c_COMBS(X13,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X13),c_Groups_Ominus__class_Ominus(X10)),X2)),X1)),X154) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X10),X2),X154)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X10),X1),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__subtractf) ).
fof(fact_setsum__addf,axiom,
! [X154,X1,X2,X13,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X10),hAPP(hAPP(c_COMBS(X13,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X13),c_Groups_Oplus__class_Oplus(X10)),X2)),X1)),X154) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X10),X2),X154)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X10),X1),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__addf) ).
fof(fact_setprod__timesf,axiom,
! [X154,X1,X2,X13,X10] :
( class_Groups_Ocomm__monoid__mult(X10)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X13,X10),hAPP(hAPP(c_COMBS(X13,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X13),c_Groups_Otimes__class_Otimes(X10)),X2)),X1)),X154) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X13,X10),X2),X154)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X13,X10),X1),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__timesf) ).
fof(fact_divmod__nat__rel__mult2__eq,axiom,
! [X81,X143,X149,X92,X84] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X84,X92),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X149),X143)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X81))
=> hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X84,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X92),X81)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X149),X81)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X92),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X149,X81))),X143)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__mult2__eq) ).
fof(fact_select__weight__def,axiom,
! [X290,X10] : c_Random_Oselect__weight(X10,X290) = 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(X10,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,X10),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X10)),X290)))),hAPP(hAPP(c_COMBB(X10,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X10,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X10,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(X10,X290))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_select__weight__def) ).
fof(fact_insert__times__insert,axiom,
! [X160,X38,X154,X39,X13,X10] : hAPP(hAPP(c_Product__Type_OSigma(X10,X13),hAPP(hAPP(c_Set_Oinsert(X10),X39),X154)),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),hAPP(hAPP(c_Set_Oinsert(X13),X38),X160))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X39),X38)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X154),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),hAPP(hAPP(c_Set_Oinsert(X13),X38),X160)))),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),hAPP(hAPP(c_Set_Oinsert(X10),X39),X154)),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),X160)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__times__insert) ).
fof(fact_setsum__divide__distrib,axiom,
! [X177,X154,X2,X13,X10] :
( class_Fields_Ofield(X10)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X10),X2),X154)),X177) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X10),hAPP(hAPP(c_COMBC(X13,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X13),c_Rings_Oinverse__class_Odivide(X10)),X2)),X177)),X154) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__divide__distrib) ).
fof(fact_setsum__left__distrib,axiom,
! [X177,X154,X2,X13,X10] :
( class_Rings_Osemiring__0(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X10),X2),X154)),X177) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X10),hAPP(hAPP(c_COMBC(X13,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X13),c_Groups_Otimes__class_Otimes(X10)),X2)),X177)),X154) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__left__distrib) ).
fof(fact_zmult2__lemma,axiom,
! [X81,X143,X149,X92,X84] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X84,X92),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X149),X143)))
=> ( X92 != 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)),X81))
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(X84,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X92),X81)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X149),X81)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X92),c_Divides_Odiv__class_Omod(tc_Int_Oint,X149,X81))),X143)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma) ).
fof(fact_listrel__rtrancl__trans,axiom,
! [X299,X177,X289,X290,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X290),X289)),c_List_Olistrel(X10,c_Transitive__Closure_Ortrancl(X10,X177))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X289),X299)),c_List_Olistrel(X10,c_Transitive__Closure_Ortrancl(X10,X177))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X290),X299)),c_List_Olistrel(X10,c_Transitive__Closure_Ortrancl(X10,X177)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__rtrancl__trans) ).
fof(fact_pred__subset__eq,axiom,
! [X216,X196,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X196)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X216)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X196),X216)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq) ).
fof(fact_reduction__pair__lemma,axiom,
! [X216,X196,X19,X10] :
( c_FunDef_Oreduction__pair(X10,X19)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X196),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X19)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X216),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X19)))
=> ( c_Wellfounded_Owf(X10,X216)
=> c_Wellfounded_Owf(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X196),X216)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reduction__pair__lemma) ).
fof(fact_Union__Int__subset,axiom,
! [X160,X154,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),X154),X160))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X154)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X160)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__Int__subset) ).
fof(fact_Image__subset__eq,axiom,
! [X160,X154,X177,X13,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_OImage(X13,X10,X177),X154)),X160))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool)),X154),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X13,tc_HOL_Obool)),hAPP(c_Relation_OImage(X10,X13,hAPP(c_Relation_Oconverse(X13,X10),X177)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X160))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__subset__eq) ).
fof(fact_image__eq__UN,axiom,
! [X154,X2,X10,X13] : hAPP(c_Set_Oimage(X13,X10,X2),X154) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBC(X13,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X10,tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X13),c_Set_Oinsert(X10)),X2)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__eq__UN) ).
fof(fact_option__map__o__sum__case,axiom,
! [X204,X1,X2,X13,X10,X125,X195] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(X195),tc_Option_Ooption(X125),tc_sum(X10,X13),hAPP(c_Option_Omap(X195,X125),X2)),c_Sum__Type_Osum_Osum__case(X10,tc_Option_Ooption(X195),X13,X1,X204)) = c_Sum__Type_Osum_Osum__case(X10,tc_Option_Ooption(X125),X13,hAPP(c_Fun_Ocomp(tc_Option_Ooption(X195),tc_Option_Ooption(X125),X10,hAPP(c_Option_Omap(X195,X125),X2)),X1),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X195),tc_Option_Ooption(X125),X13,hAPP(c_Option_Omap(X195,X125),X2)),X204)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option__map__o__sum__case) ).
fof(fact_rtrancl__listrel1__ConsI1,axiom,
! [X16,X177,X289,X290,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X290),X289)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X10),c_List_Olistrel1(X10,X177))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290)),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X289))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X10),c_List_Olistrel1(X10,X177)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__listrel1__ConsI1) ).
fof(fact_option__map__o__map__upd,axiom,
! [X38,X39,X102,X2,X10,X13,X125] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(X125),tc_Option_Ooption(X13),X10,hAPP(c_Option_Omap(X125,X13),X2)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X125)),X102),X39),hAPP(c_Option_Ooption_OSome(X125),X38))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X125),tc_Option_Ooption(X13),X10,hAPP(c_Option_Omap(X125,X13),X2)),X102)),X39),hAPP(c_Option_Ooption_OSome(X13),hAPP(X2,X38))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option__map__o__map__upd) ).
fof(fact_pair__leqI2,axiom,
! [X53,X54,X38,X39] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X39),X38))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X54),X53))
=> 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),X39),X54)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X38),X53))),c_FunDef_Opair__leq)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__leqI2) ).
fof(fact_pair__lessI2,axiom,
! [X53,X54,X38,X39] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X39),X38))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X54),X53))
=> 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),X39),X54)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X38),X53))),c_FunDef_Opair__less)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__lessI2) ).
fof(fact_rtrancl__Un__subset,axiom,
! [X216,X196,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X10,X196)),c_Transitive__Closure_Ortrancl(X10,X216))),c_Transitive__Closure_Ortrancl(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X196),X216)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__subset) ).
fof(fact_Image__Int__subset,axiom,
! [X160,X154,X196,X13,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_OImage(X13,X10,X196),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13,tc_HOL_Obool)),X154),X160))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_OImage(X13,X10,X196),X154)),hAPP(c_Relation_OImage(X13,X10,X196),X160)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Int__subset) ).
fof(fact_image__Int__subset,axiom,
! [X160,X154,X2,X13,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X13,X10,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13,tc_HOL_Obool)),X154),X160))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X13,X10,X2),X154)),hAPP(c_Set_Oimage(X13,X10,X2),X160)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Int__subset) ).
fof(fact_transfer__nat__int__set__cong,axiom,
! [X272,X19] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
=> ( hBOOL(hAPP(X19,X3))
<=> hBOOL(hAPP(X272,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)))),X19)) = 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)))),X272)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__set__cong) ).
fof(fact_pair__leqI1,axiom,
! [X53,X54,X38,X39] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X39),X38))
=> 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),X39),X54)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X38),X53))),c_FunDef_Opair__leq)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__leqI1) ).
fof(fact_pair__lessI1,axiom,
! [X53,X54,X38,X39] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X39),X38))
=> 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),X39),X54)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X38),X53))),c_FunDef_Opair__less)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__lessI1) ).
fof(fact_lists__eq__set,axiom,
! [X154,X10] : c_List_Olists(X10,X154) = hAPP(c_Set_OCollect(tc_List_Olist(X10)),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X10)),c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool))),c_List_Oset(X10))),X154)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__eq__set) ).
fof(fact_append__listrel1I,axiom,
! [X320,X321,X177,X289,X290,X10] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X290),X289)),c_List_Olistrel1(X10,X177)))
& X321 = X320 )
| ( X290 = X289
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X321),X320)),c_List_Olistrel1(X10,X177))) ) )
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Oappend(X10),X290),X321)),hAPP(hAPP(c_List_Oappend(X10),X289),X320))),c_List_Olistrel1(X10,X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__listrel1I) ).
fof(fact_lexord__append__leftI,axiom,
! [X16,X177,X168,X165,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X165),X168)),c_List_Olexord(X10,X177)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Oappend(X10),X16),X165)),hAPP(hAPP(c_List_Oappend(X10),X16),X168))),c_List_Olexord(X10,X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__append__leftI) ).
fof(fact_listrel1I2,axiom,
! [X16,X177,X289,X290,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X290),X289)),c_List_Olistrel1(X10,X177)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290)),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X289))),c_List_Olistrel1(X10,X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1I2) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
! [X19] : 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)))),X19))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J) ).
fof(fact_finite__range__updI,axiom,
! [X38,X39,X2,X13,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X10)),hAPP(c_Set_Oimage(X13,tc_Option_Ooption(X10),X2),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X10)),hAPP(c_Set_Oimage(X13,tc_Option_Ooption(X10),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X13,tc_Option_Ooption(X10)),X2),X39),hAPP(c_Option_Ooption_OSome(X10),X38))),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__range__updI) ).
fof(fact_zip__map1,axiom,
! [X289,X290,X2,X125,X13,X10] : hAPP(hAPP(c_List_Ozip(X10,X13),hAPP(hAPP(c_List_Omap(X125,X10),X2),X290)),X289) = hAPP(hAPP(c_List_Omap(tc_prod(X125,X13),tc_prod(X10,X13)),hAPP(c_Product__Type_Oprod_Oprod__case(X125,X13,tc_prod(X10,X13)),hAPP(hAPP(c_COMBB(X10,tc_fun(X13,tc_prod(X10,X13)),X125),c_Product__Type_OPair(X10,X13)),X2))),hAPP(hAPP(c_List_Ozip(X125,X13),X290),X289)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__map1) ).
fof(fact_mlex__prod__def,axiom,
! [X196,X2,X10] : c_Wellfounded_Omlex__prod(X10,X2,X196) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X10),X10),c_Wellfounded_Olex__prod(tc_Nat_Onat,X10,c_Wellfounded_Oless__than,X196)),hAPP(hAPP(c_COMBS(X10,X10,tc_prod(tc_Nat_Onat,X10)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X10,tc_prod(tc_Nat_Onat,X10)),X10),c_Product__Type_OPair(tc_Nat_Onat,X10)),X2)),c_COMBI(X10))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__prod__def) ).
fof(fact_finite__empty__induct,axiom,
! [X19,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(X19,X154))
=> ( ! [X116,X246] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X246))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X116),X246))
=> ( hBOOL(hAPP(X19,X246))
=> hBOOL(hAPP(X19,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X246),hAPP(hAPP(c_Set_Oinsert(X10),X116),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) )
=> hBOOL(hAPP(X19,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__empty__induct) ).
fof(fact_Times__subset__cancel2,axiom,
! [X160,X154,X13,X198,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X16),X198))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X13,X10),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X13,X10),X154),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X13),X198))),hAPP(hAPP(c_Product__Type_OSigma(X13,X10),X160),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X13),X198))))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool)),X154),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__subset__cancel2) ).
fof(fact_rel__pow__Suc__I2,axiom,
! [X20,X73,X196,X25,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),X196))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X25),X73)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X20),X196)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X73)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),hAPP(c_Nat_OSuc,X20)),X196))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__Suc__I2) ).
fof(fact_rel__pow__Suc__I,axiom,
! [X73,X196,X20,X25,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X20),X196)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X25),X73)),X196))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X73)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),hAPP(c_Nat_OSuc,X20)),X196))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__Suc__I) ).
fof(fact_image__Pow__mono,axiom,
! [X160,X154,X2,X13,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X13,X10,X2),X154)),X160))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(X13,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),c_Set_Oimage(X13,X10,X2)),hAPP(c_Set_OPow(X13),X154))),hAPP(c_Set_OPow(X10),X160))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Pow__mono) ).
fof(fact_select__weight__member,axiom,
! [X54,X290,X10] :
( 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,X10),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X10)),X290))))
=> hBOOL(hAPP(hAPP(c_member(X10),hAPP(c_Product__Type_Ofst(X10,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(X10,X290),X54))),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X10),X10),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X10)),X290)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_select__weight__member) ).
fof(fact_setsum__abs,axiom,
! [X154,X2,X13,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Groups_Oabs__class_Oabs(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X10),X2),X154))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X10),hAPP(hAPP(c_COMBB(X10,X10,X13),c_Groups_Oabs__class_Oabs(X10)),X2)),X154))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__abs) ).
fof(fact_set__minus__filter__out,axiom,
! [X25,X290,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),X290)),hAPP(hAPP(c_Set_Oinsert(X10),X25),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = hAPP(c_List_Oset(X10),hAPP(c_List_Ofilter(X10,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10),c_fNot),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X25))),X290)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__minus__filter__out) ).
fof(fact_filter__filter,axiom,
! [X290,X17,X19,X10] : hAPP(c_List_Ofilter(X10,X19),hAPP(c_List_Ofilter(X10,X17),X290)) = hAPP(c_List_Ofilter(X10,hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),X17)),X19)),X290),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__filter) ).
fof(fact_Domain__Diff__subset,axiom,
! [X160,X154,X13,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X10,X13),X154)),hAPP(c_Relation_ODomain(X10,X13),X160))),hAPP(c_Relation_ODomain(X10,X13),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),X154),X160)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Diff__subset) ).
fof(fact_Range__Diff__subset,axiom,
! [X160,X154,X13,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_ORange(X13,X10),X154)),hAPP(c_Relation_ORange(X13,X10),X160))),hAPP(c_Relation_ORange(X13,X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X13,X10),tc_HOL_Obool)),X154),X160)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Diff__subset) ).
fof(fact_fun__left__comm__idem__remove,axiom,
! [X10] : c_Finite__Set_Ofun__left__comm__idem(X10,tc_fun(X10,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),hAPP(c_COMBC(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Set_Oinsert(X10)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem__remove) ).
fof(fact_card__Diff1__less,axiom,
! [X16,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X10),X154))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff1__less) ).
fof(fact_split__comp__eq,axiom,
! [X1,X2,X195,X125,X13,X10] : hAPP(hAPP(c_COMBS(tc_prod(X10,X13),X13,X125),hAPP(hAPP(c_COMBB(X195,tc_fun(X13,X125),tc_prod(X10,X13)),X2),hAPP(hAPP(c_COMBB(X10,X195,tc_prod(X10,X13)),X1),c_Product__Type_Ofst(X10,X13)))),c_Product__Type_Osnd(X10,X13)) = hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,X125),hAPP(hAPP(c_COMBB(X195,tc_fun(X13,X125),X10),X2),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__comp__eq) ).
fof(fact_insort__key__remove1,axiom,
! [X2,X290,X39,X10,X13] :
( class_Orderings_Olinorder(X13)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),hAPP(c_List_Oset(X10),X290)))
=> ( c_List_Olinorder__class_Osorted(X13,hAPP(hAPP(c_List_Omap(X10,X13),X2),X290))
=> ( hAPP(c_List_Ohd(X10),hAPP(c_List_Ofilter(X10,hAPP(hAPP(c_COMBB(X13,tc_HOL_Obool,X10),hAPP(c_fequal,hAPP(X2,X39))),X2)),X290)) = X39
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X13,X2),X39),c_List_Oremove1(X10,X39,X290)) = X290 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__key__remove1) ).
fof(fact_sum_Orecs_I1_J,axiom,
! [X39,X37,X12,X125,X10,X13] : c_Sum__Type_Osum_Osum__rec(X13,X10,X125,X12,X37,hAPP(c_Sum__Type_OInl(X13,X125),X39)) = hAPP(X12,X39),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Orecs_I1_J) ).
fof(fact_sum_Orecs_I2_J,axiom,
! [X38,X37,X12,X125,X10,X13] : c_Sum__Type_Osum_Osum__rec(X13,X10,X125,X12,X37,hAPP(c_Sum__Type_OInr(X125,X13),X38)) = hAPP(X37,X38),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Orecs_I2_J) ).
fof(fact_equiv__intrel__iff,axiom,
! [X25,X16] :
( 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)),X16),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)),X25),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)),X16),X25)),c_Int_Ointrel)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__intrel__iff) ).
fof(fact_fold__graph_H_Ointros_I1_J,axiom,
! [X73,X2,X13,X10] : c_Nitpick_Ofold__graph_H(X10,X13,X2,X73,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),X73),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_H_Ointros_I1_J) ).
fof(fact_fold__graph_H_Oequations_I1_J,axiom,
! [X52,X51,X13,X10] : c_Nitpick_Ofold__graph_H(X10,X13,X51,X52,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),X52),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_H_Oequations_I1_J) ).
fof(fact_map__pair_Oid,axiom,
! [X13,X10] : c_Product__Type_Omap__pair(X10,X10,X13,X13,c_Fun_Oid(X10),c_Fun_Oid(X13)) = c_Fun_Oid(tc_prod(X10,X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair_Oid) ).
fof(fact_map__pair_Oidentity,axiom,
! [X13,X10] : c_Product__Type_Omap__pair(X10,X10,X13,X13,c_COMBI(X10),c_COMBI(X13)) = c_Fun_Oid(tc_prod(X10,X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair_Oidentity) ).
fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
! [X73,X154,X2,X13,X10] :
( c_Finite__Set_Ofun__left__comm(X10,X13,X2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X13,X2,X73,X154),hAPP(hAPP(c_Finite__Set_Ofold(X10,X13,X2),X73),X154))) ) ),
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,
! [X16,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X10),X154))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff1__le) ).
fof(fact_rel__comp__mono,axiom,
! [X54,X209,X125,X177,X224,X13,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),X224),X177))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X13,X125),tc_HOL_Obool)),X209),X54))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X125),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X10,X13,X125),X224),X209)),hAPP(hAPP(c_Relation_Orel__comp(X10,X13,X125),X177),X54))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__mono) ).
fof(fact_equiv__class__subset,axiom,
! [X38,X39,X177,X154,X10] :
( c_Equiv__Relations_Oequiv(X10,X154,X177)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),X177))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_OImage(X10,X10,X177),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X10,X10,X177),hAPP(hAPP(c_Set_Oinsert(X10),X38),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__class__subset) ).
fof(fact_the__inv__into__into,axiom,
! [X160,X16,X154,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,X154)
=> ( hBOOL(hAPP(hAPP(c_member(X13),X16),hAPP(c_Set_Oimage(X10,X13,X2),X154)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> hBOOL(hAPP(hAPP(c_member(X10),hAPP(c_Fun_Othe__inv__into(X10,X13,X154,X2),X16)),X160)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__into) ).
fof(fact_finite__range__imageI,axiom,
! [X2,X125,X1,X13,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Set_Oimage(X13,X10,X1),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X125),hAPP(c_Set_Oimage(X13,X125,hAPP(hAPP(c_COMBB(X10,X125,X13),X2),X1)),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__range__imageI) ).
fof(fact_Inter__Un__subset,axiom,
! [X160,X154,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X154)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X160))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),X154),X160)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__Un__subset) ).
fof(fact_listrel__subset,axiom,
! [X154,X177,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X177),hAPP(hAPP(c_Product__Type_OSigma(X10,X10),X154),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X10),X154))))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_HOL_Obool)),c_List_Olistrel(X10,X177)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olists(X10,X154)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_List_Olist(X10)),c_List_Olists(X10,X154))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__subset) ).
fof(fact_fold__image__reindex,axiom,
! [X73,X1,X204,X13,X154,X10,X125] :
( class_Groups_Oab__semigroup__mult(X125)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( c_Fun_Oinj__on(X10,X13,X204,X154)
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X125,X13,c_Groups_Otimes__class_Otimes(X125)),X1),X73),hAPP(c_Set_Oimage(X10,X13,X204),X154)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X125,X10,c_Groups_Otimes__class_Otimes(X125)),hAPP(c_Fun_Ocomp(X13,X125,X10,X1),X204)),X73),X154) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__reindex) ).
fof(fact_zmult2__lemma__aux4,axiom,
! [X149,X92,X143,X81] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X81))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X143))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X143),X92))
=> 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),X92),c_Divides_Odiv__class_Omod(tc_Int_Oint,X149,X81))),X143)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X92),X81))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma__aux4) ).
fof(fact_restrict__map__upds,axiom,
! [X102,X197,X289,X13,X290,X10] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13)),X289)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),X290)),X197))
=> c_Map_Orestrict__map(X10,X13,c_Map_Omap__upds(X10,X13,X102,X290,X289),X197) = c_Map_Omap__upds(X10,X13,c_Map_Orestrict__map(X10,X13,X102,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X197),hAPP(c_List_Oset(X10),X290))),X290,X289) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__map__upds) ).
fof(fact_fold__sup__le__sup,axiom,
! [X18,X38,X154,X10] :
( class_Lattices_Osemilattice__sup(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X3),X38)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__sup__class_Osup(X10)),X18),X154)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X38),X18))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__sup__le__sup) ).
fof(fact_min__max_Ofold__sup__le__sup,axiom,
! [X18,X38,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X3),X38)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omax(X10)),X18),X154)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X38),X18))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ofold__sup__le__sup) ).
fof(fact_listrel1I1,axiom,
! [X290,X177,X25,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),X177))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290)),hAPP(hAPP(c_List_Olist_OCons(X10),X25),X290))),c_List_Olistrel1(X10,X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1I1) ).
fof(fact_transpose__column,axiom,
! [X113,X290,X10] :
( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X10))),X290)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X113),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),X290)))
=> hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),X10),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_Nat_Onat,X10),c_List_Onth(X10)),X113)),hAPP(c_List_Ofilter(tc_List_Olist(X10),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X10)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X113)),c_Nat_Osize__class_Osize(tc_List_Olist(X10)))),c_List_Otranspose(X10,X290))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(X10)),X290),X113) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__column) ).
fof(fact_split__paired__Eps,axiom,
! [X19,X13,X10] : c_Hilbert__Choice_OEps(tc_prod(X10,X13),X19) = c_Hilbert__Choice_OEps(tc_prod(X10,X13),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_prod(X10,X13)),tc_fun(X13,tc_HOL_Obool),X10),hAPP(c_COMBB(tc_prod(X10,X13),tc_HOL_Obool,X13),X19)),c_Product__Type_OPair(X10,X13)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__paired__Eps) ).
fof(fact_split__paired__The,axiom,
! [X19,X13,X10] : c_HOL_OThe(tc_prod(X10,X13),X19) = c_HOL_OThe(tc_prod(X10,X13),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_prod(X10,X13)),tc_fun(X13,tc_HOL_Obool),X10),hAPP(c_COMBB(tc_prod(X10,X13),tc_HOL_Obool,X13),X19)),c_Product__Type_OPair(X10,X13)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__paired__The) ).
fof(fact_Comp,axiom,
! [X196,X141,X17,X18,X19,X210,X10] :
( c_Hoare__Mirabelle_Ohoare__derivs(X10,X210,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X10)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X10),X19),X18),X17)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X10),tc_HOL_Obool))))
=> ( c_Hoare__Mirabelle_Ohoare__derivs(X10,X210,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X10)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X10),X17),X141),X196)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X10),tc_HOL_Obool))))
=> c_Hoare__Mirabelle_Ohoare__derivs(X10,X210,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X10)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X10),X19),c_Com_Ocom_OSemi(X18,X141)),X196)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X10),tc_HOL_Obool)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Comp) ).
fof(fact_total__on__def,axiom,
! [X177,X154,X10] :
( c_Relation_Ototal__on(X10,X154,X177)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> ! [X227] :
( hBOOL(hAPP(hAPP(c_member(X10),X227),X154))
=> ( X3 != X227
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X227)),X177))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X227),X3)),X177)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__def) ).
fof(fact_mod__lemma,axiom,
! [X149,X92,X143,X81] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X81))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X143),X92))
=> 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),X92),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X149,X81))),X143)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X92),X81))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__lemma) ).
fof(fact_single__valued__confluent,axiom,
! [X73,X25,X16,X177,X10] :
( c_Relation_Osingle__valued(X10,X10,X177)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),c_Transitive__Closure_Ortrancl(X10,X177)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X73)),c_Transitive__Closure_Ortrancl(X10,X177)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X25),X73)),c_Transitive__Closure_Ortrancl(X10,X177)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X73),X25)),c_Transitive__Closure_Ortrancl(X10,X177))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__confluent) ).
fof(fact_reduction__pairI,axiom,
! [X216,X196,X10] :
( c_Wellfounded_Owf(X10,X196)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X196),X216)),X196))
=> c_FunDef_Oreduction__pair(X10,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X196),X216)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reduction__pairI) ).
fof(fact_zmult2__lemma__aux2,axiom,
! [X149,X143,X92,X81] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X81))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X92),X143))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X143),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),X92),c_Divides_Odiv__class_Omod(tc_Int_Oint,X149,X81))),X143)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma__aux2) ).
fof(fact_select__def,axiom,
! [X290,X10] : c_Random_Oselect(X10,X290) = 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(X10,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(X10)),X290)))),hAPP(hAPP(c_COMBB(X10,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X10,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X10,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(X10),X290)),c_Code__Numeral_Onat__of))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_select__def) ).
fof(fact_of__int,axiom,
! [X163,X113,X10] :
( class_Rings_Oring__1(X10)
=> hAPP(c_Int_Oring__1__class_Oof__int(X10),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),X113),X163)),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(X10),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),X113)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),X163)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int) ).
fof(fact_dom__option__map,axiom,
! [X102,X2,X125,X13,X10] : c_Map_Odom(X10,X13,hAPP(hAPP(c_COMBS(X10,tc_Option_Ooption(X125),tc_Option_Ooption(X13)),hAPP(hAPP(c_COMBB(tc_fun(X125,X13),tc_fun(tc_Option_Ooption(X125),tc_Option_Ooption(X13)),X10),c_Option_Omap(X125,X13)),X2)),X102)) = c_Map_Odom(X10,X125,X102),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__option__map) ).
fof(fact_diff__single__insert,axiom,
! [X160,X16,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),X160))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),X160))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__single__insert) ).
fof(fact_nat,axiom,
! [X25,X16] : 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),X16),X25)),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),X16),X25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat) ).
fof(fact_inj__on__Un,axiom,
! [X160,X154,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160))
<=> ( c_Fun_Oinj__on(X10,X13,X2,X154)
& c_Fun_Oinj__on(X10,X13,X2,X160)
& hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X13,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160))),hAPP(c_Set_Oimage(X10,X13,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X160),X154))) = c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__Un) ).
fof(fact_in__finite__psubset,axiom,
! [X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X154),X160)),c_Wellfounded_Ofinite__psubset(X10)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X154),X160))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__finite__psubset) ).
fof(fact_Domain__iff,axiom,
! [X177,X13,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X39),hAPP(c_Relation_ODomain(X10,X13),X177)))
<=> ? [X90] : hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X39),X90)),X177)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__iff) ).
fof(fact_Un__Pow__subset,axiom,
! [X160,X154,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X10),X154)),hAPP(c_Set_OPow(X10),X160))),hAPP(c_Set_OPow(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Pow__subset) ).
fof(fact_nat__diff__add__eq1,axiom,
! [X42,X97,X80,X120,X119] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X119),X120))
=> 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),X120),X80)),X97)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X119),X80)),X42)) = 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),X120),X119)),X80)),X97)),X42) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__add__eq1) ).
fof(fact_pick__member,axiom,
! [X290,X10,X113] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X113),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X10),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X10)),X290))))
=> hBOOL(hAPP(hAPP(c_member(X10),hAPP(c_Random_Opick(X10,X290),X113)),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X10),X10),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X10)),X290)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pick__member) ).
fof(fact_rel__compI,axiom,
! [X54,X18,X125,X177,X38,X39,X13,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X39),X38)),X177))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X13,X125)),hAPP(hAPP(c_Product__Type_OPair(X13,X125),X38),X18)),X54))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X125)),hAPP(hAPP(c_Product__Type_OPair(X10,X125),X39),X18)),hAPP(hAPP(c_Relation_Orel__comp(X10,X13,X125),X177),X54))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__compI) ).
fof(fact_sorted__insort__insert__key,axiom,
! [X16,X290,X2,X13,X10] :
( class_Orderings_Olinorder(X10)
=> ( c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Omap(X13,X10),X2),X290))
=> c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Omap(X13,X10),X2),c_List_Olinorder__class_Oinsort__insert__key(X13,X10,X2,X16,X290))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__insort__insert__key) ).
fof(fact_bex__Un,axiom,
! [X19,X160,X154,X10] :
( ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)))
& hBOOL(hAPP(X19,X3)) )
<=> ( ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
& hBOOL(hAPP(X19,X3)) )
| ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X160))
& hBOOL(hAPP(X19,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bex__Un) ).
fof(fact_ball__Un,axiom,
! [X19,X160,X154,X10] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)))
=> hBOOL(hAPP(X19,X3)) )
<=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> hBOOL(hAPP(X19,X3)) )
& ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X160))
=> hBOOL(hAPP(X19,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ball__Un) ).
fof(fact_INF2__D,axiom,
! [X39,X18,X38,X160,X154,X125,X13,X10] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_fun(X125,tc_HOL_Obool))),X154),X160),X38),X18))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hBOOL(hAPP(hAPP(hAPP(X160,X39),X38),X18)) ) ),
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,
! [X25,X16,X1,X2,X10,X13,X125] : hAPP(c_Fun_Ocomp(X125,X13,X10,X2),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,X125),X1),X16),X25)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,X13),hAPP(c_Fun_Ocomp(X125,X13,X10,X2),X1)),X16),hAPP(X2,X25)),
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,
! [X160,X2,X13,X10] : hAPP(c_Set_Ovimage(X10,X13,X2),X160) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBC(X10,tc_fun(X13,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(X13,tc_fun(tc_fun(X13,tc_HOL_Obool),tc_HOL_Obool),X10),c_member(X13)),X2)),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__def) ).
fof(fact_zip__append2,axiom,
! [X296,X298,X297,X10,X94] : hAPP(hAPP(c_List_Ozip(X94,X10),X297),hAPP(hAPP(c_List_Oappend(X10),X298),X296)) = hAPP(hAPP(c_List_Oappend(tc_prod(X94,X10)),hAPP(hAPP(c_List_Ozip(X94,X10),hAPP(hAPP(c_List_Otake(X94),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X298)),X297)),X298)),hAPP(hAPP(c_List_Ozip(X94,X10),hAPP(hAPP(c_List_Odrop(X94),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X298)),X297)),X296)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__append2) ).
fof(fact_in__listrel1__converse,axiom,
! [X177,X25,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X16),X25)),c_List_Olistrel1(X10,hAPP(c_Relation_Oconverse(X10,X10),X177))))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X16),X25)),hAPP(c_Relation_Oconverse(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olistrel1(X10,X177)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__listrel1__converse) ).
fof(fact_map__filter__simps_I1_J,axiom,
! [X290,X16,X2,X10,X13] : c_List_Omap__filter(X13,X10,X2,hAPP(hAPP(c_List_Olist_OCons(X13),X16),X290)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(X10),X10,c_List_Omap__filter(X13,X10,X2,X290),hAPP(hAPP(c_COMBC(X10,tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_OCons(X10)),c_List_Omap__filter(X13,X10,X2,X290))),hAPP(X2,X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__filter__simps_I1_J) ).
fof(fact_Cons__eq__append__conv,axiom,
! [X299,X289,X290,X16,X10] :
( hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290) = hAPP(hAPP(c_List_Oappend(X10),X289),X299)
<=> ( ( X289 = c_List_Olist_ONil(X10)
& hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290) = X299 )
| ? [X314] :
( hAPP(hAPP(c_List_Olist_OCons(X10),X16),X314) = X289
& X290 = hAPP(hAPP(c_List_Oappend(X10),X314),X299) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__eq__append__conv) ).
fof(fact_append__eq__Cons__conv,axiom,
! [X290,X16,X299,X289,X10] :
( hAPP(hAPP(c_List_Oappend(X10),X289),X299) = hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290)
<=> ( ( X289 = c_List_Olist_ONil(X10)
& X299 = hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290) )
| ? [X314] :
( X289 = hAPP(hAPP(c_List_Olist_OCons(X10),X16),X314)
& hAPP(hAPP(c_List_Oappend(X10),X314),X299) = X290 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__eq__Cons__conv) ).
fof(fact_min__max_OInf__fin_Oclosed,axiom,
! [X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( ! [X3,X90] : hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X3),X90)),hAPP(hAPP(c_Set_Oinsert(X10),X3),hAPP(hAPP(c_Set_Oinsert(X10),X90),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(X10),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X154)),X154)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oclosed) ).
fof(fact_min__max_OSup__fin_Oclosed,axiom,
! [X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( ! [X3,X90] : hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X3),X90)),hAPP(hAPP(c_Set_Oinsert(X10),X3),hAPP(hAPP(c_Set_Oinsert(X10),X90),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(X10),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X154)),X154)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oclosed) ).
fof(fact_triple__valid__def2,axiom,
! [X17,X18,X19,X20,X10] :
( c_Hoare__Mirabelle_Otriple__valid(X10,X20,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X10),X19),X18),X17))
<=> ! [X21,X22] :
( hBOOL(hAPP(hAPP(X19,X21),X22))
=> ! [X23] :
( c_Natural_Oevaln(X18,X22,X20,X23)
=> hBOOL(hAPP(hAPP(X17,X21),X23)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triple__valid__def2) ).
fof(fact_map__of__map__restrict,axiom,
! [X294,X2,X13,X10] : c_Map_Omap__of(X10,X13,hAPP(hAPP(c_List_Omap(X10,tc_prod(X10,X13)),hAPP(hAPP(c_COMBS(X10,X13,tc_prod(X10,X13)),c_Product__Type_OPair(X10,X13)),X2)),X294)) = c_Map_Orestrict__map(X10,X13,hAPP(c_Fun_Ocomp(X13,tc_Option_Ooption(X13),X10,c_Option_Ooption_OSome(X13)),X2),hAPP(c_List_Oset(X10),X294)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__map__restrict) ).
fof(fact_card__SigmaI,axiom,
! [X160,X13,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X13),hAPP(X160,X3))) )
=> hAPP(c_Finite__Set_Ocard(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X154),X160)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_Nat_Onat,X10),c_Finite__Set_Ocard(X13)),X160)),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__SigmaI) ).
fof(fact_fold__graph_Oequations_I1_J,axiom,
! [X73,X2,X13,X10] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X13,X2,X73,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),X73)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_Oequations_I1_J) ).
fof(fact_fold__graph_OemptyI,axiom,
! [X73,X2,X13,X10] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X13,X2,X73,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),X73)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_OemptyI) ).
fof(fact_wf__union__compatible,axiom,
! [X216,X196,X10] :
( c_Wellfounded_Owf(X10,X196)
=> ( c_Wellfounded_Owf(X10,X216)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X196),X216)),X196))
=> c_Wellfounded_Owf(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X196),X216)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__union__compatible) ).
fof(fact_fold1__in,axiom,
! [X154,X10] :
( class_Groups_Oab__semigroup__mult(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( ! [X3,X90] : hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X3),X90)),hAPP(hAPP(c_Set_Oinsert(X10),X3),hAPP(hAPP(c_Set_Oinsert(X10),X90),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(X10),hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),X154)),X154)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__in) ).
fof(fact_unique__quotient__lemma,axiom,
! [X143,X149,X150,X151,X92] :
( 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),X92),X151)),X150)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X92),X149)),X143)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X150))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X150),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X143),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X151),X149)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).
fof(fact_unique__quotient__lemma__neg,axiom,
! [X143,X149,X150,X151,X92] :
( 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),X92),X151)),X150)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X92),X149)),X143)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X143),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X92),X143))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X92),X150))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X149),X151)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).
fof(fact_distinct__insort__insert,axiom,
! [X16,X2,X290,X10,X13] :
( class_Orderings_Olinorder(X13)
=> ( hBOOL(hAPP(c_List_Odistinct(X10),X290))
=> hBOOL(hAPP(c_List_Odistinct(X10),c_List_Olinorder__class_Oinsort__insert__key(X10,X13,X2,X16,X290))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__insort__insert) ).
fof(fact_nth__transpose,axiom,
! [X290,X10,X113] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X113),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),c_List_Otranspose(X10,X290))))
=> hAPP(hAPP(c_List_Onth(tc_List_Olist(X10)),c_List_Otranspose(X10,X290)),X113) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),X10),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_Nat_Onat,X10),c_List_Onth(X10)),X113)),hAPP(c_List_Ofilter(tc_List_Olist(X10),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X10)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X113)),c_Nat_Osize__class_Osize(tc_List_Olist(X10)))),X290)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__transpose) ).
fof(fact_Powp__Pow__eq,axiom,
! [X16,X154,X10] :
( hBOOL(hAPP(c_Predicate_OPowp(X10,hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X154)),X16))
<=> hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X16),hAPP(c_Set_OPow(X10),X154))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Powp__Pow__eq) ).
fof(fact_card__bij__eq,axiom,
! [X1,X160,X154,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,X154)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X13,X2),X154)),X160))
=> ( c_Fun_Oinj__on(X13,X10,X1,X160)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X13,X10,X1),X160)),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X160))
=> hAPP(c_Finite__Set_Ocard(X10),X154) = hAPP(c_Finite__Set_Ocard(X13),X160) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__bij__eq) ).
fof(fact_Eps__split,axiom,
! [X19,X13,X10] : c_Hilbert__Choice_OEps(tc_prod(X10,X13),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,tc_HOL_Obool),X19)) = c_Hilbert__Choice_OEps(tc_prod(X10,X13),hAPP(hAPP(c_COMBS(tc_prod(X10,X13),X13,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X10,tc_fun(X13,tc_HOL_Obool),tc_prod(X10,X13)),X19),c_Product__Type_Ofst(X10,X13))),c_Product__Type_Osnd(X10,X13))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Eps__split) ).
fof(fact_The__split,axiom,
! [X19,X13,X10] : c_HOL_OThe(tc_prod(X10,X13),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,tc_HOL_Obool),X19)) = c_HOL_OThe(tc_prod(X10,X13),hAPP(hAPP(c_COMBS(tc_prod(X10,X13),X13,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X10,tc_fun(X13,tc_HOL_Obool),tc_prod(X10,X13)),X19),c_Product__Type_Ofst(X10,X13))),c_Product__Type_Osnd(X10,X13))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_The__split) ).
fof(fact_inf__period_I3_J,axiom,
! [X53,X197,X141,X10] :
( ( class_Rings_Ocomm__ring(X10)
& class_Rings_Odvd(X10) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X141),X197))
=> ! [X3,X124] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X141),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X3),X53)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X141),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X124),X197))),X53))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__period_I3_J) ).
fof(fact_inf__period_I4_J,axiom,
! [X53,X197,X141,X10] :
( ( class_Rings_Ocomm__ring(X10)
& class_Rings_Odvd(X10) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X141),X197))
=> ! [X3,X124] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X141),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X3),X53)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X141),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X124),X197))),X53))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__period_I4_J) ).
fof(fact_div__mod__equality,axiom,
! [X81,X92,X84,X94] :
( class_Divides_Osemiring__div(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),X84),X92)),X92)),c_Divides_Odiv__class_Omod(X94,X84,X92))),X81) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X81) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mod__equality) ).
fof(fact_fold__Un__disjoint,axiom,
! [X1,X160,X154,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13,X10,c_Groups_Otimes__class_Otimes(X13)),X1),c_Groups_Oone__class_Oone(X13)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13,X10,c_Groups_Otimes__class_Otimes(X13)),X1),c_Groups_Oone__class_Oone(X13)),X154)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13,X10,c_Groups_Otimes__class_Otimes(X13)),X1),c_Groups_Oone__class_Oone(X13)),X160)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__Un__disjoint) ).
fof(fact_uminus__listsum__map,axiom,
! [X290,X2,X13,X10] :
( class_Groups_Oab__group__add(X10)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X10),hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(X13,X10),X2),X290))) = hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(X13,X10),hAPP(c_Fun_Ocomp(X10,X10,X13,c_Groups_Ouminus__class_Ouminus(X10)),X2)),X290)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_uminus__listsum__map) ).
fof(fact_neg__map__def,axiom,
! [X19,X2,X10,X13] : c_New__Random__Sequence_Oneg__map(X13,X10,X2,X19) = c_New__Random__Sequence_Oneg__bind(X13,X10,X19,hAPP(c_Fun_Ocomp(X10,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(X10)))))),X13,c_New__Random__Sequence_Oneg__single(X10)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__map__def) ).
fof(fact_setsum__abs__ge__zero,axiom,
! [X154,X2,X13,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X10),hAPP(hAPP(c_COMBB(X10,X10,X13),c_Groups_Oabs__class_Oabs(X10)),X2)),X154))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__abs__ge__zero) ).
fof(fact_finite__Collect__subsets,axiom,
! [X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool))),X154)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__subsets) ).
fof(fact_sum__squares__le__zero__iff,axiom,
! [X25,X16,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X16),X16)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X25),X25))),c_Groups_Ozero__class_Ozero(X10)))
<=> ( X16 = c_Groups_Ozero__class_Ozero(X10)
& X25 = c_Groups_Ozero__class_Ozero(X10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).
fof(fact_Min_Oclosed,axiom,
! [X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( ! [X3,X90] : hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X3),X90)),hAPP(hAPP(c_Set_Oinsert(X10),X3),hAPP(hAPP(c_Set_Oinsert(X10),X90),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(X10),c_Big__Operators_Olinorder__class_OMin(X10,X154)),X154)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oclosed) ).
fof(fact_Max_Oclosed,axiom,
! [X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( ! [X3,X90] : hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X3),X90)),hAPP(hAPP(c_Set_Oinsert(X10),X3),hAPP(hAPP(c_Set_Oinsert(X10),X90),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(X10),c_Big__Operators_Olinorder__class_OMax(X10,X154)),X154)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oclosed) ).
fof(fact_Inf__fin_Oclosed,axiom,
! [X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( ! [X3,X90] : hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X3),X90)),hAPP(hAPP(c_Set_Oinsert(X10),X3),hAPP(hAPP(c_Set_Oinsert(X10),X90),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(X10),c_Big__Operators_Olattice__class_OInf__fin(X10,X154)),X154)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oclosed) ).
fof(fact_Sup__fin_Oclosed,axiom,
! [X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( ! [X3,X90] : hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X3),X90)),hAPP(hAPP(c_Set_Oinsert(X10),X3),hAPP(hAPP(c_Set_Oinsert(X10),X90),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(X10),c_Big__Operators_Olattice__class_OSup__fin(X10,X154)),X154)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oclosed) ).
fof(fact_folding__image_Oreindex,axiom,
! [X1,X204,X154,X225,X73,X2,X13,X10] :
( c_Finite__Set_Ofolding__image(X10,X13,X2,X73,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X154))
=> ( c_Fun_Oinj__on(X13,X13,X204,X154)
=> hAPP(hAPP(X225,X1),hAPP(c_Set_Oimage(X13,X13,X204),X154)) = hAPP(hAPP(X225,hAPP(c_Fun_Ocomp(X13,X10,X13,X1),X204)),X154) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image_Oreindex) ).
fof(fact_transpose__column__length,axiom,
! [X113,X290,X10] :
( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X10))),X290)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X113),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),X290)))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),hAPP(c_List_Ofilter(tc_List_Olist(X10),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X10)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X113)),c_Nat_Osize__class_Osize(tc_List_Olist(X10)))),c_List_Otranspose(X10,X290))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X10)),X290),X113)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__column__length) ).
fof(fact_pair__imageI,axiom,
! [X2,X125,X154,X38,X39,X13,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X39),X38)),X154))
=> hBOOL(hAPP(hAPP(c_member(X125),hAPP(hAPP(X2,X39),X38)),hAPP(c_Set_Oimage(tc_prod(X10,X13),X125,hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,X125),X2)),X154))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__imageI) ).
fof(fact_weak__map__of__SomeI,axiom,
! [X162,X16,X101,X13,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X101),X16)),hAPP(c_List_Oset(tc_prod(X10,X13)),X162)))
=> ? [X3] : hAPP(c_Map_Omap__of(X10,X13,X162),X101) = hAPP(c_Option_Ooption_OSome(X13),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_weak__map__of__SomeI) ).
fof(fact_length__filter__map,axiom,
! [X290,X2,X13,X19,X10] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),hAPP(c_List_Ofilter(X10,X19),hAPP(hAPP(c_List_Omap(X13,X10),X2),X290))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13)),hAPP(c_List_Ofilter(X13,hAPP(c_Fun_Ocomp(X10,tc_HOL_Obool,X13,X19),X2)),X290)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__filter__map) ).
fof(fact_trancl__subset__Sigma__aux,axiom,
! [X154,X177,X38,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),c_Transitive__Closure_Ortrancl(X10,X177)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X177),hAPP(hAPP(c_Product__Type_OSigma(X10,X10),X154),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X10),X154))))
=> ( X39 = X38
| hBOOL(hAPP(hAPP(c_member(X10),X39),X154)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__subset__Sigma__aux) ).
fof(fact_sum__length__filter__compl,axiom,
! [X290,X19,X10] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),hAPP(c_List_Ofilter(X10,X19),X290))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),hAPP(c_List_Ofilter(X10,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10),c_fNot),X19)),X290))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__length__filter__compl) ).
fof(fact_rtrancl__trans,axiom,
! [X18,X177,X38,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),c_Transitive__Closure_Ortrancl(X10,X177)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X38),X18)),c_Transitive__Closure_Ortrancl(X10,X177)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X18)),c_Transitive__Closure_Ortrancl(X10,X177))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__trans) ).
fof(fact_zdiv__zadd1__eq,axiom,
! [X81,X92,X84] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X84),X92)),X81) = 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),X84),X81)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X92),X81))),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,X84,X81)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X92,X81))),X81)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zadd1__eq) ).
fof(fact_div__add1__eq,axiom,
! [X81,X92,X84] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X84),X92)),X81) = 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),X84),X81)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X92),X81))),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,X84,X81)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X92,X81))),X81)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__add1__eq) ).
fof(fact_inf2D1,axiom,
! [X25,X16,X160,X154,X13,X10] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_fun(X13,tc_HOL_Obool))),X154),X160),X16),X25))
=> hBOOL(hAPP(hAPP(X154,X16),X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2D1) ).
fof(fact_inf2D2,axiom,
! [X25,X16,X160,X154,X13,X10] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_fun(X13,tc_HOL_Obool))),X154),X160),X16),X25))
=> hBOOL(hAPP(hAPP(X160,X16),X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2D2) ).
fof(fact_converse__rtrancl__into__rtrancl,axiom,
! [X18,X177,X38,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),X177))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X38),X18)),c_Transitive__Closure_Ortrancl(X10,X177)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X18)),c_Transitive__Closure_Ortrancl(X10,X177))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).
fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
! [X18,X177,X38,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),c_Transitive__Closure_Ortrancl(X10,X177)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X38),X18)),X177))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X18)),c_Transitive__Closure_Ortrancl(X10,X177))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__into__rtrancl) ).
fof(fact_rtrancl__listrel1__if__listrel,axiom,
! [X177,X289,X290,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X290),X289)),c_List_Olistrel(X10,X177)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X290),X289)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X10),c_List_Olistrel1(X10,X177)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__listrel1__if__listrel) ).
fof(fact_folding_Ocommute__comps_I1_J,axiom,
! [X204,X1,X205,X2,X125,X195,X194,X225,X11,X13,X10] :
( c_Finite__Set_Ofolding(X10,X13,X11,X225)
=> hAPP(c_Fun_Ocomp(X194,X195,X125,X2),hAPP(c_Fun_Ocomp(X205,X194,X125,X1),X204)) = hAPP(c_Fun_Ocomp(X205,X195,X125,hAPP(c_Fun_Ocomp(X194,X195,X205,X2),X1)),X204) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__comps_I1_J) ).
fof(fact_zdiv__mono2__neg__lemma,axiom,
! [X150,X151,X130,X143,X149,X92] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X92),X149)),X143) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X130),X151)),X150)
=> ( 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),X130),X151)),X150)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X143),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X150))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X130))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X130),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X151),X149)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
! [X19] : 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)))),X19)) = 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),X19),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,
! [X177,X289,X290,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X290),X289)),c_List_Olistrel1(X10,X177)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X290),X289)),c_List_Olistrel(X10,c_Transitive__Closure_Ortrancl(X10,X177)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__reflcl__if__listrel1) ).
fof(fact_lexord__lex,axiom,
! [X177,X25,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X16),X25)),c_List_Olex(X10,X177)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X16),X25)),c_List_Olexord(X10,X177)))
& hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X16) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__lex) ).
fof(fact_filter__map,axiom,
! [X290,X2,X13,X19,X10] : hAPP(c_List_Ofilter(X10,X19),hAPP(hAPP(c_List_Omap(X13,X10),X2),X290)) = hAPP(hAPP(c_List_Omap(X13,X10),X2),hAPP(c_List_Ofilter(X13,hAPP(c_Fun_Ocomp(X10,tc_HOL_Obool,X13,X19),X2)),X290)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__map) ).
fof(fact_wfP__SUP,axiom,
! [X10,X177,X13] :
( ! [X152] : c_Wellfounded_OwfP(X13,hAPP(X177,X152))
=> ( ! [X152,X123] :
( hAPP(X177,X152) != hAPP(X177,X123)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13,tc_HOL_Obool)),c_Predicate_ODomainP(X13,X13,hAPP(X177,X152))),c_Predicate_ORangeP(X13,X13,hAPP(X177,X123))) = c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool)) )
=> c_Wellfounded_OwfP(X13,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_fun(X13,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),X177)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__SUP) ).
fof(fact_partition__filter__conv,axiom,
! [X290,X2,X10] : c_List_Opartition(X10,X2,X290) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(c_List_Ofilter(X10,X2),X290)),hAPP(c_List_Ofilter(X10,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X10,c_fNot),X2)),X290)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition__filter__conv) ).
fof(fact_upto_Opinduct,axiom,
! [X19,X51,X192] :
( 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),X192),X51)))
=> ( ! [X152,X123] :
( 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),X152),X123)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X152),X123))
=> hBOOL(hAPP(hAPP(X19,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X152),c_Groups_Oone__class_Oone(tc_Int_Oint))),X123)) )
=> hBOOL(hAPP(hAPP(X19,X152),X123)) ) )
=> hBOOL(hAPP(hAPP(X19,X192),X51)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upto_Opinduct) ).
fof(fact_map__add__upds,axiom,
! [X289,X290,X277,X278,X13,X10] : c_Map_Omap__add(X10,X13,X278,c_Map_Omap__upds(X10,X13,X277,X290,X289)) = c_Map_Omap__upds(X10,X13,c_Map_Omap__add(X10,X13,X278,X277),X290,X289),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__upds) ).
fof(fact_Ints__odd__less__0,axiom,
! [X39,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),c_Int_Oring__1__class_OInts(X10)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),c_Groups_Oone__class_Oone(X10)),X39)),X39)),c_Groups_Ozero__class_Ozero(X10)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),c_Groups_Ozero__class_Ozero(X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__odd__less__0) ).
fof(fact_zdiv__zmod__equality2,axiom,
! [X103,X92,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),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),X92)),X92)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X92))),X103) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X84),X103),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zmod__equality2) ).
fof(fact_zdvd__period,axiom,
! [X18,X53,X16,X141,X39] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X39),X141))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X39),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16),X53)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X39),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18),X141))),X53))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__period) ).
fof(fact_dom__map__upds,axiom,
! [X289,X290,X102,X13,X10] : c_Map_Odom(X10,X13,c_Map_Omap__upds(X10,X13,X102,X290,X289)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Otake(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13)),X289)),X290))),c_Map_Odom(X10,X13,X102)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__map__upds) ).
fof(fact_INFI__set__fold,axiom,
! [X2,X290,X13,X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,X10),hAPP(c_List_Oset(X13),X290)),X2) = hAPP(c_List_Ofoldl(X10,X13,hAPP(c_COMBC(X13,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X13),c_Lattices_Osemilattice__inf__class_Oinf(X10)),X2)),c_Orderings_Otop__class_Otop(X10)),X290) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INFI__set__fold) ).
fof(fact_SUPR__set__fold,axiom,
! [X2,X290,X13,X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,X10),hAPP(c_List_Oset(X13),X290)),X2) = hAPP(c_List_Ofoldl(X10,X13,hAPP(c_COMBC(X13,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X13),c_Lattices_Osemilattice__sup__class_Osup(X10)),X2)),c_Orderings_Obot__class_Obot(X10)),X290) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUPR__set__fold) ).
fof(fact_finite__UN__I,axiom,
! [X160,X13,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ! [X116] :
( hBOOL(hAPP(hAPP(c_member(X10),X116),X154))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X13),hAPP(X160,X116))) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X13),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X154),X160))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UN__I) ).
fof(fact_finite__UN,axiom,
! [X160,X13,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X154),X160)))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X13),hAPP(X160,X3))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UN) ).
fof(fact_rel__comp__UNION__distrib,axiom,
! [X177,X241,X195,X54,X13,X125,X10] : hAPP(hAPP(c_Relation_Orel__comp(X10,X125,X13),X54),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X195,tc_fun(tc_prod(X125,X13),tc_HOL_Obool)),X241),X177)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X195,tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),X241),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X125,X13),tc_HOL_Obool),tc_fun(tc_prod(X10,X13),tc_HOL_Obool),X195),hAPP(c_Relation_Orel__comp(X10,X125,X13),X54)),X177)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__UNION__distrib) ).
fof(fact_o__assoc,axiom,
! [X204,X1,X195,X2,X10,X13,X125] : hAPP(c_Fun_Ocomp(X125,X13,X10,X2),hAPP(c_Fun_Ocomp(X195,X125,X10,X1),X204)) = hAPP(c_Fun_Ocomp(X195,X13,X10,hAPP(c_Fun_Ocomp(X125,X13,X195,X2),X1)),X204),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__assoc) ).
fof(fact_surj__Compl__image__subset,axiom,
! [X154,X2,X10,X13] :
( hAPP(c_Set_Oimage(X13,X10,X2),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X13,X10,X2),X154))),hAPP(c_Set_Oimage(X13,X10,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X13,tc_HOL_Obool)),X154)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__Compl__image__subset) ).
fof(fact_in__inv__image,axiom,
! [X2,X177,X13,X25,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),hAPP(hAPP(c_Relation_Oinv__image(X13,X10),X177),X2)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X13,X13)),hAPP(hAPP(c_Product__Type_OPair(X13,X13),hAPP(X2,X16)),hAPP(X2,X25))),X177)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__inv__image) ).
fof(fact_folding_Oremove,axiom,
! [X16,X154,X225,X2,X13,X10] :
( c_Finite__Set_Ofolding(X10,X13,X2,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(X225,X154) = hAPP(c_Fun_Ocomp(X13,X13,X13,hAPP(X225,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))),hAPP(X2,X16)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Oremove) ).
fof(fact_Image__subset,axiom,
! [X198,X160,X154,X177,X13,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),X177),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X154),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),X160))))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool)),hAPP(c_Relation_OImage(X10,X13,X177),X198)),X160)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__subset) ).
fof(fact_tl__append,axiom,
! [X289,X290,X10] : hAPP(c_List_Otl(X10),hAPP(hAPP(c_List_Oappend(X10),X290),X289)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(X10),X10,hAPP(c_List_Otl(X10),X289),hAPP(c_COMBK(tc_fun(tc_List_Olist(X10),tc_List_Olist(X10)),X10),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Oappend(X10)),X289))),X290),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl__append) ).
fof(fact_pos__map__def,axiom,
! [X19,X2,X10,X13] : c_New__Random__Sequence_Opos__map(X13,X10,X2,X19) = c_New__Random__Sequence_Opos__bind(X13,X10,X19,hAPP(c_Fun_Ocomp(X10,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(X10))))),X13,c_New__Random__Sequence_Opos__single(X10)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__map__def) ).
fof(fact_inj__image__Compl__subset,axiom,
! [X154,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X13,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X154))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X13,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X13,X2),X154)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__Compl__subset) ).
fof(fact_folding_Oinsert__remove,axiom,
! [X16,X154,X225,X2,X13,X10] :
( c_Finite__Set_Ofolding(X10,X13,X2,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(X225,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(c_Fun_Ocomp(X13,X13,X13,hAPP(X225,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))),hAPP(X2,X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Oinsert__remove) ).
fof(fact_folding_Ocommute__left__comp_H_H,axiom,
! [X1,X125,X160,X154,X225,X2,X13,X10] :
( c_Finite__Set_Ofolding(X10,X13,X2,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> hAPP(c_Fun_Ocomp(X13,X13,X125,hAPP(X225,X160)),hAPP(c_Fun_Ocomp(X13,X13,X125,hAPP(X225,X154)),X1)) = hAPP(c_Fun_Ocomp(X13,X13,X125,hAPP(X225,X154)),hAPP(c_Fun_Ocomp(X13,X13,X125,hAPP(X225,X160)),X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__left__comp_H_H) ).
fof(fact_map__of__is__SomeI,axiom,
! [X25,X16,X285,X13,X10] :
( hBOOL(hAPP(c_List_Odistinct(X10),hAPP(hAPP(c_List_Omap(tc_prod(X10,X13),X10),c_Product__Type_Ofst(X10,X13)),X285)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X16),X25)),hAPP(c_List_Oset(tc_prod(X10,X13)),X285)))
=> hAPP(c_Map_Omap__of(X10,X13,X285),X16) = hAPP(c_Option_Ooption_OSome(X13),X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__is__SomeI) ).
fof(fact_map__of__eq__Some__iff,axiom,
! [X25,X16,X285,X13,X10] :
( hBOOL(hAPP(c_List_Odistinct(X10),hAPP(hAPP(c_List_Omap(tc_prod(X10,X13),X10),c_Product__Type_Ofst(X10,X13)),X285)))
=> ( hAPP(c_Map_Omap__of(X10,X13,X285),X16) = hAPP(c_Option_Ooption_OSome(X13),X25)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X16),X25)),hAPP(c_List_Oset(tc_prod(X10,X13)),X285))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__eq__Some__iff) ).
fof(fact_Some__eq__map__of__iff,axiom,
! [X16,X25,X285,X13,X10] :
( hBOOL(hAPP(c_List_Odistinct(X10),hAPP(hAPP(c_List_Omap(tc_prod(X10,X13),X10),c_Product__Type_Ofst(X10,X13)),X285)))
=> ( hAPP(c_Option_Ooption_OSome(X13),X25) = hAPP(c_Map_Omap__of(X10,X13,X285),X16)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X16),X25)),hAPP(c_List_Oset(tc_prod(X10,X13)),X285))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Some__eq__map__of__iff) ).
fof(fact_finite__SigmaI,axiom,
! [X160,X13,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ! [X116] :
( hBOOL(hAPP(hAPP(c_member(X10),X116),X154))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X13),hAPP(X160,X116))) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X154),X160))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__SigmaI) ).
fof(fact_convex__bound__le,axiom,
! [X144,X80,X105,X84,X93,X94] :
( class_Rings_Olinordered__semiring__1(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X105),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X80))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X144))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X80),X144) = c_Groups_Oone__class_Oone(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X80),X93)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X144),X105))),X84)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_convex__bound__le) ).
fof(fact_convex__bound__lt,axiom,
! [X144,X80,X105,X84,X93,X94] :
( class_Rings_Olinordered__semiring__1__strict(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X105),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X80))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X144))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X80),X144) = c_Groups_Oone__class_Oone(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X80),X93)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X144),X105))),X84)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_convex__bound__lt) ).
fof(fact_aset_I6_J,axiom,
! [X154,X53,X197] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X197))
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X53),c_Groups_Oone__class_Oone(tc_Int_Oint))),X154))
=> ! [X3] :
( ! [X227] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X227),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X197)))
=> ! [X249] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X249),X154))
=> X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X249),X227) ) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),X53))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X197)),X53)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I6_J) ).
fof(fact_folding_Ocommute__left__comp_H,axiom,
! [X1,X16,X125,X154,X225,X2,X13,X10] :
( c_Finite__Set_Ofolding(X10,X13,X2,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(c_Fun_Ocomp(X13,X13,X125,hAPP(X2,X16)),hAPP(c_Fun_Ocomp(X13,X13,X125,hAPP(X225,X154)),X1)) = hAPP(c_Fun_Ocomp(X13,X13,X125,hAPP(X225,X154)),hAPP(c_Fun_Ocomp(X13,X13,X125,hAPP(X2,X16)),X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__left__comp_H) ).
fof(fact_listrel1I,axiom,
! [X289,X320,X321,X290,X177,X25,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),X177))
=> ( X290 = hAPP(hAPP(c_List_Oappend(X10),X321),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X320))
=> ( X289 = hAPP(hAPP(c_List_Oappend(X10),X321),hAPP(hAPP(c_List_Olist_OCons(X10),X25),X320))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X290),X289)),c_List_Olistrel1(X10,X177))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1I) ).
fof(fact_sum__case__inject,axiom,
! [X206,X207,X37,X12,X13,X125,X10] :
( c_Sum__Type_Osum_Osum__case(X10,X125,X13,X12,X37) = c_Sum__Type_Osum_Osum__case(X10,X125,X13,X207,X206)
=> ~ ( X12 = X207
=> X37 != X206 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__case__inject) ).
fof(fact_inf__le__fold__inf,axiom,
! [X18,X38,X154,X10] :
( class_Lattices_Osemilattice__inf(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X38),X3)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X38),X18)),hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__inf__class_Oinf(X10)),X18),X154))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__le__fold__inf) ).
fof(fact_min__max_Oinf__le__fold__inf,axiom,
! [X18,X38,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X38),X3)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X38),X18)),hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omin(X10)),X18),X154))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__le__fold__inf) ).
fof(fact_setsum__shift__bounds__nat__ivl,axiom,
! [X20,X101,X102,X2,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X101)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X101))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,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)),X101))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X102),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__bounds__nat__ivl) ).
fof(fact_in__rtrancl__UnI,axiom,
! [X216,X196,X16,X10] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X16),c_Transitive__Closure_Ortrancl(X10,X196)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X16),c_Transitive__Closure_Ortrancl(X10,X216))) )
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X16),c_Transitive__Closure_Ortrancl(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X196),X216)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__rtrancl__UnI) ).
fof(fact_folding_Ocommute__left__comp,axiom,
! [X1,X16,X25,X125,X225,X2,X13,X10] :
( c_Finite__Set_Ofolding(X10,X13,X2,X225)
=> hAPP(c_Fun_Ocomp(X13,X13,X125,hAPP(X2,X25)),hAPP(c_Fun_Ocomp(X13,X13,X125,hAPP(X2,X16)),X1)) = hAPP(c_Fun_Ocomp(X13,X13,X125,hAPP(X2,X16)),hAPP(c_Fun_Ocomp(X13,X13,X125,hAPP(X2,X25)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__left__comp) ).
fof(fact_range__ex1__eq,axiom,
! [X38,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_member(X13),X38),hAPP(c_Set_Oimage(X10,X13,X2),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))))
<=> ? [X3] :
( X38 = hAPP(X2,X3)
& ! [X90] :
( X38 = hAPP(X2,X90)
=> X90 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__ex1__eq) ).
fof(fact_setsum__Un,axiom,
! [X2,X160,X154,X10,X13] :
( class_Groups_Oab__group__add(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),X154)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),X160))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Un) ).
fof(fact_rev__update,axiom,
! [X105,X297,X94,X103] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X103),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)))
=> hAPP(c_List_Orev(X94),hAPP(hAPP(c_List_Olist__update(X94,X297),X103),X105)) = hAPP(hAPP(c_List_Olist__update(X94,hAPP(c_List_Orev(X94),X297)),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(X94)),X297)),X103)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X105) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__update) ).
fof(fact_equiv__imp__dvd__card,axiom,
! [X101,X177,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( c_Equiv__Relations_Oequiv(X10,X154,X177)
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X154),X177)))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X101),hAPP(c_Finite__Set_Ocard(X10),X3))) )
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X101),hAPP(c_Finite__Set_Ocard(X10),X154))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__imp__dvd__card) ).
fof(fact_Collect__imp__eq,axiom,
! [X17,X19,X10] : hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fimplies),X19)),X17)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_OCollect(X10),X19))),hAPP(c_Set_OCollect(X10),X17)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__imp__eq) ).
fof(fact_single__valued__def,axiom,
! [X177,X13,X10] :
( c_Relation_Osingle__valued(X10,X13,X177)
<=> ! [X3,X90] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X3),X90)),X177))
=> ! [X159] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X3),X159)),X177))
=> X90 = X159 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__def) ).
fof(fact_prod__size__simp,axiom,
! [X166,X1,X2,X13,X10] : c_Product__Type_Oprod_Oprod__size(X10,X13,X2,X1,X166) = 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(X10,X13),X166))),hAPP(X1,hAPP(c_Product__Type_Osnd(X10,X13),X166)))),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,
! [X20,X101,X102,X2,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X101),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X101))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,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)),X101))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X102,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__bounds__cl__nat__ivl) ).
fof(fact_bset_I8_J,axiom,
! [X160,X53,X197] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X197))
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X53),c_Groups_Oone__class_Oone(tc_Int_Oint))),X160))
=> ! [X3] :
( ! [X227] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X227),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X197)))
=> ! [X249] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X249),X160))
=> X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X249),X227) ) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X53),X3))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X53),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X197))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I8_J) ).
fof(fact_finite__equiv__class,axiom,
! [X48,X177,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X177),hAPP(hAPP(c_Product__Type_OSigma(X10,X10),X154),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X10),X154))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X48),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X154),X177)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X48)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__equiv__class) ).
fof(fact_quotient__eqI,axiom,
! [X25,X16,X78,X48,X177,X154,X10] :
( c_Equiv__Relations_Oequiv(X10,X154,X177)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X48),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X154),X177)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X78),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X154),X177)))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X48))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X25),X78))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),X177))
=> X48 = X78 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__eqI) ).
fof(fact_quotient__eq__iff,axiom,
! [X25,X16,X78,X48,X177,X154,X10] :
( c_Equiv__Relations_Oequiv(X10,X154,X177)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X48),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X154),X177)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X78),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X154),X177)))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X48))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X25),X78))
=> ( X48 = X78
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),X177)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__eq__iff) ).
fof(fact_field__le__mult__one__interval,axiom,
! [X105,X93,X94] :
( class_Fields_Olinordered__field__inverse__zero(X94)
=> ( ! [X159] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X159))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X159),c_Groups_Oone__class_Oone(X94)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X159),X93)),X105)) ) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X105)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__le__mult__one__interval) ).
fof(fact_curryD,axiom,
! [X38,X39,X2,X13,X10] :
( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X10,X13,tc_HOL_Obool,X2),X39),X38))
=> hBOOL(hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(X10,X13),X39),X38))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curryD) ).
fof(fact_curryE,axiom,
! [X38,X39,X2,X13,X10] :
( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X10,X13,tc_HOL_Obool,X2),X39),X38))
=> hBOOL(hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(X10,X13),X39),X38))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curryE) ).
fof(fact_vimage__eq__UN,axiom,
! [X160,X2,X13,X10] : hAPP(c_Set_Ovimage(X10,X13,X2),X160) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X160),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X13),c_Set_Ovimage(X10,X13,X2)),hAPP(hAPP(c_COMBC(X13,tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),c_Set_Oinsert(X13)),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__eq__UN) ).
fof(fact_Image__eq__UN,axiom,
! [X160,X177,X10,X13] : hAPP(c_Relation_OImage(X13,X10,X177),X160) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X160),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X13),c_Relation_OImage(X13,X10,X177)),hAPP(hAPP(c_COMBC(X13,tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),c_Set_Oinsert(X13)),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__eq__UN) ).
fof(fact_distrib__inf__le,axiom,
! [X104,X105,X93,X94] :
( class_Lattices_Olattice(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),X105)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),X104))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X105),X104)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distrib__inf__le) ).
fof(fact_min__max_Odistrib__inf__le,axiom,
! [X104,X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X93),X105)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X93),X104))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X93),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X105),X104)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Odistrib__inf__le) ).
fof(fact_map__of__inject__set,axiom,
! [X289,X290,X13,X10] :
( hBOOL(hAPP(c_List_Odistinct(X10),hAPP(hAPP(c_List_Omap(tc_prod(X10,X13),X10),c_Product__Type_Ofst(X10,X13)),X290)))
=> ( hBOOL(hAPP(c_List_Odistinct(X10),hAPP(hAPP(c_List_Omap(tc_prod(X10,X13),X10),c_Product__Type_Ofst(X10,X13)),X289)))
=> ( c_Map_Omap__of(X10,X13,X290) = c_Map_Omap__of(X10,X13,X289)
<=> hAPP(c_List_Oset(tc_prod(X10,X13)),X290) = hAPP(c_List_Oset(tc_prod(X10,X13)),X289) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__inject__set) ).
fof(fact_SUP2__I,axiom,
! [X125,X13,X18,X38,X160,X154,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> ( hBOOL(hAPP(hAPP(hAPP(X160,X39),X38),X18))
=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_fun(X125,tc_HOL_Obool))),X154),X160),X38),X18)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP2__I) ).
fof(fact_splitD_H,axiom,
! [X18,X38,X39,X196,X125,X13,X10] :
( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,tc_fun(X125,tc_HOL_Obool)),X196),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X39),X38)),X18))
=> hBOOL(hAPP(hAPP(hAPP(X196,X39),X38),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splitD_H) ).
fof(fact_rel__comp__distrib2,axiom,
! [X196,X232,X216,X13,X125,X10] : hAPP(hAPP(c_Relation_Orel__comp(X10,X125,X13),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X125),tc_HOL_Obool)),X216),X232)),X196) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X10,X125,X13),X216),X196)),hAPP(hAPP(c_Relation_Orel__comp(X10,X125,X13),X232),X196)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__distrib2) ).
fof(fact_inf__INFI__fold__inf,axiom,
! [X2,X160,X154,X10,X13] :
( class_Complete__Lattice_Ocomplete__lattice(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X13),X160),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,X13),X154),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X13,hAPP(hAPP(c_COMBB(X13,tc_fun(X13,X13),X10),c_Lattices_Osemilattice__inf__class_Oinf(X13)),X2)),X160),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__INFI__fold__inf) ).
fof(fact_sup__SUPR__fold__sup,axiom,
! [X2,X160,X154,X10,X13] :
( class_Complete__Lattice_Ocomplete__lattice(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X13),X160),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,X13),X154),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X13,hAPP(hAPP(c_COMBB(X13,tc_fun(X13,X13),X10),c_Lattices_Osemilattice__sup__class_Osup(X13)),X2)),X160),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__SUPR__fold__sup) ).
fof(fact_fun__upd__twist,axiom,
! [X141,X38,X102,X13,X10,X18,X39] :
( X39 != X18
=> hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,X13),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,X13),X102),X39),X38)),X18),X141) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,X13),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,X13),X102),X18),X141)),X39),X38) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__twist) ).
fof(fact_setsum__Un__nat,axiom,
! [X2,X160,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = 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(X10,tc_Nat_Onat),X2),X154)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),X160))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Un__nat) ).
fof(fact_finite__Collect__not,axiom,
! [X19,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Set_OCollect(X10),X19)))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10),c_fNot),X19))))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__not) ).
fof(fact_zmult2__lemma__aux1,axiom,
! [X149,X143,X92,X81] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X81))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X92),X143))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X143),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),X92),X81)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X92),c_Divides_Odiv__class_Omod(tc_Int_Oint,X149,X81))),X143))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma__aux1) ).
fof(fact_nat__diff__add__eq2,axiom,
! [X42,X97,X80,X119,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X120),X119))
=> 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),X120),X80)),X97)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X119),X80)),X42)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),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),X119),X120)),X80)),X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__add__eq2) ).
fof(fact_abs__setsum__abs,axiom,
! [X154,X2,X13,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> hAPP(c_Groups_Oabs__class_Oabs(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X10),hAPP(hAPP(c_COMBB(X10,X10,X13),c_Groups_Oabs__class_Oabs(X10)),X2)),X154)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X10),hAPP(hAPP(c_COMBB(X10,X10,X13),c_Groups_Oabs__class_Oabs(X10)),X2)),X154) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__setsum__abs) ).
fof(fact_map__upds__list__update2__drop,axiom,
! [X25,X102,X289,X13,X113,X290,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290)),X113))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X113),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13)),X289)))
=> c_Map_Omap__upds(X10,X13,X102,X290,hAPP(hAPP(c_List_Olist__update(X13,X289),X113),X25)) = c_Map_Omap__upds(X10,X13,X102,X290,X289) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upds__list__update2__drop) ).
fof(fact_inj__image__subset__iff,axiom,
! [X160,X154,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X13,X2),X154)),hAPP(c_Set_Oimage(X10,X13,X2),X160)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__subset__iff) ).
fof(fact_gt__half__sum,axiom,
! [X92,X84,X94] :
( class_Fields_Olinordered__field(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),c_Groups_Oone__class_Oone(X94)),c_Groups_Oone__class_Oone(X94)))),X92)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gt__half__sum) ).
fof(fact_q__neg__lemma,axiom,
! [X150,X151,X130] :
( 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),X130),X151)),X150)),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)),X150))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X130))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X151),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_q__neg__lemma) ).
fof(fact_zip__same,axiom,
! [X290,X38,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),hAPP(c_List_Oset(tc_prod(X10,X10)),hAPP(hAPP(c_List_Ozip(X10,X10),X290),X290))))
<=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),hAPP(c_List_Oset(X10),X290)))
& X39 = X38 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__same) ).
fof(fact_set__zip__leftD,axiom,
! [X289,X290,X25,X16,X13,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X16),X25)),hAPP(c_List_Oset(tc_prod(X10,X13)),hAPP(hAPP(c_List_Ozip(X10,X13),X290),X289))))
=> hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__zip__leftD) ).
fof(fact_set__zip__rightD,axiom,
! [X289,X290,X25,X16,X13,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X16),X25)),hAPP(c_List_Oset(tc_prod(X10,X13)),hAPP(hAPP(c_List_Ozip(X10,X13),X290),X289))))
=> hBOOL(hAPP(hAPP(c_member(X13),X25),hAPP(c_List_Oset(X13),X289))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__zip__rightD) ).
fof(fact_folding_Ounion__inter,axiom,
! [X160,X154,X225,X2,X13,X10] :
( c_Finite__Set_Ofolding(X10,X13,X2,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> hAPP(c_Fun_Ocomp(X13,X13,X13,hAPP(X225,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160))),hAPP(X225,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160))) = hAPP(c_Fun_Ocomp(X13,X13,X13,hAPP(X225,X154)),hAPP(X225,X160)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ounion__inter) ).
fof(fact_abs__triangle__ineq3,axiom,
! [X92,X84,X94] :
( class_Groups_Oordered__ab__group__add__abs(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),X84)),hAPP(c_Groups_Oabs__class_Oabs(X94),X92)))),hAPP(c_Groups_Oabs__class_Oabs(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X84),X92)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__triangle__ineq3) ).
fof(fact_odd__less__0,axiom,
! [X73] :
( 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)),X73)),X73)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X73),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,X154,X10,X13] :
( class_Complete__Lattice_Ocomplete__lattice(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,X13),X154),X2) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X13,hAPP(hAPP(c_COMBB(X13,tc_fun(X13,X13),X10),c_Lattices_Osemilattice__inf__class_Oinf(X13)),X2)),c_Orderings_Otop__class_Otop(X13)),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INFI__fold__inf) ).
fof(fact_SUPR__fold__sup,axiom,
! [X2,X154,X10,X13] :
( class_Complete__Lattice_Ocomplete__lattice(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,X13),X154),X2) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X13,hAPP(hAPP(c_COMBB(X13,tc_fun(X13,X13),X10),c_Lattices_Osemilattice__sup__class_Osup(X13)),X2)),c_Orderings_Obot__class_Obot(X13)),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUPR__fold__sup) ).
fof(fact_single__valuedD,axiom,
! [X73,X25,X16,X177,X13,X10] :
( c_Relation_Osingle__valued(X10,X13,X177)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X16),X25)),X177))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X16),X73)),X177))
=> X25 = X73 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valuedD) ).
fof(fact_evalc_OLocal,axiom,
! [X77,X39,X78,X85,X18] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X18),hAPP(hAPP(hAPP(c_Natural_Oupdate,X85),c_Com_Ovname_OLoc(X78)),hAPP(X39,X85))),X77))
=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(X78,X39,X18)),X85),hAPP(hAPP(hAPP(c_Natural_Oupdate,X77),c_Com_Ovname_OLoc(X78)),hAPP(hAPP(c_Natural_Ogetlocs,X85),X78)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OLocal) ).
fof(fact_Collect__disj__eq,axiom,
! [X17,X19,X10] : hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fdisj),X19)),X17)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_OCollect(X10),X19)),hAPP(c_Set_OCollect(X10),X17)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__disj__eq) ).
fof(fact_Collect__conj__eq,axiom,
! [X17,X19,X10] : hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),X19)),X17)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_OCollect(X10),X19)),hAPP(c_Set_OCollect(X10),X17)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__conj__eq) ).
fof(fact_map__of__zip__is__Some,axiom,
! [X16,X289,X13,X290,X10] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13)),X289)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
<=> ? [X90] : hAPP(c_Map_Omap__of(X10,X13,hAPP(hAPP(c_List_Ozip(X10,X13),X290),X289)),X16) = hAPP(c_Option_Ooption_OSome(X13),X90) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__zip__is__Some) ).
fof(fact_rtrancl__converseD,axiom,
! [X177,X25,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),c_Transitive__Closure_Ortrancl(X10,hAPP(c_Relation_Oconverse(X10,X10),X177))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X25),X16)),c_Transitive__Closure_Ortrancl(X10,X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__converseD) ).
fof(fact_listsum__const__mult,axiom,
! [X290,X2,X18,X13,X10] :
( class_Rings_Osemiring__0(X10)
=> hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(X13,X10),hAPP(hAPP(c_COMBB(X10,X10,X13),hAPP(c_Groups_Otimes__class_Otimes(X10),X18)),X2)),X290)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(X13,X10),X2),X290))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__const__mult) ).
fof(fact_Image__mono,axiom,
! [X154,X223,X177,X224,X13,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),X224),X177))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X223),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool)),hAPP(c_Relation_OImage(X10,X13,X224),X223)),hAPP(c_Relation_OImage(X10,X13,X177),X154))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__mono) ).
fof(fact_mlex__leq,axiom,
! [X196,X10,X25,X16,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X2,X16)),hAPP(X2,X25)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),X196))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),c_Wellfounded_Omlex__prod(X10,X2,X196))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__leq) ).
fof(fact_swap__product,axiom,
! [X160,X154,X10,X13] : hAPP(c_Set_Oimage(tc_prod(X13,X10),tc_prod(X10,X13),hAPP(c_Product__Type_Oprod_Oprod__case(X13,X10,tc_prod(X10,X13)),hAPP(c_COMBC(X10,X13,tc_prod(X10,X13)),c_Product__Type_OPair(X10,X13)))),hAPP(hAPP(c_Product__Type_OSigma(X13,X10),X154),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X13),X160))) = hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X160),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),X154)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_swap__product) ).
fof(fact_quotientI,axiom,
! [X177,X154,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_OImage(X10,X10,X177),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X154),X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotientI) ).
fof(fact_evaln_OCall,axiom,
! [X48,X77,X20,X39,X85,X49] :
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X49),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X85),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X39,X85)),X20,X77)
=> c_Natural_Oevaln(c_Com_Ocom_OCall(X48,X49,X39),X85,X20,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X77),hAPP(c_Natural_Ogetlocs,X85))),X48),hAPP(hAPP(c_Natural_Ogetlocs,X77),c_Com_ORes))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OCall) ).
fof(fact_Image__singleton__iff,axiom,
! [X39,X177,X13,X38,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X38),hAPP(c_Relation_OImage(X13,X10,X177),hAPP(hAPP(c_Set_Oinsert(X13),X39),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool))))))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X13,X10)),hAPP(hAPP(c_Product__Type_OPair(X13,X10),X39),X38)),X177)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__singleton__iff) ).
fof(fact_norm__frac_Opinduct,axiom,
! [X19,X51,X192] :
( 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),X192),X51)))
=> ( ! [X116,X193] :
( 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),X116),X193)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X193),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(hAPP(X19,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X116)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X193))) )
=> hBOOL(hAPP(hAPP(X19,X116),X193)) ) )
=> hBOOL(hAPP(hAPP(X19,X192),X51)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__frac_Opinduct) ).
fof(fact_aset_I5_J,axiom,
! [X154,X53,X197] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X197))
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X53),X154))
=> ! [X3] :
( ! [X227] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X227),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X197)))
=> ! [X249] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X249),X154))
=> X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X249),X227) ) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X53))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X197)),X53)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I5_J) ).
fof(fact_div__mod__equality2,axiom,
! [X81,X84,X92,X94] :
( class_Divides_Osemiring__div(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),X84),X92))),c_Divides_Odiv__class_Omod(X94,X84,X92))),X81) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X81) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mod__equality2) ).
fof(fact_map__upds__Cons,axiom,
! [X313,X38,X312,X39,X102,X13,X10] : c_Map_Omap__upds(X10,X13,X102,hAPP(hAPP(c_List_Olist_OCons(X10),X39),X312),hAPP(hAPP(c_List_Olist_OCons(X13),X38),X313)) = c_Map_Omap__upds(X10,X13,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),X102),X39),hAPP(c_Option_Ooption_OSome(X13),X38)),X312,X313),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upds__Cons) ).
fof(fact_lexord__Nil__left,axiom,
! [X177,X25,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_ONil(X10)),X25)),c_List_Olexord(X10,X177)))
<=> ? [X116,X3] : X25 = hAPP(hAPP(c_List_Olist_OCons(X10),X116),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__Nil__left) ).
fof(fact_image__vimage__subset,axiom,
! [X154,X2,X13,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X13,X10,X2),hAPP(c_Set_Ovimage(X13,X10,X2),X154))),X154)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__vimage__subset) ).
fof(fact_map__sorted__distinct__set__unique,axiom,
! [X289,X290,X2,X10,X13] :
( class_Orderings_Olinorder(X13)
=> ( c_Fun_Oinj__on(X10,X13,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),X290)),hAPP(c_List_Oset(X10),X289)))
=> ( c_List_Olinorder__class_Osorted(X13,hAPP(hAPP(c_List_Omap(X10,X13),X2),X290))
=> ( hBOOL(hAPP(c_List_Odistinct(X13),hAPP(hAPP(c_List_Omap(X10,X13),X2),X290)))
=> ( c_List_Olinorder__class_Osorted(X13,hAPP(hAPP(c_List_Omap(X10,X13),X2),X289))
=> ( hBOOL(hAPP(c_List_Odistinct(X13),hAPP(hAPP(c_List_Omap(X10,X13),X2),X289)))
=> ( hAPP(c_List_Oset(X10),X290) = hAPP(c_List_Oset(X10),X289)
=> X290 = X289 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__sorted__distinct__set__unique) ).
fof(fact_zmult2__lemma__aux3,axiom,
! [X149,X92,X143,X81] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X81))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X143))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X143),X92))
=> 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),X92),c_Divides_Odiv__class_Omod(tc_Int_Oint,X149,X81))),X143))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma__aux3) ).
fof(fact_finite__quotient,axiom,
! [X177,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X177),hAPP(hAPP(c_Product__Type_OSigma(X10,X10),X154),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X10),X154))))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X154),X177))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__quotient) ).
fof(fact_foldl__append,axiom,
! [X289,X290,X39,X2,X13,X10] : hAPP(c_List_Ofoldl(X10,X13,X2,X39),hAPP(hAPP(c_List_Oappend(X13),X290),X289)) = hAPP(c_List_Ofoldl(X10,X13,X2,hAPP(c_List_Ofoldl(X10,X13,X2,X39),X290)),X289),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__append) ).
fof(fact_rtrancl__converseI,axiom,
! [X177,X16,X25,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X25),X16)),c_Transitive__Closure_Ortrancl(X10,X177)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),c_Transitive__Closure_Ortrancl(X10,hAPP(c_Relation_Oconverse(X10,X10),X177)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__converseI) ).
fof(fact_zip__append1,axiom,
! [X296,X298,X297,X10,X94] : hAPP(hAPP(c_List_Ozip(X94,X10),hAPP(hAPP(c_List_Oappend(X94),X297),X298)),X296) = hAPP(hAPP(c_List_Oappend(tc_prod(X94,X10)),hAPP(hAPP(c_List_Ozip(X94,X10),X297),hAPP(hAPP(c_List_Otake(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)),X296))),hAPP(hAPP(c_List_Ozip(X94,X10),X298),hAPP(hAPP(c_List_Odrop(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)),X296))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__append1) ).
fof(fact_Diff__subset__conv,axiom,
! [X198,X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160)),X198))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X160),X198))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__subset__conv) ).
fof(fact_evaln_Oequations_I4_J,axiom,
! [X65,X50,X52,X66,X51] :
( c_Natural_Oevaln(c_Com_Ocom_OSemi(X51,X66),X52,X50,X65)
<=> ? [X67] :
( c_Natural_Oevaln(X51,X52,X50,X67)
& c_Natural_Oevaln(X66,X67,X50,X65) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I4_J) ).
fof(fact_map__add__upd,axiom,
! [X25,X16,X1,X2,X13,X10] : c_Map_Omap__add(X10,X13,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),X1),X16),hAPP(c_Option_Ooption_OSome(X13),X25))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),c_Map_Omap__add(X10,X13,X2,X1)),X16),hAPP(c_Option_Ooption_OSome(X13),X25)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__upd) ).
fof(fact_bset_I6_J,axiom,
! [X53,X160,X197] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X197))
=> ! [X3] :
( ! [X227] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X227),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X197)))
=> ! [X249] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X249),X160))
=> X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X249),X227) ) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),X53))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X197)),X53)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I6_J) ).
fof(fact_bset_I5_J,axiom,
! [X53,X160,X197] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X197))
=> ! [X3] :
( ! [X227] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X227),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X197)))
=> ! [X249] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X249),X160))
=> X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X249),X227) ) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X53))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X197)),X53)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I5_J) ).
fof(fact_setprod__Un__Int,axiom,
! [X1,X160,X154,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),X154)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),X160)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__Un__Int) ).
fof(fact_setprod_Ounion__inter,axiom,
! [X1,X160,X154,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),X154)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),X160)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Ounion__inter) ).
fof(fact_setsum__Un__Int,axiom,
! [X1,X160,X154,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1),X154)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1),X160)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Un__Int) ).
fof(fact_inf2I,axiom,
! [X13,X10,X160,X25,X16,X154] :
( hBOOL(hAPP(hAPP(X154,X16),X25))
=> ( hBOOL(hAPP(hAPP(X160,X16),X25))
=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_fun(X13,tc_HOL_Obool))),X154),X160),X16),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2I) ).
fof(fact_vimage__subsetD,axiom,
! [X154,X160,X2,X10,X13] :
( hAPP(c_Set_Oimage(X13,X10,X2),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X13,X10,X2),X160)),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),hAPP(c_Set_Oimage(X13,X10,X2),X154))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__subsetD) ).
fof(fact_bset_I7_J,axiom,
! [X160,X53,X197] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X197))
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X53),X160))
=> ! [X3] :
( ! [X227] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X227),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X197)))
=> ! [X249] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X249),X160))
=> X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X249),X227) ) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X53),X3))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X53),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X197))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I7_J) ).
fof(fact_zdiv__mono2__lemma,axiom,
! [X150,X151,X130,X143,X149,X92] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X92),X149)),X143) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X130),X151)),X150)
=> ( 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),X130),X151)),X150)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X150),X130))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X143))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X130))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X130),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X149),X151)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).
fof(fact_converse__INTER,axiom,
! [X177,X216,X125,X10,X13] : hAPP(c_Relation_Oconverse(X13,X10),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X125,tc_fun(tc_prod(X13,X10),tc_HOL_Obool)),X216),X177)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X125,tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),X216),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X13,X10),tc_HOL_Obool),tc_fun(tc_prod(X10,X13),tc_HOL_Obool),X125),c_Relation_Oconverse(X13,X10)),X177)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__INTER) ).
fof(fact_converse__UNION,axiom,
! [X177,X216,X125,X10,X13] : hAPP(c_Relation_Oconverse(X13,X10),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X125,tc_fun(tc_prod(X13,X10),tc_HOL_Obool)),X216),X177)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X125,tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),X216),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X13,X10),tc_HOL_Obool),tc_fun(tc_prod(X10,X13),tc_HOL_Obool),X125),c_Relation_Oconverse(X13,X10)),X177)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__UNION) ).
fof(fact_eq__Abs__Integ,axiom,
! [X73] :
~ ! [X3,X90] : X73 != 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),X90)),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,
! [X154,X2,X13,X73,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X73),hAPP(c_Set_Oimage(X13,X10,X2),X154)))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X13),X3),X154))
& X73 = hAPP(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__iff) ).
fof(fact_eq__equiv__class__iff2,axiom,
! [X25,X16,X177,X154,X10] :
( c_Equiv__Relations_Oequiv(X10,X154,X177)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X25),X154))
=> ( hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),X177) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),hAPP(hAPP(c_Set_Oinsert(X10),X25),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),X177)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),X177)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__equiv__class__iff2) ).
fof(fact_split__comp,axiom,
! [X16,X1,X2,X195,X10,X125,X13] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X13,X125,X10),hAPP(c_Fun_Ocomp(X195,tc_fun(X125,X10),X13,X2),X1)),X16) = hAPP(hAPP(X2,hAPP(X1,hAPP(c_Product__Type_Ofst(X13,X125),X16))),hAPP(c_Product__Type_Osnd(X13,X125),X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__comp) ).
fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
! [X160,X154] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X154),X160))
<=> 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)),X154)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X160))) ),
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,
! [X160,X154] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X154),X160))
<=> 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)),X154)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X160))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I4_J) ).
fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
! [X226,X204,X10] :
( class_Orderings_Olinorder(X10)
=> ( ! [X3,X90] : hAPP(X204,hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X3),X90)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),hAPP(X204,X3)),hAPP(X204,X90))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X226))
=> ( X226 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(X204,c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X226)) = c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(c_Set_Oimage(X10,X10,X204),X226)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Ohom__commute) ).
fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
! [X226,X204,X10] :
( class_Orderings_Olinorder(X10)
=> ( ! [X3,X90] : hAPP(X204,hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X3),X90)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),hAPP(X204,X3)),hAPP(X204,X90))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X226))
=> ( X226 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(X204,c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X226)) = c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(c_Set_Oimage(X10,X10,X204),X226)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Ohom__commute) ).
fof(fact_vimage__subsetI,axiom,
! [X154,X160,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool)),X160),hAPP(c_Set_Oimage(X10,X13,X2),X154)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X10,X13,X2),X160)),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__subsetI) ).
fof(fact_converse__iff,axiom,
! [X177,X38,X39,X13,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X39),X38)),hAPP(c_Relation_Oconverse(X13,X10),X177)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X13,X10)),hAPP(hAPP(c_Product__Type_OPair(X13,X10),X38),X39)),X177)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__iff) ).
fof(fact_converseD,axiom,
! [X177,X38,X39,X13,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X39),X38)),hAPP(c_Relation_Oconverse(X13,X10),X177)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X13,X10)),hAPP(hAPP(c_Product__Type_OPair(X13,X10),X38),X39)),X177)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converseD) ).
fof(fact_sup2I1,axiom,
! [X160,X13,X10,X25,X16,X154] :
( hBOOL(hAPP(hAPP(X154,X16),X25))
=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_fun(X13,tc_HOL_Obool))),X154),X160),X16),X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2I1) ).
fof(fact_sup2I2,axiom,
! [X154,X13,X10,X25,X16,X160] :
( hBOOL(hAPP(hAPP(X160,X16),X25))
=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_fun(X13,tc_HOL_Obool))),X154),X160),X16),X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2I2) ).
fof(fact_Int__mono,axiom,
! [X197,X160,X198,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X198))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),X197))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X198),X197))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__mono) ).
fof(fact_Un__mono,axiom,
! [X197,X160,X198,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X198))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),X197))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X198),X197))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__mono) ).
fof(fact_Diff__mono,axiom,
! [X160,X197,X198,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X198))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X197),X160))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X198),X197))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__mono) ).
fof(fact_hom__fold1__commute,axiom,
! [X226,X204,X10] :
( class_Lattices_Oab__semigroup__idem__mult(X10)
=> ( ! [X3,X90] : hAPP(X204,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X3),X90)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(X204,X3)),hAPP(X204,X90))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X226))
=> ( X226 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(X204,hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),X226)) = hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),hAPP(c_Set_Oimage(X10,X10,X204),X226)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hom__fold1__commute) ).
fof(fact_setsum_Oreindex,axiom,
! [X1,X204,X154,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( c_Fun_Oinj__on(X10,X10,X204,X154)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1),hAPP(c_Set_Oimage(X10,X10,X204),X154)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),hAPP(c_Fun_Ocomp(X10,X13,X10,X1),X204)),X154) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oreindex) ).
fof(fact_setprod_Oreindex,axiom,
! [X1,X204,X154,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( c_Fun_Oinj__on(X10,X10,X204,X154)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),hAPP(c_Set_Oimage(X10,X10,X204),X154)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),hAPP(c_Fun_Ocomp(X10,X13,X10,X1),X204)),X154) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Oreindex) ).
fof(fact_acc_OaccI,axiom,
! [X177,X16,X10] :
( ! [X90] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X90),X16)),X177))
=> hBOOL(hAPP(hAPP(c_member(X10),X90),c_Wellfounded_Oacc(X10,X177))) )
=> hBOOL(hAPP(hAPP(c_member(X10),X16),c_Wellfounded_Oacc(X10,X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc_OaccI) ).
fof(fact_acc_Osimps,axiom,
! [X177,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X39),c_Wellfounded_Oacc(X10,X177)))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X39)),X177))
=> hBOOL(hAPP(hAPP(c_member(X10),X3),c_Wellfounded_Oacc(X10,X177))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc_Osimps) ).
fof(fact_rtrancl__listrel1__eq__len,axiom,
! [X177,X25,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X16),X25)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X10),c_List_Olistrel1(X10,X177))))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X16) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__listrel1__eq__len) ).
fof(fact_list__update_Osimps_I2_J,axiom,
! [X168,X113,X290,X16,X10] : hAPP(hAPP(c_List_Olist__update(X10,hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290)),X113),X168) = c_Nat_Onat_Onat__case(tc_List_Olist(X10),hAPP(hAPP(c_List_Olist_OCons(X10),X168),X290),hAPP(hAPP(c_COMBB(tc_List_Olist(X10),tc_List_Olist(X10),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X10),X16)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X10,tc_List_Olist(X10)),c_List_Olist__update(X10,X290)),X168)),X113),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update_Osimps_I2_J) ).
fof(fact_split__eta,axiom,
! [X2,X125,X13,X10] : hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,X125),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_prod(X10,X13)),tc_fun(X13,X125),X10),hAPP(c_COMBB(tc_prod(X10,X13),X125,X13),X2)),c_Product__Type_OPair(X10,X13))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__eta) ).
fof(fact_aset_I8_J,axiom,
! [X53,X154,X197] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X197))
=> ! [X3] :
( ! [X227] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X227),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X197)))
=> ! [X249] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X249),X154))
=> X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X249),X227) ) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X53),X3))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X53),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X197))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I8_J) ).
fof(fact_aset_I7_J,axiom,
! [X53,X154,X197] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X197))
=> ! [X3] :
( ! [X227] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X227),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X197)))
=> ! [X249] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X249),X154))
=> X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X249),X227) ) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X53),X3))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X53),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X197))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I7_J) ).
fof(fact_nth__take__lemma,axiom,
! [X298,X297,X94,X103] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X103),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X103),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X298)))
=> ( ! [X152] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X152),X103))
=> hAPP(hAPP(c_List_Onth(X94),X297),X152) = hAPP(hAPP(c_List_Onth(X94),X298),X152) )
=> hAPP(hAPP(c_List_Otake(X94),X103),X297) = hAPP(hAPP(c_List_Otake(X94),X103),X298) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__take__lemma) ).
fof(fact_rel__pow__0__E,axiom,
! [X196,X25,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X196)))
=> X16 = X25 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__0__E) ).
fof(fact_exI__realizer,axiom,
! [X10,X13,X16,X25,X19] :
( hBOOL(hAPP(hAPP(X19,X25),X16))
=> hBOOL(hAPP(hAPP(X19,hAPP(c_Product__Type_Osnd(X13,X10),hAPP(hAPP(c_Product__Type_OPair(X13,X10),X16),X25))),hAPP(c_Product__Type_Ofst(X13,X10),hAPP(hAPP(c_Product__Type_OPair(X13,X10),X16),X25)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_exI__realizer) ).
fof(fact_comp__inj__on__iff,axiom,
! [X255,X125,X154,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,X154)
=> ( c_Fun_Oinj__on(X13,X125,X255,hAPP(c_Set_Oimage(X10,X13,X2),X154))
<=> c_Fun_Oinj__on(X10,X125,hAPP(c_Fun_Ocomp(X13,X125,X10,X255),X2),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__inj__on__iff) ).
fof(fact_comp__surj,axiom,
! [X1,X125,X2,X10,X13] :
( hAPP(c_Set_Oimage(X13,X10,X2),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))
=> ( hAPP(c_Set_Oimage(X10,X125,X1),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X125,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(X13,X125,hAPP(c_Fun_Ocomp(X10,X125,X13,X1),X2)),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X125,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__surj) ).
fof(fact_zdiv__zmod__equality,axiom,
! [X103,X84,X92] : 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),X92),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),X92))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X92))),X103) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X84),X103),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zmod__equality) ).
fof(fact_setsum__reindex,axiom,
! [X204,X160,X2,X13,X10,X125] :
( class_Groups_Ocomm__monoid__add(X125)
=> ( c_Fun_Oinj__on(X10,X13,X2,X160)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X125),X204),hAPP(c_Set_Oimage(X10,X13,X2),X160)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X125),hAPP(c_Fun_Ocomp(X13,X125,X10,X204),X2)),X160) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__reindex) ).
fof(fact_setprod__reindex,axiom,
! [X204,X160,X2,X13,X10,X125] :
( class_Groups_Ocomm__monoid__mult(X125)
=> ( c_Fun_Oinj__on(X10,X13,X2,X160)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X13,X125),X204),hAPP(c_Set_Oimage(X10,X13,X2),X160)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X125),hAPP(c_Fun_Ocomp(X13,X125,X10,X204),X2)),X160) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__reindex) ).
fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
! [X160,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160))),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X154)),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X160)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Ounion__inter) ).
fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
! [X160,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160))),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X154)),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X160)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Ounion__inter) ).
fof(fact_lexn__length,axiom,
! [X20,X177,X289,X290,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X290),X289)),hAPP(c_List_Olexn(X10,X177),X20)))
=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290) = X20
& hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X289) = X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexn__length) ).
fof(fact_converseI,axiom,
! [X177,X38,X39,X13,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X39),X38)),X177))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X13,X10)),hAPP(hAPP(c_Product__Type_OPair(X13,X10),X38),X39)),hAPP(c_Relation_Oconverse(X10,X13),X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converseI) ).
fof(fact_rel__comp__distrib,axiom,
! [X232,X216,X196,X13,X125,X10] : hAPP(hAPP(c_Relation_Orel__comp(X10,X125,X13),X196),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X125,X13),tc_HOL_Obool)),X216),X232)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X10,X125,X13),X196),X216)),hAPP(hAPP(c_Relation_Orel__comp(X10,X125,X13),X196),X232)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__distrib) ).
fof(fact_bot__empty__eq2,axiom,
! [X25,X16,X13,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X10,tc_fun(X13,tc_HOL_Obool))),X16),X25))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X16),X25)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__empty__eq2) ).
fof(fact_transpose__transpose,axiom,
! [X290,X10] :
( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X10))),X290)))
=> c_List_Otranspose(X10,c_List_Otranspose(X10,X290)) = c_List_OtakeWhile(tc_List_Olist(X10),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X10)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_List_Olist(X10),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X10))),X290) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__transpose) ).
fof(fact_Min_Ohom__commute,axiom,
! [X226,X204,X10] :
( class_Orderings_Olinorder(X10)
=> ( ! [X3,X90] : hAPP(X204,hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X3),X90)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),hAPP(X204,X3)),hAPP(X204,X90))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X226))
=> ( X226 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(X204,c_Big__Operators_Olinorder__class_OMin(X10,X226)) = c_Big__Operators_Olinorder__class_OMin(X10,hAPP(c_Set_Oimage(X10,X10,X204),X226)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Ohom__commute) ).
fof(fact_Max_Ohom__commute,axiom,
! [X226,X204,X10] :
( class_Orderings_Olinorder(X10)
=> ( ! [X3,X90] : hAPP(X204,hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X3),X90)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),hAPP(X204,X3)),hAPP(X204,X90))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X226))
=> ( X226 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(X204,c_Big__Operators_Olinorder__class_OMax(X10,X226)) = c_Big__Operators_Olinorder__class_OMax(X10,hAPP(c_Set_Oimage(X10,X10,X204),X226)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Ohom__commute) ).
fof(fact_Inf__fin_Ohom__commute,axiom,
! [X226,X204,X10] :
( class_Lattices_Olattice(X10)
=> ( ! [X3,X90] : hAPP(X204,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X3),X90)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),hAPP(X204,X3)),hAPP(X204,X90))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X226))
=> ( X226 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(X204,c_Big__Operators_Olattice__class_OInf__fin(X10,X226)) = c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(c_Set_Oimage(X10,X10,X204),X226)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Ohom__commute) ).
fof(fact_Sup__fin_Ohom__commute,axiom,
! [X226,X204,X10] :
( class_Lattices_Olattice(X10)
=> ( ! [X3,X90] : hAPP(X204,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X3),X90)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),hAPP(X204,X3)),hAPP(X204,X90))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X226))
=> ( X226 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(X204,c_Big__Operators_Olattice__class_OSup__fin(X10,X226)) = c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(c_Set_Oimage(X10,X10,X204),X226)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Ohom__commute) ).
fof(fact_periodic__finite__ex,axiom,
! [X19,X141] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X141))
=> ( ! [X3,X124] :
( hBOOL(hAPP(X19,X3))
<=> hBOOL(hAPP(X19,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X124),X141)))) )
=> ( ? [X147] : hBOOL(hAPP(X19,X147))
<=> ? [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),X141)))
& hBOOL(hAPP(X19,X3)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_periodic__finite__ex) ).
fof(fact_listrel__Nil1,axiom,
! [X177,X290,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_ONil(X10)),X290)),c_List_Olistrel(X10,X177)))
=> X290 = c_List_Olist_ONil(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__Nil1) ).
fof(fact_the__elem__def,axiom,
! [X48,X10] : c_Set_Othe__elem(X10,X48) = c_HOL_OThe(X10,hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),hAPP(c_fequal,X48)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Set_Oinsert(X10)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__elem__def) ).
fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
! [X160,X154] :
( c_Nat__Transfer_Onat__set(X154)
=> ( c_Nat__Transfer_Onat__set(X160)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X154),X160))
<=> 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),X154)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X160))) ) ) ),
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,
! [X160,X154] :
( c_Nat__Transfer_Onat__set(X154)
=> ( c_Nat__Transfer_Onat__set(X160)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X154),X160))
<=> 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),X154)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X160))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I4_J) ).
fof(fact_union__comp__emptyL,axiom,
! [X160,X198,X154,X10] :
( hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X154),X198) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool))
=> ( hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X160),X198) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool))
=> hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X154),X160)),X198) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_union__comp__emptyL) ).
fof(fact_int__def,axiom,
! [X102] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X102) = 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),X102),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,
! [X104,X105,X93,X94] :
( class_Lattices_Olattice(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X105),X104))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),X105)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),X104)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distrib__sup__le) ).
fof(fact_min__max_Odistrib__sup__le,axiom,
! [X104,X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X93),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X105),X104))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X93),X105)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X93),X104)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Odistrib__sup__le) ).
fof(fact_fold__inf__le__inf,axiom,
! [X38,X39,X154,X10] :
( class_Lattices_Osemilattice__inf(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__inf__class_Oinf(X10)),X38),X154)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X39),X38))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__inf__le__inf) ).
fof(fact_min__max_Ofold__inf__le__inf,axiom,
! [X38,X39,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omin(X10)),X38),X154)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X39),X38))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ofold__inf__le__inf) ).
fof(fact_set__update__subsetI,axiom,
! [X113,X16,X154,X290,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),X290)),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Olist__update(X10,X290),X113),X16))),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__update__subsetI) ).
fof(fact_setsum__ub__add__nat,axiom,
! [X166,X2,X20,X102,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X102,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X166))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X102,X20))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X166)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__ub__add__nat) ).
fof(fact_Times__Int__distrib1,axiom,
! [X198,X160,X154,X13,X10] : hAPP(hAPP(c_Product__Type_OSigma(X10,X13),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),X198)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X154),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),X198))),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X160),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),X198))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__Int__distrib1) ).
fof(fact_Times__Un__distrib1,axiom,
! [X198,X160,X154,X13,X10] : hAPP(hAPP(c_Product__Type_OSigma(X10,X13),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),X198)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X154),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),X198))),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X160),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),X198))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__Un__distrib1) ).
fof(fact_Times__Diff__distrib1,axiom,
! [X198,X160,X154,X13,X10] : hAPP(hAPP(c_Product__Type_OSigma(X10,X13),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160)),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),X198)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X154),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),X198))),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X160),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),X198))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__Diff__distrib1) ).
fof(fact_card__inj__on__le,axiom,
! [X160,X154,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,X154)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X13,X2),X154)),X160))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X160))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X154)),hAPP(c_Finite__Set_Ocard(X13),X160))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__inj__on__le) ).
fof(fact_fold__image__1,axiom,
! [X2,X216,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X216))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X216))
=> hAPP(X2,X3) = c_Groups_Oone__class_Oone(X13) )
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13,X10,c_Groups_Otimes__class_Otimes(X13)),X2),c_Groups_Oone__class_Oone(X13)),X216) = c_Groups_Oone__class_Oone(X13) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__1) ).
fof(fact_surjective__sum,axiom,
! [X2,X13,X125,X10] : c_Sum__Type_Osum_Osum__case(X10,X125,X13,hAPP(hAPP(c_COMBB(tc_sum(X10,X13),X125,X10),X2),c_Sum__Type_OInl(X10,X13)),hAPP(hAPP(c_COMBB(tc_sum(X10,X13),X125,X13),X2),c_Sum__Type_OInr(X13,X10))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surjective__sum) ).
fof(fact_sum__case__KK,axiom,
! [X16,X39,X125,X10,X13] : hAPP(c_Sum__Type_Osum_Osum__case(X13,X10,X125,hAPP(c_COMBK(X10,X13),X39),hAPP(c_COMBK(X10,X125),X39)),X16) = X39,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__case__KK) ).
fof(fact_map__of__filter__in,axiom,
! [X19,X73,X101,X290,X10,X13] :
( hAPP(c_Map_Omap__of(X13,X10,X290),X101) = hAPP(c_Option_Ooption_OSome(X10),X73)
=> ( hBOOL(hAPP(hAPP(X19,X101),X73))
=> hAPP(c_Map_Omap__of(X13,X10,hAPP(c_List_Ofilter(tc_prod(X13,X10),hAPP(c_Product__Type_Oprod_Oprod__case(X13,X10,tc_HOL_Obool),X19)),X290)),X101) = hAPP(c_Option_Ooption_OSome(X10),X73) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__filter__in) ).
fof(fact_listrel__Nil2,axiom,
! [X177,X290,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X290),c_List_Olist_ONil(X10))),c_List_Olistrel(X10,X177)))
=> X290 = c_List_Olist_ONil(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__Nil2) ).
fof(fact_INF__commute,axiom,
! [X2,X160,X125,X154,X13,X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,X10),X154),hAPP(hAPP(c_COMBB(tc_fun(X125,X10),X10,X13),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X125,X10),X160)),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X125,X10),X160),hAPP(hAPP(c_COMBB(tc_fun(X13,X10),X10,X125),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,X10),X154)),hAPP(c_COMBC(X13,X125,X10),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__commute) ).
fof(fact_SUP__commute,axiom,
! [X2,X160,X125,X154,X13,X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,X10),X154),hAPP(hAPP(c_COMBB(tc_fun(X125,X10),X10,X13),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X125,X10),X160)),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X125,X10),X160),hAPP(hAPP(c_COMBB(tc_fun(X13,X10),X10,X125),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,X10),X154)),hAPP(c_COMBC(X13,X125,X10),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__commute) ).
fof(fact_eq__equiv__class__iff,axiom,
! [X25,X16,X177,X154,X10] :
( c_Equiv__Relations_Oequiv(X10,X154,X177)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X25),X154))
=> ( hAPP(c_Relation_OImage(X10,X10,X177),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X10,X10,X177),hAPP(hAPP(c_Set_Oinsert(X10),X25),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),X177)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__equiv__class__iff) ).
fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
! [X2,X154,X10] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> c_Nat__Transfer_Ois__nat(hAPP(X2,X3)) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Int_Oint),X2),X154) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X10),c_Int_Onat),X2)),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__sum__prod2_I1_J) ).
fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
! [X2,X154,X10] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> c_Nat__Transfer_Ois__nat(hAPP(X2,X3)) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,tc_Int_Oint),X2),X154) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X10),c_Int_Onat),X2)),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__sum__prod2_I2_J) ).
fof(fact_listrel1__eq__len,axiom,
! [X177,X289,X290,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X290),X289)),c_List_Olistrel1(X10,X177)))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X289) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1__eq__len) ).
fof(fact_listrel__eq__len,axiom,
! [X177,X289,X290,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X290),X289)),c_List_Olistrel(X10,X177)))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X289) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__eq__len) ).
fof(fact_Sigma__Union,axiom,
! [X160,X48,X13,X10] : hAPP(hAPP(c_Product__Type_OSigma(X10,X13),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X48)),X160) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),X48),hAPP(hAPP(c_COMBC(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_fun(X13,tc_HOL_Obool)),tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),c_Product__Type_OSigma(X10,X13)),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Union) ).
fof(fact_bset_I4_J,axiom,
! [X160,X53,X197] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X197))
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X53),X160))
=> ! [X3] :
( ! [X227] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X227),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X197)))
=> ! [X249] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X249),X160))
=> X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X249),X227) ) )
=> ( X3 != X53
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X197) != X53 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I4_J) ).
fof(fact_aset_I4_J,axiom,
! [X154,X53,X197] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X197))
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X53),X154))
=> ! [X3] :
( ! [X227] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X227),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X197)))
=> ! [X249] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X249),X154))
=> X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X249),X227) ) )
=> ( X3 != X53
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X197) != X53 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I4_J) ).
fof(fact_fold__def,axiom,
! [X154,X73,X2,X10,X13] : hAPP(hAPP(c_Finite__Set_Ofold(X13,X10,X2),X73),X154) = c_HOL_OThe(X10,c_Finite__Set_Ofold__graph(X13,X10,X2,X73,X154)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__def) ).
fof(fact_split__paired__All,axiom,
! [X13,X10,X19] :
( ! [X147] : hBOOL(hAPP(X19,X147))
<=> ! [X116,X193] : hBOOL(hAPP(X19,hAPP(hAPP(c_Product__Type_OPair(X10,X13),X116),X193))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__paired__All) ).
fof(fact_curryI,axiom,
! [X38,X39,X13,X10,X2] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(X10,X13),X39),X38)))
=> hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X10,X13,tc_HOL_Obool,X2),X39),X38)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curryI) ).
fof(fact_diff__card__le__card__Diff,axiom,
! [X154,X160,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> 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(X10),X154)),hAPP(c_Finite__Set_Ocard(X10),X160))),hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__card__le__card__Diff) ).
fof(fact_inj__on__Inter,axiom,
! [X2,X13,X10,X216] :
( X216 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool))
=> ( ! [X246] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X246),X216))
=> c_Fun_Oinj__on(X10,X13,X2,X246) )
=> c_Fun_Oinj__on(X10,X13,X2,c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X216)) ) ),
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,
! [X177,X10] :
( c_Nitpick_Orefl_H(X10,X177)
<=> ! [X3] : hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X3)),X177)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Orefl_H__def) ).
fof(fact_decr__mult__lemma,axiom,
! [X101,X19,X141] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X141))
=> ( ! [X3] :
( hBOOL(hAPP(X19,X3))
=> hBOOL(hAPP(X19,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X141))) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X101))
=> ! [X3] :
( hBOOL(hAPP(X19,X3))
=> hBOOL(hAPP(X19,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X101),X141)))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_decr__mult__lemma) ).
fof(fact_incr__mult__lemma,axiom,
! [X101,X19,X141] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X141))
=> ( ! [X3] :
( hBOOL(hAPP(X19,X3))
=> hBOOL(hAPP(X19,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X141))) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X101))
=> ! [X3] :
( hBOOL(hAPP(X19,X3))
=> hBOOL(hAPP(X19,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X101),X141)))) ) ) ) ),
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,X16,X125,X225,X2,X13,X10] :
( c_Finite__Set_Ofolding__idem(X10,X13,X2,X225)
=> hAPP(c_Fun_Ocomp(X13,X13,X125,hAPP(X2,X16)),hAPP(c_Fun_Ocomp(X13,X13,X125,hAPP(X2,X16)),X1)) = hAPP(c_Fun_Ocomp(X13,X13,X125,hAPP(X2,X16)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Oidem__left__comp) ).
fof(fact_mem__splitI,axiom,
! [X125,X13,X38,X39,X18,X73,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X73),hAPP(hAPP(X18,X39),X38)))
=> hBOOL(hAPP(hAPP(c_member(X10),X73),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X13,X125,tc_fun(X10,tc_HOL_Obool)),X18),hAPP(hAPP(c_Product__Type_OPair(X13,X125),X39),X38)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__splitI) ).
fof(fact_listrel__Cons,axiom,
! [X290,X16,X177,X10] : hAPP(c_Relation_OImage(tc_List_Olist(X10),tc_List_Olist(X10),c_List_Olistrel(X10,X177)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X10),tc_HOL_Obool)))) = c_List_Oset__Cons(X10,hAPP(c_Relation_OImage(X10,X10,X177),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(X10),tc_List_Olist(X10),c_List_Olistrel(X10,X177)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X10)),X290),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X10),tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__Cons) ).
fof(fact_UN__le__add__shift,axiom,
! [X101,X230,X20,X10] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X20)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool),tc_Nat_Onat),X230),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X101))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X101,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X101))),X230),
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,
! [X299,X102,X289,X13,X290,X10] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13)),X289)
=> c_Map_Omap__upds(X10,X13,X102,hAPP(hAPP(c_List_Oappend(X10),X290),X299),X289) = c_Map_Omap__upds(X10,X13,X102,X290,X289) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upds__append__drop) ).
fof(fact_fun__upds__append2__drop,axiom,
! [X299,X102,X289,X13,X290,X10] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13)),X289)
=> c_Map_Omap__upds(X10,X13,X102,X290,hAPP(hAPP(c_List_Oappend(X13),X289),X299)) = c_Map_Omap__upds(X10,X13,X102,X290,X289) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upds__append2__drop) ).
fof(fact_option__map__eq__Some,axiom,
! [X25,X215,X2,X10,X13] :
( hAPP(hAPP(c_Option_Omap(X13,X10),X2),X215) = hAPP(c_Option_Ooption_OSome(X10),X25)
<=> ? [X159] :
( X215 = hAPP(c_Option_Ooption_OSome(X13),X159)
& hAPP(X2,X159) = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option__map__eq__Some) ).
fof(fact_override__on__apply__in,axiom,
! [X1,X2,X13,X154,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(c_Fun_Ooverride__on(X10,X13,X2,X1,X154),X39) = hAPP(X1,X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_override__on__apply__in) ).
fof(fact_restrict__map__insert,axiom,
! [X154,X39,X2,X13,X10] : c_Map_Orestrict__map(X10,X13,X2,hAPP(hAPP(c_Set_Oinsert(X10),X39),X154)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),c_Map_Orestrict__map(X10,X13,X2,X154)),X39),hAPP(X2,X39)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__map__insert) ).
fof(fact_lexord__append__rightI,axiom,
! [X177,X16,X10,X25] :
( ? [X193,X159] : X25 = hAPP(hAPP(c_List_Olist_OCons(X10),X193),X159)
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X16),hAPP(hAPP(c_List_Oappend(X10),X16),X25))),c_List_Olexord(X10,X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__append__rightI) ).
fof(fact_list__eq__iff__zip__eq,axiom,
! [X10,X289,X290] :
( X290 = X289
<=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X289)
& ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X3),hAPP(c_List_Oset(tc_prod(X10,X10)),hAPP(hAPP(c_List_Ozip(X10,X10),X290),X289))))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X10,X10,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,
! [X19,X51,X192] :
( 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),X192),X51)))
=> ( ! [X3,X90] :
( 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),X90)))
=> ( ( X90 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(hAPP(X19,X90),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X90))) )
=> hBOOL(hAPP(hAPP(X19,X3),X90)) ) )
=> hBOOL(hAPP(hAPP(X19,X192),X51)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__gcd_Opinduct) ).
fof(fact_inj__on__strict__subset,axiom,
! [X154,X160,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,X160)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X13,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X13,X2),X154)),hAPP(c_Set_Oimage(X10,X13,X2),X160))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__strict__subset) ).
fof(fact_evalc_Oequations_I4_J,axiom,
! [X66,X52,X72,X51] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X51,X72)),X52),X66))
<=> ? [X67] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X51),X52),X67))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X72),X67),X66)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I4_J) ).
fof(fact_inj__on__image__Int,axiom,
! [X160,X154,X198,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,X198)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X198))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),X198))
=> hAPP(c_Set_Oimage(X10,X13,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X13,X2),X154)),hAPP(c_Set_Oimage(X10,X13,X2),X160)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__image__Int) ).
fof(fact_inj__on__image__set__diff,axiom,
! [X160,X154,X198,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,X198)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X198))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),X198))
=> hAPP(c_Set_Oimage(X10,X13,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X13,X2),X154)),hAPP(c_Set_Oimage(X10,X13,X2),X160)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__image__set__diff) ).
fof(fact_filter__in__sublist,axiom,
! [X54,X290,X10] :
( hBOOL(hAPP(c_List_Odistinct(X10),X290))
=> hAPP(c_List_Ofilter(X10,hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),hAPP(c_List_Oset(X10),c_List_Osublist(X10,X290,X54)))),X290) = c_List_Osublist(X10,X290,X54) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__in__sublist) ).
fof(fact_endo__inj__surj,axiom,
! [X2,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X10,X2),X154)),X154))
=> ( c_Fun_Oinj__on(X10,X10,X2,X154)
=> hAPP(c_Set_Oimage(X10,X10,X2),X154) = X154 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_endo__inj__surj) ).
fof(fact_insort__insert__key__triv,axiom,
! [X290,X13,X16,X2,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_member(X10),hAPP(X2,X16)),hAPP(c_Set_Oimage(X13,X10,X2),hAPP(c_List_Oset(X13),X290))))
=> c_List_Olinorder__class_Oinsort__insert__key(X13,X10,X2,X16,X290) = X290 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__insert__key__triv) ).
fof(fact_set__insort__insert,axiom,
! [X290,X16,X10] :
( class_Orderings_Olinorder(X10)
=> hAPP(c_List_Oset(X10),c_List_Olinorder__class_Oinsort__insert__key(X10,X10,c_COMBI(X10),X16,X290)) = hAPP(hAPP(c_Set_Oinsert(X10),X16),hAPP(c_List_Oset(X10),X290)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__insort__insert) ).
fof(fact_listrel1__subset__listrel,axiom,
! [X224,X177,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X177),X224))
=> ( c_Relation_Orefl__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X224)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_HOL_Obool)),c_List_Olistrel1(X10,X177)),c_List_Olistrel(X10,X224))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1__subset__listrel) ).
fof(fact_folding__image_Oeq__fold,axiom,
! [X1,X154,X225,X73,X2,X13,X10] :
( c_Finite__Set_Ofolding__image(X10,X13,X2,X73,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X154))
=> hAPP(hAPP(X225,X1),X154) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X10,X13,X2),X1),X73),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image_Oeq__fold) ).
fof(fact_fun__left__comm_Ofold__rec,axiom,
! [X73,X16,X154,X2,X13,X10] :
( c_Finite__Set_Ofun__left__comm(X10,X13,X2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(hAPP(c_Finite__Set_Ofold(X10,X13,X2),X73),X154) = hAPP(hAPP(X2,X16),hAPP(hAPP(c_Finite__Set_Ofold(X10,X13,X2),X73),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__rec) ).
fof(fact_hoare__valids__def,axiom,
! [X211,X210,X10] :
( c_Hoare__Mirabelle_Ohoare__valids(X10,X210,X211)
<=> ! [X83] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X10)),X3),X210))
=> c_Hoare__Mirabelle_Otriple__valid(X10,X83,X3) )
=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X10)),X3),X211))
=> c_Hoare__Mirabelle_Otriple__valid(X10,X83,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__valids__def) ).
fof(fact_sum_Osimps_I5_J,axiom,
! [X39,X37,X12,X125,X10,X13] : hAPP(c_Sum__Type_Osum_Osum__case(X13,X10,X125,X12,X37),hAPP(c_Sum__Type_OInl(X13,X125),X39)) = hAPP(X12,X39),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I5_J) ).
fof(fact_sum_Osimps_I6_J,axiom,
! [X38,X37,X12,X125,X10,X13] : hAPP(c_Sum__Type_Osum_Osum__case(X13,X10,X125,X12,X37),hAPP(c_Sum__Type_OInr(X125,X13),X38)) = hAPP(X37,X38),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I6_J) ).
fof(fact_vimage__compose,axiom,
! [X16,X2,X1,X125,X13,X10] : hAPP(c_Set_Ovimage(X10,X13,hAPP(c_Fun_Ocomp(X125,X13,X10,X1),X2)),X16) = hAPP(c_Set_Ovimage(X10,X125,X2),hAPP(c_Set_Ovimage(X125,X13,X1),X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__compose) ).
fof(fact_image__compose,axiom,
! [X177,X1,X2,X125,X10,X13] : hAPP(c_Set_Oimage(X13,X10,hAPP(c_Fun_Ocomp(X125,X10,X13,X2),X1)),X177) = hAPP(c_Set_Oimage(X125,X10,X2),hAPP(c_Set_Oimage(X13,X125,X1),X177)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__compose) ).
fof(fact_rtrancl__power,axiom,
! [X196,X166,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X166),c_Transitive__Closure_Ortrancl(X10,X196)))
<=> ? [X83] : hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X166),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X83),X196))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__power) ).
fof(fact_scomp__unfold,axiom,
! [X16,X1,X2,X10,X195,X125,X13] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X13,X125,X195,X10),X2),X1),X16) = hAPP(hAPP(X1,hAPP(c_Product__Type_Ofst(X125,X195),hAPP(X2,X16))),hAPP(c_Product__Type_Osnd(X125,X195),hAPP(X2,X16))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_scomp__unfold) ).
fof(fact_equiv__class__eq__iff,axiom,
! [X25,X16,X177,X154,X10] :
( c_Equiv__Relations_Oequiv(X10,X154,X177)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),X177))
<=> ( hAPP(c_Relation_OImage(X10,X10,X177),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X10,X10,X177),hAPP(hAPP(c_Set_Oinsert(X10),X25),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))
& hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
& hBOOL(hAPP(hAPP(c_member(X10),X25),X154)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__class__eq__iff) ).
fof(fact_sum__squares__gt__zero__iff,axiom,
! [X25,X16,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X16),X16)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X25),X25))))
<=> ( X16 != c_Groups_Ozero__class_Ozero(X10)
| X25 != c_Groups_Ozero__class_Ozero(X10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__gt__zero__iff) ).
fof(fact_rtrancl__is__UN__rel__pow,axiom,
! [X196,X10] : c_Transitive__Closure_Ortrancl(X10,X196) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X10,X10),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(X10,X10),tc_HOL_Obool),tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool)),X196)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__is__UN__rel__pow) ).
fof(fact_inj__on__imageI,axiom,
! [X154,X2,X1,X125,X13,X10] :
( c_Fun_Oinj__on(X10,X13,hAPP(c_Fun_Ocomp(X125,X13,X10,X1),X2),X154)
=> c_Fun_Oinj__on(X125,X13,X1,hAPP(c_Set_Oimage(X10,X125,X2),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__imageI) ).
fof(fact_setsum__eq__Suc0__iff,axiom,
! [X2,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),X154) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
& hAPP(X2,X3) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& ! [X227] :
( hBOOL(hAPP(hAPP(c_member(X10),X227),X154))
=> ( X3 != X227
=> hAPP(X2,X227) = 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,
! [X16,X290,X10] :
( class_Orderings_Olinorder(X10)
=> ( c_List_Olinorder__class_Osorted(X10,X290)
=> c_List_Olinorder__class_Osorted(X10,c_List_Olinorder__class_Oinsort__insert__key(X10,X10,c_COMBI(X10),X16,X290)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__insort__insert) ).
fof(fact_abs__mult__less,axiom,
! [X112,X92,X81,X84,X94] :
( class_Rings_Olinordered__idom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),X84)),X81))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),X92)),X112))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),X84)),hAPP(c_Groups_Oabs__class_Oabs(X94),X92))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),X112))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult__less) ).
fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
! [X16,X73,X154,X2,X13,X10] :
( c_Finite__Set_Ofun__left__comm(X10,X13,X2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Finite__Set_Ofold(X10,X13,X2),X73),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(X2,X16),hAPP(hAPP(c_Finite__Set_Ofold(X10,X13,X2),X73),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__insert__remove) ).
fof(fact_takeWhile__map,axiom,
! [X290,X2,X13,X19,X10] : c_List_OtakeWhile(X10,X19,hAPP(hAPP(c_List_Omap(X13,X10),X2),X290)) = hAPP(hAPP(c_List_Omap(X13,X10),X2),c_List_OtakeWhile(X13,hAPP(c_Fun_Ocomp(X10,tc_HOL_Obool,X13,X19),X2),X290)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__map) ).
fof(fact_setsum__eq__1__iff,axiom,
! [X2,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),X154) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
& hAPP(X2,X3) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& ! [X227] :
( hBOOL(hAPP(hAPP(c_member(X10),X227),X154))
=> ( X3 != X227
=> hAPP(X2,X227) = 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,
! [X177,X154,X10] :
( c_Relation_Orefl__on(X10,X154,X177)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X177),hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),hAPP(c_Relation_Oconverse(X10,X10),X177)),X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__comp__subset) ).
fof(fact_comp__inj__on,axiom,
! [X1,X125,X154,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,X154)
=> ( c_Fun_Oinj__on(X13,X125,X1,hAPP(c_Set_Oimage(X10,X13,X2),X154))
=> c_Fun_Oinj__on(X10,X125,hAPP(c_Fun_Ocomp(X13,X125,X10,X1),X2),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__inj__on) ).
fof(fact_elem__le__sum,axiom,
! [X305,X20] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X20),hAPP(c_List_Oset(tc_Nat_Onat),X305)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20),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)),X305))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_elem__le__sum) ).
fof(fact_rev__ImageI,axiom,
! [X177,X38,X13,X154,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X39),X38)),X177))
=> hBOOL(hAPP(hAPP(c_member(X13),X38),hAPP(c_Relation_OImage(X10,X13,X177),X154))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__ImageI) ).
fof(fact_Option_Omap_Ocompositionality,axiom,
! [X293,X1,X125,X2,X10,X13] : hAPP(hAPP(c_Option_Omap(X13,X10),X2),hAPP(hAPP(c_Option_Omap(X125,X13),X1),X293)) = hAPP(hAPP(c_Option_Omap(X125,X10),hAPP(c_Fun_Ocomp(X13,X10,X125,X2),X1)),X293),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Option_Omap_Ocompositionality) ).
fof(fact_option__map__comp,axiom,
! [X292,X1,X125,X2,X10,X13] : hAPP(hAPP(c_Option_Omap(X13,X10),X2),hAPP(hAPP(c_Option_Omap(X125,X13),X1),X292)) = hAPP(hAPP(c_Option_Omap(X125,X10),hAPP(c_Fun_Ocomp(X13,X10,X125,X2),X1)),X292),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option__map__comp) ).
fof(fact_map__map,axiom,
! [X290,X1,X125,X2,X10,X13] : hAPP(hAPP(c_List_Omap(X13,X10),X2),hAPP(hAPP(c_List_Omap(X125,X13),X1),X290)) = hAPP(hAPP(c_List_Omap(X125,X10),hAPP(c_Fun_Ocomp(X13,X10,X125,X2),X1)),X290),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__map) ).
fof(fact_List_Omap_Ocompositionality,axiom,
! [X291,X1,X125,X2,X10,X13] : hAPP(hAPP(c_List_Omap(X13,X10),X2),hAPP(hAPP(c_List_Omap(X125,X13),X1),X291)) = hAPP(hAPP(c_List_Omap(X125,X10),hAPP(c_Fun_Ocomp(X13,X10,X125,X2),X1)),X291),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Omap_Ocompositionality) ).
fof(fact_take__Cons,axiom,
! [X290,X16,X20,X10] : hAPP(hAPP(c_List_Otake(X10),X20),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290)) = c_Nat_Onat_Onat__case(tc_List_Olist(X10),c_List_Olist_ONil(X10),hAPP(hAPP(c_COMBB(tc_List_Olist(X10),tc_List_Olist(X10),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X10),X16)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Otake(X10)),X290)),X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Cons) ).
fof(fact_Un__Image,axiom,
! [X154,X216,X196,X10,X13] : hAPP(c_Relation_OImage(X13,X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X13,X10),tc_HOL_Obool)),X196),X216)),X154) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_OImage(X13,X10,X196),X154)),hAPP(c_Relation_OImage(X13,X10,X216),X154)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Image) ).
fof(fact_iterate_Osimps,axiom,
! [X16,X2,X10,X13,X101] :
( ( X101 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_Random_Oiterate(X13,X10,X101,X2),X16) = hAPP(c_Product__Type_OPair(X13,X10),X16) )
& ( X101 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_Random_Oiterate(X13,X10,X101,X2),X16) = hAPP(hAPP(c_Product__Type_Oscomp(X10,X13,X10,tc_prod(X13,X10)),hAPP(X2,X16)),c_Random_Oiterate(X13,X10,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X101),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,
! [X38,X39,X177,X154,X10] :
( c_Equiv__Relations_Oequiv(X10,X154,X177)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),X177))
=> hAPP(c_Relation_OImage(X10,X10,X177),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X10,X10,X177),hAPP(hAPP(c_Set_Oinsert(X10),X38),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__class__eq) ).
fof(fact_mem__Sigma__iff,axiom,
! [X160,X154,X38,X39,X13,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X39),X38)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X154),X160)))
<=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
& hBOOL(hAPP(hAPP(c_member(X13),X38),hAPP(X160,X39))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__Sigma__iff) ).
fof(fact_SigmaD2,axiom,
! [X160,X154,X38,X39,X13,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X39),X38)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X154),X160)))
=> hBOOL(hAPP(hAPP(c_member(X13),X38),hAPP(X160,X39))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaD2) ).
fof(fact_listrel1__mono,axiom,
! [X54,X177,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X177),X54))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_HOL_Obool)),c_List_Olistrel1(X10,X177)),c_List_Olistrel1(X10,X54))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1__mono) ).
fof(fact_listrel__mono,axiom,
! [X54,X177,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X177),X54))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_HOL_Obool)),c_List_Olistrel(X10,X177)),c_List_Olistrel(X10,X54))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__mono) ).
fof(fact_scomp__def,axiom,
! [X16,X1,X2,X10,X195,X125,X13] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X13,X125,X195,X10),X2),X1),X16) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X125,X195,X10),X1),hAPP(X2,X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_scomp__def) ).
fof(fact_scomp__apply,axiom,
! [X16,X1,X2,X10,X195,X125,X13] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X13,X125,X195,X10),X2),X1),X16) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X125,X195,X10),X1),hAPP(X2,X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_scomp__apply) ).
fof(fact_Un__least,axiom,
! [X160,X198,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X198))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),X198))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)),X198)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__least) ).
fof(fact_folding__one_Ounion__inter,axiom,
! [X160,X154,X225,X2,X10] :
( c_Finite__Set_Ofolding__one(X10,X2,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(X2,hAPP(X225,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160))),hAPP(X225,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160))) = hAPP(hAPP(X2,hAPP(X225,X154)),hAPP(X225,X160)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Ounion__inter) ).
fof(fact_f__the__inv__into__f,axiom,
! [X25,X154,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,X154)
=> ( hBOOL(hAPP(hAPP(c_member(X13),X25),hAPP(c_Set_Oimage(X10,X13,X2),X154)))
=> hAPP(X2,hAPP(c_Fun_Othe__inv__into(X10,X13,X154,X2),X25)) = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_f__the__inv__into__f) ).
fof(fact_INT__extend__simps_I8_J,axiom,
! [X160,X154,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X13,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBC(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool))),X160)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X13,tc_HOL_Obool),X154)),X160),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I8_J) ).
fof(fact_UN__extend__simps_I8_J,axiom,
! [X160,X154,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X13,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBC(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool))),X160)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X13,tc_HOL_Obool),X154)),X160),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I8_J) ).
fof(fact_INT__simps_I8_J,axiom,
! [X160,X154,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X13,tc_HOL_Obool),X154)),X160) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X13,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBC(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool))),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I8_J) ).
fof(fact_UN__simps_I8_J,axiom,
! [X160,X154,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X13,tc_HOL_Obool),X154)),X160) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X13,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBC(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool))),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I8_J) ).
fof(fact_inj__on__def,axiom,
! [X154,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,X154)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> ! [X227] :
( hBOOL(hAPP(hAPP(c_member(X10),X227),X154))
=> ( hAPP(X2,X3) = hAPP(X2,X227)
=> X3 = X227 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__def) ).
fof(fact_rtrancl__subset,axiom,
! [X216,X196,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X196),X216))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X216),c_Transitive__Closure_Ortrancl(X10,X196)))
=> c_Transitive__Closure_Ortrancl(X10,X216) = c_Transitive__Closure_Ortrancl(X10,X196) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__subset) ).
fof(fact_eq__equiv__class,axiom,
! [X154,X38,X39,X177,X10] :
( hAPP(c_Relation_OImage(X10,X10,X177),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X10,X10,X177),hAPP(hAPP(c_Set_Oinsert(X10),X38),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))
=> ( c_Equiv__Relations_Oequiv(X10,X154,X177)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X38),X154))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),X177)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__equiv__class) ).
fof(fact_map__of__Cons__code_I2_J,axiom,
! [X301,X144,X13,X10,X103,X121] :
( ( X121 = X103
=> hAPP(c_Map_Omap__of(X10,X13,hAPP(hAPP(c_List_Olist_OCons(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X121),X144)),X301)),X103) = hAPP(c_Option_Ooption_OSome(X13),X144) )
& ( X121 != X103
=> hAPP(c_Map_Omap__of(X10,X13,hAPP(hAPP(c_List_Olist_OCons(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X121),X144)),X301)),X103) = hAPP(c_Map_Omap__of(X10,X13,X301),X103) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__Cons__code_I2_J) ).
fof(fact_SigmaD1,axiom,
! [X160,X154,X38,X39,X13,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X39),X38)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X154),X160)))
=> hBOOL(hAPP(hAPP(c_member(X10),X39),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaD1) ).
fof(fact_setprod__zero__iff,axiom,
! [X2,X154,X10,X13] :
( ( class_Rings_Ocomm__semiring__1(X13)
& class_Rings_Ono__zero__divisors(X13) )
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),X154) = c_Groups_Ozero__class_Ozero(X13)
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
& hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X13) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__zero__iff) ).
fof(fact_card__image__le,axiom,
! [X2,X13,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X13),hAPP(c_Set_Oimage(X10,X13,X2),X154))),hAPP(c_Finite__Set_Ocard(X10),X154))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__image__le) ).
fof(fact_INTER__UNIV__conv_I2_J,axiom,
! [X160,X154,X10,X13] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X154),X160) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X13),X3),X154))
=> hAPP(X160,X3) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INTER__UNIV__conv_I2_J) ).
fof(fact_UNION__empty__conv_I2_J,axiom,
! [X160,X154,X10,X13] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X154),X160) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X13),X3),X154))
=> hAPP(X160,X3) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNION__empty__conv_I2_J) ).
fof(fact_INTER__UNIV__conv_I1_J,axiom,
! [X160,X154,X13,X10] :
( c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X154),X160)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X13),X3),X154))
=> hAPP(X160,X3) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INTER__UNIV__conv_I1_J) ).
fof(fact_UNION__empty__conv_I1_J,axiom,
! [X160,X154,X13,X10] :
( c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X154),X160)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X13),X3),X154))
=> hAPP(X160,X3) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNION__empty__conv_I1_J) ).
fof(fact_setsum__SucD,axiom,
! [X20,X154,X2,X10] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),X154) = hAPP(c_Nat_OSuc,X20)
=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
& 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,
! [X160,X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160))),c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),c_Big__Operators_Olattice__class_OInf__fin(X10,X154)),c_Big__Operators_Olattice__class_OInf__fin(X10,X160)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Ounion__inter) ).
fof(fact_Sup__fin_Ounion__inter,axiom,
! [X160,X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160))),c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),c_Big__Operators_Olattice__class_OSup__fin(X10,X154)),c_Big__Operators_Olattice__class_OSup__fin(X10,X160)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Ounion__inter) ).
fof(fact_Max_Ounion__inter,axiom,
! [X160,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),c_Big__Operators_Olinorder__class_OMax(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160))),c_Big__Operators_Olinorder__class_OMax(X10,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),c_Big__Operators_Olinorder__class_OMax(X10,X154)),c_Big__Operators_Olinorder__class_OMax(X10,X160)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Ounion__inter) ).
fof(fact_Min_Ounion__inter,axiom,
! [X160,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),c_Big__Operators_Olinorder__class_OMin(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160))),c_Big__Operators_Olinorder__class_OMin(X10,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),c_Big__Operators_Olinorder__class_OMin(X10,X154)),c_Big__Operators_Olinorder__class_OMin(X10,X160)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Ounion__inter) ).
fof(fact_type__definition_OAbs__inject,axiom,
! [X25,X16,X154,X256,X257,X13,X10] :
( c_Typedef_Otype__definition(X10,X13,X257,X256,X154)
=> ( hBOOL(hAPP(hAPP(c_member(X13),X16),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X13),X25),X154))
=> ( hAPP(X256,X16) = hAPP(X256,X25)
<=> X16 = X25 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_OAbs__inject) ).
fof(fact_Field__insert,axiom,
! [X177,X38,X39,X10] : hAPP(c_Relation_OField(X10),hAPP(hAPP(c_Set_Oinsert(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),X177)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X39),hAPP(hAPP(c_Set_Oinsert(X10),X38),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),hAPP(c_Relation_OField(X10),X177)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__insert) ).
fof(fact_start__le__sum,axiom,
! [X305,X20,X102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X305))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_start__le__sum) ).
fof(fact_pair__box_Osize_I1_J,axiom,
! [X38,X39,X115,X11,X13,X10] : c_Nitpick_Opair__box_Opair__box__size(X10,X13,X11,X115,c_Nitpick_Opair__box_OPairBox(X10,X13,X39,X38)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X11,X39)),hAPP(X115,X38))),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,
! [X101,X198,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X10,tc_HOL_Obool)),X198))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X198)))
=> ( ! [X266] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X266),X198))
=> hAPP(c_Finite__Set_Ocard(X10),X266) = X101 )
=> ( ! [X267] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X267),X198))
=> ! [X268] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X268),X198))
=> ( X267 != X268
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X267),X268) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ) )
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X101),hAPP(c_Finite__Set_Ocard(tc_fun(X10,tc_HOL_Obool)),X198)) = hAPP(c_Finite__Set_Ocard(X10),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X198)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__partition) ).
fof(fact_sorted__same,axiom,
! [X290,X1,X10] :
( class_Orderings_Olinorder(X10)
=> c_List_Olinorder__class_Osorted(X10,hAPP(c_List_Ofilter(X10,hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),hAPP(X1,X290))),X290)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__same) ).
fof(fact_inj__comp,axiom,
! [X1,X125,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> ( c_Fun_Oinj__on(X125,X10,X1,c_Orderings_Otop__class_Otop(tc_fun(X125,tc_HOL_Obool)))
=> c_Fun_Oinj__on(X125,X13,hAPP(c_Fun_Ocomp(X10,X13,X125,X2),X1),c_Orderings_Otop__class_Otop(tc_fun(X125,tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__comp) ).
fof(fact_set__update__subset__insert,axiom,
! [X16,X113,X290,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Olist__update(X10,X290),X113),X16))),hAPP(hAPP(c_Set_Oinsert(X10),X16),hAPP(c_List_Oset(X10),X290)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__update__subset__insert) ).
fof(fact_min__max_OInf__fin_Oremove,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X154) = X16 )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X154) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X16),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oremove) ).
fof(fact_min__max_OSup__fin_Oremove,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X154) = X16 )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X154) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X16),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oremove) ).
fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
! [X154,X2,X10] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),X154) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X10),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X154)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod2_I1_J) ).
fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
! [X154,X2,X10] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,tc_Nat_Onat),X2),X154) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X10),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X154)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod2_I2_J) ).
fof(fact_vimage__singleton__eq,axiom,
! [X38,X2,X13,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X39),hAPP(c_Set_Ovimage(X10,X13,X2),hAPP(hAPP(c_Set_Oinsert(X13),X38),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool))))))
<=> hAPP(X2,X39) = X38 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__singleton__eq) ).
fof(fact_inj__on__imageI2,axiom,
! [X154,X2,X255,X125,X13,X10] :
( c_Fun_Oinj__on(X10,X13,hAPP(c_Fun_Ocomp(X125,X13,X10,X255),X2),X154)
=> c_Fun_Oinj__on(X10,X125,X2,X154) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__imageI2) ).
fof(fact_finite__Diff__insert,axiom,
! [X160,X39,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),X160))))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Diff__insert) ).
fof(fact_insert__def,axiom,
! [X160,X39,X10] : hAPP(hAPP(c_Set_Oinsert(X10),X39),X160) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X39))),X160),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__def) ).
fof(fact_eq__add__iff1,axiom,
! [X141,X38,X18,X161,X39,X10] :
( class_Rings_Oring(X10)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X161)),X18) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X38),X161)),X141)
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X39),X38)),X161)),X18) = X141 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__add__iff1) ).
fof(fact_eq__add__iff2,axiom,
! [X141,X38,X18,X161,X39,X10] :
( class_Rings_Oring(X10)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X161)),X18) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X38),X161)),X141)
<=> X18 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X38),X39)),X161)),X141) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__add__iff2) ).
fof(fact_Image__INT__eq,axiom,
! [X160,X125,X154,X177,X13,X10] :
( c_Relation_Osingle__valued(X10,X13,hAPP(c_Relation_Oconverse(X13,X10),X177))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X125,tc_HOL_Obool))
=> hAPP(c_Relation_OImage(X13,X10,X177),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X125,tc_fun(X13,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X125,tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X125),c_Relation_OImage(X13,X10,X177)),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__INT__eq) ).
fof(fact_partition__filter2,axiom,
! [X290,X19,X10] : hAPP(c_Product__Type_Osnd(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Opartition(X10,X19,X290)) = hAPP(c_List_Ofilter(X10,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X10,c_fNot),X19)),X290),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition__filter2) ).
fof(fact_vimage__mono,axiom,
! [X2,X13,X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X13,X10,X2),X154)),hAPP(c_Set_Ovimage(X13,X10,X2),X160))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__mono) ).
fof(fact_image__mono,axiom,
! [X2,X13,X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X13,X2),X154)),hAPP(c_Set_Oimage(X10,X13,X2),X160))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__mono) ).
fof(fact_UN__equiv__class,axiom,
! [X39,X2,X13,X177,X154,X10] :
( c_Equiv__Relations_Oequiv(X10,X154,X177)
=> ( c_Equiv__Relations_Ocongruent(X10,tc_fun(X13,tc_HOL_Obool),X177,X2)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),hAPP(c_Relation_OImage(X10,X10,X177),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),X2) = hAPP(X2,X39) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__equiv__class) ).
fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = X16 )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X16),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,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,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = X16 )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X16),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oinsert__remove) ).
fof(fact_comp__cong,axiom,
! [X194,X195,X125,X10,X13,X253,X254,X255,X16,X1,X2] :
( hAPP(X2,hAPP(X1,X16)) = hAPP(X255,hAPP(X254,X253))
=> hAPP(hAPP(c_Fun_Ocomp(X13,X10,X125,X2),X1),X16) = hAPP(hAPP(c_Fun_Ocomp(X195,X10,X194,X255),X254),X253) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__cong) ).
fof(fact_folding__one_Oremove,axiom,
! [X16,X154,X225,X2,X10] :
( c_Finite__Set_Ofolding__one(X10,X2,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(X225,X154) = X16 )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(X225,X154) = hAPP(hAPP(X2,X16),hAPP(X225,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oremove) ).
fof(fact_card_Ounion__inter,axiom,
! [X160,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160))),hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X154)),hAPP(c_Finite__Set_Ocard(X10),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Ounion__inter) ).
fof(fact_card__Un__Int,axiom,
! [X160,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X154)),hAPP(c_Finite__Set_Ocard(X10),X160)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160))),hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Un__Int) ).
fof(fact_wf__same__fst,axiom,
! [X10,X196,X13,X19] :
( ! [X3] :
( hBOOL(hAPP(X19,X3))
=> c_Wellfounded_Owf(X13,hAPP(X196,X3)) )
=> c_Wellfounded_Owf(tc_prod(X10,X13),c_Recdef_Osame__fst(X10,X13,X19,X196)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__same__fst) ).
fof(fact_in__rel__def,axiom,
! [X25,X16,X196,X13,X10] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X10,X13,X196),X16),X25))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X16),X25)),X196)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__rel__def) ).
fof(fact_ran__distinct,axiom,
! [X295,X13,X10] :
( hBOOL(hAPP(c_List_Odistinct(X10),hAPP(hAPP(c_List_Omap(tc_prod(X10,X13),X10),c_Product__Type_Ofst(X10,X13)),X295)))
=> c_Map_Oran(X10,X13,c_Map_Omap__of(X10,X13,X295)) = hAPP(c_Set_Oimage(tc_prod(X10,X13),X13,c_Product__Type_Osnd(X10,X13)),hAPP(c_List_Oset(tc_prod(X10,X13)),X295)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ran__distinct) ).
fof(fact_restrict__upd__same,axiom,
! [X25,X16,X102,X13,X10] : c_Map_Orestrict__map(X10,X13,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),X102),X16),hAPP(c_Option_Ooption_OSome(X13),X25)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = c_Map_Orestrict__map(X10,X13,X102,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__upd__same) ).
fof(fact_Image__closed__trancl,axiom,
! [X48,X177,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_OImage(X10,X10,X177),X48)),X48))
=> hAPP(c_Relation_OImage(X10,X10,c_Transitive__Closure_Ortrancl(X10,X177)),X48) = X48 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__closed__trancl) ).
fof(fact_acc__downwards__aux,axiom,
! [X177,X39,X38,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X38),X39)),c_Transitive__Closure_Ortrancl(X10,X177)))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),c_Wellfounded_Oacc(X10,X177)))
=> hBOOL(hAPP(hAPP(c_member(X10),X38),c_Wellfounded_Oacc(X10,X177))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__downwards__aux) ).
fof(fact_acc__downwards,axiom,
! [X38,X177,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X39),c_Wellfounded_Oacc(X10,X177)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X38),X39)),c_Transitive__Closure_Ortrancl(X10,X177)))
=> hBOOL(hAPP(hAPP(c_member(X10),X38),c_Wellfounded_Oacc(X10,X177))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__downwards) ).
fof(fact_INT__simps_I2_J,axiom,
! [X160,X154,X13,X10,X198] :
( ( X198 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool),X10),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13,tc_HOL_Obool)),X154)),X160)) = c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)) )
& ( X198 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool),X10),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13,tc_HOL_Obool)),X154)),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13,tc_HOL_Obool)),X154),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X198),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I2_J) ).
fof(fact_INT__simps_I4_J,axiom,
! [X160,X154,X13,X10,X198] :
( ( X198 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool),X10),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13,tc_HOL_Obool)),X154)),X160)) = c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)) )
& ( X198 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool),X10),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13,tc_HOL_Obool)),X154)),X160)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13,tc_HOL_Obool)),X154),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X198),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I4_J) ).
fof(fact_UN__simps_I3_J,axiom,
! [X160,X154,X13,X10,X198] :
( ( X198 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool),X10),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13,tc_HOL_Obool)),X154)),X160)) = c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool)) )
& ( X198 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool),X10),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13,tc_HOL_Obool)),X154)),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13,tc_HOL_Obool)),X154),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X198),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I3_J) ).
fof(fact_INT__extend__simps_I2_J,axiom,
! [X160,X154,X13,X10,X198] :
( ( X198 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13,tc_HOL_Obool)),X154),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X198),X160)) = X154 )
& ( X198 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13,tc_HOL_Obool)),X154),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X198),X160)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool),X10),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13,tc_HOL_Obool)),X154)),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I2_J) ).
fof(fact_UN__extend__simps_I3_J,axiom,
! [X160,X154,X13,X10,X198] :
( ( X198 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13,tc_HOL_Obool)),X154),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X198),X160)) = X154 )
& ( X198 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13,tc_HOL_Obool)),X154),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X198),X160)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool),X10),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13,tc_HOL_Obool)),X154)),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I3_J) ).
fof(fact_INT__extend__simps_I4_J,axiom,
! [X160,X154,X13,X10,X198] :
( ( X198 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13,tc_HOL_Obool)),X154),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X198),X160)) = X154 )
& ( X198 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13,tc_HOL_Obool)),X154),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X198),X160)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool),X10),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13,tc_HOL_Obool)),X154)),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I4_J) ).
fof(fact_folding__one_Oinsert__remove,axiom,
! [X16,X154,X225,X2,X10] :
( c_Finite__Set_Ofolding__one(X10,X2,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(X225,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = X16 )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(X225,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(X2,X16),hAPP(X225,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oinsert__remove) ).
fof(fact_Min_Oremove,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(X10,X154) = X16 )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(X10,X154) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X16),c_Big__Operators_Olinorder__class_OMin(X10,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oremove) ).
fof(fact_Max_Oremove,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(X10,X154) = X16 )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(X10,X154) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X16),c_Big__Operators_Olinorder__class_OMax(X10,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oremove) ).
fof(fact_Inf__fin_Oremove,axiom,
! [X16,X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(X10,X154) = X16 )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(X10,X154) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X16),c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oremove) ).
fof(fact_Sup__fin_Oremove,axiom,
! [X16,X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(X10,X154) = X16 )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(X10,X154) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X16),c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oremove) ).
fof(fact_type__definition_ORep,axiom,
! [X16,X154,X256,X257,X13,X10] :
( c_Typedef_Otype__definition(X10,X13,X257,X256,X154)
=> hBOOL(hAPP(hAPP(c_member(X13),hAPP(X257,X16)),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep) ).
fof(fact_type__definition_OAbs__inverse,axiom,
! [X25,X154,X256,X257,X13,X10] :
( c_Typedef_Otype__definition(X10,X13,X257,X256,X154)
=> ( hBOOL(hAPP(hAPP(c_member(X13),X25),X154))
=> hAPP(X257,hAPP(X256,X25)) = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_OAbs__inverse) ).
fof(fact_sorted__insort__key,axiom,
! [X290,X16,X2,X13,X10] :
( class_Orderings_Olinorder(X10)
=> ( c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Omap(X13,X10),X2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X13,X10,X2),X16),X290)))
<=> c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Omap(X13,X10),X2),X290)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__insort__key) ).
fof(fact_mod__induct__0,axiom,
! [X113,X19,X166] :
( ! [X152] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X152),X166))
=> ( hBOOL(hAPP(X19,X152))
=> hBOOL(hAPP(X19,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X152),X166))) ) )
=> ( hBOOL(hAPP(X19,X113))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X113),X166))
=> hBOOL(hAPP(X19,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,
! [X81,X92,X84] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),X92)),X81) = 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),X92),X81))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),c_Divides_Odiv__class_Omod(tc_Int_Oint,X92,X81))),X81)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zmult1__eq) ).
fof(fact_div__mult1__eq,axiom,
! [X81,X92,X84] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X84),X92)),X81) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X84),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X92),X81))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X84),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X92,X81))),X81)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult1__eq) ).
fof(fact_nat__eq__add__iff1,axiom,
! [X20,X102,X165,X113,X163] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X163),X113))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X113),X165)),X102) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X163),X165)),X20)
<=> 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),X163)),X165)),X102) = X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__add__iff1) ).
fof(fact_nat__eq__add__iff2,axiom,
! [X20,X102,X165,X163,X113] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X113),X163))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X113),X165)),X102) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X163),X165)),X20)
<=> X102 = 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),X163),X113)),X165)),X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__add__iff2) ).
fof(fact_Un__Int__assoc__eq,axiom,
! [X198,X160,X154,X10] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)),X198) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X160),X198))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X198),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__assoc__eq) ).
fof(fact_INT__simps_I7_J,axiom,
! [X160,X154,X198,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X13),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154)),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X198),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I7_J) ).
fof(fact_UN__simps_I5_J,axiom,
! [X160,X154,X198,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X13),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154)),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X198),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I5_J) ).
fof(fact_UN__simps_I7_J,axiom,
! [X160,X154,X198,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X13),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154)),X160)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X198),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I7_J) ).
fof(fact_Int__UN__distrib,axiom,
! [X154,X241,X13,X160,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X160),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X241),X154)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X241),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X13),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X160)),X154)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__UN__distrib) ).
fof(fact_UN__extend__simps_I5_J,axiom,
! [X160,X198,X13,X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X198),X160)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X13),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154)),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I5_J) ).
fof(fact_Un__INT__distrib,axiom,
! [X154,X241,X13,X160,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X160),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X241),X154)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X241),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X13),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X160)),X154)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__INT__distrib) ).
fof(fact_INT__extend__simps_I7_J,axiom,
! [X160,X198,X13,X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X198),X160)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X13),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154)),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I7_J) ).
fof(fact_UN__extend__simps_I7_J,axiom,
! [X160,X198,X13,X154,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X198),X160)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X13),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154)),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I7_J) ).
fof(fact_union__comp__emptyR,axiom,
! [X198,X160,X154,X10] :
( hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X154),X160) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool))
=> ( hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X154),X198) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool))
=> hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X154),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X160),X198)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_union__comp__emptyR) ).
fof(fact_type__definition_ORep__range,axiom,
! [X154,X256,X257,X13,X10] :
( c_Typedef_Otype__definition(X10,X13,X257,X256,X154)
=> hAPP(c_Set_Oimage(X10,X13,X257),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = X154 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep__range) ).
fof(fact_singleton__quotient,axiom,
! [X177,X16,X10] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),X177) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_OImage(X10,X10,X177),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__quotient) ).
fof(fact_congruentD,axiom,
! [X73,X25,X2,X177,X13,X10] :
( c_Equiv__Relations_Ocongruent(X10,X13,X177,X2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X25),X73)),X177))
=> hAPP(X2,X25) = hAPP(X2,X73) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_congruentD) ).
fof(fact_rtrancl__subset__rtrancl,axiom,
! [X54,X177,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X177),c_Transitive__Closure_Ortrancl(X10,X54)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X10,X177)),c_Transitive__Closure_Ortrancl(X10,X54))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__subset__rtrancl) ).
fof(fact_rel__pow__imp__rtrancl,axiom,
! [X196,X20,X166,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X166),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X20),X196)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X166),c_Transitive__Closure_Ortrancl(X10,X196))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__imp__rtrancl) ).
fof(fact_acc__downward,axiom,
! [X39,X177,X38,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X38),c_Wellfounded_Oacc(X10,X177)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),X177))
=> hBOOL(hAPP(hAPP(c_member(X10),X39),c_Wellfounded_Oacc(X10,X177))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__downward) ).
fof(fact_Min_Oinsert__remove,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = X16 )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X16),c_Big__Operators_Olinorder__class_OMin(X10,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oinsert__remove) ).
fof(fact_Max_Oinsert__remove,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = X16 )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X16),c_Big__Operators_Olinorder__class_OMax(X10,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oinsert__remove) ).
fof(fact_Inf__fin_Oinsert__remove,axiom,
! [X16,X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = X16 )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X16),c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oinsert__remove) ).
fof(fact_Sup__fin_Oinsert__remove,axiom,
! [X16,X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = X16 )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X16),c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oinsert__remove) ).
fof(fact_type__definition_OAbs__image,axiom,
! [X154,X256,X257,X13,X10] :
( c_Typedef_Otype__definition(X10,X13,X257,X256,X154)
=> hAPP(c_Set_Oimage(X13,X10,X256),X154) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_OAbs__image) ).
fof(fact_inj__on__mapI,axiom,
! [X154,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(X10),tc_fun(X10,tc_HOL_Obool),c_List_Oset(X10)),X154)))
=> c_Fun_Oinj__on(tc_List_Olist(X10),tc_List_Olist(X13),hAPP(c_List_Omap(X10,X13),X2),X154) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__mapI) ).
fof(fact_update__zip,axiom,
! [X307,X120,X298,X297,X10,X94] : hAPP(hAPP(c_List_Olist__update(tc_prod(X94,X10),hAPP(hAPP(c_List_Ozip(X94,X10),X297),X298)),X120),X307) = hAPP(hAPP(c_List_Ozip(X94,X10),hAPP(hAPP(c_List_Olist__update(X94,X297),X120),hAPP(c_Product__Type_Ofst(X94,X10),X307))),hAPP(hAPP(c_List_Olist__update(X10,X298),X120),hAPP(c_Product__Type_Osnd(X94,X10),X307))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_update__zip) ).
fof(fact_finite__Collect__le__nat,axiom,
! [X101] : 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)),X101)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__le__nat) ).
fof(fact_finite__Collect__less__nat,axiom,
! [X101] : 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)),X101)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__less__nat) ).
fof(fact_O__assoc,axiom,
! [X232,X216,X196,X195,X13,X125,X10] : hAPP(hAPP(c_Relation_Orel__comp(X10,X125,X13),hAPP(hAPP(c_Relation_Orel__comp(X10,X195,X125),X196),X216)),X232) = hAPP(hAPP(c_Relation_Orel__comp(X10,X195,X13),X196),hAPP(hAPP(c_Relation_Orel__comp(X195,X125,X13),X216),X232)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_O__assoc) ).
fof(fact_setsum_Oremove,axiom,
! [X1,X16,X154,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1),X154) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(X1,X16)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oremove) ).
fof(fact_setsum__diff1_H,axiom,
! [X2,X39,X154,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),X154) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(X2,X39)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff1_H) ).
fof(fact_setprod_Oremove,axiom,
! [X1,X16,X154,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),X154) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),hAPP(X1,X16)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Oremove) ).
fof(fact_Pow__INT__eq,axiom,
! [X160,X154,X13,X10] : hAPP(c_Set_OPow(X10),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),X13),c_Set_OPow(X10)),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__INT__eq) ).
fof(fact_q__pos__lemma,axiom,
! [X150,X151,X130] :
( 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),X130),X151)),X150)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X150),X130))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X130))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X151)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_q__pos__lemma) ).
fof(fact_UN__le__eq__Un0,axiom,
! [X230,X20,X10] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X20)),X230) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X20)),X230)),hAPP(X230,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,
! [X160,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)))
=> hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X154)),hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160))) ),
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,
! [X230,X160,X154,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13,tc_HOL_Obool)),X154),X160)),X230) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X154),X230)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X160),X230)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__Un) ).
fof(fact_UN__Un,axiom,
! [X230,X160,X154,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13,tc_HOL_Obool)),X154),X160)),X230) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X154),X230)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X160),X230)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__Un) ).
fof(fact_dom__eq__singleton__conv,axiom,
! [X16,X2,X13,X10] :
( c_Map_Odom(X10,X13,X2) = hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))
<=> ? [X252] : X2 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),hAPP(c_COMBK(tc_Option_Ooption(X13),X10),c_Option_Ooption_ONone(X13))),X16),hAPP(c_Option_Ooption_OSome(X13),X252)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__eq__singleton__conv) ).
fof(fact_Compl__subset__Compl__iff,axiom,
! [X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X154)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X160)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__subset__Compl__iff) ).
fof(fact_INT__lower,axiom,
! [X160,X13,X154,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X154),X160)),hAPP(X160,X39))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__lower) ).
fof(fact_rtrancl__mono,axiom,
! [X54,X177,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X177),X54))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X10,X177)),c_Transitive__Closure_Ortrancl(X10,X54))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__mono) ).
fof(fact_vimage__INT,axiom,
! [X160,X154,X125,X2,X13,X10] : hAPP(c_Set_Ovimage(X10,X13,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X125,tc_fun(X13,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X125,tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X125),c_Set_Ovimage(X10,X13,X2)),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__INT) ).
fof(fact_vimage__UN,axiom,
! [X160,X154,X125,X2,X13,X10] : hAPP(c_Set_Ovimage(X10,X13,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X125,tc_fun(X13,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X125,tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X125),c_Set_Ovimage(X10,X13,X2)),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__UN) ).
fof(fact_Image__UN,axiom,
! [X160,X154,X125,X177,X10,X13] : hAPP(c_Relation_OImage(X13,X10,X177),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X125,tc_fun(X13,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X125,tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X125),c_Relation_OImage(X13,X10,X177)),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__UN) ).
fof(fact_image__UN,axiom,
! [X160,X154,X125,X2,X10,X13] : hAPP(c_Set_Oimage(X13,X10,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X125,tc_fun(X13,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X125,tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X125),c_Set_Oimage(X13,X10,X2)),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__UN) ).
fof(fact_diff__frac__eq,axiom,
! [X133,X93,X104,X105,X94] :
( class_Fields_Ofield(X94)
=> ( X105 != c_Groups_Ozero__class_Ozero(X94)
=> ( X104 != c_Groups_Ozero__class_Ozero(X94)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X93),X105)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X133),X104)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X93),X104)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X133),X105))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X105),X104)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__frac__eq) ).
fof(fact_add__frac__eq,axiom,
! [X133,X93,X104,X105,X94] :
( class_Fields_Ofield(X94)
=> ( X105 != c_Groups_Ozero__class_Ozero(X94)
=> ( X104 != c_Groups_Ozero__class_Ozero(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X93),X105)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X133),X104)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X93),X104)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X133),X105))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X105),X104)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__frac__eq) ).
fof(fact_Compl__eq,axiom,
! [X154,X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X154) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10),c_fNot),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X154))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__eq) ).
fof(fact_Suc__mult__le__cancel1,axiom,
! [X20,X102,X101] :
( 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,X101)),X102)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X101)),X20)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).
fof(fact_Suc__mult__less__cancel1,axiom,
! [X20,X102,X101] :
( 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,X101)),X102)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X101)),X20)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).
fof(fact_split__pos__lemma,axiom,
! [X20,X19,X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X101))
=> ( hBOOL(hAPP(hAPP(X19,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20),X101)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20,X101)))
<=> ! [X152,X123] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X123))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X123),X101))
& X20 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X101),X152)),X123) )
=> hBOOL(hAPP(hAPP(X19,X152),X123)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__pos__lemma) ).
fof(fact_UN__o,axiom,
! [X2,X1,X125,X154,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X154),hAPP(c_Fun_Ocomp(X125,tc_fun(X10,tc_HOL_Obool),X13,X1),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X125,tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X13,X125,X2),X154)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__o) ).
fof(fact_setsum_Oinsert__remove,axiom,
! [X16,X1,X154,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(X1,X16)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oinsert__remove) ).
fof(fact_setprod_Oinsert__remove,axiom,
! [X16,X1,X154,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),hAPP(X1,X16)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Oinsert__remove) ).
fof(fact_fun__upd__upd,axiom,
! [X73,X25,X16,X2,X13,X10] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,X13),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,X13),X2),X16),X25)),X16),X73) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,X13),X2),X16),X73),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__upd) ).
fof(fact_split__neg__lemma,axiom,
! [X20,X19,X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(X19,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20),X101)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20,X101)))
<=> ! [X152,X123] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),X123))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X123),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& X20 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X101),X152)),X123) )
=> hBOOL(hAPP(hAPP(X19,X152),X123)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__neg__lemma) ).
fof(fact_zip__same__conv__map,axiom,
! [X290,X10] : hAPP(hAPP(c_List_Ozip(X10,X10),X290),X290) = hAPP(hAPP(c_List_Omap(X10,tc_prod(X10,X10)),hAPP(hAPP(c_COMBS(X10,X10,tc_prod(X10,X10)),c_Product__Type_OPair(X10,X10)),c_COMBI(X10))),X290),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__same__conv__map) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
! [X160,X154] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X154),X160) = 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)),X154)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X160))),
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,
! [X160,X154] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X154),X160) = 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)),X154)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X160))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J) ).
fof(fact_Plus__def,axiom,
! [X160,X154,X13,X10] : c_Sum__Type_OPlus(X10,X13,X154,X160) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_sum(X10,X13),tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,tc_sum(X10,X13),c_Sum__Type_OInl(X10,X13)),X154)),hAPP(c_Set_Oimage(X13,tc_sum(X10,X13),c_Sum__Type_OInr(X13,X10)),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Plus__def) ).
fof(fact_power__Suc__less,axiom,
! [X42,X84,X94] :
( class_Rings_Olinordered__semidom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),c_Groups_Oone__class_Oone(X94)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42))),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__less) ).
fof(fact_type__definition_ORep__inject,axiom,
! [X25,X16,X154,X256,X257,X13,X10] :
( c_Typedef_Otype__definition(X10,X13,X257,X256,X154)
=> ( hAPP(X257,X16) = hAPP(X257,X25)
<=> X16 = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep__inject) ).
fof(fact_finite__cartesian__productD2,axiom,
! [X160,X154,X13,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X154),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),X160))))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__cartesian__productD2) ).
fof(fact_finite__cartesian__productD1,axiom,
! [X160,X154,X13,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X154),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),X160))))
=> ( X160 != c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__cartesian__productD1) ).
fof(fact_type__definition_ORep__inverse,axiom,
! [X16,X154,X256,X257,X13,X10] :
( c_Typedef_Otype__definition(X10,X13,X257,X256,X154)
=> hAPP(X256,hAPP(X257,X16)) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep__inverse) ).
fof(fact_abs__triangle__ineq2,axiom,
! [X92,X84,X94] :
( class_Groups_Oordered__ab__group__add__abs(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),X84)),hAPP(c_Groups_Oabs__class_Oabs(X94),X92))),hAPP(c_Groups_Oabs__class_Oabs(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X84),X92)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__triangle__ineq2) ).
fof(fact_abs__triangle__ineq2__sym,axiom,
! [X92,X84,X94] :
( class_Groups_Oordered__ab__group__add__abs(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),X84)),hAPP(c_Groups_Oabs__class_Oabs(X94),X92))),hAPP(c_Groups_Oabs__class_Oabs(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X92),X84)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__triangle__ineq2__sym) ).
fof(fact_vimage__insert,axiom,
! [X160,X39,X2,X13,X10] : hAPP(c_Set_Ovimage(X10,X13,X2),hAPP(hAPP(c_Set_Oinsert(X13),X39),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X10,X13,X2),hAPP(hAPP(c_Set_Oinsert(X13),X39),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(X10,X13,X2),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__insert) ).
fof(fact_DomainI,axiom,
! [X177,X38,X39,X13,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X39),X38)),X177))
=> hBOOL(hAPP(hAPP(c_member(X10),X39),hAPP(c_Relation_ODomain(X10,X13),X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainI) ).
fof(fact_RangeI,axiom,
! [X177,X38,X39,X13,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X39),X38)),X177))
=> hBOOL(hAPP(hAPP(c_member(X13),X38),hAPP(c_Relation_ORange(X10,X13),X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeI) ).
fof(fact_set__drop__subset__set__drop,axiom,
! [X290,X10,X102,X20] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20),X102))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Odrop(X10),X102),X290))),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Odrop(X10),X20),X290)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__drop__subset__set__drop) ).
fof(fact_set__take__subset__set__take,axiom,
! [X290,X10,X20,X102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Otake(X10),X102),X290))),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Otake(X10),X20),X290)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__take__subset__set__take) ).
fof(fact_sorted__list__of__set__insert,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> c_List_Olinorder__class_Osorted__list__of__set(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X10,c_COMBI(X10)),X16),c_List_Olinorder__class_Osorted__list__of__set(X10,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__list__of__set__insert) ).
fof(fact_power__le__imp__le__base,axiom,
! [X92,X42,X84,X94] :
( class_Rings_Olinordered__semidom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),hAPP(c_Nat_OSuc,X42))),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X92),hAPP(c_Nat_OSuc,X42))))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X92)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__le__imp__le__base) ).
fof(fact_sup__le__fold__sup,axiom,
! [X38,X39,X154,X10] :
( class_Lattices_Osemilattice__sup(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X39),X38)),hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__sup__class_Osup(X10)),X38),X154))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__le__fold__sup) ).
fof(fact_min__max_Osup__le__fold__sup,axiom,
! [X38,X39,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X39),X38)),hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omax(X10)),X38),X154))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__le__fold__sup) ).
fof(fact_Domain__mono,axiom,
! [X54,X177,X13,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),X177),X54))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X10,X13),X177)),hAPP(c_Relation_ODomain(X10,X13),X54))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__mono) ).
fof(fact_less__half__sum,axiom,
! [X92,X84,X94] :
( class_Fields_Olinordered__field(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),c_Groups_Oone__class_Oone(X94)),c_Groups_Oone__class_Oone(X94))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__half__sum) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
! [X160,X154] :
( c_Nat__Transfer_Onat__set(X154)
=> ( c_Nat__Transfer_Onat__set(X160)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X154),X160) = 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),X154)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X160))) ) ),
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,
! [X160,X154] :
( c_Nat__Transfer_Onat__set(X154)
=> ( c_Nat__Transfer_Onat__set(X160)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X154),X160) = 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),X154)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X160))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J) ).
fof(fact_combine__common__factor,axiom,
! [X81,X92,X142,X84,X94] :
( class_Rings_Osemiring(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X142)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X142)),X81)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92)),X142)),X81) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_combine__common__factor) ).
fof(fact_Id__on__subset__Times,axiom,
! [X154,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Relation_OId__on(X10,X154)),hAPP(hAPP(c_Product__Type_OSigma(X10,X10),X154),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X10),X154)))),
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,
! [X19,X10,X13] : hAPP(c_Relation_ORange(X13,X10),hAPP(c_Set_OCollect(tc_prod(X13,X10)),hAPP(c_Product__Type_Oprod_Oprod__case(X13,X10,tc_HOL_Obool),X19))) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X13)),hAPP(c_COMBC(X13,X10,tc_HOL_Obool),X19))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Collect__split) ).
fof(fact_equiv__type,axiom,
! [X177,X154,X10] :
( c_Equiv__Relations_Oequiv(X10,X154,X177)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X177),hAPP(hAPP(c_Product__Type_OSigma(X10,X10),X154),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X10),X154)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__type) ).
fof(fact_map__comp__map,axiom,
! [X1,X2,X10,X13,X125] : hAPP(c_Fun_Ocomp(tc_List_Olist(X125),tc_List_Olist(X13),tc_List_Olist(X10),hAPP(c_List_Omap(X125,X13),X2)),hAPP(c_List_Omap(X10,X125),X1)) = hAPP(c_List_Omap(X10,X13),hAPP(c_Fun_Ocomp(X125,X13,X10,X2),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__map) ).
fof(fact_List_Omap_Ocomp,axiom,
! [X1,X2,X10,X13,X125] : hAPP(c_Fun_Ocomp(tc_List_Olist(X125),tc_List_Olist(X13),tc_List_Olist(X10),hAPP(c_List_Omap(X125,X13),X2)),hAPP(c_List_Omap(X10,X125),X1)) = hAPP(c_List_Omap(X10,X13),hAPP(c_Fun_Ocomp(X125,X13,X10,X2),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Omap_Ocomp) ).
fof(fact_Option_Omap_Ocomp,axiom,
! [X1,X2,X10,X13,X125] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(X125),tc_Option_Ooption(X13),tc_Option_Ooption(X10),hAPP(c_Option_Omap(X125,X13),X2)),hAPP(c_Option_Omap(X10,X125),X1)) = hAPP(c_Option_Omap(X10,X13),hAPP(c_Fun_Ocomp(X125,X13,X10,X2),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Option_Omap_Ocomp) ).
fof(fact_refl__onD1,axiom,
! [X25,X16,X177,X154,X10] :
( c_Relation_Orefl__on(X10,X154,X177)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),X177))
=> hBOOL(hAPP(hAPP(c_member(X10),X16),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onD1) ).
fof(fact_refl__onD2,axiom,
! [X25,X16,X177,X154,X10] :
( c_Relation_Orefl__on(X10,X154,X177)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),X177))
=> hBOOL(hAPP(hAPP(c_member(X10),X25),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onD2) ).
fof(fact_listrel_ONil,axiom,
! [X177,X10] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_ONil(X10)),c_List_Olist_ONil(X10))),c_List_Olistrel(X10,X177))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel_ONil) ).
fof(fact_Int__Union2,axiom,
! [X154,X160,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X160)),X154) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X160),hAPP(hAPP(c_COMBC(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool))),X154)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Union2) ).
fof(fact_Id__on__iff,axiom,
! [X154,X25,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),c_Relation_OId__on(X10,X154)))
<=> ( X16 = X25
& hBOOL(hAPP(hAPP(c_member(X10),X16),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__iff) ).
fof(fact_finite__Plus__iff,axiom,
! [X160,X154,X13,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X10,X13)),c_Sum__Type_OPlus(X10,X13,X154,X160)))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus__iff) ).
fof(fact_finite__PlusD_I1_J,axiom,
! [X160,X154,X13,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X10,X13)),c_Sum__Type_OPlus(X10,X13,X154,X160)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__PlusD_I1_J) ).
fof(fact_finite__PlusD_I2_J,axiom,
! [X160,X154,X13,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X10,X13)),c_Sum__Type_OPlus(X10,X13,X154,X160)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X160)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__PlusD_I2_J) ).
fof(fact_SigmaI,axiom,
! [X160,X38,X13,X154,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X13),X38),hAPP(X160,X39)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X39),X38)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X154),X160))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaI) ).
fof(fact_foldl__assoc,axiom,
! [X299,X25,X16,X10] :
( class_Groups_Osemigroup__add(X10)
=> hAPP(c_List_Ofoldl(X10,X10,c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X16),X25)),X299) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X16),hAPP(c_List_Ofoldl(X10,X10,c_Groups_Oplus__class_Oplus(X10),X25),X299)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__assoc) ).
fof(fact_rel__pow__0__I,axiom,
! [X196,X16,X10] : hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X16)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X196))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__0__I) ).
fof(fact_quotient__disj,axiom,
! [X78,X48,X177,X154,X10] :
( c_Equiv__Relations_Oequiv(X10,X154,X177)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X48),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X154),X177)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X78),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X154),X177)))
=> ( X48 = X78
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X48),X78) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__disj) ).
fof(fact_pick__same,axiom,
! [X290,X10,X162] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X162),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290)))
=> hAPP(c_Random_Opick(X10,hAPP(hAPP(c_List_Omap(X10,tc_prod(tc_Code__Numeral_Ocode__numeral,X10)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X10),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X290)),hAPP(c_Code__Numeral_Oof__nat,X162)) = hAPP(hAPP(c_List_Onth(X10),X290),X162) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pick__same) ).
fof(fact_subset__card__intvl__is__intvl,axiom,
! [X101,X154] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X154),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X101),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X101),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X154)))))
=> X154 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X101),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X101),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X154))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__card__intvl__is__intvl) ).
fof(fact_ord_OatLeastAtMost__iff,axiom,
! [X165,X162,X228,X113,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X113),c_SetInterval_Oord_OatLeastAtMost(X10,X228,X162,X165)))
<=> ( hBOOL(hAPP(hAPP(X228,X162),X113))
& hBOOL(hAPP(hAPP(X228,X113),X165)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OatLeastAtMost__iff) ).
fof(fact_ord_OgreaterThanLessThan__iff,axiom,
! [X165,X162,X229,X113,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X113),c_SetInterval_Oord_OgreaterThanLessThan(X10,X229,X162,X165)))
<=> ( hBOOL(hAPP(hAPP(X229,X162),X113))
& hBOOL(hAPP(hAPP(X229,X113),X165)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OgreaterThanLessThan__iff) ).
fof(fact_set__Cons__sing__Nil,axiom,
! [X154,X10] : c_List_Oset__Cons(X10,X154,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X10)),c_List_Olist_ONil(X10)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X10),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(X10,tc_List_Olist(X10),hAPP(hAPP(c_COMBC(X10,tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_OCons(X10)),c_List_Olist_ONil(X10))),X154),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__Cons__sing__Nil) ).
fof(fact_INT__insert__distrib,axiom,
! [X160,X39,X13,X154,X165,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X165),X154))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool),X10),hAPP(c_Set_Oinsert(X13),X39)),X160)) = hAPP(hAPP(c_Set_Oinsert(X13),X39),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X154),X160)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__insert__distrib) ).
fof(fact_UN__insert__distrib,axiom,
! [X160,X39,X13,X154,X165,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X165),X154))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool),X10),hAPP(c_Set_Oinsert(X13),X39)),X160)) = hAPP(hAPP(c_Set_Oinsert(X13),X39),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X154),X160)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__insert__distrib) ).
fof(fact_finite__conv__nat__seg__image,axiom,
! [X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
<=> ? [X83,X247] : X154 = hAPP(c_Set_Oimage(tc_Nat_Onat,X10,X247),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)),X83))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__conv__nat__seg__image) ).
fof(fact_nat__seg__image__imp__finite,axiom,
! [X20,X2,X10,X154] :
( X154 = hAPP(c_Set_Oimage(tc_Nat_Onat,X10,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)),X20)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__seg__image__imp__finite) ).
fof(fact_take__hd__drop,axiom,
! [X297,X94,X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)))
=> hAPP(hAPP(c_List_Oappend(X94),hAPP(hAPP(c_List_Otake(X94),X42),X297)),hAPP(hAPP(c_List_Olist_OCons(X94),hAPP(c_List_Ohd(X94),hAPP(hAPP(c_List_Odrop(X94),X42),X297))),c_List_Olist_ONil(X94))) = hAPP(hAPP(c_List_Otake(X94),hAPP(c_Nat_OSuc,X42)),X297) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__hd__drop) ).
fof(fact_Diff__insert2,axiom,
! [X160,X39,X154,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),X160)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),X160),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__insert2) ).
fof(fact_listrel__rtrancl__refl,axiom,
! [X177,X290,X10] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X290),X290)),c_List_Olistrel(X10,c_Transitive__Closure_Ortrancl(X10,X177)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__rtrancl__refl) ).
fof(fact_InlI,axiom,
! [X160,X13,X154,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hBOOL(hAPP(hAPP(c_member(tc_sum(X10,X13)),hAPP(c_Sum__Type_OInl(X10,X13),X39)),c_Sum__Type_OPlus(X10,X13,X154,X160))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_InlI) ).
fof(fact_InrI,axiom,
! [X154,X13,X160,X38,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X38),X160))
=> hBOOL(hAPP(hAPP(c_member(tc_sum(X13,X10)),hAPP(c_Sum__Type_OInr(X10,X13),X38)),c_Sum__Type_OPlus(X13,X10,X154,X160))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_InrI) ).
fof(fact_Inter__subset,axiom,
! [X160,X154,X10] :
( ! [X270] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X270),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X270),X160)) )
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X154)),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__subset) ).
fof(fact_zmod__zmult2__eq,axiom,
! [X92,X84,X81] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X81))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X92),X81)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X92),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),X92),X81))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zmult2__eq) ).
fof(fact_Int__greatest,axiom,
! [X160,X154,X198,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X198),X154))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X198),X160))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X198),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__greatest) ).
fof(fact_max__Suc2,axiom,
! [X20,X102] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X102),hAPP(c_Nat_OSuc,X20)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X20),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)),X20)),X102),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__Suc2) ).
fof(fact_rel__pow__add,axiom,
! [X196,X20,X102,X10] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X20)),X196) = hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X102),X196)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X20),X196)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__add) ).
fof(fact_Union__mono,axiom,
! [X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),X154),X160))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X154)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X160))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__mono) ).
fof(fact_Inter__anti__mono,axiom,
! [X154,X160,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),X160),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X154)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X160))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__anti__mono) ).
fof(fact_abs__triangle__ineq4,axiom,
! [X92,X84,X94] :
( class_Groups_Oordered__ab__group__add__abs(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X84),X92))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),X84)),hAPP(c_Groups_Oabs__class_Oabs(X94),X92)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__triangle__ineq4) ).
fof(fact_abs__triangle__ineq,axiom,
! [X92,X84,X94] :
( class_Groups_Oordered__ab__group__add__abs(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),X84)),hAPP(c_Groups_Oabs__class_Oabs(X94),X92)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__triangle__ineq) ).
fof(fact_min__Suc2,axiom,
! [X20,X102] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X102),hAPP(c_Nat_OSuc,X20)) = 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)),X20)),X102),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__Suc2) ).
fof(fact_card_Oremove,axiom,
! [X16,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Finite__Set_Ocard(X10),X154) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oremove) ).
fof(fact_zip__update,axiom,
! [X105,X298,X93,X120,X297,X10,X94] : hAPP(hAPP(c_List_Ozip(X94,X10),hAPP(hAPP(c_List_Olist__update(X94,X297),X120),X93)),hAPP(hAPP(c_List_Olist__update(X10,X298),X120),X105)) = hAPP(hAPP(c_List_Olist__update(tc_prod(X94,X10),hAPP(hAPP(c_List_Ozip(X94,X10),X297),X298)),X120),hAPP(hAPP(c_Product__Type_OPair(X94,X10),X93),X105)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__update) ).
fof(fact_image__Int,axiom,
! [X160,X154,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> hAPP(c_Set_Oimage(X10,X13,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X13,X2),X154)),hAPP(c_Set_Oimage(X10,X13,X2),X160)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Int) ).
fof(fact_image__set__diff,axiom,
! [X160,X154,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> hAPP(c_Set_Oimage(X10,X13,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X13,X2),X154)),hAPP(c_Set_Oimage(X10,X13,X2),X160)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__set__diff) ).
fof(fact_the__inv__into__onto,axiom,
! [X154,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,X154)
=> hAPP(c_Set_Oimage(X13,X10,c_Fun_Othe__inv__into(X10,X13,X154,X2)),hAPP(c_Set_Oimage(X10,X13,X2),X154)) = X154 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__onto) ).
fof(fact_pair__box_Orecs,axiom,
! [X38,X39,X12,X10,X125,X13] : c_Nitpick_Opair__box_Opair__box__rec(X13,X125,X10,X12,c_Nitpick_Opair__box_OPairBox(X13,X125,X39,X38)) = hAPP(hAPP(X12,X39),X38),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__box_Orecs) ).
fof(fact_pair__box_Osimps_I2_J,axiom,
! [X38,X39,X12,X10,X125,X13] : c_Nitpick_Opair__box_Opair__box__case(X13,X125,X10,X12,c_Nitpick_Opair__box_OPairBox(X13,X125,X39,X38)) = hAPP(hAPP(X12,X39),X38),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__box_Osimps_I2_J) ).
fof(fact_setprod__dvd__setprod__subset,axiom,
! [X2,X154,X160,X10,X13] :
( ( class_Groups_Ocomm__monoid__mult(X13)
& class_Rings_Odvd(X13) )
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X13),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),X154)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),X160))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__dvd__setprod__subset) ).
fof(fact_zip__takeWhile__fst,axiom,
! [X289,X290,X19,X13,X10] : hAPP(hAPP(c_List_Ozip(X10,X13),c_List_OtakeWhile(X10,X19,X290)),X289) = c_List_OtakeWhile(tc_prod(X10,X13),hAPP(c_Fun_Ocomp(X10,tc_HOL_Obool,tc_prod(X10,X13),X19),c_Product__Type_Ofst(X10,X13)),hAPP(hAPP(c_List_Ozip(X10,X13),X290),X289)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__takeWhile__fst) ).
fof(fact_zmult__zless__mono2__lemma,axiom,
! [X103,X119,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X120),X119))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X103))
=> 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),X103)),X120)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X103)),X119))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__zless__mono2__lemma) ).
fof(fact_Diff__Int2,axiom,
! [X160,X198,X154,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X198)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X160),X198)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X198)),X160),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Int2) ).
fof(fact_Int__Un__distrib2,axiom,
! [X154,X198,X160,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X160),X198)),X154) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X160),X154)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X198),X154)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Un__distrib2) ).
fof(fact_Diff__Int__distrib2,axiom,
! [X198,X160,X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160)),X198) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X198)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X160),X198)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Int__distrib2) ).
fof(fact_Un__Int__distrib2,axiom,
! [X154,X198,X160,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X160),X198)),X154) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X160),X154)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X198),X154)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__distrib2) ).
fof(fact_Un__Diff,axiom,
! [X198,X160,X154,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)),X198) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X198)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X160),X198)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff) ).
fof(fact_bset_I3_J,axiom,
! [X160,X53,X197] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X197))
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X53),c_Groups_Oone__class_Oone(tc_Int_Oint))),X160))
=> ( ! [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),X197)))
=> ! [X227] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X227),X160))
=> X53 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X227),X3) ) )
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X53),X197) = X53 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I3_J) ).
fof(fact_aset_I3_J,axiom,
! [X154,X53,X197] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X197))
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X53),c_Groups_Oone__class_Oone(tc_Int_Oint))),X154))
=> ( ! [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),X197)))
=> ! [X227] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X227),X154))
=> X53 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X227),X3) ) )
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X53),X197) = X53 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I3_J) ).
fof(fact_take__add,axiom,
! [X297,X94,X119,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X120),X119)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)))
=> hAPP(hAPP(c_List_Otake(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X120),X119)),X297) = hAPP(hAPP(c_List_Oappend(X94),hAPP(hAPP(c_List_Otake(X94),X120),X297)),hAPP(hAPP(c_List_Otake(X94),X119),hAPP(hAPP(c_List_Odrop(X94),X120),X297))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__add) ).
fof(fact_card_Ounion__inter__neutral,axiom,
! [X160,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( ( ? [X3] : hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)))
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
=> hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X154)),hAPP(c_Finite__Set_Ocard(X10),X160)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Ounion__inter__neutral) ).
fof(fact_inj__on__map__add__dom,axiom,
! [X283,X102,X13,X10] :
( c_Fun_Oinj__on(X10,tc_Option_Ooption(X13),c_Map_Omap__add(X10,X13,X102,X283),c_Map_Odom(X10,X13,X283))
<=> c_Fun_Oinj__on(X10,tc_Option_Ooption(X13),X283,c_Map_Odom(X10,X13,X283)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__map__add__dom) ).
fof(fact_card__Suc__Diff1,axiom,
! [X16,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(X10),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Suc__Diff1) ).
fof(fact_folding_Ocommute__comp_H_H,axiom,
! [X160,X154,X225,X2,X13,X10] :
( c_Finite__Set_Ofolding(X10,X13,X2,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> hAPP(c_Fun_Ocomp(X13,X13,X13,hAPP(X225,X160)),hAPP(X225,X154)) = hAPP(c_Fun_Ocomp(X13,X13,X13,hAPP(X225,X154)),hAPP(X225,X160)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__comp_H_H) ).
fof(fact_Compl__INT,axiom,
! [X160,X154,X13,X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X13),c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool))),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__INT) ).
fof(fact_Compl__UN,axiom,
! [X160,X154,X13,X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X13),c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool))),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__UN) ).
fof(fact_fold1Set__sing,axiom,
! [X38,X39,X2,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X10,X2,hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),X38))
<=> X39 = X38 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1Set__sing) ).
fof(fact_folding_Ounion,axiom,
! [X160,X154,X225,X2,X13,X10] :
( c_Finite__Set_Ofolding(X10,X13,X2,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(X225,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(c_Fun_Ocomp(X13,X13,X13,hAPP(X225,X154)),hAPP(X225,X160)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ounion) ).
fof(fact_split__div_H,axiom,
! [X20,X102,X19] :
( hBOOL(hAPP(X19,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X102),X20)))
<=> ( ( X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& hBOOL(hAPP(X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X153] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X153)),X102))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),hAPP(c_Nat_OSuc,X153))))
& hBOOL(hAPP(X19,X153)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__div_H) ).
fof(fact_card_Oinsert__remove,axiom,
! [X16,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oinsert__remove) ).
fof(fact_o__eq__elim,axiom,
! [X141,X18,X195,X38,X39,X10,X13,X125] :
( hAPP(c_Fun_Ocomp(X125,X13,X10,X39),X38) = hAPP(c_Fun_Ocomp(X195,X13,X10,X18),X141)
=> ! [X252] : hAPP(X39,hAPP(X38,X252)) = hAPP(X18,hAPP(X141,X252)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__elim) ).
fof(fact_o__eq__dest,axiom,
! [X168,X141,X18,X195,X38,X39,X10,X13,X125] :
( hAPP(c_Fun_Ocomp(X125,X13,X10,X39),X38) = hAPP(c_Fun_Ocomp(X195,X13,X10,X18),X141)
=> hAPP(X39,hAPP(X38,X168)) = hAPP(X18,hAPP(X141,X168)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__dest) ).
fof(fact_insort__left__comm,axiom,
! [X290,X25,X16,X10] :
( class_Orderings_Olinorder(X10)
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X10,c_COMBI(X10)),X16),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X10,c_COMBI(X10)),X25),X290)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X10,c_COMBI(X10)),X25),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X10,c_COMBI(X10)),X16),X290)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__left__comm) ).
fof(fact_o__eq__id__dest,axiom,
! [X168,X18,X38,X39,X10,X13,X125] :
( hAPP(c_Fun_Ocomp(X125,X13,X10,X39),X38) = hAPP(c_Fun_Ocomp(X13,X13,X10,c_Fun_Oid(X13)),X18)
=> hAPP(X39,hAPP(X38,X168)) = hAPP(X18,X168) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__id__dest) ).
fof(fact_equiv__class__self,axiom,
! [X39,X177,X154,X10] :
( c_Equiv__Relations_Oequiv(X10,X154,X177)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hBOOL(hAPP(hAPP(c_member(X10),X39),hAPP(c_Relation_OImage(X10,X10,X177),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__class__self) ).
fof(fact_inj__image__mem__iff,axiom,
! [X154,X39,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_member(X13),hAPP(X2,X39)),hAPP(c_Set_Oimage(X10,X13,X2),X154)))
<=> hBOOL(hAPP(hAPP(c_member(X10),X39),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__mem__iff) ).
fof(fact_INF__subset,axiom,
! [X2,X160,X154,X10,X13] :
( class_Complete__Lattice_Ocomplete__lattice(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,X13),X160),X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,X13),X154),X2))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__subset) ).
fof(fact_SUP__subset,axiom,
! [X2,X160,X154,X10,X13] :
( class_Complete__Lattice_Ocomplete__lattice(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,X13),X154),X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,X13),X160),X2))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__subset) ).
fof(fact_finite__range__map__of,axiom,
! [X285,X13,X10] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X10)),hAPP(c_Set_Oimage(X13,tc_Option_Ooption(X10),c_Map_Omap__of(X13,X10,X285)),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__range__map__of) ).
fof(fact_UN__simps_I1_J,axiom,
! [X160,X39,X13,X10,X198] :
( ( X198 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool),X10),hAPP(c_Set_Oinsert(X13),X39)),X160)) = c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool)) )
& ( X198 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool),X10),hAPP(c_Set_Oinsert(X13),X39)),X160)) = hAPP(hAPP(c_Set_Oinsert(X13),X39),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X198),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I1_J) ).
fof(fact_UN__extend__simps_I1_J,axiom,
! [X160,X39,X13,X10,X198] :
( ( X198 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Set_Oinsert(X13),X39),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X198),X160)) = hAPP(hAPP(c_Set_Oinsert(X13),X39),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool))) )
& ( X198 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Set_Oinsert(X13),X39),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X198),X160)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool),X10),hAPP(c_Set_Oinsert(X13),X39)),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I1_J) ).
fof(fact_setsum__right__distrib,axiom,
! [X154,X2,X13,X177,X10] :
( class_Rings_Osemiring__0(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X177),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X10),X2),X154)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X10),hAPP(hAPP(c_COMBB(X10,X10,X13),hAPP(c_Groups_Otimes__class_Otimes(X10),X177)),X2)),X154) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__right__distrib) ).
fof(fact_mlex__less,axiom,
! [X196,X10,X25,X16,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X16)),hAPP(X2,X25)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),c_Wellfounded_Omlex__prod(X10,X2,X196))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__less) ).
fof(fact_range__composition,axiom,
! [X1,X2,X125,X10,X13] : hAPP(c_Set_Oimage(X13,X10,hAPP(hAPP(c_COMBB(X125,X10,X13),X2),X1)),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))) = hAPP(c_Set_Oimage(X125,X10,X2),hAPP(c_Set_Oimage(X13,X125,X1),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__composition) ).
fof(fact_sorted__equals__nth__mono,axiom,
! [X290,X10] :
( class_Orderings_Olinorder(X10)
=> ( c_List_Olinorder__class_Osorted(X10,X290)
<=> ! [X123] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X123),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290)))
=> ! [X152] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X152),X123))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_List_Onth(X10),X290),X152)),hAPP(hAPP(c_List_Onth(X10),X290),X123))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__equals__nth__mono) ).
fof(fact_INT__D,axiom,
! [X39,X160,X154,X13,X38,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X38),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X154),X160)))
=> ( hBOOL(hAPP(hAPP(c_member(X13),X39),X154))
=> hBOOL(hAPP(hAPP(c_member(X10),X38),hAPP(X160,X39))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__D) ).
fof(fact_foldl__absorb0,axiom,
! [X299,X16,X10] :
( class_Groups_Omonoid__add(X10)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X16),hAPP(c_List_Ofoldl(X10,X10,c_Groups_Oplus__class_Oplus(X10),c_Groups_Ozero__class_Ozero(X10)),X299)) = hAPP(c_List_Ofoldl(X10,X10,c_Groups_Oplus__class_Oplus(X10),X16),X299) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__absorb0) ).
fof(fact_list__update__swap,axiom,
! [X309,X93,X297,X94,X310,X120] :
( X120 != X310
=> hAPP(hAPP(c_List_Olist__update(X94,hAPP(hAPP(c_List_Olist__update(X94,X297),X120),X93)),X310),X309) = hAPP(hAPP(c_List_Olist__update(X94,hAPP(hAPP(c_List_Olist__update(X94,X297),X310),X309)),X120),X93) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__swap) ).
fof(fact_rel__pow__commute,axiom,
! [X20,X196,X10] : hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X196),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X20),X196)) = hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X20),X196)),X196),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__commute) ).
fof(fact_card__insert,axiom,
! [X16,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert) ).
fof(fact_divide__left__mono,axiom,
! [X81,X84,X92,X94] :
( class_Fields_Olinordered__field(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X92),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X81))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X81),X84)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X81),X92))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__left__mono) ).
fof(fact_divide__strict__left__mono,axiom,
! [X81,X84,X92,X94] :
( class_Fields_Olinordered__field(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X92),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X81))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X81),X84)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X81),X92))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__left__mono) ).
fof(fact_mono__Field,axiom,
! [X54,X177,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X177),X54))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_OField(X10),X177)),hAPP(c_Relation_OField(X10),X54))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mono__Field) ).
fof(fact_folding_Ocommute__comp_H,axiom,
! [X16,X154,X225,X2,X13,X10] :
( c_Finite__Set_Ofolding(X10,X13,X2,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(c_Fun_Ocomp(X13,X13,X13,hAPP(X2,X16)),hAPP(X225,X154)) = hAPP(c_Fun_Ocomp(X13,X13,X13,hAPP(X225,X154)),hAPP(X2,X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__comp_H) ).
fof(fact_INT__simps_I5_J,axiom,
! [X160,X39,X198,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X13),hAPP(c_Set_Oinsert(X10),X39)),X160)) = hAPP(hAPP(c_Set_Oinsert(X10),X39),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X198),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I5_J) ).
fof(fact_INT__extend__simps_I5_J,axiom,
! [X160,X198,X13,X39,X10] : hAPP(hAPP(c_Set_Oinsert(X10),X39),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X198),X160)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X198),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X13),hAPP(c_Set_Oinsert(X10),X39)),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I5_J) ).
fof(fact_left__add__mult__distrib,axiom,
! [X103,X119,X80,X120] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X120),X80)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X119),X80)),X103)) = 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),X120),X119)),X80)),X103),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).
fof(fact_zip__takeWhile__snd,axiom,
! [X289,X19,X290,X13,X10] : hAPP(hAPP(c_List_Ozip(X10,X13),X290),c_List_OtakeWhile(X13,X19,X289)) = c_List_OtakeWhile(tc_prod(X10,X13),hAPP(c_Fun_Ocomp(X13,tc_HOL_Obool,tc_prod(X10,X13),X19),c_Product__Type_Osnd(X10,X13)),hAPP(hAPP(c_List_Ozip(X10,X13),X290),X289)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__takeWhile__snd) ).
fof(fact_option__map__o__empty,axiom,
! [X16,X2,X125,X10,X13] : hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(X13),tc_Option_Ooption(X10),X125,hAPP(c_Option_Omap(X13,X10),X2)),hAPP(c_COMBK(tc_Option_Ooption(X13),X125),c_Option_Ooption_ONone(X13))),X16) = c_Option_Ooption_ONone(X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option__map__o__empty) ).
fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
! [X2,X16,X10,X13,X113] :
( ( X113 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_New__DSequence_Oneg__decr__bind(X13,X10,X16,X2),X113) = c_Lazy__Sequence_Ohit__bound(X10) )
& ( X113 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_New__DSequence_Oneg__decr__bind(X13,X10,X16,X2),X113) = c_Lazy__Sequence_Ohb__bind(X13,X10,hAPP(X16,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X113),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X13,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X10))),X2),X113)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__decr__bind__def) ).
fof(fact_inj__fun,axiom,
! [X125,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> c_Fun_Oinj__on(X10,tc_fun(X125,X13),hAPP(hAPP(c_COMBB(X13,tc_fun(X125,X13),X10),c_COMBK(X13,X125)),X2),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__fun) ).
fof(fact_Int__eq__Inter,axiom,
! [X160,X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(tc_fun(X10,tc_HOL_Obool)),X160),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__eq__Inter) ).
fof(fact_Un__eq__Union,axiom,
! [X160,X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(tc_fun(X10,tc_HOL_Obool)),X160),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__eq__Union) ).
fof(fact_divide__left__mono__neg,axiom,
! [X81,X92,X84,X94] :
( class_Fields_Olinordered__field__inverse__zero(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X81),c_Groups_Ozero__class_Ozero(X94)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X81),X84)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X81),X92))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__left__mono__neg) ).
fof(fact_divide__strict__left__mono__neg,axiom,
! [X81,X92,X84,X94] :
( class_Fields_Olinordered__field(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X81),c_Groups_Ozero__class_Ozero(X94)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X81),X84)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X81),X92))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__left__mono__neg) ).
fof(fact_nth__zip,axiom,
! [X298,X10,X297,X94,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X298)))
=> hAPP(hAPP(c_List_Onth(tc_prod(X94,X10)),hAPP(hAPP(c_List_Ozip(X94,X10),X297),X298)),X120) = hAPP(hAPP(c_Product__Type_OPair(X94,X10),hAPP(hAPP(c_List_Onth(X94),X297),X120)),hAPP(hAPP(c_List_Onth(X10),X298),X120)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__zip) ).
fof(fact_mod__mult2__eq,axiom,
! [X81,X92,X84] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X84,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X92),X81)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X92),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X84),X92),X81))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X84,X92)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult2__eq) ).
fof(fact_list__update__length,axiom,
! [X105,X298,X93,X297,X94] : hAPP(hAPP(c_List_Olist__update(X94,hAPP(hAPP(c_List_Oappend(X94),X297),hAPP(hAPP(c_List_Olist_OCons(X94),X93),X298))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)),X105) = hAPP(hAPP(c_List_Oappend(X94),X297),hAPP(hAPP(c_List_Olist_OCons(X94),X105),X298)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__length) ).
fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
! [X177,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_HOL_Obool)),c_List_Olistrel1(X10,c_Transitive__Closure_Ortrancl(X10,X177))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X10),c_List_Olistrel1(X10,X177)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1__rtrancl__subset__rtrancl__listrel1) ).
fof(fact_rtrancl__Un__rtrancl,axiom,
! [X216,X196,X10] : c_Transitive__Closure_Ortrancl(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X10,X196)),c_Transitive__Closure_Ortrancl(X10,X216))) = c_Transitive__Closure_Ortrancl(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X196),X216)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__rtrancl) ).
fof(fact_div__dvd__div,axiom,
! [X18,X38,X39,X10] :
( class_Divides_Osemiring__div(X10)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X39),X38))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X39),X18))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X10),X38),X39)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X10),X18),X39)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X38),X18)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__dvd__div) ).
fof(fact_unity__coeff__ex,axiom,
! [X162,X19,X10] :
( ( class_Rings_Odvd(X10)
& class_Rings_Osemiring__0(X10) )
=> ( ? [X3] : hBOOL(hAPP(X19,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X162),X3)))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X162),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X3),c_Groups_Ozero__class_Ozero(X10))))
& hBOOL(hAPP(X19,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unity__coeff__ex) ).
fof(fact_zip__map__fst__snd,axiom,
! [X299,X13,X10] : hAPP(hAPP(c_List_Ozip(X10,X13),hAPP(hAPP(c_List_Omap(tc_prod(X10,X13),X10),c_Product__Type_Ofst(X10,X13)),X299)),hAPP(hAPP(c_List_Omap(tc_prod(X10,X13),X13),c_Product__Type_Osnd(X10,X13)),X299)) = X299,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__map__fst__snd) ).
fof(fact_setprod__reindex__cong,axiom,
! [X204,X1,X160,X154,X2,X13,X10,X125] :
( class_Groups_Ocomm__monoid__mult(X125)
=> ( c_Fun_Oinj__on(X10,X13,X2,X154)
=> ( X160 = hAPP(c_Set_Oimage(X10,X13,X2),X154)
=> ( X1 = hAPP(c_Fun_Ocomp(X13,X125,X10,X204),X2)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X13,X125),X204),X160) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X125),X1),X154) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__reindex__cong) ).
fof(fact_sum__squares__ge__zero,axiom,
! [X105,X93,X94] :
( class_Rings_Olinordered__ring(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X93),X93)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X105),X105)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).
fof(fact_pred__nat__trancl__eq__le,axiom,
! [X20,X102] :
( 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),X102),X20)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__nat__trancl__eq__le) ).
fof(fact_folding_Ocommute__comp,axiom,
! [X16,X25,X225,X2,X13,X10] :
( c_Finite__Set_Ofolding(X10,X13,X2,X225)
=> hAPP(c_Fun_Ocomp(X13,X13,X13,hAPP(X2,X25)),hAPP(X2,X16)) = hAPP(c_Fun_Ocomp(X13,X13,X13,hAPP(X2,X16)),hAPP(X2,X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__comp) ).
fof(fact_Sigma__Int__distrib1,axiom,
! [X198,X242,X241,X13,X10] : hAPP(hAPP(c_Product__Type_OSigma(X10,X13),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X241),X242)),X198) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X241),X198)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X242),X198)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Int__distrib1) ).
fof(fact_Sigma__Un__distrib1,axiom,
! [X198,X242,X241,X13,X10] : hAPP(hAPP(c_Product__Type_OSigma(X10,X13),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X241),X242)),X198) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X241),X198)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X242),X198)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Un__distrib1) ).
fof(fact_Sigma__Diff__distrib1,axiom,
! [X198,X242,X241,X13,X10] : hAPP(hAPP(c_Product__Type_OSigma(X10,X13),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X241),X242)),X198) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X241),X198)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X242),X198)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Diff__distrib1) ).
fof(fact_in__set__butlast__appendI,axiom,
! [X289,X290,X16,X10] :
( ( hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),c_List_Obutlast(X10,X290))))
| hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),c_List_Obutlast(X10,X289)))) )
=> hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),c_List_Obutlast(X10,hAPP(hAPP(c_List_Oappend(X10),X290),X289))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__butlast__appendI) ).
fof(fact_acc__subset,axiom,
! [X190,X191,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X191),X190))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),c_Wellfounded_Oacc(X10,X190)),c_Wellfounded_Oacc(X10,X191))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__subset) ).
fof(fact_insort__key__left__comm,axiom,
! [X290,X13,X25,X16,X2,X10] :
( class_Orderings_Olinorder(X10)
=> ( hAPP(X2,X16) != hAPP(X2,X25)
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X13,X10,X2),X25),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X13,X10,X2),X16),X290)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X13,X10,X2),X16),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X13,X10,X2),X25),X290)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__key__left__comm) ).
fof(fact_map__of__SomeD,axiom,
! [X25,X101,X290,X10,X13] :
( hAPP(c_Map_Omap__of(X13,X10,X290),X101) = hAPP(c_Option_Ooption_OSome(X10),X25)
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X13,X10)),hAPP(hAPP(c_Product__Type_OPair(X13,X10),X101),X25)),hAPP(c_List_Oset(tc_prod(X13,X10)),X290))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__SomeD) ).
fof(fact_map__of__is__SomeD,axiom,
! [X25,X16,X285,X10,X13] :
( hAPP(c_Map_Omap__of(X13,X10,X285),X16) = hAPP(c_Option_Ooption_OSome(X10),X25)
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X13,X10)),hAPP(hAPP(c_Product__Type_OPair(X13,X10),X16),X25)),hAPP(c_List_Oset(tc_prod(X13,X10)),X285))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__is__SomeD) ).
fof(fact_divmod__int__rel__div__mod,axiom,
! [X84,X92] :
( X92 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(X84,X92),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),X92)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X92)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__div__mod) ).
fof(fact_INT__extend__simps_I10_J,axiom,
! [X2,X160,X125,X154,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBB(X125,tc_fun(X10,tc_HOL_Obool),X13),X160),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X125,tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X13,X125,X2),X154)),X160),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I10_J) ).
fof(fact_UN__extend__simps_I10_J,axiom,
! [X2,X160,X125,X154,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBB(X125,tc_fun(X10,tc_HOL_Obool),X13),X160),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X125,tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X13,X125,X2),X154)),X160),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I10_J) ).
fof(fact_INT__simps_I10_J,axiom,
! [X160,X154,X2,X125,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X125,X13,X2),X154)),X160) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X125,tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBB(X13,tc_fun(X10,tc_HOL_Obool),X125),X160),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I10_J) ).
fof(fact_UN__simps_I10_J,axiom,
! [X160,X154,X2,X125,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X125,X13,X2),X154)),X160) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X125,tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBB(X13,tc_fun(X10,tc_HOL_Obool),X125),X160),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I10_J) ).
fof(fact_divmod__nat__rel,axiom,
! [X42,X97] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X97,X42),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X97),X42)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X97,X42)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel) ).
fof(fact_Compl__anti__mono,axiom,
! [X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X160)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X154))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__anti__mono) ).
fof(fact_finite__surj__inj,axiom,
! [X2,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(c_Set_Oimage(X10,X10,X2),X154)))
=> c_Fun_Oinj__on(X10,X10,X2,X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__surj__inj) ).
fof(fact_Compl__Times__UNIV1,axiom,
! [X154,X13,X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),X154))) = hAPP(hAPP(c_Product__Type_OSigma(X10,X13),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X13,tc_HOL_Obool)),X154))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__Times__UNIV1) ).
fof(fact_Compl__Times__UNIV2,axiom,
! [X154,X13,X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X154),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(X10,X13),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X154)),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__Times__UNIV2) ).
fof(fact_Cons__acc__listrel1I,axiom,
! [X290,X177,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X16),c_Wellfounded_Oacc(X10,X177)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X290),c_Wellfounded_Oacc(tc_List_Olist(X10),c_List_Olistrel1(X10,X177))))
=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290)),c_Wellfounded_Oacc(tc_List_Olist(X10),c_List_Olistrel1(X10,X177)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__acc__listrel1I) ).
fof(fact_neg__divide__le__eq,axiom,
! [X39,X38,X18,X10] :
( class_Fields_Olinordered__field(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),X18)),X39))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X18)),X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__divide__le__eq) ).
fof(fact_neg__divide__less__eq,axiom,
! [X39,X38,X18,X10] :
( class_Fields_Olinordered__field(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),X18)),X39))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X18)),X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__divide__less__eq) ).
fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
! [X2,X16,X10,X13,X113] :
( ( X113 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_New__DSequence_Opos__decr__bind(X13,X10,X16,X2),X113) = c_Lazy__Sequence_Oempty(X10) )
& ( X113 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_New__DSequence_Opos__decr__bind(X13,X10,X16,X2),X113) = c_Lazy__Sequence_Obind(X13,X10,hAPP(X16,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X113),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X13,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X10)),X2),X113)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__decr__bind__def) ).
fof(fact_accp__subset,axiom,
! [X190,X191,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),X191),X190))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),c_Wellfounded_Oaccp(X10,X190)),c_Wellfounded_Oaccp(X10,X191))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__subset) ).
fof(fact_folding__idem_Osubset__comp__idem,axiom,
! [X160,X154,X225,X2,X13,X10] :
( c_Finite__Set_Ofolding__idem(X10,X13,X2,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),X154))
=> hAPP(c_Fun_Ocomp(X13,X13,X13,hAPP(X225,X154)),hAPP(X225,X160)) = hAPP(X225,X154) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Osubset__comp__idem) ).
fof(fact_insort__insert__triv,axiom,
! [X290,X16,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
=> c_List_Olinorder__class_Oinsort__insert__key(X10,X10,c_COMBI(X10),X16,X290) = X290 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__insert__triv) ).
fof(fact_split__div__lemma,axiom,
! [X102,X158,X20] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X158)),X102))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),hAPP(c_Nat_OSuc,X158)))) )
<=> X158 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X102),X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__div__lemma) ).
fof(fact_setsum__diff,axiom,
! [X2,X160,X154,X10,X13] :
( class_Groups_Oab__group__add(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X13),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),X154)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),X160)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff) ).
fof(fact_id__take__nth__drop,axiom,
! [X297,X94,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)))
=> X297 = hAPP(hAPP(c_List_Oappend(X94),hAPP(hAPP(c_List_Otake(X94),X120),X297)),hAPP(hAPP(c_List_Olist_OCons(X94),hAPP(hAPP(c_List_Onth(X94),X297),X120)),hAPP(hAPP(c_List_Odrop(X94),hAPP(c_Nat_OSuc,X120)),X297))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__take__nth__drop) ).
fof(fact_less__than__iff,axiom,
! [X25,X16] :
( 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),X16),X25)),c_Wellfounded_Oless__than))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16),X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__than__iff) ).
fof(fact_image__image,axiom,
! [X154,X1,X125,X2,X10,X13] : hAPP(c_Set_Oimage(X13,X10,X2),hAPP(c_Set_Oimage(X125,X13,X1),X154)) = hAPP(c_Set_Oimage(X125,X10,hAPP(hAPP(c_COMBB(X13,X10,X125),X2),X1)),X154),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__image) ).
fof(fact_inj__on__map__eq__map,axiom,
! [X289,X290,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),X290)),hAPP(c_List_Oset(X10),X289)))
=> ( hAPP(hAPP(c_List_Omap(X10,X13),X2),X290) = hAPP(hAPP(c_List_Omap(X10,X13),X2),X289)
<=> X290 = X289 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__map__eq__map) ).
fof(fact_map__inj__on,axiom,
! [X289,X290,X2,X10,X13] :
( hAPP(hAPP(c_List_Omap(X13,X10),X2),X290) = hAPP(hAPP(c_List_Omap(X13,X10),X2),X289)
=> ( c_Fun_Oinj__on(X13,X10,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13,tc_HOL_Obool)),hAPP(c_List_Oset(X13),X290)),hAPP(c_List_Oset(X13),X289)))
=> X290 = X289 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__inj__on) ).
fof(fact_zdiff__int__split,axiom,
! [X25,X16,X19] :
( hBOOL(hAPP(X19,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16),X25))))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X16))
=> hBOOL(hAPP(X19,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X16)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25)))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16),X25))
=> hBOOL(hAPP(X19,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,
! [X97,X92,X42,X84,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42)),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),X42))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X97)),X92)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__le__dvd) ).
fof(fact_map__add__assoc,axiom,
! [X280,X277,X278,X13,X10] : c_Map_Omap__add(X10,X13,X278,c_Map_Omap__add(X10,X13,X277,X280)) = c_Map_Omap__add(X10,X13,c_Map_Omap__add(X10,X13,X278,X277),X280),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__assoc) ).
fof(fact_Image__Int__eq,axiom,
! [X160,X154,X196,X13,X10] :
( c_Relation_Osingle__valued(X10,X13,hAPP(c_Relation_Oconverse(X13,X10),X196))
=> hAPP(c_Relation_OImage(X13,X10,X196),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_OImage(X13,X10,X196),X154)),hAPP(c_Relation_OImage(X13,X10,X196),X160)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Int__eq) ).
fof(fact_frac__le,axiom,
! [X104,X133,X105,X93,X94] :
( class_Fields_Olinordered__field(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X93))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X105))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X133))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X133),X104))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X93),X104)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X105),X133))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_frac__le) ).
fof(fact_mult__mono_H,axiom,
! [X112,X81,X92,X84,X94] :
( class_Rings_Oordered__semiring(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X81),X112))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X81))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X81)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X112))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__mono_H) ).
fof(fact_mult__mono,axiom,
! [X112,X81,X92,X84,X94] :
( class_Rings_Oordered__semiring(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X81),X112))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X81))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X81)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X112))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__mono) ).
fof(fact_frac__less,axiom,
! [X104,X133,X105,X93,X94] :
( class_Fields_Olinordered__field(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X93))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X105))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X133))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X133),X104))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X93),X104)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X105),X133))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_frac__less) ).
fof(fact_frac__less2,axiom,
! [X104,X133,X105,X93,X94] :
( class_Fields_Olinordered__field(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X93))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X105))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X133))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X133),X104))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X93),X104)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X105),X133))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_frac__less2) ).
fof(fact_mult__less__le__imp__less,axiom,
! [X112,X81,X92,X84,X94] :
( class_Rings_Olinordered__semiring__strict(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X81),X112))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X81))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X81)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X112))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__le__imp__less) ).
fof(fact_mult__le__less__imp__less,axiom,
! [X112,X81,X92,X84,X94] :
( class_Rings_Olinordered__semiring__strict(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X81),X112))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X81))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X81)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X112))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__less__imp__less) ).
fof(fact_mult__strict__mono_H,axiom,
! [X112,X81,X92,X84,X94] :
( class_Rings_Olinordered__semiring__strict(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X81),X112))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X81))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X81)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X112))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__mono_H) ).
fof(fact_mult__strict__mono,axiom,
! [X112,X81,X92,X84,X94] :
( class_Rings_Olinordered__semiring__strict(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X81),X112))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X81))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X81)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X112))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__mono) ).
fof(fact_setsum__diff1__ring,axiom,
! [X2,X39,X154,X10,X13] :
( class_Rings_Oring(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X13),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),X154)),hAPP(X2,X39)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff1__ring) ).
fof(fact_geometric__sum,axiom,
! [X20,X16,X10] :
( class_Fields_Ofield(X10)
=> ( X16 != c_Groups_Oone__class_Oone(X10)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),hAPP(c_Power_Opower__class_Opower(X10),X16)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X16),X20)),c_Groups_Oone__class_Oone(X10))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X16),c_Groups_Oone__class_Oone(X10))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_geometric__sum) ).
fof(fact_listsum__abs,axiom,
! [X290,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Groups_Oabs__class_Oabs(X10),hAPP(c_List_Omonoid__add__class_Olistsum(X10),X290))),hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(X10,X10),c_Groups_Oabs__class_Oabs(X10)),X290)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__abs) ).
fof(fact_evaln_OLocal,axiom,
! [X77,X20,X39,X78,X85,X18] :
( c_Natural_Oevaln(X18,hAPP(hAPP(hAPP(c_Natural_Oupdate,X85),c_Com_Ovname_OLoc(X78)),hAPP(X39,X85)),X20,X77)
=> c_Natural_Oevaln(c_Com_Ocom_OLocal(X78,X39,X18),X85,X20,hAPP(hAPP(hAPP(c_Natural_Oupdate,X77),c_Com_Ovname_OLoc(X78)),hAPP(hAPP(c_Natural_Ogetlocs,X85),X78))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OLocal) ).
fof(fact_image__add__atLeastLessThan,axiom,
! [X163,X113,X101] : 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)),X101)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X113),X163)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X113),X101)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X163),X101)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__add__atLeastLessThan) ).
fof(fact_setsum__diff__nat__ivl,axiom,
! [X2,X166,X20,X102,X10] :
( class_Groups_Oab__group__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20),X166))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X102),X166))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X102),X20))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X20),X166)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff__nat__ivl) ).
fof(fact_setsum__add__nat__ivl,axiom,
! [X2,X166,X20,X102,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20),X166))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X102),X20))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X20),X166))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X102),X166)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__add__nat__ivl) ).
fof(fact_mult__right__le__imp__le,axiom,
! [X92,X81,X84,X94] :
( class_Rings_Olinordered__semiring__strict(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X81)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X81)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X81))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X92)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__le__imp__le) ).
fof(fact_mult__left__le__imp__le,axiom,
! [X92,X84,X81,X94] :
( class_Rings_Olinordered__semiring__strict(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),X84)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),X92)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X81))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X92)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__le__imp__le) ).
fof(fact_mult__le__cancel__left__pos,axiom,
! [X38,X39,X18,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X39)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X38)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel__left__pos) ).
fof(fact_mult__right__less__imp__less,axiom,
! [X92,X81,X84,X94] :
( class_Rings_Olinordered__semiring(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X81)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X81)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X81))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),X92)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__less__imp__less) ).
fof(fact_mult__less__imp__less__right,axiom,
! [X92,X81,X84,X94] :
( class_Rings_Olinordered__semiring__strict(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X81)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X81)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X81))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),X92)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__imp__less__right) ).
fof(fact_power__less__imp__less__base,axiom,
! [X92,X42,X84,X94] :
( class_Rings_Olinordered__semidom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X92),X42)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),X92)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__imp__less__base) ).
fof(fact_mult__left__less__imp__less,axiom,
! [X92,X84,X81,X94] :
( class_Rings_Olinordered__semiring(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),X84)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),X92)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X81))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),X92)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__less__imp__less) ).
fof(fact_mult__less__imp__less__left,axiom,
! [X92,X84,X81,X94] :
( class_Rings_Olinordered__semiring__strict(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),X84)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),X92)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X81))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),X92)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__imp__less__left) ).
fof(fact_mult__less__cancel__left__pos,axiom,
! [X38,X39,X18,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X39)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X38)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).
fof(fact_setsum__diff__nat,axiom,
! [X2,X154,X160,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),X154)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff__nat) ).
fof(fact_fold1__strict__below__iff,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Finite__Set_Ofold1(X10,c_Orderings_Oord__class_Omin(X10)),X154)),X16))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X3),X16)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__strict__below__iff) ).
fof(fact_fold1__below__iff,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Finite__Set_Ofold1(X10,c_Orderings_Oord__class_Omin(X10)),X154)),X16))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X3),X16)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__below__iff) ).
fof(fact_INF1__D,axiom,
! [X39,X38,X160,X154,X13,X10] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X154),X160),X38))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hBOOL(hAPP(hAPP(X160,X39),X38)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF1__D) ).
fof(fact_power__increasing__iff,axiom,
! [X25,X16,X38,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Oone__class_Oone(X10)),X38))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X38),X16)),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X38),X25)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X16),X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__increasing__iff) ).
fof(fact_power__le__imp__le__exp,axiom,
! [X42,X97,X84,X94] :
( class_Rings_Olinordered__semidom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Oone__class_Oone(X94)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X97)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),X42)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__le__imp__le__exp) ).
fof(fact_power__less__imp__less__exp,axiom,
! [X42,X97,X84,X94] :
( class_Rings_Olinordered__semidom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Oone__class_Oone(X94)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X97)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).
fof(fact_power__strict__increasing__iff,axiom,
! [X25,X16,X38,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Oone__class_Oone(X10)),X38))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X38),X16)),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X38),X25)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16),X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__increasing__iff) ).
fof(fact_select,axiom,
! [X54,X10,X290] :
( X290 != c_List_Olist_ONil(X10)
=> hBOOL(hAPP(hAPP(c_member(X10),hAPP(c_Product__Type_Ofst(X10,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(X10,X290),X54))),hAPP(c_List_Oset(X10),X290))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_select) ).
fof(fact_card__cartesian__product__singleton,axiom,
! [X154,X16,X13,X10] : hAPP(c_Finite__Set_Ocard(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),X154))) = hAPP(c_Finite__Set_Ocard(X13),X154),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__cartesian__product__singleton) ).
fof(fact_evalc_Oequations_I9_J,axiom,
! [X50,X52,X51] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X51)),X52),X50))
<=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X51))),X52),X50)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I9_J) ).
fof(fact_evalc_OBody,axiom,
! [X59,X60,X86] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X86))),X60),X59))
=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X86)),X60),X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OBody) ).
fof(fact_splitD,axiom,
! [X38,X39,X2,X13,X10] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,tc_HOL_Obool),X2),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X39),X38)))
=> hBOOL(hAPP(hAPP(X2,X39),X38)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splitD) ).
fof(fact_swap__inj__on,axiom,
! [X154,X13,X10] : c_Fun_Oinj__on(tc_prod(X10,X13),tc_prod(X13,X10),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,tc_prod(X13,X10)),hAPP(c_COMBC(X13,X10,tc_prod(X13,X10)),c_Product__Type_OPair(X13,X10))),X154),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_swap__inj__on) ).
fof(fact_setprod__pos__nat,axiom,
! [X2,X216,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X216))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X216))
=> 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(X10,tc_Nat_Onat),X2),X216))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__pos__nat) ).
fof(fact_setprod__pos__nat__iff,axiom,
! [X2,X216,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X216))
=> ( 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(X10,tc_Nat_Onat),X2),X216)))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X216))
=> 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,
! [X20,X102,X2,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X102),hAPP(c_Nat_OSuc,X20))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,tc_Nat_Onat),X2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X102,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__bounds__cl__Suc__ivl) ).
fof(fact_mult__le__cancel__left__neg,axiom,
! [X38,X39,X18,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X39)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X38)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X38),X39)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).
fof(fact_mult__less__cancel__left__neg,axiom,
! [X38,X39,X18,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X39)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X38)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X38),X39)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).
fof(fact_empty__upd__none,axiom,
! [X220,X16,X10,X13] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X13,tc_Option_Ooption(X10)),hAPP(c_COMBK(tc_Option_Ooption(X10),X13),c_Option_Ooption_ONone(X10))),X16),c_Option_Ooption_ONone(X10)),X220) = c_Option_Ooption_ONone(X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__upd__none) ).
fof(fact_Int__lower1,axiom,
! [X160,X154,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)),X154)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__lower1) ).
fof(fact_Int__lower2,axiom,
! [X160,X154,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__lower2) ).
fof(fact_Diff__subset,axiom,
! [X160,X154,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160)),X154)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__subset) ).
fof(fact_listsum__map__remove1,axiom,
! [X2,X290,X16,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
=> hAPP(c_List_Omonoid__add__class_Olistsum(X13),hAPP(hAPP(c_List_Omap(X10,X13),X2),X290)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(X2,X16)),hAPP(c_List_Omonoid__add__class_Olistsum(X13),hAPP(hAPP(c_List_Omap(X10,X13),X2),c_List_Oremove1(X10,X16,X290)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__map__remove1) ).
fof(fact_Int__Un__distrib,axiom,
! [X198,X160,X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X160),X198)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X198)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Un__distrib) ).
fof(fact_Diff__Int__distrib,axiom,
! [X160,X154,X198,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X198),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X198),X154)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X198),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Int__distrib) ).
fof(fact_Un__Int__distrib,axiom,
! [X198,X160,X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X160),X198)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X198)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__distrib) ).
fof(fact_Diff__Int,axiom,
! [X198,X160,X154,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X160),X198)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X198)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Int) ).
fof(fact_Diff__Un,axiom,
! [X198,X160,X154,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X160),X198)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X198)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Un) ).
fof(fact_prod_Orecs,axiom,
! [X38,X39,X12,X10,X125,X13] : c_Product__Type_Oprod_Oprod__rec(X13,X125,X10,X12,hAPP(hAPP(c_Product__Type_OPair(X13,X125),X39),X38)) = hAPP(hAPP(X12,X39),X38),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod_Orecs) ).
fof(fact_New__DSequence_Oneg__bind__def,axiom,
! [X113,X2,X16,X10,X13] : hAPP(c_New__DSequence_Oneg__bind(X13,X10,X16,X2),X113) = c_Lazy__Sequence_Ohb__bind(X13,X10,hAPP(X16,X113),hAPP(hAPP(c_COMBC(X13,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X10))),X2),X113)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__bind__def) ).
fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
! [X20,X102,X2,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X102)),hAPP(c_Nat_OSuc,X20))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,tc_Nat_Onat),X2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X102),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__bounds__Suc__ivl) ).
fof(fact_image__add__atLeastAtMost,axiom,
! [X163,X113,X101] : 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)),X101)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X113,X163)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X113),X101),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X163),X101)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__add__atLeastAtMost) ).
fof(fact_Int__Collect,axiom,
! [X19,X154,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(c_Set_OCollect(X10),X19))))
<=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
& hBOOL(hAPP(X19,X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Collect) ).
fof(fact_atLeastLessThan__subset__iff,axiom,
! [X141,X18,X38,X39,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X39),X38)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X18),X141)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X38),X39))
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X18),X39))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X38),X141)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__subset__iff) ).
fof(fact_sum_Osize_I1_J,axiom,
! [X39,X115,X11,X13,X10] : c_Sum__Type_Osum_Osum__size(X10,X13,X11,X115,hAPP(c_Sum__Type_OInl(X10,X13),X39)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X11,X39)),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,
! [X38,X115,X11,X13,X10] : c_Sum__Type_Osum_Osum__size(X10,X13,X11,X115,hAPP(c_Sum__Type_OInr(X13,X10),X38)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X115,X38)),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,
! [X160,X154,X225,X2,X13,X10] :
( c_Finite__Set_Ofolding__idem(X10,X13,X2,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> hAPP(X225,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(c_Fun_Ocomp(X13,X13,X13,hAPP(X225,X154)),hAPP(X225,X160)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Ounion__idem) ).
fof(fact_wf__Un,axiom,
! [X54,X177,X10] :
( c_Wellfounded_Owf(X10,X177)
=> ( c_Wellfounded_Owf(X10,X54)
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X10,X10),X177)),hAPP(c_Relation_ORange(X10,X10),X54)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Wellfounded_Owf(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X177),X54)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__Un) ).
fof(fact_le__diff__iff,axiom,
! [X20,X102,X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X101),X102))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X101),X20))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X102),X101)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20),X101)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__iff) ).
fof(fact_less__diff__iff,axiom,
! [X20,X102,X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X101),X102))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X101),X20))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X102),X101)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20),X101)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__diff__iff) ).
fof(fact_mult__less__cancel__left__disj,axiom,
! [X38,X39,X18,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X39)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X38)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),X38)) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X38),X39)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).
fof(fact_mult__less__cancel__right__disj,axiom,
! [X38,X18,X39,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X18)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X38),X18)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),X38)) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X38),X39)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).
fof(fact_insert__subset,axiom,
! [X160,X154,X16,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)),X160))
<=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X160))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__subset) ).
fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
! [X2,X154,X10] :
( ( class_Groups_Ocomm__monoid__add(X10)
& class_Groups_Ocomm__monoid__mult(X10) )
=> ( c_Nat__Transfer_Onat__set(X154)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X10),X2),X154) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),hAPP(hAPP(c_COMBB(tc_Int_Oint,X10,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),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__sum__prod_I1_J) ).
fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
! [X2,X154,X10] :
( ( class_Groups_Ocomm__monoid__add(X10)
& class_Groups_Ocomm__monoid__mult(X10) )
=> ( c_Nat__Transfer_Onat__set(X154)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X10),X2),X154) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X10),hAPP(hAPP(c_COMBB(tc_Int_Oint,X10,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),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__sum__prod_I2_J) ).
fof(fact_map__of_Osimps_I2_J,axiom,
! [X286,X166,X13,X10] : c_Map_Omap__of(X10,X13,hAPP(hAPP(c_List_Olist_OCons(tc_prod(X10,X13)),X166),X286)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),c_Map_Omap__of(X10,X13,X286)),hAPP(c_Product__Type_Ofst(X10,X13),X166)),hAPP(c_Option_Ooption_OSome(X13),hAPP(c_Product__Type_Osnd(X10,X13),X166))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of_Osimps_I2_J) ).
fof(fact_setsum__Un__disjoint,axiom,
! [X1,X160,X154,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1),X154)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1),X160)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Un__disjoint) ).
fof(fact_setprod__Un__disjoint,axiom,
! [X1,X160,X154,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),X154)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),X160)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__Un__disjoint) ).
fof(fact_setprod_Ounion__disjoint,axiom,
! [X1,X160,X154,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),X154)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),X160)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Ounion__disjoint) ).
fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
! [X154,X2,X10] :
( ( class_Groups_Ocomm__monoid__add(X10)
& class_Groups_Ocomm__monoid__mult(X10) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),X154) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X10),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,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)),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod_I1_J) ).
fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
! [X154,X2,X10] :
( ( class_Groups_Ocomm__monoid__add(X10)
& class_Groups_Ocomm__monoid__mult(X10) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X10),X2),X154) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X10),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,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)),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod_I2_J) ).
fof(fact_listrel__subset__rtrancl__listrel1,axiom,
! [X177,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_HOL_Obool)),c_List_Olistrel(X10,X177)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X10),c_List_Olistrel1(X10,X177)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__subset__rtrancl__listrel1) ).
fof(fact_image__add__int__atLeastLessThan,axiom,
! [X165,X162] : 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)),X162)),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),X165),X162))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X162),X165),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__add__int__atLeastLessThan) ).
fof(fact_drop__append,axiom,
! [X298,X297,X42,X94] : hAPP(hAPP(c_List_Odrop(X94),X42),hAPP(hAPP(c_List_Oappend(X94),X297),X298)) = hAPP(hAPP(c_List_Oappend(X94),hAPP(hAPP(c_List_Odrop(X94),X42),X297)),hAPP(hAPP(c_List_Odrop(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297))),X298)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__append) ).
fof(fact_take__append,axiom,
! [X298,X297,X42,X94] : hAPP(hAPP(c_List_Otake(X94),X42),hAPP(hAPP(c_List_Oappend(X94),X297),X298)) = hAPP(hAPP(c_List_Oappend(X94),hAPP(hAPP(c_List_Otake(X94),X42),X297)),hAPP(hAPP(c_List_Otake(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297))),X298)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__append) ).
fof(fact_set__sublist__subset,axiom,
! [X241,X290,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),c_List_Osublist(X10,X290,X241))),hAPP(c_List_Oset(X10),X290))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__sublist__subset) ).
fof(fact_set__remove1__subset,axiom,
! [X290,X16,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),c_List_Oremove1(X10,X16,X290))),hAPP(c_List_Oset(X10),X290))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__remove1__subset) ).
fof(fact_inj__on__the__inv__into,axiom,
! [X154,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,X154)
=> c_Fun_Oinj__on(X13,X10,c_Fun_Othe__inv__into(X10,X13,X154,X2),hAPP(c_Set_Oimage(X10,X13,X2),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__the__inv__into) ).
fof(fact_Domain__Collect__split,axiom,
! [X19,X13,X10] : hAPP(c_Relation_ODomain(X10,X13),hAPP(c_Set_OCollect(tc_prod(X10,X13)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,tc_HOL_Obool),X19))) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X13,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X13)),X19)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Collect__split) ).
fof(fact_fun__left__comm__idem_Ofold__set,axiom,
! [X290,X25,X2,X13,X10] :
( c_Finite__Set_Ofun__left__comm__idem(X10,X13,X2)
=> hAPP(hAPP(c_Finite__Set_Ofold(X10,X13,X2),X25),hAPP(c_List_Oset(X10),X290)) = hAPP(c_List_Ofoldl(X13,X10,hAPP(c_COMBC(X10,X13,X13),X2),X25),X290) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofold__set) ).
fof(fact_setsum__negf,axiom,
! [X154,X2,X13,X10] :
( class_Groups_Oab__group__add(X10)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X10),hAPP(hAPP(c_COMBB(X10,X10,X13),c_Groups_Ouminus__class_Ouminus(X10)),X2)),X154) = hAPP(c_Groups_Ouminus__class_Ouminus(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X10),X2),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__negf) ).
fof(fact_abs__setprod,axiom,
! [X154,X2,X13,X10] :
( class_Fields_Olinordered__field(X10)
=> hAPP(c_Groups_Oabs__class_Oabs(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X13,X10),X2),X154)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X13,X10),hAPP(hAPP(c_COMBB(X10,X10,X13),c_Groups_Oabs__class_Oabs(X10)),X2)),X154) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__setprod) ).
fof(fact_all__set__conv__all__nth,axiom,
! [X19,X290,X10] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X290)))
=> hBOOL(hAPP(X19,X3)) )
<=> ! [X152] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X152),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290)))
=> hBOOL(hAPP(X19,hAPP(hAPP(c_List_Onth(X10),X290),X152))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__set__conv__all__nth) ).
fof(fact_insert__mono,axiom,
! [X39,X197,X198,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X198),X197))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X39),X198)),hAPP(hAPP(c_Set_Oinsert(X10),X39),X197))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__mono) ).
fof(fact_sorted__append,axiom,
! [X289,X290,X10] :
( class_Orderings_Olinorder(X10)
=> ( c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Oappend(X10),X290),X289))
<=> ( c_List_Olinorder__class_Osorted(X10,X290)
& c_List_Olinorder__class_Osorted(X10,X289)
& ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X290)))
=> ! [X227] :
( hBOOL(hAPP(hAPP(c_member(X10),X227),hAPP(c_List_Oset(X10),X289)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X3),X227)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__append) ).
fof(fact_power__less__power__Suc,axiom,
! [X42,X84,X94] :
( class_Rings_Olinordered__semidom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Oone__class_Oone(X94)),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).
fof(fact_double__diff,axiom,
! [X198,X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),X198))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X160),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X198),X154)) = X154 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__diff) ).
fof(fact_Pow__mono,axiom,
! [X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X10),X154)),hAPP(c_Set_OPow(X10),X160))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__mono) ).
fof(fact_K__record__comp,axiom,
! [X16,X2,X18,X125,X10,X13] : hAPP(hAPP(c_Fun_Ocomp(X13,X10,X125,hAPP(c_COMBK(X10,X13),X18)),X2),X16) = X18,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_K__record__comp) ).
fof(fact_set__drop__subset,axiom,
! [X290,X20,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Odrop(X10),X20),X290))),hAPP(c_List_Oset(X10),X290))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__drop__subset) ).
fof(fact_set__take__subset,axiom,
! [X290,X20,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Otake(X10),X20),X290))),hAPP(c_List_Oset(X10),X290))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__take__subset) ).
fof(fact_pos__le__divide__eq,axiom,
! [X38,X39,X18,X10] :
( class_Fields_Olinordered__field(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),X18)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X18)),X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__le__divide__eq) ).
fof(fact_pos__divide__le__eq,axiom,
! [X39,X38,X18,X10] :
( class_Fields_Olinordered__field(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),X18)),X39))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X18))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__divide__le__eq) ).
fof(fact_mult__imp__le__div__pos,axiom,
! [X93,X104,X105,X94] :
( class_Fields_Olinordered__field(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X105))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X104),X105)),X93))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X104),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X93),X105))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__imp__le__div__pos) ).
fof(fact_pos__less__divide__eq,axiom,
! [X38,X39,X18,X10] :
( class_Fields_Olinordered__field(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),X18)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X18)),X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__less__divide__eq) ).
fof(fact_pos__divide__less__eq,axiom,
! [X39,X38,X18,X10] :
( class_Fields_Olinordered__field(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),X18)),X39))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X18))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__divide__less__eq) ).
fof(fact_mult__imp__less__div__pos,axiom,
! [X93,X104,X105,X94] :
( class_Fields_Olinordered__field(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X105))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X104),X105)),X93))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X104),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X93),X105))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__imp__less__div__pos) ).
fof(fact_of__int__setprod,axiom,
! [X154,X2,X13,X10] :
( ( class_Groups_Ocomm__monoid__mult(X10)
& class_Rings_Oring__1(X10) )
=> hAPP(c_Int_Oring__1__class_Oof__int(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X13,tc_Int_Oint),X2),X154)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X13,X10),hAPP(hAPP(c_COMBB(tc_Int_Oint,X10,X13),c_Int_Oring__1__class_Oof__int(X10)),X2)),X154) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__setprod) ).
fof(fact_of__nat__setprod,axiom,
! [X154,X2,X13,X10] :
( ( class_Groups_Ocomm__monoid__mult(X10)
& class_Rings_Osemiring__1(X10) )
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X13,tc_Nat_Onat),X2),X154)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X13,X10),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,X13),c_Nat_Osemiring__1__class_Oof__nat(X10)),X2)),X154) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__setprod) ).
fof(fact_converse__Int,axiom,
! [X54,X177,X10,X13] : hAPP(c_Relation_Oconverse(X13,X10),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X13,X10),tc_HOL_Obool)),X177),X54)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X13,X10),X177)),hAPP(c_Relation_Oconverse(X13,X10),X54)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__Int) ).
fof(fact_converse__Un,axiom,
! [X54,X177,X10,X13] : hAPP(c_Relation_Oconverse(X13,X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X13,X10),tc_HOL_Obool)),X177),X54)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X13,X10),X177)),hAPP(c_Relation_Oconverse(X13,X10),X54)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__Un) ).
fof(fact_length__takeWhile__le,axiom,
! [X290,X19,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_List_OtakeWhile(X10,X19,X290))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__takeWhile__le) ).
fof(fact_funpow__add,axiom,
! [X2,X20,X102,X10] : hAPP(hAPP(c_Nat_Ocompow(X10,X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X20)),X2) = hAPP(c_Fun_Ocomp(X10,X10,X10,hAPP(hAPP(c_Nat_Ocompow(X10,X10),X102),X2)),hAPP(hAPP(c_Nat_Ocompow(X10,X10),X20),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow__add) ).
fof(fact_of__int__setsum,axiom,
! [X154,X2,X13,X10] :
( class_Rings_Oring__1(X10)
=> hAPP(c_Int_Oring__1__class_Oof__int(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,tc_Int_Oint),X2),X154)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X10),hAPP(hAPP(c_COMBB(tc_Int_Oint,X10,X13),c_Int_Oring__1__class_Oof__int(X10)),X2)),X154) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__setsum) ).
fof(fact_of__nat__setsum,axiom,
! [X154,X2,X13,X10] :
( class_Rings_Osemiring__1(X10)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,tc_Nat_Onat),X2),X154)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X10),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,X13),c_Nat_Osemiring__1__class_Oof__nat(X10)),X2)),X154) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__setsum) ).
fof(fact_inj__singleton,axiom,
! [X10] : c_Fun_Oinj__on(X10,tc_fun(X10,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Set_Oinsert(X10)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__singleton) ).
fof(fact_New__DSequence_Opos__bind__def,axiom,
! [X113,X2,X16,X10,X13] : hAPP(c_New__DSequence_Opos__bind(X13,X10,X16,X2),X113) = c_Lazy__Sequence_Obind(X13,X10,hAPP(X16,X113),hAPP(hAPP(c_COMBC(X13,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X10)),X2),X113)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__bind__def) ).
fof(fact_finite__cartesian__product,axiom,
! [X160,X13,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X160))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X154),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),X160)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__cartesian__product) ).
fof(fact_card__psubset,axiom,
! [X154,X160,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X154)),hAPP(c_Finite__Set_Ocard(X10),X160)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X154),X160)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__psubset) ).
fof(fact_finite__surj,axiom,
! [X2,X160,X13,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool)),X160),hAPP(c_Set_Oimage(X10,X13,X2),X154)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__surj) ).
fof(fact_inj__on__Int,axiom,
! [X160,X154,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,X154)
=> ( c_Fun_Oinj__on(X10,X13,X2,X160)
=> c_Fun_Oinj__on(X10,X13,X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__Int) ).
fof(fact_nth__drop,axiom,
! [X297,X94,X120,X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),X120)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)))
=> hAPP(hAPP(c_List_Onth(X94),hAPP(hAPP(c_List_Odrop(X94),X42),X297)),X120) = hAPP(hAPP(c_List_Onth(X94),X297),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),X120)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__drop) ).
fof(fact_sorted__rev__nth__mono,axiom,
! [X119,X120,X297,X94] :
( class_Orderings_Olinorder(X94)
=> ( c_List_Olinorder__class_Osorted(X94,hAPP(c_List_Orev(X94),X297))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X120),X119))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X119),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_List_Onth(X94),X297),X119)),hAPP(hAPP(c_List_Onth(X94),X297),X120))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__rev__nth__mono) ).
fof(fact_zip__append,axiom,
! [X316,X298,X317,X10,X297,X94] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X317)
=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X298) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X316)
=> hAPP(hAPP(c_List_Ozip(X94,X10),hAPP(hAPP(c_List_Oappend(X94),X297),X298)),hAPP(hAPP(c_List_Oappend(X10),X317),X316)) = hAPP(hAPP(c_List_Oappend(tc_prod(X94,X10)),hAPP(hAPP(c_List_Ozip(X94,X10),X297),X317)),hAPP(hAPP(c_List_Ozip(X94,X10),X298),X316)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__append) ).
fof(fact_list__size__map,axiom,
! [X290,X1,X13,X2,X10] : c_List_Olist_Olist__size(X10,X2,hAPP(hAPP(c_List_Omap(X13,X10),X1),X290)) = c_List_Olist_Olist__size(X13,hAPP(c_Fun_Ocomp(X10,tc_Nat_Onat,X13,X2),X1),X290),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__size__map) ).
fof(fact_refl__onD,axiom,
! [X39,X177,X154,X10] :
( c_Relation_Orefl__on(X10,X154,X177)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X39)),X177)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onD) ).
fof(fact_UN__upper,axiom,
! [X160,X13,X154,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool)),hAPP(X160,X39)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X154),X160))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__upper) ).
fof(fact_take__Cons__number__of,axiom,
! [X297,X93,X94,X144] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Otake(X94),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)) = c_List_Olist_ONil(X94) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Otake(X94),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)) = hAPP(hAPP(c_List_Olist_OCons(X94),X93),hAPP(hAPP(c_List_Otake(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X297)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Cons__number__of) ).
fof(fact_evalc_Oequations_I7_J,axiom,
! [X52,X50,X51] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X51,X50)),X52),X52))
<=> ( hBOOL(hAPP(X51,X52))
=> ? [X67] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X50),X52),X67))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X51,X50)),X67),X52)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I7_J) ).
fof(fact_predicate2D,axiom,
! [X25,X16,X17,X19,X13,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_fun(X13,tc_HOL_Obool))),X19),X17))
=> ( hBOOL(hAPP(hAPP(X19,X16),X25))
=> hBOOL(hAPP(hAPP(X17,X16),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate2D) ).
fof(fact_rev__predicate2D,axiom,
! [X17,X13,X10,X25,X16,X19] :
( hBOOL(hAPP(hAPP(X19,X16),X25))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_fun(X13,tc_HOL_Obool))),X19),X17))
=> hBOOL(hAPP(hAPP(X17,X16),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate2D) ).
fof(fact_fold1__antimono,axiom,
! [X160,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Finite__Set_Ofold1(X10,c_Orderings_Oord__class_Omin(X10)),X160)),hAPP(c_Finite__Set_Ofold1(X10,c_Orderings_Oord__class_Omin(X10)),X154))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__antimono) ).
fof(fact_Un__iff,axiom,
! [X160,X154,X18,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X18),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)))
<=> ( hBOOL(hAPP(hAPP(c_member(X10),X18),X154))
| hBOOL(hAPP(hAPP(c_member(X10),X18),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__iff) ).
fof(fact_field__le__epsilon,axiom,
! [X105,X93,X94] :
( class_Fields_Olinordered__field(X94)
=> ( ! [X178] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X178))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X105),X178))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X105)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__le__epsilon) ).
fof(fact_restrict__restrict,axiom,
! [X160,X154,X102,X13,X10] : c_Map_Orestrict__map(X10,X13,c_Map_Orestrict__map(X10,X13,X102,X154),X160) = c_Map_Orestrict__map(X10,X13,X102,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__restrict) ).
fof(fact_foldl__Cons,axiom,
! [X290,X16,X39,X2,X13,X10] : hAPP(c_List_Ofoldl(X10,X13,X2,X39),hAPP(hAPP(c_List_Olist_OCons(X13),X16),X290)) = hAPP(c_List_Ofoldl(X10,X13,X2,hAPP(hAPP(X2,X39),X16)),X290),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__Cons) ).
fof(fact_length__transpose__sorted,axiom,
! [X290,X10] :
( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X10))),X290)))
=> ( ( X290 = c_List_Olist_ONil(tc_List_Olist(X10))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),c_List_Otranspose(X10,X290)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X290 != c_List_Olist_ONil(tc_List_Olist(X10))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),c_List_Otranspose(X10,X290)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X10)),X290),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,
! [X42,X92,X84,X94] :
( class_Rings_Olinordered__semidom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X42))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X92),X42))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__mono) ).
fof(fact_power__decreasing,axiom,
! [X84,X169,X42,X94] :
( class_Rings_Olinordered__semidom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),X169))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),c_Groups_Oone__class_Oone(X94)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X169)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__decreasing) ).
fof(fact_power__strict__decreasing,axiom,
! [X84,X169,X42,X94] :
( class_Rings_Olinordered__semidom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),X169))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),c_Groups_Oone__class_Oone(X94)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X169)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__decreasing) ).
fof(fact_vimage__Int,axiom,
! [X160,X154,X2,X13,X10] : hAPP(c_Set_Ovimage(X10,X13,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X10,X13,X2),X154)),hAPP(c_Set_Ovimage(X10,X13,X2),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Int) ).
fof(fact_vimage__Un,axiom,
! [X160,X154,X2,X13,X10] : hAPP(c_Set_Ovimage(X10,X13,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X10,X13,X2),X154)),hAPP(c_Set_Ovimage(X10,X13,X2),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Un) ).
fof(fact_vimage__Diff,axiom,
! [X160,X154,X2,X13,X10] : hAPP(c_Set_Ovimage(X10,X13,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X10,X13,X2),X154)),hAPP(c_Set_Ovimage(X10,X13,X2),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Diff) ).
fof(fact_Image__Un,axiom,
! [X160,X154,X196,X10,X13] : hAPP(c_Relation_OImage(X13,X10,X196),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_OImage(X13,X10,X196),X154)),hAPP(c_Relation_OImage(X13,X10,X196),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Un) ).
fof(fact_image__Un,axiom,
! [X160,X154,X2,X10,X13] : hAPP(c_Set_Oimage(X13,X10,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X13,X10,X2),X154)),hAPP(c_Set_Oimage(X13,X10,X2),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Un) ).
fof(fact_append__in__lists__conv,axiom,
! [X154,X289,X290,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),hAPP(hAPP(c_List_Oappend(X10),X290),X289)),c_List_Olists(X10,X154)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X290),c_List_Olists(X10,X154)))
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X289),c_List_Olists(X10,X154))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__in__lists__conv) ).
fof(fact_Powp__mono,axiom,
! [X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(X10,X154)),c_Predicate_OPowp(X10,X160))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Powp__mono) ).
fof(fact_map__add__comm,axiom,
! [X277,X278,X13,X10] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_Map_Odom(X10,X13,X278)),c_Map_Odom(X10,X13,X277)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Map_Omap__add(X10,X13,X278,X277) = c_Map_Omap__add(X10,X13,X277,X278) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__comm) ).
fof(fact_finite__Plus,axiom,
! [X160,X13,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X160))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X10,X13)),c_Sum__Type_OPlus(X10,X13,X154,X160))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus) ).
fof(fact_Id__on__eqI,axiom,
! [X154,X10,X38,X39] :
( X39 = X38
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X38)),c_Relation_OId__on(X10,X154))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__eqI) ).
fof(fact_Rep__Integ__induct,axiom,
! [X19,X25] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X25),c_Int_OInteg))
=> ( ! [X3] : hBOOL(hAPP(X19,hAPP(c_Int_ORep__Integ,X3)))
=> hBOOL(hAPP(X19,X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ__induct) ).
fof(fact_list__update__append1,axiom,
! [X93,X298,X297,X94,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)))
=> hAPP(hAPP(c_List_Olist__update(X94,hAPP(hAPP(c_List_Oappend(X94),X297),X298)),X120),X93) = hAPP(hAPP(c_List_Oappend(X94),hAPP(hAPP(c_List_Olist__update(X94,X297),X120),X93)),X298) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__append1) ).
fof(fact_nat__mult__dvd__cancel1,axiom,
! [X20,X102,X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X101))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X101),X102)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X101),X20)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X102),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel1) ).
fof(fact_dvd__mult__cancel,axiom,
! [X42,X97,X103] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X103),X97)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X103),X42)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X103))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X97),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel) ).
fof(fact_mult__le__cancel2,axiom,
! [X20,X101,X102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X102),X101)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X101)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X101))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).
fof(fact_power__dvd__imp__le,axiom,
! [X42,X97,X120] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X120),X97)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X120),X42)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X120))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__dvd__imp__le) ).
fof(fact_nat__mult__le__cancel1,axiom,
! [X20,X102,X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X101))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X101),X102)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X101),X20)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).
fof(fact_mult__le__cancel1,axiom,
! [X20,X102,X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X101),X102)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X101),X20)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X101))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).
fof(fact_nat__power__less__imp__less,axiom,
! [X42,X97,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X120))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X120),X97)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X120),X42)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__power__less__imp__less) ).
fof(fact_nat__mult__less__cancel1,axiom,
! [X20,X102,X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X101))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X101),X102)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X101),X20)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).
fof(fact_wfE__pf,axiom,
! [X154,X196,X10] :
( c_Wellfounded_Owf(X10,X196)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(c_Relation_OImage(X10,X10,X196),X154)))
=> X154 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfE__pf) ).
fof(fact_int__setsum,axiom,
! [X154,X2,X10] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),X154)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X10),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X154),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__setsum) ).
fof(fact_int__setprod,axiom,
! [X154,X2,X10] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,tc_Nat_Onat),X2),X154)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X10),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X154),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__setprod) ).
fof(fact_override__on__emptyset,axiom,
! [X1,X2,X13,X10] : c_Fun_Ooverride__on(X10,X13,X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_override__on__emptyset) ).
fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
! [X25,X16,X2,X13,X10] :
( c_Finite__Set_Ofun__left__comm(X10,X13,X2)
=> hAPP(c_Fun_Ocomp(X13,X13,X13,hAPP(X2,X16)),hAPP(X2,X25)) = hAPP(c_Fun_Ocomp(X13,X13,X13,hAPP(X2,X25)),hAPP(X2,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__comp__comm) ).
fof(fact_hoare__derivs_OSkip,axiom,
! [X19,X210,X10] : c_Hoare__Mirabelle_Ohoare__derivs(X10,X210,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X10)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X10),X19),c_Com_Ocom_OSKIP),X19)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X10),tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_OSkip) ).
fof(fact_hoare__derivs_Oequations_I7_J,axiom,
! [X52,X51,X10] : c_Hoare__Mirabelle_Ohoare__derivs(X10,X51,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X10)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X10),X52),c_Com_Ocom_OSKIP),X52)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X10),tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_Oequations_I7_J) ).
fof(fact_option_Orecs_I2_J,axiom,
! [X39,X37,X12,X13,X10] : c_Option_Ooption_Ooption__rec(X10,X13,X12,X37,hAPP(c_Option_Ooption_OSome(X13),X39)) = hAPP(X37,X39),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Orecs_I2_J) ).
fof(fact_set__update__memI,axiom,
! [X16,X290,X10,X20] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290)))
=> hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Olist__update(X10,X290),X20),X16)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__update__memI) ).
fof(fact_UN__I,axiom,
! [X160,X38,X13,X154,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X13),X38),hAPP(X160,X39)))
=> hBOOL(hAPP(hAPP(c_member(X13),X38),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X154),X160))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__I) ).
fof(fact_unique__quotient,axiom,
! [X150,X151,X143,X149,X92,X84] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X84,X92),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X149),X143)))
=> ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X84,X92),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X151),X150)))
=> ( X92 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> X149 = X151 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unique__quotient) ).
fof(fact_unique__remainder,axiom,
! [X150,X151,X143,X149,X92,X84] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X84,X92),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X149),X143)))
=> ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X84,X92),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X151),X150)))
=> ( X92 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> X143 = X150 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unique__remainder) ).
fof(fact_finite__imageD,axiom,
! [X154,X2,X13,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Set_Oimage(X13,X10,X2),X154)))
=> ( c_Fun_Oinj__on(X13,X10,X2,X154)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageD) ).
fof(fact_dvd__mult__cancel__left,axiom,
! [X38,X39,X18,X10] :
( class_Rings_Oidom(X10)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X39)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X38)))
<=> ( X18 = c_Groups_Ozero__class_Ozero(X10)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X39),X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel__left) ).
fof(fact_dvd__mult__cancel__right,axiom,
! [X38,X18,X39,X10] :
( class_Rings_Oidom(X10)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X18)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X38),X18)))
<=> ( X18 = c_Groups_Ozero__class_Ozero(X10)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X39),X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel__right) ).
fof(fact_single__valued__subset,axiom,
! [X54,X177,X13,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),X177),X54))
=> ( c_Relation_Osingle__valued(X10,X13,X54)
=> c_Relation_Osingle__valued(X10,X13,X177) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__subset) ).
fof(fact_add__le__cancel__right,axiom,
! [X38,X18,X39,X10] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X39),X18)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X38),X18)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),X38)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
fof(fact_add__le__imp__le__right,axiom,
! [X92,X81,X84,X94] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X81)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X92),X81)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X92)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).
fof(fact_add__le__cancel__left,axiom,
! [X38,X39,X18,X10] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X18),X39)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X18),X38)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),X38)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).
fof(fact_add__le__imp__le__left,axiom,
! [X92,X84,X81,X94] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X81),X84)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X81),X92)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X92)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).
fof(fact_add__less__imp__less__right,axiom,
! [X92,X81,X84,X94] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X81)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X92),X81)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),X92)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
fof(fact_add__less__cancel__right,axiom,
! [X38,X18,X39,X10] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X39),X18)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X38),X18)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),X38)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
fof(fact_add__less__imp__less__left,axiom,
! [X92,X84,X81,X94] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X81),X84)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X81),X92)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),X92)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
fof(fact_add__less__cancel__left,axiom,
! [X38,X39,X18,X10] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X18),X39)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X18),X38)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),X38)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
fof(fact_evaln_Oequations_I7_J,axiom,
! [X72,X52,X50,X51] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X51,X50),X52,X72,X52)
<=> ( hBOOL(hAPP(X51,X52))
=> ? [X67] :
( c_Natural_Oevaln(X50,X52,X72,X67)
& c_Natural_Oevaln(c_Com_Ocom_OWhile(X51,X50),X67,X72,X52) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I7_J) ).
fof(fact_sorted__nth__mono,axiom,
! [X119,X120,X297,X94] :
( class_Orderings_Olinorder(X94)
=> ( c_List_Olinorder__class_Osorted(X94,X297)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X120),X119))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X119),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_List_Onth(X94),X297),X120)),hAPP(hAPP(c_List_Onth(X94),X297),X119))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__nth__mono) ).
fof(fact_relpow_Osimps_I2_J,axiom,
! [X196,X20,X10] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),hAPP(c_Nat_OSuc,X20)),X196) = hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X20),X196)),X196),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_relpow_Osimps_I2_J) ).
fof(fact_diff__divide__eq__iff,axiom,
! [X105,X93,X104,X94] :
( class_Fields_Ofield(X94)
=> ( X104 != c_Groups_Ozero__class_Ozero(X94)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X93),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X105),X104)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X104),X93)),X105)),X104) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__divide__eq__iff) ).
fof(fact_add__divide__eq__iff,axiom,
! [X105,X93,X104,X94] :
( class_Fields_Ofield(X94)
=> ( X104 != c_Groups_Ozero__class_Ozero(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X93),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X105),X104)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X104),X93)),X105)),X104) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__divide__eq__iff) ).
fof(fact_filter__insort,axiom,
! [X16,X19,X290,X2,X13,X10] :
( class_Orderings_Olinorder(X10)
=> ( c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Omap(X13,X10),X2),X290))
=> ( hBOOL(hAPP(X19,X16))
=> hAPP(c_List_Ofilter(X13,X19),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X13,X10,X2),X16),X290)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X13,X10,X2),X16),hAPP(c_List_Ofilter(X13,X19),X290)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__insort) ).
fof(fact_subset__singletonD,axiom,
! [X16,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))
=> ( X154 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
| X154 = hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__singletonD) ).
fof(fact_DiffE,axiom,
! [X160,X154,X18,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X18),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(X10),X18),X154))
=> hBOOL(hAPP(hAPP(c_member(X10),X18),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffE) ).
fof(fact_folding__idem_Oin__comp__idem,axiom,
! [X16,X154,X225,X2,X13,X10] :
( c_Finite__Set_Ofolding__idem(X10,X13,X2,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Fun_Ocomp(X13,X13,X13,hAPP(X225,X154)),hAPP(X2,X16)) = hAPP(X225,X154) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Oin__comp__idem) ).
fof(fact_take__Suc__conv__app__nth,axiom,
! [X297,X94,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)))
=> hAPP(hAPP(c_List_Otake(X94),hAPP(c_Nat_OSuc,X120)),X297) = hAPP(hAPP(c_List_Oappend(X94),hAPP(hAPP(c_List_Otake(X94),X120),X297)),hAPP(hAPP(c_List_Olist_OCons(X94),hAPP(hAPP(c_List_Onth(X94),X297),X120)),c_List_Olist_ONil(X94))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Suc__conv__app__nth) ).
fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
! [X160,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( X160 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X154)),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X160)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Ounion__disjoint) ).
fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
! [X160,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( X160 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X154)),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X160)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Ounion__disjoint) ).
fof(fact_comp__funpow,axiom,
! [X2,X20,X13,X10] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(X10,X13),tc_fun(X10,X13)),X20),c_Fun_Ocomp(X13,X13,X10,X2)) = c_Fun_Ocomp(X13,X13,X10,hAPP(hAPP(c_Nat_Ocompow(X13,X13),X20),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__funpow) ).
fof(fact_curry__conv,axiom,
! [X38,X39,X2,X10,X125,X13] : hAPP(hAPP(c_Product__Type_Ocurry(X13,X125,X10,X2),X39),X38) = hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(X13,X125),X39),X38)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curry__conv) ).
fof(fact_curry__def,axiom,
! [X25,X16,X18,X10,X125,X13] : hAPP(hAPP(c_Product__Type_Ocurry(X13,X125,X10,X18),X16),X25) = hAPP(X18,hAPP(hAPP(c_Product__Type_OPair(X13,X125),X16),X25)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curry__def) ).
fof(fact_inj__on__Un__image__eq__iff,axiom,
! [X160,X154,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> ( hAPP(c_Set_Oimage(X10,X13,X2),X154) = hAPP(c_Set_Oimage(X10,X13,X2),X160)
<=> X154 = X160 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__Un__image__eq__iff) ).
fof(fact_mult__imp__div__pos__le,axiom,
! [X104,X93,X105,X94] :
( class_Fields_Olinordered__field(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X105))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X104),X105)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X93),X105)),X104)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__imp__div__pos__le) ).
fof(fact_mult__imp__div__pos__less,axiom,
! [X104,X93,X105,X94] :
( class_Fields_Olinordered__field(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X105))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X104),X105)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X93),X105)),X104)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__imp__div__pos__less) ).
fof(fact_refl__on__Int,axiom,
! [X54,X160,X177,X154,X10] :
( c_Relation_Orefl__on(X10,X154,X177)
=> ( c_Relation_Orefl__on(X10,X160,X54)
=> c_Relation_Orefl__on(X10,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X177),X54)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__Int) ).
fof(fact_refl__on__Un,axiom,
! [X54,X160,X177,X154,X10] :
( c_Relation_Orefl__on(X10,X154,X177)
=> ( c_Relation_Orefl__on(X10,X160,X54)
=> c_Relation_Orefl__on(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X177),X54)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__Un) ).
fof(fact_map__upds__Nil1,axiom,
! [X313,X102,X13,X10] : c_Map_Omap__upds(X10,X13,X102,c_List_Olist_ONil(X10),X313) = X102,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upds__Nil1) ).
fof(fact_map__upds__Nil2,axiom,
! [X312,X102,X13,X10] : c_Map_Omap__upds(X10,X13,X102,X312,c_List_Olist_ONil(X13)) = X102,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upds__Nil2) ).
fof(fact_option_Orecs_I1_J,axiom,
! [X37,X12,X13,X10] : c_Option_Ooption_Ooption__rec(X10,X13,X12,X37,c_Option_Ooption_ONone(X13)) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Orecs_I1_J) ).
fof(fact_Domain__insert,axiom,
! [X177,X38,X39,X13,X10] : hAPP(c_Relation_ODomain(X10,X13),hAPP(hAPP(c_Set_Oinsert(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X39),X38)),X177)) = hAPP(hAPP(c_Set_Oinsert(X10),X39),hAPP(c_Relation_ODomain(X10,X13),X177)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__insert) ).
fof(fact_Range__insert,axiom,
! [X177,X38,X39,X10,X13] : hAPP(c_Relation_ORange(X13,X10),hAPP(hAPP(c_Set_Oinsert(tc_prod(X13,X10)),hAPP(hAPP(c_Product__Type_OPair(X13,X10),X39),X38)),X177)) = hAPP(hAPP(c_Set_Oinsert(X10),X38),hAPP(c_Relation_ORange(X13,X10),X177)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__insert) ).
fof(fact_subset__trans,axiom,
! [X198,X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),X198))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X198)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__trans) ).
fof(fact_psubset__subset__trans,axiom,
! [X198,X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),X198))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X154),X198)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__subset__trans) ).
fof(fact_subset__psubset__trans,axiom,
! [X198,X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X160),X198))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X154),X198)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__psubset__trans) ).
fof(fact_psubset__trans,axiom,
! [X198,X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X160),X198))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X154),X198)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__trans) ).
fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
! [X154,X16] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X16),X154))
<=> hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X16)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X154))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I2_J) ).
fof(fact_Pair__scomp,axiom,
! [X2,X16,X13,X125,X10] : hAPP(hAPP(c_Product__Type_Oscomp(X10,X125,X10,X13),hAPP(c_Product__Type_OPair(X125,X10),X16)),X2) = hAPP(X2,X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__scomp) ).
fof(fact_mod__div__equality,axiom,
! [X92,X84,X94] :
( class_Divides_Osemiring__div(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),X84),X92)),X92)),c_Divides_Odiv__class_Omod(X94,X84,X92)) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__div__equality) ).
fof(fact_mod__div__decomp,axiom,
! [X92,X84,X94] :
( class_Divides_Osemiring__div(X94)
=> X84 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),X84),X92)),X92)),c_Divides_Odiv__class_Omod(X94,X84,X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__div__decomp) ).
fof(fact_evalc__elim__cases_I6_J,axiom,
! [X59,X45,X87] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X87)),X45),X59))
=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X87))),X45),X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I6_J) ).
fof(fact_UN__singleton,axiom,
! [X154,X10] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Set_Oinsert(X10)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = X154,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__singleton) ).
fof(fact_upd__conv__take__nth__drop,axiom,
! [X84,X297,X94,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)))
=> hAPP(hAPP(c_List_Olist__update(X94,X297),X120),X84) = hAPP(hAPP(c_List_Oappend(X94),hAPP(hAPP(c_List_Otake(X94),X120),X297)),hAPP(hAPP(c_List_Olist_OCons(X94),X84),hAPP(hAPP(c_List_Odrop(X94),hAPP(c_Nat_OSuc,X120)),X297))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upd__conv__take__nth__drop) ).
fof(fact_Pow__insert,axiom,
! [X154,X39,X10] : hAPP(c_Set_OPow(X10),hAPP(hAPP(c_Set_Oinsert(X10),X39),X154)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X10),X154)),hAPP(c_Set_Oimage(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),hAPP(c_Set_Oinsert(X10),X39)),hAPP(c_Set_OPow(X10),X154))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__insert) ).
fof(fact_evalc_OIfTrue,axiom,
! [X75,X77,X76,X54,X38] :
( hBOOL(hAPP(X38,X54))
=> ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X76),X54),X77))
=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X38,X76,X75)),X54),X77)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OIfTrue) ).
fof(fact_finite__vimageD,axiom,
! [X225,X204,X13,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Set_Ovimage(X10,X13,X204),X225)))
=> ( hAPP(c_Set_Oimage(X10,X13,X204),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X225)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__vimageD) ).
fof(fact_Cons__in__lists__iff,axiom,
! [X154,X290,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290)),c_List_Olists(X10,X154)))
<=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X290),c_List_Olists(X10,X154))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__in__lists__iff) ).
fof(fact_range,axiom,
! [X45,X103] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X103))
=> 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(X103),X45))),X103)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range) ).
fof(fact_IntD1,axiom,
! [X160,X154,X18,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X18),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)))
=> hBOOL(hAPP(hAPP(c_member(X10),X18),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntD1) ).
fof(fact_Int__iff,axiom,
! [X160,X154,X18,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X18),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)))
<=> ( hBOOL(hAPP(hAPP(c_member(X10),X18),X154))
& hBOOL(hAPP(hAPP(c_member(X10),X18),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__iff) ).
fof(fact_DiffD1,axiom,
! [X160,X154,X18,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X18),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160)))
=> hBOOL(hAPP(hAPP(c_member(X10),X18),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffD1) ).
fof(fact_IntD2,axiom,
! [X160,X154,X18,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X18),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)))
=> hBOOL(hAPP(hAPP(c_member(X10),X18),X160)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntD2) ).
fof(fact_Diff__insert,axiom,
! [X160,X39,X154,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),X160)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160)),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__insert) ).
fof(fact_fold1__Un,axiom,
! [X160,X154,X10] :
( class_Groups_Oab__semigroup__mult(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( X160 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),X154)),hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),X160)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__Un) ).
fof(fact_dvd_OmonoI,axiom,
! [X2,X10] :
( class_Orderings_Oorder(X10)
=> ( ! [X3,X90] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X90))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(X2,X3)),hAPP(X2,X90))) )
=> c_Orderings_Oorder_Omono(tc_Nat_Onat,X10,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,
! [X16,X154,X225,X2,X13,X10] :
( c_Finite__Set_Ofolding__idem(X10,X13,X2,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(X225,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(c_Fun_Ocomp(X13,X13,X13,hAPP(X225,X154)),hAPP(X2,X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Oinsert__idem) ).
fof(fact_scomp__Pair,axiom,
! [X16,X125,X13,X10] : hAPP(hAPP(c_Product__Type_Oscomp(X10,X13,X125,tc_prod(X13,X125)),X16),c_Product__Type_OPair(X13,X125)) = X16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_scomp__Pair) ).
fof(fact_Pow__def,axiom,
! [X154,X10] : hAPP(c_Set_OPow(X10),X154) = hAPP(c_Set_OCollect(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool))),X154)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__def) ).
fof(fact_rev__foldl__cons,axiom,
! [X290,X10] : hAPP(c_List_Orev(X10),X290) = hAPP(c_List_Ofoldl(tc_List_Olist(X10),X10,hAPP(c_COMBC(X10,tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_OCons(X10)),c_List_Olist_ONil(X10)),X290),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__foldl__cons) ).
fof(fact_gauss__sum,axiom,
! [X20,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),c_Groups_Oone__class_Oone(X10)),c_Groups_Oone__class_Oone(X10))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),c_Nat_Osemiring__1__class_Oof__nat(X10)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X20))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),X20)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),X20)),c_Groups_Oone__class_Oone(X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gauss__sum) ).
fof(fact_acyclic__subset,axiom,
! [X177,X54,X10] :
( c_Wellfounded_Oacyclic(X10,X54)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X177),X54))
=> c_Wellfounded_Oacyclic(X10,X177) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__subset) ).
fof(fact_wf__subset,axiom,
! [X166,X177,X10] :
( c_Wellfounded_Owf(X10,X177)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X166),X177))
=> c_Wellfounded_Owf(X10,X166) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__subset) ).
fof(fact_in__set__remove1,axiom,
! [X290,X10,X38,X39] :
( X39 != X38
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),hAPP(c_List_Oset(X10),c_List_Oremove1(X10,X38,X290))))
<=> hBOOL(hAPP(hAPP(c_member(X10),X39),hAPP(c_List_Oset(X10),X290))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__remove1) ).
fof(fact_Int__assoc,axiom,
! [X198,X160,X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)),X198) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X160),X198)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__assoc) ).
fof(fact_Un__assoc,axiom,
! [X198,X160,X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)),X198) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X160),X198)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__assoc) ).
fof(fact_Int__Diff,axiom,
! [X198,X160,X154,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)),X198) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X160),X198)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Diff) ).
fof(fact_le__add__diff,axiom,
! [X97,X42,X103] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X103),X42))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),X97)),X103))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff) ).
fof(fact_set__takeWhileD,axiom,
! [X290,X19,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),c_List_OtakeWhile(X10,X19,X290))))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
& hBOOL(hAPP(X19,X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__takeWhileD) ).
fof(fact_in__set__sublistD,axiom,
! [X241,X290,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),c_List_Osublist(X10,X290,X241))))
=> hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__sublistD) ).
fof(fact_evaln_OWhileTrue,axiom,
! [X88,X77,X20,X18,X85,X38] :
( hBOOL(hAPP(X38,X85))
=> ( c_Natural_Oevaln(X18,X85,X20,X77)
=> ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X38,X18),X77,X20,X88)
=> c_Natural_Oevaln(c_Com_Ocom_OWhile(X38,X18),X85,X20,X88) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OWhileTrue) ).
fof(fact_filter__is__subset,axiom,
! [X290,X19,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),hAPP(c_List_Ofilter(X10,X19),X290))),hAPP(c_List_Oset(X10),X290))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__is__subset) ).
fof(fact_crossproduct__noteq,axiom,
! [X141,X18,X38,X39,X10] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X10)
=> ( ( X39 != X38
& X18 != X141 )
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X18)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X38),X141)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X141)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X38),X18)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).
fof(fact_crossproduct__eq,axiom,
! [X73,X16,X25,X131,X10] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X10)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X131),X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X16),X73)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X131),X73)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X16),X25))
<=> ( X131 = X16
| X25 = X73 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_crossproduct__eq) ).
fof(fact_reflp__def,axiom,
! [X177,X10] :
( c_Predicate_Oreflp(X10,X177)
<=> c_Relation_Orefl__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X10,X10)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X10,tc_HOL_Obool),X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reflp__def) ).
fof(fact_le__diff__conv2,axiom,
! [X113,X163,X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X101),X163))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X113),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X163),X101)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X113),X101)),X163)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv2) ).
fof(fact_vimageD,axiom,
! [X154,X2,X13,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X39),hAPP(c_Set_Ovimage(X10,X13,X2),X154)))
=> hBOOL(hAPP(hAPP(c_member(X13),hAPP(X2,X39)),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimageD) ).
fof(fact_vimage__eq,axiom,
! [X160,X2,X13,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X39),hAPP(c_Set_Ovimage(X10,X13,X2),X160)))
<=> hBOOL(hAPP(hAPP(c_member(X13),hAPP(X2,X39)),X160)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__eq) ).
fof(fact_drop__Cons,axiom,
! [X290,X16,X20,X10] : hAPP(hAPP(c_List_Odrop(X10),X20),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290)) = c_Nat_Onat_Onat__case(tc_List_Olist(X10),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Odrop(X10)),X290),X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__Cons) ).
fof(fact_mult__right__le__one__le,axiom,
! [X105,X93,X94] :
( class_Rings_Olinordered__idom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X93))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X105))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X105),c_Groups_Oone__class_Oone(X94)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X93),X105)),X93)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).
fof(fact_mult__left__le__one__le,axiom,
! [X105,X93,X94] :
( class_Rings_Olinordered__idom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X93))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X105))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X105),c_Groups_Oone__class_Oone(X94)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X105),X93)),X93)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).
fof(fact_Union__disjoint,axiom,
! [X154,X198,X10] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X198)),X154) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X3),X198))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X3),X154) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__disjoint) ).
fof(fact_zdiv__mono2,axiom,
! [X92,X130,X84] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X130))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X130),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),X92)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),X130))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2) ).
fof(fact_Domain__Un__eq,axiom,
! [X160,X154,X13,X10] : hAPP(c_Relation_ODomain(X10,X13),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X10,X13),X154)),hAPP(c_Relation_ODomain(X10,X13),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Un__eq) ).
fof(fact_Range__Un__eq,axiom,
! [X160,X154,X10,X13] : hAPP(c_Relation_ORange(X13,X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X13,X10),tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_ORange(X13,X10),X154)),hAPP(c_Relation_ORange(X13,X10),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Un__eq) ).
fof(fact_map__update,axiom,
! [X25,X101,X290,X2,X10,X13] : hAPP(hAPP(c_List_Omap(X13,X10),X2),hAPP(hAPP(c_List_Olist__update(X13,X290),X101),X25)) = hAPP(hAPP(c_List_Olist__update(X10,hAPP(hAPP(c_List_Omap(X13,X10),X2),X290)),X101),hAPP(X2,X25)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__update) ).
fof(fact_map__add__def,axiom,
! [X16,X277,X278,X10,X13] : hAPP(c_Map_Omap__add(X13,X10,X278,X277),X16) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X10),X10,hAPP(X278,X16),c_Option_Ooption_OSome(X10)),hAPP(X277,X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__def) ).
fof(fact_set__ConsD,axiom,
! [X290,X16,X25,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X25),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290))))
=> ( X25 = X16
| hBOOL(hAPP(hAPP(c_member(X10),X25),hAPP(c_List_Oset(X10),X290))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__ConsD) ).
fof(fact_code__numeral__decr,axiom,
! [X103] :
( X103 != 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,X103)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,X103))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral__decr) ).
fof(fact_in__set__dropD,axiom,
! [X290,X20,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Odrop(X10),X20),X290))))
=> hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__dropD) ).
fof(fact_in__set__takeD,axiom,
! [X290,X20,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Otake(X10),X20),X290))))
=> hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__takeD) ).
fof(fact_dom__fun__upd,axiom,
! [X16,X2,X13,X10,X25] :
( ( X25 = c_Option_Ooption_ONone(X10)
=> c_Map_Odom(X13,X10,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X13,tc_Option_Ooption(X10)),X2),X16),X25)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13,tc_HOL_Obool)),c_Map_Odom(X13,X10,X2)),hAPP(hAPP(c_Set_Oinsert(X13),X16),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool)))) )
& ( X25 != c_Option_Ooption_ONone(X10)
=> c_Map_Odom(X13,X10,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X13,tc_Option_Ooption(X10)),X2),X16),X25)) = hAPP(hAPP(c_Set_Oinsert(X13),X16),c_Map_Odom(X13,X10,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__fun__upd) ).
fof(fact_power__Suc__less__one,axiom,
! [X42,X84,X94] :
( class_Rings_Olinordered__semidom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),c_Groups_Oone__class_Oone(X94)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),hAPP(c_Nat_OSuc,X42))),c_Groups_Oone__class_Oone(X94))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__less__one) ).
fof(fact_zdiv__mono2__neg,axiom,
! [X92,X130,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),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X130))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X130),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),X130)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),X92))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2__neg) ).
fof(fact_Id__onE,axiom,
! [X154,X18,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X18),c_Relation_OId__on(X10,X154)))
=> ~ ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> X18 != hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__onE) ).
fof(fact_the__inv__f__f,axiom,
! [X16,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> hAPP(c_Fun_Othe__inv__into(X10,X13,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X2),hAPP(X2,X16)) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__f__f) ).
fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
! [X73,X16,X154,X2,X13,X10] :
( c_Finite__Set_Ofun__left__comm(X10,X13,X2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(X2,X16),hAPP(hAPP(c_Finite__Set_Ofold(X10,X13,X2),X73),X154)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X13,X2),hAPP(hAPP(X2,X16),X73)),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__fun__comm) ).
fof(fact_wfP__subset,axiom,
! [X166,X177,X10] :
( c_Wellfounded_OwfP(X10,X177)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),X166),X177))
=> c_Wellfounded_OwfP(X10,X166) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__subset) ).
fof(fact_pred__equals__eq,axiom,
! [X216,X196,X10] :
( hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X196) = hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X216)
<=> X196 = X216 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq) ).
fof(fact_mult__less__cancel1,axiom,
! [X20,X102,X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X101),X102)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X101),X20)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X101))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).
fof(fact_mult__less__cancel2,axiom,
! [X20,X101,X102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X102),X101)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X101)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X101))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).
fof(fact_divide__right__mono,axiom,
! [X81,X92,X84,X94] :
( class_Fields_Olinordered__field__inverse__zero(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X81))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X84),X81)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X92),X81))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__right__mono) ).
fof(fact_power__mono,axiom,
! [X42,X92,X84,X94] :
( class_Rings_Olinordered__semidom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X92),X42))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mono) ).
fof(fact_mult__right__mono,axiom,
! [X81,X92,X84,X94] :
( class_Rings_Oordered__semiring(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X81))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X81)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X81))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__mono) ).
fof(fact_comm__mult__left__mono,axiom,
! [X81,X92,X84,X94] :
( class_Rings_Oordered__comm__semiring(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X81))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),X84)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),X92))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).
fof(fact_mult__left__mono,axiom,
! [X81,X92,X84,X94] :
( class_Rings_Oordered__semiring(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X81))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),X84)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),X92))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__mono) ).
fof(fact_divide__strict__right__mono,axiom,
! [X81,X92,X84,X94] :
( class_Fields_Olinordered__field(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X81))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X84),X81)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X92),X81))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__right__mono) ).
fof(fact_mult__strict__right__mono,axiom,
! [X81,X92,X84,X94] :
( class_Rings_Olinordered__semiring__strict(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X81))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X81)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X81))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).
fof(fact_comm__mult__strict__left__mono,axiom,
! [X81,X92,X84,X94] :
( class_Rings_Olinordered__comm__semiring__strict(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X81))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),X84)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),X92))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).
fof(fact_mult__strict__left__mono,axiom,
! [X81,X92,X84,X94] :
( class_Rings_Olinordered__semiring__strict(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X81))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),X84)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),X92))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).
fof(fact_zip__Cons__Cons,axiom,
! [X298,X105,X297,X93,X10,X94] : hAPP(hAPP(c_List_Ozip(X94,X10),hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)),hAPP(hAPP(c_List_Olist_OCons(X10),X105),X298)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(X94,X10)),hAPP(hAPP(c_Product__Type_OPair(X94,X10),X93),X105)),hAPP(hAPP(c_List_Ozip(X94,X10),X297),X298)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__Cons__Cons) ).
fof(fact_divide__le__0__iff,axiom,
! [X38,X39,X10] :
( class_Fields_Olinordered__field__inverse__zero(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X39),X38)),c_Groups_Ozero__class_Ozero(X10)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X39))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X38),c_Groups_Ozero__class_Ozero(X10))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),c_Groups_Ozero__class_Ozero(X10)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X38)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__le__0__iff) ).
fof(fact_mult__le__0__iff,axiom,
! [X38,X39,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X38)),c_Groups_Ozero__class_Ozero(X10)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X39))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X38),c_Groups_Ozero__class_Ozero(X10))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),c_Groups_Ozero__class_Ozero(X10)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X38)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).
fof(fact_divide__less__0__iff,axiom,
! [X38,X39,X10] :
( class_Fields_Olinordered__field__inverse__zero(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X39),X38)),c_Groups_Ozero__class_Ozero(X10)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X39))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X38),c_Groups_Ozero__class_Ozero(X10))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),c_Groups_Ozero__class_Ozero(X10)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X38)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__less__0__iff) ).
fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
! [X154,X16] :
( c_Nat__Transfer_Ois__nat(X16)
=> ( c_Nat__Transfer_Onat__set(X154)
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X16),X154))
<=> hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X16)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X154))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I2_J) ).
fof(fact_Max__eqI,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ! [X90] :
( hBOOL(hAPP(hAPP(c_member(X10),X90),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X90),X16)) )
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> c_Big__Operators_Olinorder__class_OMax(X10,X154) = X16 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max__eqI) ).
fof(fact_zdvd__mono,axiom,
! [X53,X102,X101] :
( X101 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X102),X53))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X101),X102)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X101),X53))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__mono) ).
fof(fact_zdvd__mult__cancel,axiom,
! [X42,X97,X103] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X103),X97)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X103),X42)))
=> ( X103 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X97),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__mult__cancel) ).
fof(fact_nat__mult__dvd__cancel__disj,axiom,
! [X20,X102,X101] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X101),X102)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X101),X20)))
<=> ( X101 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X102),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel__disj) ).
fof(fact_mod__pos__neg__1__number__of,axiom,
! [X133] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)),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),X133)) = 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),X133))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__neg__1__number__of) ).
fof(fact_subset__inj__on,axiom,
! [X154,X160,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,X160)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> c_Fun_Oinj__on(X10,X13,X2,X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__inj__on) ).
fof(fact_length__filter__le,axiom,
! [X290,X19,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),hAPP(c_List_Ofilter(X10,X19),X290))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__filter__le) ).
fof(fact_rtrancl_Ortrancl__refl,axiom,
! [X177,X39,X10] : hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X39)),c_Transitive__Closure_Ortrancl(X10,X177))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).
fof(fact_nat__add__left__cancel__le,axiom,
! [X20,X102,X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X101),X102)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X101),X20)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
fof(fact_nat__add__left__cancel__less,axiom,
! [X20,X102,X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X101),X102)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X101),X20)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
fof(fact_zdvd__reduce,axiom,
! [X102,X20,X101] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X101),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X101),X102))))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X101),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__reduce) ).
fof(fact_the__inv__into__f__f,axiom,
! [X16,X154,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,X154)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Fun_Othe__inv__into(X10,X13,X154,X2),hAPP(X2,X16)) = X16 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__f__f) ).
fof(fact_div__pos__neg__1__number__of,axiom,
! [X133] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)),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),X133)) = 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),X133))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__pos__neg__1__number__of) ).
fof(fact_the__inv__into__f__eq,axiom,
! [X25,X16,X154,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,X154)
=> ( hAPP(X2,X16) = X25
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Fun_Othe__inv__into(X10,X13,X154,X2),X25) = X16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__f__eq) ).
fof(fact_finite__INT,axiom,
! [X154,X13,X241,X10] :
( ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X241))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X13),hAPP(X154,X3))) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X13),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X241),X154))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__INT) ).
fof(fact_power__increasing,axiom,
! [X84,X169,X42,X94] :
( class_Rings_Olinordered__semidom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),X169))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Oone__class_Oone(X94)),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X169))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__increasing) ).
fof(fact_power__strict__increasing,axiom,
! [X84,X169,X42,X94] :
( class_Rings_Olinordered__semidom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),X169))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Oone__class_Oone(X94)),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X169))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__increasing) ).
fof(fact_divide__right__mono__neg,axiom,
! [X81,X92,X84,X94] :
( class_Fields_Olinordered__field__inverse__zero(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X81),c_Groups_Ozero__class_Ozero(X94)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X92),X81)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X84),X81))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__right__mono__neg) ).
fof(fact_mult__right__mono__neg,axiom,
! [X81,X84,X92,X94] :
( class_Rings_Oordered__ring(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X92),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X81),c_Groups_Ozero__class_Ozero(X94)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X81)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X81))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).
fof(fact_mult__left__mono__neg,axiom,
! [X81,X84,X92,X94] :
( class_Rings_Oordered__ring(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X92),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X81),c_Groups_Ozero__class_Ozero(X94)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),X84)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),X92))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).
fof(fact_divide__strict__right__mono__neg,axiom,
! [X81,X84,X92,X94] :
( class_Fields_Olinordered__field(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X92),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X81),c_Groups_Ozero__class_Ozero(X94)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X84),X81)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X92),X81))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__right__mono__neg) ).
fof(fact_mult__strict__right__mono__neg,axiom,
! [X81,X84,X92,X94] :
( class_Rings_Olinordered__ring__strict(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X92),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X81),c_Groups_Ozero__class_Ozero(X94)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X81)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X81))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).
fof(fact_mult__strict__left__mono__neg,axiom,
! [X81,X84,X92,X94] :
( class_Rings_Olinordered__ring__strict(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X92),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X81),c_Groups_Ozero__class_Ozero(X94)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),X84)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),X92))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).
fof(fact_card__Diff__singleton,axiom,
! [X16,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X154)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff__singleton) ).
fof(fact_finite__Diff2,axiom,
! [X154,X160,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Diff2) ).
fof(fact_listsum__update__nat,axiom,
! [X42,X306,X103] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X103),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X306)))
=> hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,X306),X103),X42)) = 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),X306)),X42)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X306),X103)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__update__nat) ).
fof(fact_o__def,axiom,
! [X16,X1,X2,X125,X10,X13] : hAPP(hAPP(c_Fun_Ocomp(X13,X10,X125,X2),X1),X16) = hAPP(X2,hAPP(X1,X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__def) ).
fof(fact_o__apply,axiom,
! [X16,X1,X2,X125,X10,X13] : hAPP(hAPP(c_Fun_Ocomp(X13,X10,X125,X2),X1),X16) = hAPP(X2,hAPP(X1,X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__apply) ).
fof(fact_mult__dvd__mono,axiom,
! [X112,X81,X92,X84,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X84),X92))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X81),X112))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X81)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X112))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__dvd__mono) ).
fof(fact_inf__mono,axiom,
! [X112,X92,X81,X84,X94] :
( class_Lattices_Osemilattice__inf(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X81))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X92),X112))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X84),X92)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X81),X112))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__mono) ).
fof(fact_sup__mono,axiom,
! [X112,X92,X81,X84,X94] :
( class_Lattices_Osemilattice__sup(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X81))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X92),X112))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X84),X92)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X81),X112))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__mono) ).
fof(fact_min__max_Osup__mono,axiom,
! [X112,X92,X81,X84,X94] :
( class_Orderings_Olinorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X81))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X92),X112))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X84),X92)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X81),X112))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__mono) ).
fof(fact_min__max_Oinf__mono,axiom,
! [X112,X92,X81,X84,X94] :
( class_Orderings_Olinorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X81))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X92),X112))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X84),X92)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X81),X112))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__mono) ).
fof(fact_add__mono,axiom,
! [X112,X81,X92,X84,X94] :
( class_Groups_Oordered__ab__semigroup__add(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X81),X112))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X81)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X92),X112))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mono) ).
fof(fact_add__less__le__mono,axiom,
! [X112,X81,X92,X84,X94] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X81),X112))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X81)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X92),X112))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
fof(fact_add__le__less__mono,axiom,
! [X112,X81,X92,X84,X94] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X81),X112))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X81)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X92),X112))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
fof(fact_add__strict__mono,axiom,
! [X112,X81,X92,X84,X94] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X81),X112))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X81)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X92),X112))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__mono) ).
fof(fact_right__diff__distrib__number__of,axiom,
! [X81,X92,X144,X10] :
( ( class_Int_Onumber(X10)
& class_Rings_Oring(X10) )
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X144)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X92),X81)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X144)),X92)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X144)),X81)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__diff__distrib__number__of) ).
fof(fact_right__distrib__number__of,axiom,
! [X81,X92,X144,X10] :
( ( class_Int_Onumber(X10)
& class_Rings_Osemiring(X10) )
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X144)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X92),X81)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X144)),X92)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X144)),X81)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__distrib__number__of) ).
fof(fact_div__mult__div__if__dvd,axiom,
! [X133,X104,X93,X105,X94] :
( class_Divides_Osemiring__div(X94)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X105),X93))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X104),X133))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),X93),X105)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),X133),X104)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X93),X133)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X105),X104)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__div__if__dvd) ).
fof(fact_fold__inf__insert,axiom,
! [X39,X38,X154,X10] :
( class_Lattices_Osemilattice__inf(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__inf__class_Oinf(X10)),X38),hAPP(hAPP(c_Set_Oinsert(X10),X39),X154)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X39),hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__inf__class_Oinf(X10)),X38),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__inf__insert) ).
fof(fact_fold__sup__insert,axiom,
! [X39,X38,X154,X10] :
( class_Lattices_Osemilattice__sup(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__sup__class_Osup(X10)),X38),hAPP(hAPP(c_Set_Oinsert(X10),X39),X154)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X39),hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__sup__class_Osup(X10)),X38),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__sup__insert) ).
fof(fact_min__max_Ofold__sup__insert,axiom,
! [X39,X38,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omax(X10)),X38),hAPP(hAPP(c_Set_Oinsert(X10),X39),X154)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X39),hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omax(X10)),X38),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ofold__sup__insert) ).
fof(fact_min__max_Ofold__inf__insert,axiom,
! [X39,X38,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omin(X10)),X38),hAPP(hAPP(c_Set_Oinsert(X10),X39),X154)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X39),hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omin(X10)),X38),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ofold__inf__insert) ).
fof(fact_finite__vimageI,axiom,
! [X204,X13,X225,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X225))
=> ( c_Fun_Oinj__on(X13,X10,X204,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X13),hAPP(c_Set_Ovimage(X13,X10,X204),X225))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__vimageI) ).
fof(fact_INF__leI,axiom,
! [X230,X154,X113,X10,X13] :
( class_Complete__Lattice_Ocomplete__lattice(X13)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X113),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,X13),X154),X230)),hAPP(X230,X113))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__leI) ).
fof(fact_add__number__of__diff2,axiom,
! [X133,X81,X144,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),X144)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X81),hAPP(c_Int_Onumber__class_Onumber__of(X94),X133))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X144),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X133)))),X81) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__number__of__diff2) ).
fof(fact_less__eq__nat_Osimps_I2_J,axiom,
! [X20,X102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X102)),X20))
<=> hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I2_J) ).
fof(fact_SUP1__I,axiom,
! [X13,X38,X160,X154,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> ( hBOOL(hAPP(hAPP(X160,X39),X38))
=> hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X154),X160),X38)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP1__I) ).
fof(fact_Sup__le__iff,axiom,
! [X38,X154,X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Complete__Lattice_OSup__class_OSup(X10,X154)),X38))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X3),X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__le__iff) ).
fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
! [X16,X73,X154,X2,X13,X10] :
( c_Finite__Set_Ofun__left__comm__idem(X10,X13,X2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Finite__Set_Ofold(X10,X13,X2),X73),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(X2,X16),hAPP(hAPP(c_Finite__Set_Ofold(X10,X13,X2),X73),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofold__insert__idem) ).
fof(fact_sum__eq__0__conv,axiom,
! [X305,X102] :
( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X305) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X102 = 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),X305)))
=> 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,
! [X57,X58,X59,X42,X60,X61] :
( c_Natural_Oevaln(X61,X60,X42,X59)
=> ( c_Natural_Oevaln(X58,X59,X42,X57)
=> c_Natural_Oevaln(c_Com_Ocom_OSemi(X61,X58),X60,X42,X57) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OSemi) ).
fof(fact_one__le__mult__iff,axiom,
! [X20,X102] :
( 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),X102),X20)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X102))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__le__mult__iff) ).
fof(fact_one__less__mult,axiom,
! [X97,X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X42))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X97))
=> 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),X97),X42))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__mult) ).
fof(fact_mod__mult__self4,axiom,
! [X97,X42,X103] : 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),X103),X42)),X97)),X42) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X97),X42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self4) ).
fof(fact_Union__Un__distrib,axiom,
! [X160,X154,X10] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X154)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__Un__distrib) ).
fof(fact_Inter__Un__distrib,axiom,
! [X160,X154,X10] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X154)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__Un__distrib) ).
fof(fact_split__mod,axiom,
! [X101,X20,X19] :
( hBOOL(hAPP(X19,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20,X101)))
<=> ( ( X101 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(X19,X20)) )
& ( X101 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ! [X152,X123] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X123),X101))
=> ( X20 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X101),X152)),X123)
=> hBOOL(hAPP(X19,X123)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__mod) ).
fof(fact_in__lists__conv__set,axiom,
! [X154,X290,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X290),c_List_Olists(X10,X154)))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X290)))
=> hBOOL(hAPP(hAPP(c_member(X10),X3),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__lists__conv__set) ).
fof(fact_list_Osize_I2_J,axiom,
! [X291,X39,X11,X10] : c_List_Olist_Olist__size(X10,X11,hAPP(hAPP(c_List_Olist_OCons(X10),X39),X291)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X11,X39)),c_List_Olist_Olist__size(X10,X11,X291))),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,
! [X97,X42,X105,X93,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X93),X105))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),X97))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),X42)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X105),X97))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__power__le) ).
fof(fact_restrict__complement__singleton__eq,axiom,
! [X16,X2,X13,X10] : c_Map_Orestrict__map(X10,X13,X2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),X2),X16),c_Option_Ooption_ONone(X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__complement__singleton__eq) ).
fof(fact_select__weight__cons__zero,axiom,
! [X290,X16,X10] : c_Random_Oselect__weight(X10,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X10)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X10),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X16)),X290)) = c_Random_Oselect__weight(X10,X290),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_select__weight__cons__zero) ).
fof(fact_transpose_Opsimps_I2_J,axiom,
! [X328,X10] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X10)),c_List_Otranspose__rel(X10)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X10)),c_List_Olist_ONil(X10)),X328)))
=> c_List_Otranspose(X10,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X10)),c_List_Olist_ONil(X10)),X328)) = c_List_Otranspose(X10,X328) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose_Opsimps_I2_J) ).
fof(fact_disjoint__eq__subset__Compl,axiom,
! [X160,X154,X10] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X160))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_disjoint__eq__subset__Compl) ).
fof(fact_card__seteq,axiom,
! [X154,X160,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X160)),hAPP(c_Finite__Set_Ocard(X10),X154)))
=> X154 = X160 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__seteq) ).
fof(fact_Inter__lower,axiom,
! [X154,X160,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X160),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X154)),X160)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__lower) ).
fof(fact_converse__rel__comp,axiom,
! [X54,X177,X125,X10,X13] : hAPP(c_Relation_Oconverse(X13,X10),hAPP(hAPP(c_Relation_Orel__comp(X13,X125,X10),X177),X54)) = hAPP(hAPP(c_Relation_Orel__comp(X10,X125,X13),hAPP(c_Relation_Oconverse(X125,X10),X54)),hAPP(c_Relation_Oconverse(X13,X125),X177)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rel__comp) ).
fof(fact_min__le__iff__disj,axiom,
! [X73,X25,X16,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X16),X25)),X73))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X73))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X25),X73)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__le__iff__disj) ).
fof(fact_min__less__iff__disj,axiom,
! [X73,X25,X16,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X16),X25)),X73))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X16),X73))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X25),X73)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__less__iff__disj) ).
fof(fact_split__div,axiom,
! [X101,X20,X19] :
( hBOOL(hAPP(X19,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20),X101)))
<=> ( ( X101 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( X101 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ! [X152,X123] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X123),X101))
=> ( X20 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X101),X152)),X123)
=> hBOOL(hAPP(X19,X152)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__div) ).
fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
! [X160,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X160 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),X154))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X160)),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X154)) = c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X154) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Osubset__idem) ).
fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
! [X160,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X160 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),X154))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X160)),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X154)) = c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X154) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Osubset__idem) ).
fof(fact_map__add__dom__app__simps_I1_J,axiom,
! [X282,X281,X13,X102,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X102),c_Map_Odom(X10,X13,X281)))
=> hAPP(c_Map_Omap__add(X10,X13,X282,X281),X102) = hAPP(X281,X102) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__dom__app__simps_I1_J) ).
fof(fact_evalc_OWhileTrue,axiom,
! [X88,X77,X18,X85,X38] :
( hBOOL(hAPP(X38,X85))
=> ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X18),X85),X77))
=> ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X38,X18)),X77),X88))
=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X38,X18)),X85),X88)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OWhileTrue) ).
fof(fact_subset__Pow__Union,axiom,
! [X154,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),X154),hAPP(c_Set_OPow(X10),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X154)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__Pow__Union) ).
fof(fact_map__of__zip__inject,axiom,
! [X299,X290,X13,X289,X10] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X289) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13)),X290)
=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X299) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13)),X290)
=> ( hBOOL(hAPP(c_List_Odistinct(X13),X290))
=> ( c_Map_Omap__of(X13,X10,hAPP(hAPP(c_List_Ozip(X13,X10),X290),X289)) = c_Map_Omap__of(X13,X10,hAPP(hAPP(c_List_Ozip(X13,X10),X290),X299))
=> X289 = X299 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__zip__inject) ).
fof(fact_IntI,axiom,
! [X160,X154,X18,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X18),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X18),X160))
=> hBOOL(hAPP(hAPP(c_member(X10),X18),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntI) ).
fof(fact_dom__map__add,axiom,
! [X20,X102,X13,X10] : c_Map_Odom(X10,X13,c_Map_Omap__add(X10,X13,X102,X20)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_Map_Odom(X10,X13,X20)),c_Map_Odom(X10,X13,X102)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__map__add) ).
fof(fact_conjI__realizer,axiom,
! [X13,X10,X158,X17,X166,X19] :
( hBOOL(hAPP(X19,X166))
=> ( hBOOL(hAPP(X17,X158))
=> ( hBOOL(hAPP(X19,hAPP(c_Product__Type_Ofst(X10,X13),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X166),X158))))
& hBOOL(hAPP(X17,hAPP(c_Product__Type_Osnd(X10,X13),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X166),X158)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conjI__realizer) ).
fof(fact_INFI__apply,axiom,
! [X16,X2,X154,X125,X13,X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X125,X10)),X154),X2),X16) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,X10),X154),hAPP(hAPP(c_COMBC(X13,X125,X10),X2),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INFI__apply) ).
fof(fact_SUPR__apply,axiom,
! [X16,X2,X154,X125,X13,X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X125,X10)),X154),X2),X16) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,X10),X154),hAPP(hAPP(c_COMBC(X13,X125,X10),X2),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUPR__apply) ).
fof(fact_finite__Un,axiom,
! [X210,X225,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X225),X210)))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X225))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X210)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Un) ).
fof(fact_Un__Diff__Int,axiom,
! [X160,X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = X154,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff__Int) ).
fof(fact_lists__mono,axiom,
! [X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),c_List_Olists(X10,X154)),c_List_Olists(X10,X160))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__mono) ).
fof(fact_neg__le__divide__eq,axiom,
! [X38,X39,X18,X10] :
( class_Fields_Olinordered__field(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),X18)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X18))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__le__divide__eq) ).
fof(fact_neg__less__divide__eq,axiom,
! [X38,X39,X18,X10] :
( class_Fields_Olinordered__field(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),X18)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X18))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__divide__eq) ).
fof(fact_wfP__def,axiom,
! [X177,X10] :
( c_Wellfounded_OwfP(X10,X177)
<=> c_Wellfounded_Owf(X10,hAPP(c_Set_OCollect(tc_prod(X10,X10)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X10,tc_HOL_Obool),X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__def) ).
fof(fact_pos__imp__zdiv__neg__iff,axiom,
! [X39,X38] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X38))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X39),X38)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X39),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,
! [X160,X154,X13,X198,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X16),X198))
=> ( hAPP(hAPP(c_Product__Type_OSigma(X13,X10),X154),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X13),X198)) = hAPP(hAPP(c_Product__Type_OSigma(X13,X10),X160),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X13),X198))
<=> X154 = X160 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__eq__cancel2) ).
fof(fact_mod__pos__neg__trivial,axiom,
! [X92,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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X84),X92)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X92) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X84),X92) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__neg__trivial) ).
fof(fact_wfI__pf,axiom,
! [X196,X10] :
( ! [X246] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X246),hAPP(c_Relation_OImage(X10,X10,X196),X246)))
=> X246 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) )
=> c_Wellfounded_Owf(X10,X196) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfI__pf) ).
fof(fact_splitI,axiom,
! [X13,X10,X38,X39,X2] :
( hBOOL(hAPP(hAPP(X2,X39),X38))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,tc_HOL_Obool),X2),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X39),X38))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splitI) ).
fof(fact_prod__caseI,axiom,
! [X13,X10,X38,X39,X12] :
( hBOOL(hAPP(hAPP(X12,X39),X38))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,tc_HOL_Obool),X12),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X39),X38))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod__caseI) ).
fof(fact_neg__imp__zdiv__neg__iff,axiom,
! [X39,X38] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X38),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),X39),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)),X39)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__imp__zdiv__neg__iff) ).
fof(fact_le__diff__conv,axiom,
! [X113,X101,X163] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X163),X101)),X113))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X163),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X113),X101))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv) ).
fof(fact_less__diff__conv,axiom,
! [X101,X163,X113] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X113),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X163),X101)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X113),X101)),X163)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__diff__conv) ).
fof(fact_card__Diff__subset,axiom,
! [X154,X160,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),X154))
=> hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X154)),hAPP(c_Finite__Set_Ocard(X10),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff__subset) ).
fof(fact_folding__idem_Oidem__comp,axiom,
! [X16,X225,X2,X13,X10] :
( c_Finite__Set_Ofolding__idem(X10,X13,X2,X225)
=> hAPP(c_Fun_Ocomp(X13,X13,X13,hAPP(X2,X16)),hAPP(X2,X16)) = hAPP(X2,X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Oidem__comp) ).
fof(fact_Field__Un,axiom,
! [X54,X177,X10] : hAPP(c_Relation_OField(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X177),X54)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_OField(X10),X177)),hAPP(c_Relation_OField(X10),X54)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__Un) ).
fof(fact_zip__eq__conv,axiom,
! [X299,X289,X13,X290,X10] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13)),X289)
=> ( hAPP(hAPP(c_List_Ozip(X10,X13),X290),X289) = X299
<=> ( hAPP(hAPP(c_List_Omap(tc_prod(X10,X13),X10),c_Product__Type_Ofst(X10,X13)),X299) = X290
& hAPP(hAPP(c_List_Omap(tc_prod(X10,X13),X13),c_Product__Type_Osnd(X10,X13)),X299) = X289 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__eq__conv) ).
fof(fact_map__upd__Some__unfold,axiom,
! [X25,X16,X38,X39,X102,X10,X13] :
( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X13,tc_Option_Ooption(X10)),X102),X39),hAPP(c_Option_Ooption_OSome(X10),X38)),X16) = hAPP(c_Option_Ooption_OSome(X10),X25)
<=> ( ( X16 = X39
& X38 = X25 )
| ( X16 != X39
& hAPP(X102,X16) = hAPP(c_Option_Ooption_OSome(X10),X25) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upd__Some__unfold) ).
fof(fact_inf1D1,axiom,
! [X16,X160,X154,X10] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160),X16))
=> hBOOL(hAPP(X154,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1D1) ).
fof(fact_inf1D2,axiom,
! [X16,X160,X154,X10] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160),X16))
=> hBOOL(hAPP(X160,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1D2) ).
fof(fact_listrelp_Oequations_I2_J,axiom,
! [X72,X52,X50,X51,X177,X10] :
( c_List_Olistrelp(X10,X177,hAPP(hAPP(c_List_Olist_OCons(X10),X51),X50),hAPP(hAPP(c_List_Olist_OCons(X10),X52),X72))
<=> ( hBOOL(hAPP(hAPP(X177,X51),X52))
& c_List_Olistrelp(X10,X177,X50,X72) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrelp_Oequations_I2_J) ).
fof(fact_listrelp_OCons,axiom,
! [X289,X290,X10,X25,X16,X177] :
( hBOOL(hAPP(hAPP(X177,X16),X25))
=> ( c_List_Olistrelp(X10,X177,X290,X289)
=> c_List_Olistrelp(X10,X177,hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290),hAPP(hAPP(c_List_Olist_OCons(X10),X25),X289)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrelp_OCons) ).
fof(fact_Rep__Integ__cases,axiom,
! [X25] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X25),c_Int_OInteg))
=> ~ ! [X3] : X25 != hAPP(c_Int_ORep__Integ,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ__cases) ).
fof(fact_InterI,axiom,
! [X154,X198,X10] :
( ! [X270] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X270),X198))
=> hBOOL(hAPP(hAPP(c_member(X10),X154),X270)) )
=> hBOOL(hAPP(hAPP(c_member(X10),X154),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X198))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_InterI) ).
fof(fact_lists_Osimps,axiom,
! [X154,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X39),c_List_Olists(X10,X154)))
<=> ( X39 = c_List_Olist_ONil(X10)
| ? [X116,X327] :
( X39 = hAPP(hAPP(c_List_Olist_OCons(X10),X116),X327)
& hBOOL(hAPP(hAPP(c_member(X10),X116),X154))
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X327),c_List_Olists(X10,X154))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists_Osimps) ).
fof(fact_folding__one_Ounion__disjoint,axiom,
! [X160,X154,X225,X2,X10] :
( c_Finite__Set_Ofolding__one(X10,X2,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( X160 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(X225,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(X2,hAPP(X225,X154)),hAPP(X225,X160)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Ounion__disjoint) ).
fof(fact_mod__diff__eq,axiom,
! [X81,X92,X84,X94] :
( class_Divides_Oring__div(X94)
=> c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X84),X92),X81) = c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),c_Divides_Odiv__class_Omod(X94,X84,X81)),c_Divides_Odiv__class_Omod(X94,X92,X81)),X81) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__diff__eq) ).
fof(fact_mod__mult__eq,axiom,
! [X81,X92,X84,X94] :
( class_Divides_Osemiring__div(X94)
=> c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92),X81) = c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),c_Divides_Odiv__class_Omod(X94,X84,X81)),c_Divides_Odiv__class_Omod(X94,X92,X81)),X81) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__eq) ).
fof(fact_mod__add__eq,axiom,
! [X81,X92,X84,X94] :
( class_Divides_Osemiring__div(X94)
=> c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92),X81) = c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),c_Divides_Odiv__class_Omod(X94,X84,X81)),c_Divides_Odiv__class_Omod(X94,X92,X81)),X81) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__eq) ).
fof(fact_div__add,axiom,
! [X105,X93,X104,X94] :
( class_Divides_Osemiring__div(X94)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X104),X93))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X104),X105))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X93),X105)),X104) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),X93),X104)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),X105),X104)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__add) ).
fof(fact_power__gt1__lemma,axiom,
! [X42,X84,X94] :
( class_Rings_Olinordered__semidom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Oone__class_Oone(X94)),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Oone__class_Oone(X94)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__gt1__lemma) ).
fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
! [X39,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X39),X39)),c_Groups_Ozero__class_Ozero(X10)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),c_Groups_Ozero__class_Ozero(X10))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
fof(fact_even__less__0__iff,axiom,
! [X39,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X39),X39)),c_Groups_Ozero__class_Ozero(X10)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),c_Groups_Ozero__class_Ozero(X10))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
! [X39,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X39),X39)),c_Groups_Ozero__class_Ozero(X10)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),c_Groups_Ozero__class_Ozero(X10))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
fof(fact_inj__on__diff__nat,axiom,
! [X101,X226] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X226))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X101),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)),X101),X226) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__diff__nat) ).
fof(fact_InterE,axiom,
! [X48,X198,X154,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X154),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X198)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X48),X198))
=> hBOOL(hAPP(hAPP(c_member(X10),X154),X48)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_InterE) ).
fof(fact_InterD,axiom,
! [X48,X198,X154,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X154),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X198)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X48),X198))
=> hBOOL(hAPP(hAPP(c_member(X10),X154),X48)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_InterD) ).
fof(fact_div__pos__neg__trivial,axiom,
! [X92,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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X84),X92)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),X92) = 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,
! [X13,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X10,X13)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X10,X13),tc_HOL_Obool))))
=> ( hAPP(c_Finite__Set_Ocard(X13),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__fun__UNIVD1) ).
fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
! [X160,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( X160 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X154)),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X160)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Ounion__idem) ).
fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
! [X160,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( X160 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X154)),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X160)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Ounion__idem) ).
fof(fact_zdiv__mono1,axiom,
! [X92,X95,X84] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X84),X95))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),X92)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X95),X92))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono1) ).
fof(fact_div__le__mono2,axiom,
! [X103,X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X97))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),X42))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X103),X42)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X103),X97))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__le__mono2) ).
fof(fact_zmult__zless__mono2,axiom,
! [X103,X119,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X120),X119))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X103))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X103),X120)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X103),X119))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).
fof(fact_mult__less__mono1,axiom,
! [X103,X119,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),X119))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X103))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X120),X103)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X119),X103))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__mono1) ).
fof(fact_mult__less__mono2,axiom,
! [X103,X119,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),X119))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X103))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X103),X120)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X103),X119))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__mono2) ).
fof(fact_inj__mapD,axiom,
! [X2,X13,X10] :
( c_Fun_Oinj__on(tc_List_Olist(X10),tc_List_Olist(X13),hAPP(c_List_Omap(X10,X13),X2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X10),tc_HOL_Obool)))
=> c_Fun_Oinj__on(X10,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__mapD) ).
fof(fact_inj__map,axiom,
! [X2,X13,X10] :
( c_Fun_Oinj__on(tc_List_Olist(X10),tc_List_Olist(X13),hAPP(c_List_Omap(X10,X13),X2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X10),tc_HOL_Obool)))
<=> c_Fun_Oinj__on(X10,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__map) ).
fof(fact_subset__insertI2,axiom,
! [X38,X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X38),X160))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI2) ).
fof(fact_INT__insert,axiom,
! [X160,X154,X39,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X13),X39),X154)),X160) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(X160,X39)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X154),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__insert) ).
fof(fact_UN__insert,axiom,
! [X160,X154,X39,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X13),X39),X154)),X160) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(X160,X39)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X154),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__insert) ).
fof(fact_strict__below__fold1__iff,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X16),hAPP(c_Finite__Set_Ofold1(X10,c_Orderings_Oord__class_Omin(X10)),X154)))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X16),X3)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_strict__below__fold1__iff) ).
fof(fact_min__max_Obelow__fold1__iff,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),hAPP(c_Finite__Set_Ofold1(X10,c_Orderings_Oord__class_Omin(X10)),X154)))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X3)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Obelow__fold1__iff) ).
fof(fact_below__fold1__iff,axiom,
! [X16,X154,X10] :
( class_Lattices_Osemilattice__inf(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),hAPP(c_Finite__Set_Ofold1(X10,c_Lattices_Osemilattice__inf__class_Oinf(X10)),X154)))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X3)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_below__fold1__iff) ).
fof(fact_le__iff__diff__le__0,axiom,
! [X38,X39,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),X38))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X39),X38)),c_Groups_Ozero__class_Ozero(X10))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__diff__le__0) ).
fof(fact_less__iff__diff__less__0,axiom,
! [X38,X39,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),X38))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X39),X38)),c_Groups_Ozero__class_Ozero(X10))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__diff__less__0) ).
fof(fact_zdiv__mono1__neg,axiom,
! [X92,X95,X84] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X84),X95))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X92),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),X95),X92)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),X92))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono1__neg) ).
fof(fact_nth__mem,axiom,
! [X290,X10,X20] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290)))
=> hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(c_List_Onth(X10),X290),X20)),hAPP(c_List_Oset(X10),X290))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__mem) ).
fof(fact_n__less__n__mult__m,axiom,
! [X97,X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X42))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X97))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),X97))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).
fof(fact_n__less__m__mult__n,axiom,
! [X97,X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X42))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X97))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X97),X42))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).
fof(fact_card_Oeq__fold__g,axiom,
! [X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(c_Finite__Set_Ocard(X10),X154) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X10,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X10),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X154) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oeq__fold__g) ).
fof(fact_divide__diff__eq__iff,axiom,
! [X105,X93,X104,X94] :
( class_Fields_Ofield(X94)
=> ( X104 != c_Groups_Ozero__class_Ozero(X94)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X93),X104)),X105) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X93),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X104),X105))),X104) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__diff__eq__iff) ).
fof(fact_divide__add__eq__iff,axiom,
! [X105,X93,X104,X94] :
( class_Fields_Ofield(X94)
=> ( X104 != c_Groups_Ozero__class_Ozero(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X93),X104)),X105) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X93),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X104),X105))),X104) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__add__eq__iff) ).
fof(fact_add__frac__num,axiom,
! [X104,X93,X105,X94] :
( class_Fields_Ofield__inverse__zero(X94)
=> ( X105 != c_Groups_Ozero__class_Ozero(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X93),X105)),X104) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X93),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X104),X105))),X105) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__frac__num) ).
fof(fact_in__set__conv__nth,axiom,
! [X290,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
<=> ? [X152] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X152),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290)))
& hAPP(hAPP(c_List_Onth(X10),X290),X152) = X16 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__conv__nth) ).
fof(fact_mult__le__mono,axiom,
! [X121,X103,X119,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X120),X119))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X103),X121))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X120),X103)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X119),X121))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono) ).
fof(fact_add__le__mono,axiom,
! [X121,X103,X119,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X120),X119))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X103),X121))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X120),X103)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X119),X121))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono) ).
fof(fact_zadd__zless__mono,axiom,
! [X104,X145,X133,X148] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X148),X133))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X145),X104))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X148),X145)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X133),X104))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).
fof(fact_diff__less__mono,axiom,
! [X81,X92,X84] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X84),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X81),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X84),X81)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X92),X81))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono) ).
fof(fact_diff__less__mono2,axiom,
! [X121,X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X121))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X121),X42)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X121),X97))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono2) ).
fof(fact_add__less__mono,axiom,
! [X121,X103,X119,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),X119))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X103),X121))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X120),X103)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X119),X121))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
! [X137,X138,X140,X139,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X139),X140)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X138),X137)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X138),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X139),X140)),X137)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
fof(fact_lessThan__subset__iff,axiom,
! [X25,X16,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X10),X16)),hAPP(c_SetInterval_Oord__class_OlessThan(X10),X25)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__subset__iff) ).
fof(fact_atMost__subset__iff,axiom,
! [X25,X16,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X10),X16)),hAPP(c_SetInterval_Oord__class_OatMost(X10),X25)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atMost__subset__iff) ).
fof(fact_greaterThan__subset__iff,axiom,
! [X25,X16,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),X16)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),X25)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X25),X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__subset__iff) ).
fof(fact_atLeast__subset__iff,axiom,
! [X25,X16,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X10),X16)),hAPP(c_SetInterval_Oord__class_OatLeast(X10),X25)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X25),X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__subset__iff) ).
fof(fact_lessThan__strict__subset__iff,axiom,
! [X20,X102,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X10),X102)),hAPP(c_SetInterval_Oord__class_OlessThan(X10),X20)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X102),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__strict__subset__iff) ).
fof(fact_divide__nonpos__pos,axiom,
! [X105,X93,X94] :
( class_Fields_Olinordered__field(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),c_Groups_Ozero__class_Ozero(X94)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X105))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X93),X105)),c_Groups_Ozero__class_Ozero(X94))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__nonpos__pos) ).
fof(fact_divide__nonneg__neg,axiom,
! [X105,X93,X94] :
( class_Fields_Olinordered__field(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X93))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X105),c_Groups_Ozero__class_Ozero(X94)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X93),X105)),c_Groups_Ozero__class_Ozero(X94))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__nonneg__neg) ).
fof(fact_mult__nonpos__nonneg,axiom,
! [X92,X84,X94] :
( class_Rings_Oordered__cancel__semiring(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),c_Groups_Ozero__class_Ozero(X94)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92)),c_Groups_Ozero__class_Ozero(X94))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonpos__nonneg) ).
fof(fact_split__mult__neg__le,axiom,
! [X92,X84,X94] :
( class_Rings_Oordered__cancel__semiring(X94)
=> ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X92),c_Groups_Ozero__class_Ozero(X94))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),c_Groups_Ozero__class_Ozero(X94)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X92)) ) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92)),c_Groups_Ozero__class_Ozero(X94))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__mult__neg__le) ).
fof(fact_mult__nonneg__nonpos,axiom,
! [X92,X84,X94] :
( class_Rings_Oordered__cancel__semiring(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X92),c_Groups_Ozero__class_Ozero(X94)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92)),c_Groups_Ozero__class_Ozero(X94))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos) ).
fof(fact_mult__nonneg__nonpos2,axiom,
! [X92,X84,X94] :
( class_Rings_Oordered__cancel__semiring(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X92),c_Groups_Ozero__class_Ozero(X94)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X84)),c_Groups_Ozero__class_Ozero(X94))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos2) ).
fof(fact_divide__neg__pos,axiom,
! [X105,X93,X94] :
( class_Fields_Olinordered__field(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),c_Groups_Ozero__class_Ozero(X94)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X105))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X93),X105)),c_Groups_Ozero__class_Ozero(X94))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__neg__pos) ).
fof(fact_divide__pos__neg,axiom,
! [X105,X93,X94] :
( class_Fields_Olinordered__field(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X93))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X105),c_Groups_Ozero__class_Ozero(X94)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X93),X105)),c_Groups_Ozero__class_Ozero(X94))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__pos__neg) ).
fof(fact_mult__neg__pos,axiom,
! [X92,X84,X94] :
( class_Rings_Olinordered__semiring__strict(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),c_Groups_Ozero__class_Ozero(X94)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92)),c_Groups_Ozero__class_Ozero(X94))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__neg__pos) ).
fof(fact_mult__pos__neg,axiom,
! [X92,X84,X94] :
( class_Rings_Olinordered__semiring__strict(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X92),c_Groups_Ozero__class_Ozero(X94)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92)),c_Groups_Ozero__class_Ozero(X94))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__neg) ).
fof(fact_mult__pos__neg2,axiom,
! [X92,X84,X94] :
( class_Rings_Olinordered__semiring__strict(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X92),c_Groups_Ozero__class_Ozero(X94)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X84)),c_Groups_Ozero__class_Ozero(X94))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__neg2) ).
fof(fact_set__subset__Cons,axiom,
! [X16,X290,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),X290)),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__subset__Cons) ).
fof(fact_transpose__map__map,axiom,
! [X290,X2,X13,X10] : c_List_Otranspose(X10,hAPP(hAPP(c_List_Omap(tc_List_Olist(X13),tc_List_Olist(X10)),hAPP(c_List_Omap(X13,X10),X2)),X290)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X13),tc_List_Olist(X10)),hAPP(c_List_Omap(X13,X10),X2)),c_List_Otranspose(X13,X290)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__map__map) ).
fof(fact_dvd__mult__left,axiom,
! [X81,X92,X84,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92)),X81))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X84),X81)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__left) ).
fof(fact_dvd__mult__right,axiom,
! [X81,X92,X84,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92)),X81))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X92),X81)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__right) ).
fof(fact_le__sup__iff,axiom,
! [X73,X25,X16,X10] :
( class_Lattices_Osemilattice__sup(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X16),X25)),X73))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X73))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X25),X73)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__sup__iff) ).
fof(fact_min__max_Ole__sup__iff,axiom,
! [X73,X25,X16,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X16),X25)),X73))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X73))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X25),X73)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__sup__iff) ).
fof(fact_max__less__iff__conj,axiom,
! [X73,X25,X16,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X16),X25)),X73))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X16),X73))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X25),X73)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__less__iff__conj) ).
fof(fact_nth__eq__iff__index__eq,axiom,
! [X163,X113,X290,X10] :
( hBOOL(hAPP(c_List_Odistinct(X10),X290))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X113),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X163),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290)))
=> ( hAPP(hAPP(c_List_Onth(X10),X290),X113) = hAPP(hAPP(c_List_Onth(X10),X290),X163)
<=> X113 = X163 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__eq__iff__index__eq) ).
fof(fact_distinct__conv__nth,axiom,
! [X290,X10] :
( hBOOL(hAPP(c_List_Odistinct(X10),X290))
<=> ! [X152] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X152),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290)))
=> ! [X123] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X123),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290)))
=> ( X152 != X123
=> hAPP(hAPP(c_List_Onth(X10),X290),X152) != hAPP(hAPP(c_List_Onth(X10),X290),X123) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__conv__nth) ).
fof(fact_distinct__map,axiom,
! [X290,X2,X13,X10] :
( hBOOL(hAPP(c_List_Odistinct(X10),hAPP(hAPP(c_List_Omap(X13,X10),X2),X290)))
<=> ( hBOOL(hAPP(c_List_Odistinct(X13),X290))
& c_Fun_Oinj__on(X13,X10,X2,hAPP(c_List_Oset(X13),X290)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__map) ).
fof(fact_min__max_OInf__le__Sup,axiom,
! [X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X154)),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X154))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__le__Sup) ).
fof(fact_inj__on__diff,axiom,
! [X160,X154,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,X154)
=> c_Fun_Oinj__on(X10,X13,X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__diff) ).
fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
! [X16,X73,X154,X2,X13,X10] :
( c_Finite__Set_Ofun__left__comm__idem(X10,X13,X2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Finite__Set_Ofold(X10,X13,X2),X73),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X13,X2),hAPP(hAPP(X2,X16),X73)),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofold__insert__idem2) ).
fof(fact_insert__Diff,axiom,
! [X154,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(c_Set_Oinsert(X10),X39),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = X154 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Diff) ).
fof(fact_finite__Prod__UNIV,axiom,
! [X13,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10,X13)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Prod__UNIV) ).
fof(fact_finite__Plus__UNIV__iff,axiom,
! [X13,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X10,X13)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X10,X13),tc_HOL_Obool))))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X13),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus__UNIV__iff) ).
fof(fact_setsum__head__Suc,axiom,
! [X2,X20,X102,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X102,X20)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(X2,X102)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X102),X20))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__head__Suc) ).
fof(fact_vimageI2,axiom,
! [X13,X154,X39,X2,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),hAPP(X2,X39)),X154))
=> hBOOL(hAPP(hAPP(c_member(X13),X39),hAPP(c_Set_Ovimage(X13,X10,X2),X154))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimageI2) ).
fof(fact_sorted__insort,axiom,
! [X290,X16,X10] :
( class_Orderings_Olinorder(X10)
=> ( c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X10,c_COMBI(X10)),X16),X290))
<=> c_List_Olinorder__class_Osorted(X10,X290) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__insort) ).
fof(fact_setsum__head__upt__Suc,axiom,
! [X2,X20,X102,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X20))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X102),X20)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(X2,X102)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X102)),X20))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__head__upt__Suc) ).
fof(fact_set__eq__subset,axiom,
! [X10,X160,X154] :
( X154 = X160
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__eq__subset) ).
fof(fact_equalityI,axiom,
! [X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),X154))
=> X154 = X160 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityI) ).
fof(fact_rev__nth,axiom,
! [X297,X94,X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)))
=> hAPP(hAPP(c_List_Onth(X94),hAPP(c_List_Orev(X94),X297)),X42) = hAPP(hAPP(c_List_Onth(X94),X297),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)),hAPP(c_Nat_OSuc,X42))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__nth) ).
fof(fact_INT__absorb,axiom,
! [X154,X13,X241,X101,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X101),X241))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13,tc_HOL_Obool)),hAPP(X154,X101)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X241),X154)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X241),X154) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__absorb) ).
fof(fact_UN__absorb,axiom,
! [X154,X13,X241,X101,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X101),X241))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13,tc_HOL_Obool)),hAPP(X154,X101)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X241),X154)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X241),X154) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__absorb) ).
fof(fact_list__update__overwrite,axiom,
! [X105,X93,X120,X297,X94] : hAPP(hAPP(c_List_Olist__update(X94,hAPP(hAPP(c_List_Olist__update(X94,X297),X120),X93)),X120),X105) = hAPP(hAPP(c_List_Olist__update(X94,X297),X120),X105),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__overwrite) ).
fof(fact_negative__zless,axiom,
! [X97,X42] : 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,X42)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X97))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__zless) ).
fof(fact_Ints__diff,axiom,
! [X38,X39,X10] :
( class_Rings_Oring__1(X10)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),c_Int_Oring__1__class_OInts(X10)))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X38),c_Int_Oring__1__class_OInts(X10)))
=> hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X39),X38)),c_Int_Oring__1__class_OInts(X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__diff) ).
fof(fact_Ints__mult,axiom,
! [X38,X39,X10] :
( class_Rings_Oring__1(X10)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),c_Int_Oring__1__class_OInts(X10)))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X38),c_Int_Oring__1__class_OInts(X10)))
=> hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X38)),c_Int_Oring__1__class_OInts(X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__mult) ).
fof(fact_Nats__mult,axiom,
! [X38,X39,X10] :
( class_Rings_Osemiring__1(X10)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),c_Nat_Osemiring__1__class_ONats(X10)))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X38),c_Nat_Osemiring__1__class_ONats(X10)))
=> hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X38)),c_Nat_Osemiring__1__class_ONats(X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nats__mult) ).
fof(fact_Ints__add,axiom,
! [X38,X39,X10] :
( class_Rings_Oring__1(X10)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),c_Int_Oring__1__class_OInts(X10)))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X38),c_Int_Oring__1__class_OInts(X10)))
=> hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X39),X38)),c_Int_Oring__1__class_OInts(X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__add) ).
fof(fact_Nats__add,axiom,
! [X38,X39,X10] :
( class_Rings_Osemiring__1(X10)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),c_Nat_Osemiring__1__class_ONats(X10)))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X38),c_Nat_Osemiring__1__class_ONats(X10)))
=> hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X39),X38)),c_Nat_Osemiring__1__class_ONats(X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nats__add) ).
fof(fact_add__nonpos__nonpos,axiom,
! [X92,X84,X94] :
( class_Groups_Oordered__comm__monoid__add(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),c_Groups_Ozero__class_Ozero(X94)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X92),c_Groups_Ozero__class_Ozero(X94)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92)),c_Groups_Ozero__class_Ozero(X94))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
fof(fact_add__neg__nonpos,axiom,
! [X92,X84,X94] :
( class_Groups_Oordered__comm__monoid__add(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),c_Groups_Ozero__class_Ozero(X94)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X92),c_Groups_Ozero__class_Ozero(X94)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92)),c_Groups_Ozero__class_Ozero(X94))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).
fof(fact_add__nonpos__neg,axiom,
! [X92,X84,X94] :
( class_Groups_Oordered__comm__monoid__add(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),c_Groups_Ozero__class_Ozero(X94)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X92),c_Groups_Ozero__class_Ozero(X94)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92)),c_Groups_Ozero__class_Ozero(X94))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
fof(fact_add__neg__neg,axiom,
! [X92,X84,X94] :
( class_Groups_Oordered__comm__monoid__add(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),c_Groups_Ozero__class_Ozero(X94)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X92),c_Groups_Ozero__class_Ozero(X94)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92)),c_Groups_Ozero__class_Ozero(X94))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__neg) ).
fof(fact_list__size__conv__listsum,axiom,
! [X290,X2,X10] : c_List_Olist_Olist__size(X10,X2,X290) = 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(X10,tc_Nat_Onat),X2),X290))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__size__conv__listsum) ).
fof(fact_dom__restrict,axiom,
! [X154,X102,X13,X10] : c_Map_Odom(X10,X13,c_Map_Orestrict__map(X10,X13,X102,X154)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_Map_Odom(X10,X13,X102)),X154),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__restrict) ).
fof(fact_map__of__eq__dom,axiom,
! [X289,X290,X13,X10] :
( c_Map_Omap__of(X10,X13,X290) = c_Map_Omap__of(X10,X13,X289)
=> hAPP(c_Set_Oimage(tc_prod(X10,X13),X10,c_Product__Type_Ofst(X10,X13)),hAPP(c_List_Oset(tc_prod(X10,X13)),X290)) = hAPP(c_Set_Oimage(tc_prod(X10,X13),X10,c_Product__Type_Ofst(X10,X13)),hAPP(c_List_Oset(tc_prod(X10,X13)),X289)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__eq__dom) ).
fof(fact_finite__UNIV__inj__surj,axiom,
! [X2,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))))
=> ( c_Fun_Oinj__on(X10,X10,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> hAPP(c_Set_Oimage(X10,X10,X2),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__inj__surj) ).
fof(fact_listsum__triv,axiom,
! [X290,X177,X13,X10] :
( class_Rings_Osemiring__1(X10)
=> hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(X13,X10),hAPP(c_COMBK(X10,X13),X177)),X290)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13)),X290))),X177) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__triv) ).
fof(fact_power__minus,axiom,
! [X42,X84,X94] :
( class_Rings_Oring__1(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X84)),X42) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),c_Groups_Oone__class_Oone(X94))),X42)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__minus) ).
fof(fact_rangeI,axiom,
! [X13,X16,X2,X10] : hBOOL(hAPP(hAPP(c_member(X10),hAPP(X2,X16)),hAPP(c_Set_Oimage(X13,X10,X2),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rangeI) ).
fof(fact_left__diff__distrib__number__of,axiom,
! [X144,X92,X84,X10] :
( ( class_Int_Onumber(X10)
& class_Rings_Oring(X10) )
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X84),X92)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X144)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X84),hAPP(c_Int_Onumber__class_Onumber__of(X10),X144))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X92),hAPP(c_Int_Onumber__class_Onumber__of(X10),X144))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__diff__distrib__number__of) ).
fof(fact_left__distrib__number__of,axiom,
! [X144,X92,X84,X10] :
( ( class_Int_Onumber(X10)
& class_Rings_Osemiring(X10) )
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X84),X92)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X144)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X84),hAPP(c_Int_Onumber__class_Onumber__of(X10),X144))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X92),hAPP(c_Int_Onumber__class_Onumber__of(X10),X144))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__distrib__number__of) ).
fof(fact_map__add__SomeD,axiom,
! [X16,X101,X20,X102,X10,X13] :
( hAPP(c_Map_Omap__add(X13,X10,X102,X20),X101) = hAPP(c_Option_Ooption_OSome(X10),X16)
=> ( hAPP(X20,X101) = hAPP(c_Option_Ooption_OSome(X10),X16)
| ( hAPP(X20,X101) = c_Option_Ooption_ONone(X10)
& hAPP(X102,X101) = hAPP(c_Option_Ooption_OSome(X10),X16) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__SomeD) ).
fof(fact_map__add__Some__iff,axiom,
! [X16,X101,X20,X102,X10,X13] :
( hAPP(c_Map_Omap__add(X13,X10,X102,X20),X101) = hAPP(c_Option_Ooption_OSome(X10),X16)
<=> ( hAPP(X20,X101) = hAPP(c_Option_Ooption_OSome(X10),X16)
| ( hAPP(X20,X101) = c_Option_Ooption_ONone(X10)
& hAPP(X102,X101) = hAPP(c_Option_Ooption_OSome(X10),X16) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__Some__iff) ).
fof(fact_Min_Ounion__disjoint,axiom,
! [X160,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( X160 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),c_Big__Operators_Olinorder__class_OMin(X10,X154)),c_Big__Operators_Olinorder__class_OMin(X10,X160)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Ounion__disjoint) ).
fof(fact_Max_Ounion__disjoint,axiom,
! [X160,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( X160 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),c_Big__Operators_Olinorder__class_OMax(X10,X154)),c_Big__Operators_Olinorder__class_OMax(X10,X160)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Ounion__disjoint) ).
fof(fact_Inf__fin_Ounion__disjoint,axiom,
! [X160,X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( X160 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),c_Big__Operators_Olattice__class_OInf__fin(X10,X154)),c_Big__Operators_Olattice__class_OInf__fin(X10,X160)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Ounion__disjoint) ).
fof(fact_Sup__fin_Ounion__disjoint,axiom,
! [X160,X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( X160 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),c_Big__Operators_Olattice__class_OSup__fin(X10,X154)),c_Big__Operators_Olattice__class_OSup__fin(X10,X160)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Ounion__disjoint) ).
fof(fact_dvd__power__same,axiom,
! [X42,X105,X93,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X93),X105))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),X42)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X105),X42))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__power__same) ).
fof(fact_add__right__mono,axiom,
! [X81,X92,X84,X94] :
( class_Groups_Oordered__ab__semigroup__add(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X81)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X92),X81))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__mono) ).
fof(fact_add__left__mono,axiom,
! [X81,X92,X84,X94] :
( class_Groups_Oordered__ab__semigroup__add(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X81),X84)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X81),X92))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__mono) ).
fof(fact_add__strict__right__mono,axiom,
! [X81,X92,X84,X94] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X81)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X92),X81))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
fof(fact_add__strict__left__mono,axiom,
! [X81,X92,X84,X94] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X81),X84)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X81),X92))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
fof(fact_fold1__Un2,axiom,
! [X160,X154,X10] :
( class_Lattices_Oab__semigroup__idem__mult(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( X160 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),X154)),hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),X160)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__Un2) ).
fof(fact_rev__drop,axiom,
! [X297,X120,X94] : hAPP(c_List_Orev(X94),hAPP(hAPP(c_List_Odrop(X94),X120),X297)) = hAPP(hAPP(c_List_Otake(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)),X120)),hAPP(c_List_Orev(X94),X297)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__drop) ).
fof(fact_rev__take,axiom,
! [X297,X120,X94] : hAPP(c_List_Orev(X94),hAPP(hAPP(c_List_Otake(X94),X120),X297)) = hAPP(hAPP(c_List_Odrop(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)),X120)),hAPP(c_List_Orev(X94),X297)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__take) ).
fof(fact_ivl__disj__un_I5_J,axiom,
! [X165,X162,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X162),X165))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X162),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X162,X165)) = c_SetInterval_Oord__class_OatLeastAtMost(X10,X162,X165) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I5_J) ).
fof(fact_subset__Compl__self__eq,axiom,
! [X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X154)))
<=> X154 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__Compl__self__eq) ).
fof(fact_map__upd__eqD1,axiom,
! [X25,X20,X16,X39,X102,X13,X10] :
( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),X102),X39),hAPP(c_Option_Ooption_OSome(X13),X16)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),X20),X39),hAPP(c_Option_Ooption_OSome(X13),X25))
=> X16 = X25 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upd__eqD1) ).
fof(fact_pdivmod__def,axiom,
! [X121,X103] : c_Divides_Opdivmod(X103,X121) = 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),X103)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X121))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X103),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X121))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__def) ).
fof(fact_Union__upper,axiom,
! [X154,X160,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X160),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X154))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__upper) ).
fof(fact_fold__image__def,axiom,
! [X1,X2,X13,X10] : hAPP(c_Finite__Set_Ofold__image(X10,X13,X2),X1) = c_Finite__Set_Ofold(X13,X10,hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X13),X2),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__def) ).
fof(fact_max__Suc1,axiom,
! [X102,X20] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)),X102) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X20),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),X20)),X102),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__Suc1) ).
fof(fact_Field__Union,axiom,
! [X196,X10] : hAPP(c_Relation_OField(X10),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),X196)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),c_Relation_OField(X10)),X196)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__Union) ).
fof(fact_dvd__mult__cancel2,axiom,
! [X20,X102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X102))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X102)),X102))
<=> X20 = 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,
! [X20,X102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X102))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X102),X20)),X102))
<=> X20 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel1) ).
fof(fact_Diff__partition,axiom,
! [X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X160),X154)) = X160 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__partition) ).
fof(fact_inj__mapI,axiom,
! [X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> c_Fun_Oinj__on(tc_List_Olist(X10),tc_List_Olist(X13),hAPP(c_List_Omap(X10,X13),X2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X10),tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__mapI) ).
fof(fact_Compl__Int,axiom,
! [X160,X154,X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X154)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__Int) ).
fof(fact_Compl__Un,axiom,
! [X160,X154,X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X154)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__Un) ).
fof(fact_peek__and__def,axiom,
! [X54,X171,X166,X19,X10] :
( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X10,X19,X166),X171),X54))
<=> ( hBOOL(hAPP(hAPP(X19,X171),X54))
& hBOOL(hAPP(X166,X54)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_peek__and__def) ).
fof(fact_vimage__code,axiom,
! [X16,X154,X2,X13,X10] :
( hBOOL(hAPP(hAPP(c_Set_Ovimage(X10,X13,X2),X154),X16))
<=> hBOOL(hAPP(X154,hAPP(X2,X16))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__code) ).
fof(fact_Inf__less__iff,axiom,
! [X39,X216,X10] :
( ( class_Complete__Lattice_Ocomplete__lattice(X10)
& class_Orderings_Olinorder(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Complete__Lattice_OInf__class_OInf(X10,X216)),X39))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X216))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X3),X39)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__less__iff) ).
fof(fact_mult__number__of__left,axiom,
! [X104,X133,X144,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),X144)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),X133)),X104)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X144),X133))),X104) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__number__of__left) ).
fof(fact_add__number__of__diff1,axiom,
! [X81,X133,X144,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),X144)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),X133)),X81)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X144),X133))),X81) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__number__of__diff1) ).
fof(fact_add__number__of__left,axiom,
! [X104,X133,X144,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),X144)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),X133)),X104)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X144),X133))),X104) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__number__of__left) ).
fof(fact_Option_Omap__def,axiom,
! [X2,X13,X10] : hAPP(c_Option_Omap(X10,X13),X2) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(X13),X10,c_Option_Ooption_ONone(X13),hAPP(hAPP(c_COMBB(X13,tc_Option_Ooption(X13),X10),c_Option_Ooption_OSome(X13)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Option_Omap__def) ).
fof(fact_ivl__disj__un_I3_J,axiom,
! [X165,X162,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X162),X165))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X162),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X162,X165)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X162),X165) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I3_J) ).
fof(fact_nth__map,axiom,
! [X2,X13,X290,X10,X20] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290)))
=> hAPP(hAPP(c_List_Onth(X13),hAPP(hAPP(c_List_Omap(X10,X13),X2),X290)),X20) = hAPP(X2,hAPP(hAPP(c_List_Onth(X10),X290),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__map) ).
fof(fact_le__imp__power__dvd,axiom,
! [X84,X42,X97,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),X42))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X97)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__power__dvd) ).
fof(fact_nat__gcd_Opsimps,axiom,
! [X25,X16] :
( 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),X16),X25)))
=> ( ( X25 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Nitpick_Onat__gcd(X16,X25) = X16 )
& ( X25 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Nitpick_Onat__gcd(X16,X25) = c_Nitpick_Onat__gcd(X25,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X16,X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__gcd_Opsimps) ).
fof(fact_UnionI,axiom,
! [X154,X198,X48,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X48),X198))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X154),X48))
=> hBOOL(hAPP(hAPP(c_member(X10),X154),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X198))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnionI) ).
fof(fact_zero__less__mult__pos2,axiom,
! [X84,X92,X94] :
( class_Rings_Olinordered__semiring__strict(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X84)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X92)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).
fof(fact_zero__less__mult__pos,axiom,
! [X92,X84,X94] :
( class_Rings_Olinordered__semiring__strict(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X92)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).
fof(fact_card__Un__disjoint,axiom,
! [X160,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X154)),hAPP(c_Finite__Set_Ocard(X10),X160)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Un__disjoint) ).
fof(fact_min__Suc1,axiom,
! [X102,X20] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)),X102) = 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),X20)),X102),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__Suc1) ).
fof(fact_sorted__list__of__set__remove,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> c_List_Olinorder__class_Osorted__list__of__set(X10,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = c_List_Oremove1(X10,X16,c_List_Olinorder__class_Osorted__list__of__set(X10,X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__list__of__set__remove) ).
fof(fact_finite__fun__UNIVD2,axiom,
! [X13,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X10,X13)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X10,X13),tc_HOL_Obool))))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X13),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__fun__UNIVD2) ).
fof(fact_Pow__iff,axiom,
! [X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(c_Set_OPow(X10),X160)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__iff) ).
fof(fact_PowD,axiom,
! [X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(c_Set_OPow(X10),X160)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_PowD) ).
fof(fact_zero__less__zpower__abs__iff,axiom,
! [X20,X16] :
( 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),X16)),X20)))
<=> ( X16 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X20 = 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_I22_J,axiom,
! [X165,X102,X162,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X162),X102))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X102),X165))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X162,X102)),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X102,X165)) = c_SetInterval_Oord__class_OatLeastAtMost(X10,X162,X165) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I22_J) ).
fof(fact_ivl__disj__un_I20_J,axiom,
! [X165,X102,X162,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X162),X102))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X102),X165))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X162,X102)),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X102,X165)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X162,X165) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I20_J) ).
fof(fact_ivl__disj__un_I16_J,axiom,
! [X165,X102,X162,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X162),X102))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X102),X165))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X162,X102)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X102,X165)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X162,X165) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I16_J) ).
fof(fact_ivl__disj__un_I19_J,axiom,
! [X165,X102,X162,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X162),X102))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X102),X165))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X162,X102)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X102,X165)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X162,X165) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I19_J) ).
fof(fact_Un__upper1,axiom,
! [X160,X154,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__upper1) ).
fof(fact_Un__upper2,axiom,
! [X154,X160,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__upper2) ).
fof(fact_r__into__rtrancl,axiom,
! [X177,X166,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X166),X177))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X166),c_Transitive__Closure_Ortrancl(X10,X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__into__rtrancl) ).
fof(fact_card__Plus,axiom,
! [X160,X13,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X160))
=> hAPP(c_Finite__Set_Ocard(tc_sum(X10,X13)),c_Sum__Type_OPlus(X10,X13,X154,X160)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X154)),hAPP(c_Finite__Set_Ocard(X13),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Plus) ).
fof(fact_card__Plus__conv__if,axiom,
! [X160,X13,X154,X10] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X160)) )
=> hAPP(c_Finite__Set_Ocard(tc_sum(X10,X13)),c_Sum__Type_OPlus(X10,X13,X154,X160)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X154)),hAPP(c_Finite__Set_Ocard(X13),X160)) )
& ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X160)) )
=> hAPP(c_Finite__Set_Ocard(tc_sum(X10,X13)),c_Sum__Type_OPlus(X10,X13,X154,X160)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Plus__conv__if) ).
fof(fact_sup__least,axiom,
! [X104,X93,X105,X94] :
( class_Lattices_Osemilattice__sup(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X105),X93))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X104),X93))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X105),X104)),X93)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__least) ).
fof(fact_le__supI,axiom,
! [X92,X93,X84,X94] :
( class_Lattices_Osemilattice__sup(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X93))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X92),X93))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X84),X92)),X93)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__supI) ).
fof(fact_min__max_Ole__supI,axiom,
! [X92,X93,X84,X94] :
( class_Orderings_Olinorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X93))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X92),X93))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X84),X92)),X93)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__supI) ).
fof(fact_min__max_Osup__least,axiom,
! [X104,X93,X105,X94] :
( class_Orderings_Olinorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X105),X93))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X104),X93))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X105),X104)),X93)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__least) ).
fof(fact_Int__left__commute,axiom,
! [X198,X160,X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X160),X198)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X160),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X198)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__left__commute) ).
fof(fact_Un__left__commute,axiom,
! [X198,X160,X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X160),X198)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X160),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X198)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__left__commute) ).
fof(fact_Un__Diff__cancel2,axiom,
! [X154,X160,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X160),X154)),X154) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X160),X154),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff__cancel2) ).
fof(fact_Diff__idemp,axiom,
! [X160,X154,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160)),X160) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__idemp) ).
fof(fact_imageI,axiom,
! [X2,X13,X154,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hBOOL(hAPP(hAPP(c_member(X13),hAPP(X2,X16)),hAPP(c_Set_Oimage(X10,X13,X2),X154))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_imageI) ).
fof(fact_hoare__derivs_Oinsert,axiom,
! [X211,X53,X210,X10] :
( c_Hoare__Mirabelle_Ohoare__derivs(X10,X210,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X10)),X53),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X10),tc_HOL_Obool))))
=> ( c_Hoare__Mirabelle_Ohoare__derivs(X10,X210,X211)
=> c_Hoare__Mirabelle_Ohoare__derivs(X10,X210,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X10)),X53),X211)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_Oinsert) ).
fof(fact_dvd__int__iff,axiom,
! [X102,X73] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X73),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X102)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X73))),X102)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__int__iff) ).
fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
! [X1,X125,X2,X13,X10] :
( c_Finite__Set_Ofun__left__comm(X10,X13,X2)
=> c_Finite__Set_Ofun__left__comm(X125,X13,hAPP(hAPP(c_COMBB(X10,tc_fun(X13,X13),X125),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,X125,X2,X13,X10] :
( c_Finite__Set_Ofun__left__comm__idem(X10,X13,X2)
=> c_Finite__Set_Ofun__left__comm__idem(X125,X13,hAPP(hAPP(c_COMBB(X10,tc_fun(X13,X13),X125),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,
! [X160,X198,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X39),X198))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X39),X160)),X198) = hAPP(hAPP(c_Set_Oinsert(X10),X39),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X160),X198)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__left__if1) ).
fof(fact_inj__image__eq__iff,axiom,
! [X160,X154,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> ( hAPP(c_Set_Oimage(X10,X13,X2),X154) = hAPP(c_Set_Oimage(X10,X13,X2),X160)
<=> X154 = X160 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__eq__iff) ).
fof(fact_o__eq__dest__lhs,axiom,
! [X168,X18,X38,X39,X10,X13,X125] :
( hAPP(c_Fun_Ocomp(X125,X13,X10,X39),X38) = X18
=> hAPP(X39,hAPP(X38,X168)) = hAPP(X18,X168) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__dest__lhs) ).
fof(fact_negative__zless__0,axiom,
! [X42] : 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,X42)))),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,
! [X297,X94,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)))
=> hAPP(hAPP(c_List_Olist_OCons(X94),hAPP(hAPP(c_List_Onth(X94),X297),X120)),hAPP(hAPP(c_List_Odrop(X94),hAPP(c_Nat_OSuc,X120)),X297)) = hAPP(hAPP(c_List_Odrop(X94),X120),X297) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__drop_H) ).
fof(fact_image__vimage__eq,axiom,
! [X154,X2,X10,X13] : hAPP(c_Set_Oimage(X13,X10,X2),hAPP(c_Set_Ovimage(X13,X10,X2),X154)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(c_Set_Oimage(X13,X10,X2),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__vimage__eq) ).
fof(fact_add1__zle__eq,axiom,
! [X73,X131] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X131),c_Groups_Oone__class_Oone(tc_Int_Oint))),X73))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X131),X73)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add1__zle__eq) ).
fof(fact_ivl__disj__un_I18_J,axiom,
! [X165,X102,X162,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X162),X102))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X102),X165))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X162,X102)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X102,X165)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X162),X165) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I18_J) ).
fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
! [X154] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X154))
<=> 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)),X154))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I1_J) ).
fof(fact_card__mono,axiom,
! [X154,X160,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X154)),hAPP(c_Finite__Set_Ocard(X10),X160))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__mono) ).
fof(fact_psubset__card__mono,axiom,
! [X154,X160,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X154)),hAPP(c_Finite__Set_Ocard(X10),X160))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__card__mono) ).
fof(fact_dom__minus,axiom,
! [X154,X13,X10,X16,X2] :
( hAPP(X2,X16) = c_Option_Ooption_ONone(X10)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13,tc_HOL_Obool)),c_Map_Odom(X13,X10,X2)),hAPP(hAPP(c_Set_Oinsert(X13),X16),X154)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13,tc_HOL_Obool)),c_Map_Odom(X13,X10,X2)),X154) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__minus) ).
fof(fact_UnI1,axiom,
! [X160,X154,X18,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X18),X154))
=> hBOOL(hAPP(hAPP(c_member(X10),X18),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnI1) ).
fof(fact_UnI2,axiom,
! [X154,X160,X18,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X18),X160))
=> hBOOL(hAPP(hAPP(c_member(X10),X18),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnI2) ).
fof(fact_finite__UNIV__surj__inj,axiom,
! [X2,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))))
=> ( hAPP(c_Set_Oimage(X10,X10,X2),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))
=> c_Fun_Oinj__on(X10,X10,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__surj__inj) ).
fof(fact_abs__le__iff,axiom,
! [X38,X39,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Groups_Oabs__class_Oabs(X10),X39)),X38))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),X38))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X39)),X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__le__iff) ).
fof(fact_abs__leI,axiom,
! [X92,X84,X94] :
( class_Groups_Oordered__ab__group__add__abs(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X84)),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),X84)),X92)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__leI) ).
fof(fact_abs__less__iff,axiom,
! [X38,X39,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Groups_Oabs__class_Oabs(X10),X39)),X38))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),X38))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X39)),X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__less__iff) ).
fof(fact_lists__accI,axiom,
! [X177,X290,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X290),c_Wellfounded_Oacc(tc_List_Olist(X10),c_List_Olistrel1(X10,X177))))
=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X290),c_List_Olists(X10,c_Wellfounded_Oacc(X10,X177)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__accI) ).
fof(fact_inj__vimage__image__eq,axiom,
! [X154,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> hAPP(c_Set_Ovimage(X10,X13,X2),hAPP(c_Set_Oimage(X10,X13,X2),X154)) = X154 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__vimage__image__eq) ).
fof(fact_ivl__disj__un_I15_J,axiom,
! [X165,X102,X162,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X162),X102))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X102),X165))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X162,X102)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X102),X165)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X162,X165) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I15_J) ).
fof(fact_div__mult__self2,axiom,
! [X81,X84,X92,X94] :
( class_Divides_Osemiring__div(X94)
=> ( X92 != c_Groups_Ozero__class_Ozero(X94)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X81))),X92) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X81),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),X84),X92)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self2) ).
fof(fact_div__mult__self1,axiom,
! [X81,X84,X92,X94] :
( class_Divides_Osemiring__div(X94)
=> ( X92 != c_Groups_Ozero__class_Ozero(X94)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),X92))),X92) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X81),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),X84),X92)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self1) ).
fof(fact_add__num__frac,axiom,
! [X93,X104,X105,X94] :
( class_Fields_Ofield__inverse__zero(X94)
=> ( X105 != c_Groups_Ozero__class_Ozero(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X104),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X93),X105)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X93),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X104),X105))),X105) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__num__frac) ).
fof(fact_setsum__reindex__id,axiom,
! [X160,X2,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( c_Fun_Oinj__on(X10,X13,X2,X160)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),X160) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X13),c_Fun_Oid(X13)),hAPP(c_Set_Oimage(X10,X13,X2),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__reindex__id) ).
fof(fact_setprod__reindex__id,axiom,
! [X160,X2,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( c_Fun_Oinj__on(X10,X13,X2,X160)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),X160) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X13,X13),c_Fun_Oid(X13)),hAPP(c_Set_Oimage(X10,X13,X2),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__reindex__id) ).
fof(fact_wf__comp__self,axiom,
! [X196,X10] :
( c_Wellfounded_Owf(X10,X196)
<=> c_Wellfounded_Owf(X10,hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X196),X196)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__comp__self) ).
fof(fact_less__by__empty,axiom,
! [X160,X10,X154] :
( X154 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X154),X160)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__by__empty) ).
fof(fact_distinct__append,axiom,
! [X289,X290,X10] :
( hBOOL(hAPP(c_List_Odistinct(X10),hAPP(hAPP(c_List_Oappend(X10),X290),X289)))
<=> ( hBOOL(hAPP(c_List_Odistinct(X10),X290))
& hBOOL(hAPP(c_List_Odistinct(X10),X289))
& hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),X290)),hAPP(c_List_Oset(X10),X289)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__append) ).
fof(fact_min__max_OInf__fin__set__fold,axiom,
! [X290,X16,X10] :
( class_Orderings_Olinorder(X10)
=> c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290))) = hAPP(c_List_Ofoldl(X10,X10,c_Orderings_Oord__class_Omin(X10),X16),X290) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin__set__fold) ).
fof(fact_min__max_OSup__fin__set__fold,axiom,
! [X290,X16,X10] :
( class_Orderings_Olinorder(X10)
=> c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290))) = hAPP(c_List_Ofoldl(X10,X10,c_Orderings_Oord__class_Omax(X10),X16),X290) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin__set__fold) ).
fof(fact_setsum__head,axiom,
! [X19,X20,X102,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X19),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X102,X20)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(X19,X102)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X19),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X102,X20))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__head) ).
fof(fact_funpow_Osimps_I2_J,axiom,
! [X2,X20,X10] : hAPP(hAPP(c_Nat_Ocompow(X10,X10),hAPP(c_Nat_OSuc,X20)),X2) = hAPP(c_Fun_Ocomp(X10,X10,X10,X2),hAPP(hAPP(c_Nat_Ocompow(X10,X10),X20),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow_Osimps_I2_J) ).
fof(fact_list__size__estimation_H,axiom,
! [X2,X25,X290,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),hAPP(X2,X16)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),c_List_Olist_Olist__size(X10,X2,X290))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__size__estimation_H) ).
fof(fact_list__size__estimation,axiom,
! [X2,X25,X290,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(X2,X16)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),c_List_Olist_Olist__size(X10,X2,X290))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__size__estimation) ).
fof(fact_elem__le__listsum__nat,axiom,
! [X306,X103] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X103),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X306)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X306),X103)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X306))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_elem__le__listsum__nat) ).
fof(fact_map__of__append,axiom,
! [X289,X290,X13,X10] : c_Map_Omap__of(X10,X13,hAPP(hAPP(c_List_Oappend(tc_prod(X10,X13)),X290),X289)) = c_Map_Omap__add(X10,X13,c_Map_Omap__of(X10,X13,X289),c_Map_Omap__of(X10,X13,X290)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__append) ).
fof(fact_le__div__geq,axiom,
! [X97,X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X42))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),X97))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X97),X42) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42)),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__div__geq) ).
fof(fact_lists__accD,axiom,
! [X177,X290,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X290),c_List_Olists(X10,c_Wellfounded_Oacc(X10,X177))))
=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X290),c_Wellfounded_Oacc(tc_List_Olist(X10),c_List_Olistrel1(X10,X177)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__accD) ).
fof(fact_dvd__diffD,axiom,
! [X42,X97,X103] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X103),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X103),X42))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),X97))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X103),X97)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__diffD) ).
fof(fact_dvd__diffD1,axiom,
! [X42,X97,X103] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X103),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X103),X97))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),X97))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X103),X42)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__diffD1) ).
fof(fact_semiring__1__class_Oof__nat__code,axiom,
! [X20,X10] :
( class_Rings_Osemiring__1(X10)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),X20) = c_Nat_Osemiring__1__class_Oof__nat__aux(X10,hAPP(hAPP(c_COMBC(X10,X10,X10),c_Groups_Oplus__class_Oplus(X10)),c_Groups_Oone__class_Oone(X10)),X20,c_Groups_Ozero__class_Ozero(X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__1__class_Oof__nat__code) ).
fof(fact_impossible__Cons,axiom,
! [X93,X298,X297,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X298)))
=> X297 != hAPP(hAPP(c_List_Olist_OCons(X94),X93),X298) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_impossible__Cons) ).
fof(fact_PowI,axiom,
! [X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(c_Set_OPow(X10),X160))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_PowI) ).
fof(fact_power_Opower_Opower__Suc,axiom,
! [X20,X39,X172,X173,X10] : hAPP(hAPP(c_Power_Opower_Opower(X10,X173,X172),X39),hAPP(c_Nat_OSuc,X20)) = hAPP(hAPP(X172,X39),hAPP(hAPP(c_Power_Opower_Opower(X10,X173,X172),X39),X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power_Opower_Opower__Suc) ).
fof(fact_map__add__None,axiom,
! [X101,X20,X102,X10,X13] :
( hAPP(c_Map_Omap__add(X13,X10,X102,X20),X101) = c_Option_Ooption_ONone(X10)
<=> ( hAPP(X20,X101) = c_Option_Ooption_ONone(X10)
& hAPP(X102,X101) = c_Option_Ooption_ONone(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__None) ).
fof(fact_Min__antimono,axiom,
! [X226,X230,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X230),X226))
=> ( X230 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X226))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Big__Operators_Olinorder__class_OMin(X10,X226)),c_Big__Operators_Olinorder__class_OMin(X10,X230))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min__antimono) ).
fof(fact_Max__mono,axiom,
! [X226,X230,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X230),X226))
=> ( X230 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X226))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Big__Operators_Olinorder__class_OMax(X10,X230)),c_Big__Operators_Olinorder__class_OMax(X10,X226))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max__mono) ).
fof(fact_less__bin__lemma,axiom,
! [X162,X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),X162))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X101),X162)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__bin__lemma) ).
fof(fact_singleton__iff,axiom,
! [X39,X38,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X38),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))
<=> X38 = X39 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__iff) ).
fof(fact_singletonE,axiom,
! [X39,X38,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X38),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))
=> X38 = X39 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singletonE) ).
fof(fact_range__eqI,axiom,
! [X13,X10,X16,X2,X38] :
( X38 = hAPP(X2,X16)
=> hBOOL(hAPP(hAPP(c_member(X10),X38),hAPP(c_Set_Oimage(X13,X10,X2),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__eqI) ).
fof(fact_snd__image__times,axiom,
! [X160,X13,X10,X154] :
( ( X154 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(tc_prod(X10,X13),X13,c_Product__Type_Osnd(X10,X13)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X154),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),X160))) = c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool)) )
& ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(tc_prod(X10,X13),X13,c_Product__Type_Osnd(X10,X13)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X154),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),X160))) = X160 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__image__times) ).
fof(fact_fst__image__times,axiom,
! [X154,X13,X10,X160] :
( ( X160 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(tc_prod(X13,X10),X13,c_Product__Type_Ofst(X13,X10)),hAPP(hAPP(c_Product__Type_OSigma(X13,X10),X154),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X13),X160))) = c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool)) )
& ( X160 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(tc_prod(X13,X10),X13,c_Product__Type_Ofst(X13,X10)),hAPP(hAPP(c_Product__Type_OSigma(X13,X10),X154),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X13),X160))) = X154 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__image__times) ).
fof(fact_doubleton__eq__iff,axiom,
! [X141,X18,X38,X39,X10] :
( hAPP(hAPP(c_Set_Oinsert(X10),X39),hAPP(hAPP(c_Set_Oinsert(X10),X38),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(X10),X18),hAPP(hAPP(c_Set_Oinsert(X10),X141),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))
<=> ( ( X39 = X18
& X38 = X141 )
| ( X39 = X141
& X38 = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_doubleton__eq__iff) ).
fof(fact_dvd__setprod,axiom,
! [X2,X113,X154,X10,X13] :
( class_Rings_Ocomm__semiring__1(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X113),X154))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X13),hAPP(X2,X113)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),X154))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__setprod) ).
fof(fact_nth__list__update,axiom,
! [X93,X119,X297,X94,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)))
=> ( ( X120 = X119
=> hAPP(hAPP(c_List_Onth(X94),hAPP(hAPP(c_List_Olist__update(X94,X297),X120),X93)),X119) = X93 )
& ( X120 != X119
=> hAPP(hAPP(c_List_Onth(X94),hAPP(hAPP(c_List_Olist__update(X94,X297),X120),X93)),X119) = hAPP(hAPP(c_List_Onth(X94),X297),X119) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__list__update) ).
fof(fact_dvd_OmonoD,axiom,
! [X25,X16,X2,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oorder_Omono(tc_Nat_Onat,X10,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X16),X25))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(X2,X16)),hAPP(X2,X25))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OmonoD) ).
fof(fact_add__leD1,axiom,
! [X42,X103,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X103)),X42))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD1) ).
fof(fact_add__leD2,axiom,
! [X42,X103,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X103)),X42))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X103),X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD2) ).
fof(fact_add__lessD1,axiom,
! [X103,X119,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X120),X119)),X103))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),X103)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__lessD1) ).
fof(fact_diff__Suc__less,axiom,
! [X120,X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X42))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X42),hAPP(c_Nat_OSuc,X120))),X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__less) ).
fof(fact_evaln_Oequations_I9_J,axiom,
! [X72,X50,X52,X51] :
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X51),X52,hAPP(c_Nat_OSuc,X50),X72)
<=> c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X51)),X52,X50,X72) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I9_J) ).
fof(fact_evaln_OBody,axiom,
! [X59,X42,X60,X86] :
( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X86)),X60,X42,X59)
=> c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X86),X60,hAPP(c_Nat_OSuc,X42),X59) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OBody) ).
fof(fact_ran__map__upd,axiom,
! [X38,X13,X10,X39,X102] :
( hAPP(X102,X39) = c_Option_Ooption_ONone(X10)
=> c_Map_Oran(X13,X10,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X13,tc_Option_Ooption(X10)),X102),X39),hAPP(c_Option_Ooption_OSome(X10),X38))) = hAPP(hAPP(c_Set_Oinsert(X10),X38),c_Map_Oran(X13,X10,X102)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ran__map__upd) ).
fof(fact_ivl__disj__un_I21_J,axiom,
! [X165,X102,X162,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X162),X102))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X102),X165))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X162),X102)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X102,X165)) = c_SetInterval_Oord__class_OatLeastAtMost(X10,X162,X165) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I21_J) ).
fof(fact_atLeastLessThan__add__Un,axiom,
! [X101,X163,X113] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X113),X163))
=> hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X113),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X163),X101)) = 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,X113),X163)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X163),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X163),X101))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__add__Un) ).
fof(fact_insert__Diff__single,axiom,
! [X154,X39,X10] : hAPP(hAPP(c_Set_Oinsert(X10),X39),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(X10),X39),X154),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Diff__single) ).
fof(fact_card__insert__le,axiom,
! [X16,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X154)),hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__le) ).
fof(fact_zadd__int__left,axiom,
! [X104,X42,X97] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X97)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X42)),X104)) = 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),X97),X42))),X104),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__int__left) ).
fof(fact_less__Sup__iff,axiom,
! [X216,X39,X10] :
( ( class_Complete__Lattice_Ocomplete__lattice(X10)
& class_Orderings_Olinorder(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),c_Complete__Lattice_OSup__class_OSup(X10,X216)))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X216))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Sup__iff) ).
fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
! [X154] :
( c_Nat__Transfer_Onat__set(X154)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X154))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X154))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I1_J) ).
fof(fact_transfer__nat__int__relations_I4_J,axiom,
! [X25,X16] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16))
=> ( 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_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X16)),hAPP(c_Int_Onat,X25)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X16),X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I4_J) ).
fof(fact_transfer__nat__int__relations_I3_J,axiom,
! [X25,X16] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16))
=> ( 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__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X16)),hAPP(c_Int_Onat,X25)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X16),X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I3_J) ).
fof(fact_transfer__nat__int__relations_I2_J,axiom,
! [X25,X16] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16))
=> ( 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_Nat_Onat),hAPP(c_Int_Onat,X16)),hAPP(c_Int_Onat,X25)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16),X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I2_J) ).
fof(fact_ivl__disj__un_I4_J,axiom,
! [X165,X162,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X162),X165))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X162,X165)),hAPP(hAPP(c_Set_Oinsert(X10),X165),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X162,X165) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I4_J) ).
fof(fact_evaln_OIfTrue,axiom,
! [X75,X77,X20,X76,X54,X38] :
( hBOOL(hAPP(X38,X54))
=> ( c_Natural_Oevaln(X76,X54,X20,X77)
=> c_Natural_Oevaln(c_Com_Ocom_OCond(X38,X76,X75),X54,X20,X77) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OIfTrue) ).
fof(fact_Min__eqI,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ! [X90] :
( hBOOL(hAPP(hAPP(c_member(X10),X90),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X90)) )
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> c_Big__Operators_Olinorder__class_OMin(X10,X154) = X16 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min__eqI) ).
fof(fact_map__append,axiom,
! [X289,X290,X2,X10,X13] : hAPP(hAPP(c_List_Omap(X13,X10),X2),hAPP(hAPP(c_List_Oappend(X13),X290),X289)) = hAPP(hAPP(c_List_Oappend(X10),hAPP(hAPP(c_List_Omap(X13,X10),X2),X290)),hAPP(hAPP(c_List_Omap(X13,X10),X2),X289)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__append) ).
fof(fact_finite__Union,axiom,
! [X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X10,tc_HOL_Obool)),X154))
=> ( ! [X269] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X269),X154))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X269)) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X154))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Union) ).
fof(fact_div__power,axiom,
! [X42,X93,X105,X94] :
( class_Divides_Osemiring__div(X94)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X105),X93))
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),X93),X105)),X42) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),X42)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X105),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__power) ).
fof(fact_int__div__less__self,axiom,
! [X103,X93] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X93))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X103))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X93),X103)),X93)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__div__less__self) ).
fof(fact_diff__less,axiom,
! [X97,X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X42))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X97))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42)),X97)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less) ).
fof(fact_div__less__dividend,axiom,
! [X97,X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X42))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X97))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X97),X42)),X97)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__less__dividend) ).
fof(fact_insert__inter__insert,axiom,
! [X160,X154,X39,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X39),X154)),hAPP(hAPP(c_Set_Oinsert(X10),X39),X160)) = hAPP(hAPP(c_Set_Oinsert(X10),X39),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__inter__insert) ).
fof(fact_div__nonpos__pos__le0,axiom,
! [X92,X84] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),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)),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),X92)),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,
! [X92,X84] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X92),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),X84),X92)),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,
! [X92,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),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),X92)),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,
! [X97,X44,X42,X45,X81] :
( c_Natural_Oevaln(X81,X45,X42,X44)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),X97))
=> c_Natural_Oevaln(X81,X45,X97,X44) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__nonstrict) ).
fof(fact_dvd__mod__imp__dvd,axiom,
! [X42,X97,X103,X94] :
( class_Divides_Osemiring__div(X94)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X103),c_Divides_Odiv__class_Omod(X94,X97,X42)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X103),X42))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X103),X97)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mod__imp__dvd) ).
fof(fact_dvd__mod__iff,axiom,
! [X102,X20,X101,X10] :
( class_Divides_Osemiring__div(X10)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X101),X20))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X101),c_Divides_Odiv__class_Omod(X10,X102,X20)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X101),X102)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mod__iff) ).
fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
! [X92,X84,X94] :
( class_Divides_Osemiring__div(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),c_Divides_Odiv__class_Omod(X94,X84,X92)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),X84),X92)),X92)) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__div__class_Omod__div__equality_H) ).
fof(fact_zero__le__divide__iff,axiom,
! [X38,X39,X10] :
( class_Fields_Olinordered__field__inverse__zero(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X39),X38)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X39))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X38)) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),c_Groups_Ozero__class_Ozero(X10)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X38),c_Groups_Ozero__class_Ozero(X10))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__divide__iff) ).
fof(fact_zero__le__mult__iff,axiom,
! [X38,X39,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X38)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X39))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X38)) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),c_Groups_Ozero__class_Ozero(X10)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X38),c_Groups_Ozero__class_Ozero(X10))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).
fof(fact_zero__less__divide__iff,axiom,
! [X38,X39,X10] :
( class_Fields_Olinordered__field__inverse__zero(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X39),X38)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X39))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X38)) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),c_Groups_Ozero__class_Ozero(X10)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X38),c_Groups_Ozero__class_Ozero(X10))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__divide__iff) ).
fof(fact_zadd__left__mono,axiom,
! [X103,X119,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X120),X119))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X103),X120)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X103),X119))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__mono) ).
fof(fact_diff__le__mono,axiom,
! [X121,X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),X42))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X121)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X42),X121))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono) ).
fof(fact_diff__le__mono2,axiom,
! [X121,X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),X42))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X121),X42)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X121),X97))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono2) ).
fof(fact_div__le__mono,axiom,
! [X103,X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),X42))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X97),X103)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X42),X103))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__le__mono) ).
fof(fact_mult__le__mono1,axiom,
! [X103,X119,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X120),X119))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X120),X103)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X119),X103))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono1) ).
fof(fact_mult__le__mono2,axiom,
! [X103,X119,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X120),X119))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X103),X120)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X103),X119))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono2) ).
fof(fact_add__le__mono1,axiom,
! [X103,X119,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X120),X119))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X120),X103)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X119),X103))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono1) ).
fof(fact_zadd__strict__right__mono,axiom,
! [X103,X119,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X120),X119))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X120),X103)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X119),X103))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).
fof(fact_add__less__mono1,axiom,
! [X103,X119,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),X119))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X120),X103)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X119),X103))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono1) ).
fof(fact_Min__fin__set__fold,axiom,
! [X290,X16,X10] :
( class_Orderings_Olinorder(X10)
=> c_Big__Operators_Olinorder__class_OMin(X10,hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290))) = hAPP(c_List_Ofoldl(X10,X10,c_Orderings_Oord__class_Omin(X10),X16),X290) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min__fin__set__fold) ).
fof(fact_Max__fin__set__fold,axiom,
! [X290,X16,X10] :
( class_Orderings_Olinorder(X10)
=> c_Big__Operators_Olinorder__class_OMax(X10,hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290))) = hAPP(c_List_Ofoldl(X10,X10,c_Orderings_Oord__class_Omax(X10),X16),X290) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max__fin__set__fold) ).
fof(fact_Inf__fin__set__fold,axiom,
! [X290,X16,X10] :
( class_Lattices_Olattice(X10)
=> c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290))) = hAPP(c_List_Ofoldl(X10,X10,c_Lattices_Osemilattice__inf__class_Oinf(X10),X16),X290) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin__set__fold) ).
fof(fact_Sup__fin__set__fold,axiom,
! [X290,X16,X10] :
( class_Lattices_Olattice(X10)
=> c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290))) = hAPP(c_List_Ofoldl(X10,X10,c_Lattices_Osemilattice__sup__class_Osup(X10),X16),X290) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin__set__fold) ).
fof(fact_diff__Suc__diff__eq2,axiom,
! [X97,X119,X103] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X103),X119))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X119),X103))),X97) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X119)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X103),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq2) ).
fof(fact_mod__div__equality2,axiom,
! [X84,X92,X94] :
( class_Divides_Osemiring__div(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),X84),X92))),c_Divides_Odiv__class_Omod(X94,X84,X92)) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__div__equality2) ).
fof(fact_list__update__code_I3_J,axiom,
! [X105,X120,X297,X93,X94] : hAPP(hAPP(c_List_Olist__update(X94,hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)),hAPP(c_Nat_OSuc,X120)),X105) = hAPP(hAPP(c_List_Olist_OCons(X94),X93),hAPP(hAPP(c_List_Olist__update(X94,X297),X120),X105)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__code_I3_J) ).
fof(fact_pair__box_Oinject,axiom,
! [X118,X96,X38,X39,X13,X10] :
( c_Nitpick_Opair__box_OPairBox(X10,X13,X39,X38) = c_Nitpick_Opair__box_OPairBox(X10,X13,X96,X118)
<=> ( X39 = X96
& X38 = X118 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__box_Oinject) ).
fof(fact_Sumr__inject,axiom,
! [X1,X2,X10,X125,X13] :
( c_Sum__Type_OSumr(X13,X125,X10,X2) = c_Sum__Type_OSumr(X13,X125,X10,X1)
=> X2 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sumr__inject) ).
fof(fact_Suml__inject,axiom,
! [X1,X2,X13,X125,X10] :
( c_Sum__Type_OSuml(X10,X125,X13,X2) = c_Sum__Type_OSuml(X10,X125,X13,X1)
=> X2 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suml__inject) ).
fof(fact_vimageI,axiom,
! [X13,X160,X10,X38,X39,X2] :
( hAPP(X2,X39) = X38
=> ( hBOOL(hAPP(hAPP(c_member(X10),X38),X160))
=> hBOOL(hAPP(hAPP(c_member(X13),X39),hAPP(c_Set_Ovimage(X13,X10,X2),X160))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimageI) ).
fof(fact_image__eqI,axiom,
! [X10,X154,X13,X16,X2,X38] :
( X38 = hAPP(X2,X16)
=> ( hBOOL(hAPP(hAPP(c_member(X13),X16),X154))
=> hBOOL(hAPP(hAPP(c_member(X10),X38),hAPP(c_Set_Oimage(X13,X10,X2),X154))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__eqI) ).
fof(fact_rev__image__eqI,axiom,
! [X13,X2,X38,X154,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( X38 = hAPP(X2,X16)
=> hBOOL(hAPP(hAPP(c_member(X13),X38),hAPP(c_Set_Oimage(X10,X13,X2),X154))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__image__eqI) ).
fof(fact_inj__on__iff,axiom,
! [X25,X16,X154,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,X154)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X25),X154))
=> ( hAPP(X2,X16) = hAPP(X2,X25)
<=> X16 = X25 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff) ).
fof(fact_inj__onD,axiom,
! [X25,X16,X154,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,X154)
=> ( hAPP(X2,X16) = hAPP(X2,X25)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X25),X154))
=> X16 = X25 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__onD) ).
fof(fact_inj__on__contraD,axiom,
! [X25,X16,X154,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,X154)
=> ( X16 != X25
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X25),X154))
=> hAPP(X2,X16) != hAPP(X2,X25) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__contraD) ).
fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
! [X38,X39] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X39))
=> ( 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),X39),X38)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X38),X39))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonneg1__imp__zdiv__pos__iff) ).
fof(fact_folding__one__idem_Osubset__idem,axiom,
! [X160,X154,X225,X2,X10] :
( c_Finite__Set_Ofolding__one__idem(X10,X2,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X160 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),X154))
=> hAPP(hAPP(X2,hAPP(X225,X160)),hAPP(X225,X154)) = hAPP(X225,X154) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Osubset__idem) ).
fof(fact_comp__equivI,axiom,
! [X154,X177,X10] :
( hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),hAPP(c_Relation_Oconverse(X10,X10),X177)),X177) = X177
=> ( hAPP(c_Relation_ODomain(X10,X10),X177) = X154
=> c_Equiv__Relations_Oequiv(X10,X154,X177) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__equivI) ).
fof(fact_com_Osize_I13_J,axiom,
! [X55,X56,X29] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(X29,X56,X55)) = 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),X56)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X55))),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,
! [X16,X1,X2,X10,X13] :
( class_Orderings_Oord(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X13)),X2),X1))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13),hAPP(X2,X16)),hAPP(X1,X16))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funD) ).
fof(fact_le__funE,axiom,
! [X16,X1,X2,X10,X13] :
( class_Orderings_Oord(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X13)),X2),X1))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13),hAPP(X2,X16)),hAPP(X1,X16))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funE) ).
fof(fact_map__injective,axiom,
! [X289,X290,X2,X10,X13] :
( hAPP(hAPP(c_List_Omap(X13,X10),X2),X290) = hAPP(hAPP(c_List_Omap(X13,X10),X2),X289)
=> ( c_Fun_Oinj__on(X13,X10,X2,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))
=> X290 = X289 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__injective) ).
fof(fact_inj__map__eq__map,axiom,
! [X289,X290,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> ( hAPP(hAPP(c_List_Omap(X10,X13),X2),X290) = hAPP(hAPP(c_List_Omap(X10,X13),X2),X289)
<=> X290 = X289 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__map__eq__map) ).
fof(fact_nth__list__update__eq,axiom,
! [X93,X297,X94,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)))
=> hAPP(hAPP(c_List_Onth(X94),hAPP(hAPP(c_List_Olist__update(X94,X297),X120),X93)),X120) = X93 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__list__update__eq) ).
fof(fact_setsum__atMost__Suc,axiom,
! [X20,X2,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X20))),hAPP(X2,hAPP(c_Nat_OSuc,X20))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__atMost__Suc) ).
fof(fact_ivl__disj__un_I17_J,axiom,
! [X165,X102,X162,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X162),X102))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X102),X165))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X162),X102)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X102),X165)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X162),X165) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I17_J) ).
fof(fact_butlast__conv__take,axiom,
! [X297,X94] : c_List_Obutlast(X94,X297) = hAPP(hAPP(c_List_Otake(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X297),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast__conv__take) ).
fof(fact_fold1__belowI,axiom,
! [X39,X154,X10] :
( class_Lattices_Osemilattice__inf(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Finite__Set_Ofold1(X10,c_Lattices_Osemilattice__inf__class_Oinf(X10)),X154)),X39)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__belowI) ).
fof(fact_min__max_Ofold1__belowI,axiom,
! [X39,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Finite__Set_Ofold1(X10,c_Orderings_Oord__class_Omin(X10)),X154)),X39)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ofold1__belowI) ).
fof(fact_sorted_Oequations_I2_J,axiom,
! [X51,X52,X10] :
( class_Orderings_Olinorder(X10)
=> ( c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Olist_OCons(X10),X52),X51))
<=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X51)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X52),X3)) )
& c_List_Olinorder__class_Osorted(X10,X51) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted_Oequations_I2_J) ).
fof(fact_sorted__Cons,axiom,
! [X290,X16,X10] :
( class_Orderings_Olinorder(X10)
=> ( c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290))
<=> ( c_List_Olinorder__class_Osorted(X10,X290)
& ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X290)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X3)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__Cons) ).
fof(fact_evalc_Oequations_I2_J,axiom,
! [X50,X52,X51] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(X51,X52)),X50),hAPP(hAPP(hAPP(c_Natural_Oupdate,X50),X51),hAPP(X52,X50)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I2_J) ).
fof(fact_evalc_OAssign,axiom,
! [X54,X39,X48] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(X48,X39)),X54),hAPP(hAPP(hAPP(c_Natural_Oupdate,X54),X48),hAPP(X39,X54)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OAssign) ).
fof(fact_int__power__div__base,axiom,
! [X103,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X97))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X103))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X103),X97)),X103) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X103),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),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,
! [X105,X93,X94] :
( class_Fields_Olinordered__field(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X93))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X105))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X93),X105))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__nonneg__pos) ).
fof(fact_split__mult__pos__le,axiom,
! [X92,X84,X94] :
( class_Rings_Oordered__ring(X94)
=> ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X92)) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),c_Groups_Ozero__class_Ozero(X94)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X92),c_Groups_Ozero__class_Ozero(X94))) ) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).
fof(fact_mult__nonneg__nonneg,axiom,
! [X92,X84,X94] :
( class_Rings_Oordered__cancel__semiring(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).
fof(fact_add__nonneg__nonneg,axiom,
! [X92,X84,X94] :
( class_Groups_Oordered__comm__monoid__add(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).
fof(fact_less__1__mult,axiom,
! [X42,X97,X94] :
( class_Rings_Olinordered__semidom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Oone__class_Oone(X94)),X97))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Oone__class_Oone(X94)),X42))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Oone__class_Oone(X94)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X97),X42))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__1__mult) ).
fof(fact_divide__pos__pos,axiom,
! [X105,X93,X94] :
( class_Fields_Olinordered__field(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X93))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X105))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X93),X105))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__pos__pos) ).
fof(fact_mult__pos__pos,axiom,
! [X92,X84,X94] :
( class_Rings_Olinordered__semiring__strict(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__pos) ).
fof(fact_add__pos__nonneg,axiom,
! [X92,X84,X94] :
( class_Groups_Oordered__comm__monoid__add(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).
fof(fact_add__nonneg__pos,axiom,
! [X92,X84,X94] :
( class_Groups_Oordered__comm__monoid__add(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).
fof(fact_add__pos__pos,axiom,
! [X92,X84,X94] :
( class_Groups_Oordered__comm__monoid__add(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__pos) ).
fof(fact_eq__card__imp__inj__on,axiom,
! [X2,X13,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hAPP(c_Finite__Set_Ocard(X13),hAPP(c_Set_Oimage(X10,X13,X2),X154)) = hAPP(c_Finite__Set_Ocard(X10),X154)
=> c_Fun_Oinj__on(X10,X13,X2,X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__card__imp__inj__on) ).
fof(fact_inj__on__iff__eq__card,axiom,
! [X2,X13,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( c_Fun_Oinj__on(X10,X13,X2,X154)
<=> hAPP(c_Finite__Set_Ocard(X13),hAPP(c_Set_Oimage(X10,X13,X2),X154)) = hAPP(c_Finite__Set_Ocard(X10),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__eq__card) ).
fof(fact_Compl__Diff__eq,axiom,
! [X160,X154,X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X154)),X160),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__Diff__eq) ).
fof(fact_power__eq__imp__eq__base,axiom,
! [X92,X42,X84,X94] :
( class_Rings_Olinordered__semidom(X94)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42) = hAPP(hAPP(c_Power_Opower__class_Opower(X94),X92),X42)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X42))
=> X84 = X92 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__imp__eq__base) ).
fof(fact_card__cartesian__product,axiom,
! [X160,X154,X13,X10] : hAPP(c_Finite__Set_Ocard(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X154),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),X160))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X154)),hAPP(c_Finite__Set_Ocard(X13),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__cartesian__product) ).
fof(fact_Int__insert__right__if1,axiom,
! [X160,X154,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),X160)) = hAPP(hAPP(c_Set_Oinsert(X10),X39),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__right__if1) ).
fof(fact_list__eq__iff__nth__eq,axiom,
! [X10,X289,X290] :
( X290 = X289
<=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X289)
& ! [X152] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X152),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290)))
=> hAPP(hAPP(c_List_Onth(X10),X290),X152) = hAPP(hAPP(c_List_Onth(X10),X289),X152) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__eq__iff__nth__eq) ).
fof(fact_folding_Oeq__fold,axiom,
! [X54,X154,X225,X2,X13,X10] :
( c_Finite__Set_Ofolding(X10,X13,X2,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(X225,X154),X54) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X13,X2),X54),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Oeq__fold) ).
fof(fact_weaken,axiom,
! [X211,X212,X210,X10] :
( c_Hoare__Mirabelle_Ohoare__derivs(X10,X210,X212)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X10),tc_HOL_Obool)),X211),X212))
=> c_Hoare__Mirabelle_Ohoare__derivs(X10,X210,X211) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_weaken) ).
fof(fact_le__SUPI,axiom,
! [X230,X154,X113,X10,X13] :
( class_Complete__Lattice_Ocomplete__lattice(X13)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X113),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13),hAPP(X230,X113)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,X13),X154),X230))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SUPI) ).
fof(fact_zmod__simps_I4_J,axiom,
! [X92,X81,X84,X94] :
( class_Divides_Osemiring__div(X94)
=> c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),c_Divides_Odiv__class_Omod(X94,X84,X81)),X92),X81) = c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92),X81) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__simps_I4_J) ).
fof(fact_zmod__simps_I1_J,axiom,
! [X92,X81,X84,X94] :
( class_Divides_Osemiring__div(X94)
=> c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),c_Divides_Odiv__class_Omod(X94,X84,X81)),X92),X81) = c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92),X81) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__simps_I1_J) ).
fof(fact_mod__diff__left__eq,axiom,
! [X81,X92,X84,X94] :
( class_Divides_Oring__div(X94)
=> c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X84),X92),X81) = c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),c_Divides_Odiv__class_Omod(X94,X84,X81)),X92),X81) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__diff__left__eq) ).
fof(fact_mod__mult__left__eq,axiom,
! [X81,X92,X84,X94] :
( class_Divides_Osemiring__div(X94)
=> c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92),X81) = c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),c_Divides_Odiv__class_Omod(X94,X84,X81)),X92),X81) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__left__eq) ).
fof(fact_mod__add__left__eq,axiom,
! [X81,X92,X84,X94] :
( class_Divides_Osemiring__div(X94)
=> c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92),X81) = c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),c_Divides_Odiv__class_Omod(X94,X84,X81)),X92),X81) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__left__eq) ).
fof(fact_subset__iff__psubset__eq,axiom,
! [X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X154),X160))
| X154 = X160 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__iff__psubset__eq) ).
fof(fact_psubset__eq,axiom,
! [X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X154),X160))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
& X154 != X160 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__eq) ).
fof(fact_finite__UnI,axiom,
! [X210,X225,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X225))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X210))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X225),X210))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UnI) ).
fof(fact_Pow__Int__eq,axiom,
! [X160,X154,X10] : hAPP(c_Set_OPow(X10),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X10),X154)),hAPP(c_Set_OPow(X10),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__Int__eq) ).
fof(fact_setsum_Oeq__fold,axiom,
! [X1,X154,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1),X154) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13,X10,c_Groups_Oplus__class_Oplus(X13)),X1),c_Groups_Ozero__class_Ozero(X13)),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oeq__fold) ).
fof(fact_setprod_Oeq__fold,axiom,
! [X1,X154,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),X154) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13,X10,c_Groups_Otimes__class_Otimes(X13)),X1),c_Groups_Oone__class_Oone(X13)),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Oeq__fold) ).
fof(fact_psubset__imp__subset,axiom,
! [X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__imp__subset) ).
fof(fact_mod__pos__neg,axiom,
! [X92,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),X92),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X92) = 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),X84),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X92)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__neg) ).
fof(fact_ex__nat__less,axiom,
! [X19,X20] :
( ? [X122] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X122),X20))
& hBOOL(hAPP(X19,X122)) )
<=> ? [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),X20)))
& hBOOL(hAPP(X19,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__nat__less) ).
fof(fact_restrict__map__empty,axiom,
! [X16,X197,X10,X13] : hAPP(c_Map_Orestrict__map(X13,X10,hAPP(c_COMBK(tc_Option_Ooption(X10),X13),c_Option_Ooption_ONone(X10)),X197),X16) = c_Option_Ooption_ONone(X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__map__empty) ).
fof(fact_drop__Cons__number__of,axiom,
! [X297,X93,X94,X144] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Odrop(X94),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)) = hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Odrop(X94),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)) = hAPP(hAPP(c_List_Odrop(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X297) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__Cons__number__of) ).
fof(fact_Abs__Integ__induct,axiom,
! [X16,X19] :
( ! [X90] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X90),c_Int_OInteg))
=> hBOOL(hAPP(X19,hAPP(c_Int_OAbs__Integ,X90))) )
=> hBOOL(hAPP(X19,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Abs__Integ__induct) ).
fof(fact_zdvd__mult__cancel1,axiom,
! [X20,X102] :
( X102 != 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),X102),X20)),X102))
<=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X20) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__mult__cancel1) ).
fof(fact_wf__Int1,axiom,
! [X224,X177,X10] :
( c_Wellfounded_Owf(X10,X177)
=> c_Wellfounded_Owf(X10,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X177),X224)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__Int1) ).
fof(fact_wf__Int2,axiom,
! [X224,X177,X10] :
( c_Wellfounded_Owf(X10,X177)
=> c_Wellfounded_Owf(X10,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X224),X177)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__Int2) ).
fof(fact_div__pos__neg,axiom,
! [X92,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),X92),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),X92) = 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),X84),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X92)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__pos__neg) ).
fof(fact_fold1__set,axiom,
! [X290,X10] :
( class_Lattices_Oab__semigroup__idem__mult(X10)
=> ( X290 != c_List_Olist_ONil(X10)
=> hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),hAPP(c_List_Oset(X10),X290)) = hAPP(c_List_Ofoldl(X10,X10,c_Groups_Otimes__class_Otimes(X10),hAPP(c_List_Ohd(X10),X290)),hAPP(c_List_Otl(X10),X290)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__set) ).
fof(fact_drop__zip,axiom,
! [X298,X297,X42,X10,X94] : hAPP(hAPP(c_List_Odrop(tc_prod(X94,X10)),X42),hAPP(hAPP(c_List_Ozip(X94,X10),X297),X298)) = hAPP(hAPP(c_List_Ozip(X94,X10),hAPP(hAPP(c_List_Odrop(X94),X42),X297)),hAPP(hAPP(c_List_Odrop(X10),X42),X298)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__zip) ).
fof(fact_take__zip,axiom,
! [X298,X297,X42,X10,X94] : hAPP(hAPP(c_List_Otake(tc_prod(X94,X10)),X42),hAPP(hAPP(c_List_Ozip(X94,X10),X297),X298)) = hAPP(hAPP(c_List_Ozip(X94,X10),hAPP(hAPP(c_List_Otake(X94),X42),X297)),hAPP(hAPP(c_List_Otake(X10),X42),X298)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__zip) ).
fof(fact_ivl__disj__un_I6_J,axiom,
! [X165,X162,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X162),X165))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X162),X165)),hAPP(hAPP(c_Set_Oinsert(X10),X165),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(X10,X162,X165) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I6_J) ).
fof(fact_mod__neg__neg,axiom,
! [X92,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),X92),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X92) = 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),X84),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X92)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__neg__neg) ).
fof(fact_single__valued__rel__comp,axiom,
! [X54,X125,X177,X13,X10] :
( c_Relation_Osingle__valued(X10,X13,X177)
=> ( c_Relation_Osingle__valued(X13,X125,X54)
=> c_Relation_Osingle__valued(X10,X125,hAPP(hAPP(c_Relation_Orel__comp(X10,X13,X125),X177),X54)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__rel__comp) ).
fof(fact_sorted__transpose,axiom,
! [X290,X10] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X10))),c_List_Otranspose(X10,X290)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__transpose) ).
fof(fact_Int__atLeastLessThan,axiom,
! [X141,X18,X38,X39,X10] :
( class_Orderings_Olinorder(X10)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X39),X38)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X18),X141)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X39),X18)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X38),X141)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__atLeastLessThan) ).
fof(fact_Int__atLeastAtMost,axiom,
! [X141,X18,X38,X39,X10] :
( class_Orderings_Olinorder(X10)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X39,X38)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X18,X141)) = c_SetInterval_Oord__class_OatLeastAtMost(X10,hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X39),X18),hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X38),X141)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__atLeastAtMost) ).
fof(fact_Int__greaterThanAtMost,axiom,
! [X141,X18,X38,X39,X10] :
( class_Orderings_Olinorder(X10)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X39,X38)),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X18,X141)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X10,hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X39),X18),hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X38),X141)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__greaterThanAtMost) ).
fof(fact_Int__greaterThanLessThan,axiom,
! [X141,X18,X38,X39,X10] :
( class_Orderings_Olinorder(X10)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X39,X38)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X18,X141)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X10,hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X39),X18),hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X38),X141)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__greaterThanLessThan) ).
fof(fact_set__rev__mp,axiom,
! [X160,X154,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> hBOOL(hAPP(hAPP(c_member(X10),X16),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rev__mp) ).
fof(fact_set__mp,axiom,
! [X16,X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hBOOL(hAPP(hAPP(c_member(X10),X16),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__mp) ).
fof(fact_in__mono,axiom,
! [X16,X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hBOOL(hAPP(hAPP(c_member(X10),X16),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mono) ).
fof(fact_subsetD,axiom,
! [X18,X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X18),X154))
=> hBOOL(hAPP(hAPP(c_member(X10),X18),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subsetD) ).
fof(fact_psubsetD,axiom,
! [X18,X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X18),X154))
=> hBOOL(hAPP(hAPP(c_member(X10),X18),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubsetD) ).
fof(fact_nth__append__length,axiom,
! [X298,X93,X297,X94] : hAPP(hAPP(c_List_Onth(X94),hAPP(hAPP(c_List_Oappend(X94),X297),hAPP(hAPP(c_List_Olist_OCons(X94),X93),X298))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)) = X93,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__append__length) ).
fof(fact_div__neg__neg,axiom,
! [X92,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),X92),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),X92) = 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),X84),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X92)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__neg__neg) ).
fof(fact_inj__on__add__nat,axiom,
! [X226,X101] : 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)),X101),X226),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__add__nat) ).
fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
! [X39,X38] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X38))
=> ( 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),X39),X38)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X39)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__imp__zdiv__nonneg__iff) ).
fof(fact_times__divide__times__eq,axiom,
! [X133,X104,X105,X93,X94] :
( class_Fields_Ofield__inverse__zero(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X93),X105)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X104),X133)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X93),X104)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X105),X133)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__divide__times__eq) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
! [X137,X138,X140,X139,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X139),X140)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X138),X137)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X139),X138)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X140),X137)) ),
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,
! [X112,X81,X92,X84,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X81),X112)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X81)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X92),X112)) ),
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,
! [X137,X138,X140,X139,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X139),X140)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X138),X137)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X139),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X140),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X138),X137))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
fof(fact_sorted__map__remove1,axiom,
! [X16,X290,X2,X13,X10] :
( class_Orderings_Olinorder(X10)
=> ( c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Omap(X13,X10),X2),X290))
=> c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Omap(X13,X10),X2),c_List_Oremove1(X13,X16,X290))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__map__remove1) ).
fof(fact_Domain__Union,axiom,
! [X216,X13,X10] : hAPP(c_Relation_ODomain(X10,X13),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),X216)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X10,X13),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X216),c_Relation_ODomain(X10,X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Union) ).
fof(fact_Range__Union,axiom,
! [X216,X10,X13] : hAPP(c_Relation_ORange(X13,X10),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X13,X10),tc_HOL_Obool),X216)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X13,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X216),c_Relation_ORange(X13,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Union) ).
fof(fact_all__nat__less,axiom,
! [X19,X20] :
( ! [X122] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X122),X20))
=> hBOOL(hAPP(X19,X122)) )
<=> ! [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),X20)))
=> hBOOL(hAPP(X19,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__nat__less) ).
fof(fact_Ints__power,axiom,
! [X20,X39,X10] :
( class_Rings_Oring__1(X10)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),c_Int_Oring__1__class_OInts(X10)))
=> hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X39),X20)),c_Int_Oring__1__class_OInts(X10))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__power) ).
fof(fact_Collect__mem__eq,axiom,
! [X154,X10] : hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X154)) = X154,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__mem__eq) ).
fof(fact_nat__one__le__power,axiom,
! [X42,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X120))
=> 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),X120),X42))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__one__le__power) ).
fof(fact_zdvd__zmod__imp__zdvd,axiom,
! [X42,X97,X103] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X103),c_Divides_Odiv__class_Omod(tc_Int_Oint,X97,X42)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X103),X42))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X103),X97)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__zmod__imp__zdvd) ).
fof(fact_one__less__power,axiom,
! [X42,X84,X94] :
( class_Rings_Olinordered__semidom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Oone__class_Oone(X94)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X42))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Oone__class_Oone(X94)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__power) ).
fof(fact_divide__nonpos__neg,axiom,
! [X105,X93,X94] :
( class_Fields_Olinordered__field(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),c_Groups_Ozero__class_Ozero(X94)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X105),c_Groups_Ozero__class_Ozero(X94)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X93),X105))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__nonpos__neg) ).
fof(fact_mult__nonpos__nonpos,axiom,
! [X92,X84,X94] :
( class_Rings_Oordered__ring(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),c_Groups_Ozero__class_Ozero(X94)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X92),c_Groups_Ozero__class_Ozero(X94)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).
fof(fact_divide__neg__neg,axiom,
! [X105,X93,X94] :
( class_Fields_Olinordered__field(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),c_Groups_Ozero__class_Ozero(X94)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X105),c_Groups_Ozero__class_Ozero(X94)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X93),X105))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__neg__neg) ).
fof(fact_mult__neg__neg,axiom,
! [X92,X84,X94] :
( class_Rings_Olinordered__ring__strict(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),c_Groups_Ozero__class_Ozero(X94)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X92),c_Groups_Ozero__class_Ozero(X94)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__neg__neg) ).
fof(fact_setsum__lessThan__Suc,axiom,
! [X20,X2,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X20))),hAPP(X2,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__lessThan__Suc) ).
fof(fact_dom__map__of__zip,axiom,
! [X289,X13,X290,X10] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13)),X289)
=> ( hBOOL(hAPP(c_List_Odistinct(X10),X290))
=> c_Map_Odom(X10,X13,c_Map_Omap__of(X10,X13,hAPP(hAPP(c_List_Ozip(X10,X13),X290),X289))) = hAPP(c_List_Oset(X10),X290) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__map__of__zip) ).
fof(fact_posDivAlg__div__mod,axiom,
! [X121,X103] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X103))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X121))
=> c_Divides_OposDivAlg(X103,X121) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X103),X121)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X103,X121)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg__div__mod) ).
fof(fact_pos__imp__zdiv__pos__iff,axiom,
! [X113,X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X101))
=> ( 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),X113),X101)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X101),X113)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__imp__zdiv__pos__iff) ).
fof(fact_lex__def,axiom,
! [X177,X10] : c_List_Olex(X10,X177) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(X10,X177)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lex__def) ).
fof(fact_le__max__iff__disj,axiom,
! [X25,X16,X73,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X73),hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X16),X25)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X73),X16))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X73),X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__max__iff__disj) ).
fof(fact_less__max__iff__disj,axiom,
! [X25,X16,X73,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X73),hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X16),X25)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X73),X16))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X73),X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__max__iff__disj) ).
fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
! [X39,X38] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X38),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),X39),X38)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X39),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,
! [X10,X290] :
( X290 != c_List_Olist_ONil(X10)
=> c_Random_Oselect__weight(X10,hAPP(hAPP(c_List_Omap(X10,tc_prod(tc_Code__Numeral_Ocode__numeral,X10)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X10),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X290)) = c_Random_Oselect(X10,X290) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_select__weigth__select) ).
fof(fact_finite__Inter,axiom,
! [X230,X10] :
( ? [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X3),X230))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X3)) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X230))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Inter) ).
fof(fact_abs__eq__mult,axiom,
! [X92,X84,X94] :
( class_Rings_Oordered__ring__abs(X94)
=> ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),c_Groups_Ozero__class_Ozero(X94))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X92))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X92),c_Groups_Ozero__class_Ozero(X94))) ) )
=> hAPP(c_Groups_Oabs__class_Oabs(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),X84)),hAPP(c_Groups_Oabs__class_Oabs(X94),X92)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__eq__mult) ).
fof(fact_butlast__take,axiom,
! [X297,X94,X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)))
=> c_List_Obutlast(X94,hAPP(hAPP(c_List_Otake(X94),X42),X297)) = hAPP(hAPP(c_List_Otake(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X42),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X297) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast__take) ).
fof(fact_single__Diff__lessThan,axiom,
! [X101,X10] :
( class_Orderings_Oorder(X10)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X101),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(X10),X101)) = hAPP(hAPP(c_Set_Oinsert(X10),X101),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__Diff__lessThan) ).
fof(fact_disjoint__iff__not__equal,axiom,
! [X160,X154,X10] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> ! [X227] :
( hBOOL(hAPP(hAPP(c_member(X10),X227),X160))
=> X3 != X227 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_disjoint__iff__not__equal) ).
fof(fact_insort__remove1,axiom,
! [X290,X39,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),hAPP(c_List_Oset(X10),X290)))
=> ( c_List_Olinorder__class_Osorted(X10,X290)
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X10,c_COMBI(X10)),X39),c_List_Oremove1(X10,X39,X290)) = X290 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__remove1) ).
fof(fact_negDivAlg__div__mod,axiom,
! [X121,X103] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X103),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)),X121))
=> c_Divides_OnegDivAlg(X103,X121) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X103),X121)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X103,X121)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg__div__mod) ).
fof(fact_Inf__fin_Osubset__idem,axiom,
! [X160,X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X160 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),X154))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),c_Big__Operators_Olattice__class_OInf__fin(X10,X160)),c_Big__Operators_Olattice__class_OInf__fin(X10,X154)) = c_Big__Operators_Olattice__class_OInf__fin(X10,X154) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Osubset__idem) ).
fof(fact_Sup__fin_Osubset__idem,axiom,
! [X160,X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X160 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),X154))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),c_Big__Operators_Olattice__class_OSup__fin(X10,X160)),c_Big__Operators_Olattice__class_OSup__fin(X10,X154)) = c_Big__Operators_Olattice__class_OSup__fin(X10,X154) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Osubset__idem) ).
fof(fact_Max_Osubset__idem,axiom,
! [X160,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X160 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),X154))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),c_Big__Operators_Olinorder__class_OMax(X10,X160)),c_Big__Operators_Olinorder__class_OMax(X10,X154)) = c_Big__Operators_Olinorder__class_OMax(X10,X154) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Osubset__idem) ).
fof(fact_Min_Osubset__idem,axiom,
! [X160,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X160 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),X154))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),c_Big__Operators_Olinorder__class_OMin(X10,X160)),c_Big__Operators_Olinorder__class_OMin(X10,X154)) = c_Big__Operators_Olinorder__class_OMin(X10,X154) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Osubset__idem) ).
fof(fact_zpower__zmod,axiom,
! [X105,X97,X93] : 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,X93,X97)),X105),X97) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X93),X105),X97),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__zmod) ).
fof(fact_zdiff__zmod__left,axiom,
! [X105,X97,X93] : 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,X93,X97)),X105),X97) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X93),X105),X97),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmod__left) ).
fof(fact_le__Inf__iff,axiom,
! [X154,X38,X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X38),c_Complete__Lattice_OInf__class_OInf(X10,X154)))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X38),X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Inf__iff) ).
fof(fact_take__Cons_H,axiom,
! [X297,X93,X94,X42] :
( ( X42 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Otake(X94),X42),hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)) = c_List_Olist_ONil(X94) )
& ( X42 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Otake(X94),X42),hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)) = hAPP(hAPP(c_List_Olist_OCons(X94),X93),hAPP(hAPP(c_List_Otake(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X42),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X297)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Cons_H) ).
fof(fact_inf1I,axiom,
! [X10,X160,X16,X154] :
( hBOOL(hAPP(X154,X16))
=> ( hBOOL(hAPP(X160,X16))
=> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160),X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1I) ).
fof(fact_Rep__Integ,axiom,
! [X16] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X16)),c_Int_OInteg)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ) ).
fof(fact_folding__one__idem_Ounion__idem,axiom,
! [X160,X154,X225,X2,X10] :
( c_Finite__Set_Ofolding__one__idem(X10,X2,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( X160 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(X225,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(X2,hAPP(X225,X154)),hAPP(X225,X160)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Ounion__idem) ).
fof(fact_add__increasing,axiom,
! [X81,X92,X84,X94] :
( class_Groups_Oordered__comm__monoid__add(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X92),X81))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X92),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X81))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing) ).
fof(fact_add__increasing2,axiom,
! [X84,X92,X81,X94] :
( class_Groups_Oordered__comm__monoid__add(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X81))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X92),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X92),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X81))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing2) ).
fof(fact_pos__add__strict,axiom,
! [X81,X92,X84,X94] :
( class_Rings_Olinordered__semidom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X92),X81))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X92),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X81))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__add__strict) ).
fof(fact_add__strict__increasing,axiom,
! [X81,X92,X84,X94] :
( class_Groups_Oordered__comm__monoid__add(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X92),X81))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X92),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X81))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
fof(fact_add__strict__increasing2,axiom,
! [X81,X92,X84,X94] :
( class_Groups_Oordered__comm__monoid__add(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X92),X81))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X92),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X81))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
fof(fact_zmod__zdiv__equality,axiom,
! [X92,X84] : X84 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X92),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),X92))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X92)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zdiv__equality) ).
fof(fact_le__infI1,axiom,
! [X92,X93,X84,X94] :
( class_Lattices_Osemilattice__inf(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X93))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X84),X92)),X93)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infI1) ).
fof(fact_le__infI2,axiom,
! [X84,X93,X92,X94] :
( class_Lattices_Osemilattice__inf(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X92),X93))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X84),X92)),X93)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infI2) ).
fof(fact_min__max_Ole__infI1,axiom,
! [X92,X93,X84,X94] :
( class_Orderings_Olinorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X93))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X84),X92)),X93)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__infI1) ).
fof(fact_min__max_Ole__infI2,axiom,
! [X84,X93,X92,X94] :
( class_Orderings_Olinorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X92),X93))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X84),X92)),X93)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__infI2) ).
fof(fact_less__infI1,axiom,
! [X92,X93,X84,X94] :
( class_Lattices_Osemilattice__inf(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),X93))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X84),X92)),X93)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__infI1) ).
fof(fact_less__infI2,axiom,
! [X84,X93,X92,X94] :
( class_Lattices_Osemilattice__inf(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X92),X93))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X84),X92)),X93)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__infI2) ).
fof(fact_min__max_Oless__infI1,axiom,
! [X92,X93,X84,X94] :
( class_Orderings_Olinorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),X93))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X84),X92)),X93)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oless__infI1) ).
fof(fact_min__max_Oless__infI2,axiom,
! [X84,X93,X92,X94] :
( class_Orderings_Olinorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X92),X93))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X84),X92)),X93)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oless__infI2) ).
fof(fact_listrel__Nil,axiom,
! [X177,X10] : hAPP(c_Relation_OImage(tc_List_Olist(X10),tc_List_Olist(X10),c_List_Olistrel(X10,X177)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X10)),c_List_Olist_ONil(X10)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X10),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X10)),c_List_Olist_ONil(X10)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X10),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__Nil) ).
fof(fact_setsum__eq__0__iff,axiom,
! [X2,X225,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X225))
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),X225) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X225))
=> 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_setprod__eq__1__iff,axiom,
! [X2,X225,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X225))
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,tc_Nat_Onat),X2),X225) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X225))
=> 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_restrict__in,axiom,
! [X102,X13,X154,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Map_Orestrict__map(X10,X13,X102,X154),X16) = hAPP(X102,X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__in) ).
fof(fact_nat__diff__split,axiom,
! [X38,X39,X19] :
( hBOOL(hAPP(X19,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X39),X38)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X39),X38))
=> hBOOL(hAPP(X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ! [X164] :
( X39 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X38),X164)
=> hBOOL(hAPP(X19,X164)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split) ).
fof(fact_dvd__div__mult,axiom,
! [X81,X92,X84,X94] :
( class_Divides_Osemiring__div(X94)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X84),X92))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),X92),X84)),X81) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X81)),X84) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__div__mult) ).
fof(fact_finite__compl,axiom,
! [X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X154)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__compl) ).
fof(fact_less__nat__number__of,axiom,
! [X174,X168] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X174)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X168),X174))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X174)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X168),X174)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__nat__number__of) ).
fof(fact_Un__insert__left,axiom,
! [X198,X160,X39,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X39),X160)),X198) = hAPP(hAPP(c_Set_Oinsert(X10),X39),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X160),X198)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__insert__left) ).
fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
! [X16,X2,X13,X10] :
( c_Finite__Set_Ofun__left__comm__idem(X10,X13,X2)
=> hAPP(c_Fun_Ocomp(X13,X13,X13,hAPP(X2,X16)),hAPP(X2,X16)) = hAPP(X2,X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofun__comp__idem) ).
fof(fact_finite__dom__map__of,axiom,
! [X162,X13,X10] : hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Map_Odom(X10,X13,c_Map_Omap__of(X10,X13,X162)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__dom__map__of) ).
fof(fact_com_Osize_I12_J,axiom,
! [X68,X69] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(X69,X68)) = 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),X69)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X68))),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,
! [X143,X149,X92,X84] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X84,X92),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X149),X143)))
=> ( X92 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X92) = X143 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__mod) ).
fof(fact_snd__def,axiom,
! [X166,X10,X13] : hAPP(c_Product__Type_Osnd(X13,X10),X166) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X13,X10,X10),hAPP(c_COMBK(tc_fun(X10,X10),X13),c_COMBI(X10))),X166),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__def) ).
fof(fact_Ints__odd__nonzero,axiom,
! [X39,X10] :
( class_Int_Oring__char__0(X10)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),c_Int_Oring__1__class_OInts(X10)))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),c_Groups_Oone__class_Oone(X10)),X39)),X39) != c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__odd__nonzero) ).
fof(fact_finite__Int,axiom,
! [X210,X225,X10] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X225))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X210)) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X225),X210))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Int) ).
fof(fact_finite__Diff,axiom,
! [X160,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Diff) ).
fof(fact_sorted__many__eq,axiom,
! [X299,X25,X16,X10] :
( class_Orderings_Olinorder(X10)
=> ( c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Olist_OCons(X10),X16),hAPP(hAPP(c_List_Olist_OCons(X10),X25),X299)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X25))
& c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Olist_OCons(X10),X25),X299)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__many__eq) ).
fof(fact_sorted__many,axiom,
! [X296,X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X105))
=> ( c_List_Olinorder__class_Osorted(X94,hAPP(hAPP(c_List_Olist_OCons(X94),X105),X296))
=> c_List_Olinorder__class_Osorted(X94,hAPP(hAPP(c_List_Olist_OCons(X94),X93),hAPP(hAPP(c_List_Olist_OCons(X94),X105),X296))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__many) ).
fof(fact_mod__eq,axiom,
! [X143,X149,X42,X97] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X97,X42),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X149),X143)))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X97,X42) = X143 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__eq) ).
fof(fact_zmod__le__nonneg__dividend,axiom,
! [X103,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_Divides_Odiv__class_Omod(tc_Int_Oint,X97,X103)),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__le__nonneg__dividend) ).
fof(fact_mod__le__divisor,axiom,
! [X97,X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X42))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X97,X42)),X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__le__divisor) ).
fof(fact_pos__mod__conj,axiom,
! [X84,X92] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X92))
=> ( 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,X84,X92)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X92)),X92)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__mod__conj) ).
fof(fact_pos__mod__bound,axiom,
! [X84,X92] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X92)),X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__mod__bound) ).
fof(fact_mod__less__divisor,axiom,
! [X97,X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X42))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X97,X42)),X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__less__divisor) ).
fof(fact_card__length,axiom,
! [X290,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),hAPP(c_List_Oset(X10),X290))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__length) ).
fof(fact_dvd__eq__mod__eq__0__number__of,axiom,
! [X25,X16,X10] :
( ( class_Divides_Osemiring__div(X10)
& class_Int_Onumber(X10) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X16)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X25)))
<=> c_Divides_Odiv__class_Omod(X10,hAPP(c_Int_Onumber__class_Onumber__of(X10),X25),hAPP(c_Int_Onumber__class_Onumber__of(X10),X16)) = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__eq__mod__eq__0__number__of) ).
fof(fact_image__Pow__surj,axiom,
! [X160,X154,X2,X10,X13] :
( hAPP(c_Set_Oimage(X13,X10,X2),X154) = X160
=> hAPP(c_Set_Oimage(tc_fun(X13,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),c_Set_Oimage(X13,X10,X2)),hAPP(c_Set_OPow(X13),X154)) = hAPP(c_Set_OPow(X10),X160) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Pow__surj) ).
fof(fact_surj__image__vimage__eq,axiom,
! [X154,X2,X10,X13] :
( hAPP(c_Set_Oimage(X13,X10,X2),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(X13,X10,X2),hAPP(c_Set_Ovimage(X13,X10,X2),X154)) = X154 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__image__vimage__eq) ).
fof(fact_zdvd__zdiffD,axiom,
! [X42,X97,X103] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X103),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X97),X42)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X103),X42))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X103),X97)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__zdiffD) ).
fof(fact_divmod__int__rel__div,axiom,
! [X143,X149,X92,X84] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X84,X92),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X149),X143)))
=> ( X92 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),X92) = X149 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__div) ).
fof(fact_abs__le__D2,axiom,
! [X92,X84,X94] :
( class_Groups_Oordered__ab__group__add__abs(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),X84)),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X84)),X92)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__le__D2) ).
fof(fact_minus__le__iff,axiom,
! [X38,X39,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X39)),X38))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X38)),X39)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__le__iff) ).
fof(fact_minus__less__iff,axiom,
! [X38,X39,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X39)),X38))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X38)),X39)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__less__iff) ).
fof(fact_neg__mod__conj,axiom,
! [X84,X92] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X92),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,X84,X92)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X92),c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X92))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__mod__conj) ).
fof(fact_neg__mod__sign,axiom,
! [X84,X92] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X92),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,X84,X92)),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,
! [X19,X2,X13,X10] : hAPP(c_Set_Ovimage(X10,X13,X2),hAPP(c_Set_OCollect(X13),X19)) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(X13,tc_HOL_Obool,X10),X19),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Collect__eq) ).
fof(fact_div__eq,axiom,
! [X143,X149,X42,X97] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X97,X42),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X149),X143)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X97),X42) = X149 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__eq) ).
fof(fact_card__image,axiom,
! [X154,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,X154)
=> hAPP(c_Finite__Set_Ocard(X13),hAPP(c_Set_Oimage(X10,X13,X2),X154)) = hAPP(c_Finite__Set_Ocard(X10),X154) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__image) ).
fof(fact_take__drop,axiom,
! [X297,X97,X42,X94] : hAPP(hAPP(c_List_Otake(X94),X42),hAPP(hAPP(c_List_Odrop(X94),X97),X297)) = hAPP(hAPP(c_List_Odrop(X94),X97),hAPP(hAPP(c_List_Otake(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),X97)),X297)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__drop) ).
fof(fact_sorted__filter,axiom,
! [X19,X290,X2,X13,X10] :
( class_Orderings_Olinorder(X10)
=> ( c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Omap(X13,X10),X2),X290))
=> c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Omap(X13,X10),X2),hAPP(c_List_Ofilter(X13,X19),X290))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__filter) ).
fof(fact_nat__mod__eq__lemma,axiom,
! [X105,X42,X93] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X93,X42) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X105,X42)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X105),X93))
=> ? [X153] : X93 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X105),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),X153)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mod__eq__lemma) ).
fof(fact_takeWhile__eq__all__conv,axiom,
! [X290,X19,X10] :
( c_List_OtakeWhile(X10,X19,X290) = X290
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X290)))
=> hBOOL(hAPP(X19,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__eq__all__conv) ).
fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
! [X39,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X39),X39)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X39)) ) ),
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,
! [X39,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X39),X39)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X39)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
fof(fact_add__gr__0,axiom,
! [X20,X102] :
( 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),X102),X20)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X102))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__gr__0) ).
fof(fact_asm,axiom,
! [X210,X211,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X10),tc_HOL_Obool)),X211),X210))
=> c_Hoare__Mirabelle_Ohoare__derivs(X10,X210,X211) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_asm) ).
fof(fact_mod__diff__cong,axiom,
! [X130,X92,X95,X81,X84,X94] :
( class_Divides_Oring__div(X94)
=> ( c_Divides_Odiv__class_Omod(X94,X84,X81) = c_Divides_Odiv__class_Omod(X94,X95,X81)
=> ( c_Divides_Odiv__class_Omod(X94,X92,X81) = c_Divides_Odiv__class_Omod(X94,X130,X81)
=> c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X84),X92),X81) = c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X95),X130),X81) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__diff__cong) ).
fof(fact_mod__mult__cong,axiom,
! [X130,X92,X95,X81,X84,X94] :
( class_Divides_Osemiring__div(X94)
=> ( c_Divides_Odiv__class_Omod(X94,X84,X81) = c_Divides_Odiv__class_Omod(X94,X95,X81)
=> ( c_Divides_Odiv__class_Omod(X94,X92,X81) = c_Divides_Odiv__class_Omod(X94,X130,X81)
=> c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92),X81) = c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X95),X130),X81) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__cong) ).
fof(fact_mod__add__cong,axiom,
! [X130,X92,X95,X81,X84,X94] :
( class_Divides_Osemiring__div(X94)
=> ( c_Divides_Odiv__class_Omod(X94,X84,X81) = c_Divides_Odiv__class_Omod(X94,X95,X81)
=> ( c_Divides_Odiv__class_Omod(X94,X92,X81) = c_Divides_Odiv__class_Omod(X94,X130,X81)
=> c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92),X81) = c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X95),X130),X81) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__cong) ).
fof(fact_dvd__mod,axiom,
! [X42,X97,X103,X94] :
( class_Divides_Osemiring__div(X94)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X103),X97))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X103),X42))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X103),c_Divides_Odiv__class_Omod(X94,X97,X42))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mod) ).
fof(fact_power__diff,axiom,
! [X97,X42,X84,X94] :
( class_Fields_Ofield(X94)
=> ( X84 != c_Groups_Ozero__class_Ozero(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),X97))
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X97)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__diff) ).
fof(fact_divmod__int__rel__neg,axiom,
! [X185,X92,X84] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X84),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X92)),X185))
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(X84,X92),hAPP(c_Divides_OnegateSnd,X185))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__neg) ).
fof(fact_evaln__Suc,axiom,
! [X91,X42,X45,X81] :
( c_Natural_Oevaln(X81,X45,X42,X91)
=> c_Natural_Oevaln(X81,X45,hAPP(c_Nat_OSuc,X42),X91) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__Suc) ).
fof(fact_insert__Diff1,axiom,
! [X154,X160,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X16),X160))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)),X160) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Diff1) ).
fof(fact_dom__const,axiom,
! [X2,X13,X10] : c_Map_Odom(X10,X13,hAPP(hAPP(c_COMBB(X13,tc_Option_Ooption(X13),X10),c_Option_Ooption_OSome(X13)),X2)) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__const) ).
fof(fact_Nat_Odiff__diff__eq,axiom,
! [X42,X97,X103] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X103),X97))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X103),X42))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X103)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X42),X103)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Odiff__diff__eq) ).
fof(fact_takeWhile__eq__take,axiom,
! [X290,X19,X10] : c_List_OtakeWhile(X10,X19,X290) = hAPP(hAPP(c_List_Otake(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_List_OtakeWhile(X10,X19,X290))),X290),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__eq__take) ).
fof(fact_ex__nat__less__eq,axiom,
! [X19,X20] :
( ? [X122] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X122),X20))
& hBOOL(hAPP(X19,X122)) )
<=> ? [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)),X20)))
& hBOOL(hAPP(X19,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__nat__less__eq) ).
fof(fact_Suc__diff__diff,axiom,
! [X103,X42,X97] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X97)),X42)),hAPP(c_Nat_OSuc,X103)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42)),X103),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__diff) ).
fof(fact_power__inject__base,axiom,
! [X92,X42,X84,X94] :
( class_Rings_Olinordered__semidom(X94)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),hAPP(c_Nat_OSuc,X42)) = hAPP(hAPP(c_Power_Opower__class_Opower(X94),X92),hAPP(c_Nat_OSuc,X42))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X92))
=> X84 = X92 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__inject__base) ).
fof(fact_int__zle__neg,axiom,
! [X102,X20] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X102))))
<=> ( X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X102 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__zle__neg) ).
fof(fact_wf,axiom,
! [X10] :
( class_Orderings_Owellorder(X10)
=> c_Wellfounded_Owf(X10,hAPP(c_Set_OCollect(tc_prod(X10,X10)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X10,tc_HOL_Obool),c_Orderings_Oord__class_Oless(X10)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf) ).
fof(fact_dvd__diff,axiom,
! [X104,X105,X93,X94] :
( class_Rings_Ocomm__ring__1(X94)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X93),X105))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X93),X104))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X93),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X105),X104))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__diff) ).
fof(fact_dvd__add,axiom,
! [X81,X92,X84,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X84),X92))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X84),X81))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X84),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X92),X81))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__add) ).
fof(fact_inf__greatest,axiom,
! [X104,X105,X93,X94] :
( class_Lattices_Osemilattice__inf(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X105))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X104))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X105),X104))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__greatest) ).
fof(fact_le__infI,axiom,
! [X92,X84,X93,X94] :
( class_Lattices_Osemilattice__inf(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X84),X92))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infI) ).
fof(fact_le__inf__iff,axiom,
! [X73,X25,X16,X10] :
( class_Lattices_Osemilattice__inf(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X25),X73)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X25))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X73)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__inf__iff) ).
fof(fact_min__max_Oinf__greatest,axiom,
! [X104,X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X105))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X104))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X105),X104))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__greatest) ).
fof(fact_min__max_Ole__infI,axiom,
! [X92,X84,X93,X94] :
( class_Orderings_Olinorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X84),X92))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__infI) ).
fof(fact_min__max_Ole__inf__iff,axiom,
! [X73,X25,X16,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X25),X73)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X25))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X73)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__inf__iff) ).
fof(fact_min__less__iff__conj,axiom,
! [X25,X16,X73,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X73),hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X16),X25)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X73),X16))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X73),X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__less__iff__conj) ).
fof(fact_self__quotient__aux2,axiom,
! [X149,X143,X84] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> ( X84 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X143),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),X149))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X143))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X149),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,
! [X290,X19,X10] :
( hAPP(c_List_Ofilter(X10,X19),X290) = X290
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X290)))
=> hBOOL(hAPP(X19,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__id__conv) ).
fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
! [X105,X93] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X93))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X105))
=> 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,X93,X105))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I2_J) ).
fof(fact_evalc_OSemi,axiom,
! [X57,X58,X59,X60,X61] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X61),X60),X59))
=> ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X58),X59),X57))
=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X61,X58)),X60),X57)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OSemi) ).
fof(fact_nth__append__length__plus,axiom,
! [X42,X298,X297,X94] : hAPP(hAPP(c_List_Onth(X94),hAPP(hAPP(c_List_Oappend(X94),X297),X298)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)),X42)) = hAPP(hAPP(c_List_Onth(X94),X298),X42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__append__length__plus) ).
fof(fact_list_Osimps_I5_J,axiom,
! [X291,X39,X37,X12,X13,X10] : hAPP(c_List_Olist_Olist__case(X10,X13,X12,X37),hAPP(hAPP(c_List_Olist_OCons(X13),X39),X291)) = hAPP(hAPP(X37,X39),X291),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I5_J) ).
fof(fact_sup1I1,axiom,
! [X160,X10,X16,X154] :
( hBOOL(hAPP(X154,X16))
=> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1I1) ).
fof(fact_sup1I2,axiom,
! [X154,X10,X16,X160] :
( hBOOL(hAPP(X160,X16))
=> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1I2) ).
fof(fact_zero__le__power__abs,axiom,
! [X42,X84,X94] :
( class_Rings_Olinordered__idom(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),X84)),X42))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__power__abs) ).
fof(fact_diff__Suc__diff__eq1,axiom,
! [X97,X119,X103] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X103),X119))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X119),X103))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X103)),hAPP(c_Nat_OSuc,X119)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq1) ).
fof(fact_subset__empty,axiom,
! [X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))
<=> X154 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__empty) ).
fof(fact_wfP__acyclicP,axiom,
! [X177,X10] :
( c_Wellfounded_OwfP(X10,X177)
=> c_Wellfounded_Oacyclic(X10,hAPP(c_Set_OCollect(tc_prod(X10,X10)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X10,tc_HOL_Obool),X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__acyclicP) ).
fof(fact_int__dvd__iff,axiom,
! [X73,X102] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X102)),X73))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X102),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X73)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__dvd__iff) ).
fof(fact_rel__comp__empty1,axiom,
! [X196,X13,X125,X10] : hAPP(hAPP(c_Relation_Orel__comp(X10,X125,X13),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X125),tc_HOL_Obool))),X196) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__empty1) ).
fof(fact_zdiv__zminus1__eq__if,axiom,
! [X84,X92] :
( X92 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X92) = 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),X84)),X92) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),X92)) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X92) != 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),X84)),X92) = 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),X84),X92))),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,
! [X25,X16,X10] :
( class_Lattices_Oboolean__algebra(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X16)),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X25)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X25),X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__le__compl__iff) ).
fof(fact_neg__le__iff__le,axiom,
! [X39,X38,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X38)),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X39)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),X38)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__le__iff__le) ).
fof(fact_neg__less__iff__less,axiom,
! [X39,X38,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X38)),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X39)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),X38)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__iff__less) ).
fof(fact_all__nat__less__eq,axiom,
! [X19,X20] :
( ! [X122] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X122),X20))
=> hBOOL(hAPP(X19,X122)) )
<=> ! [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)),X20)))
=> hBOOL(hAPP(X19,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__nat__less__eq) ).
fof(fact_power__gt1,axiom,
! [X42,X84,X94] :
( class_Rings_Olinordered__semidom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Oone__class_Oone(X94)),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Oone__class_Oone(X94)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),hAPP(c_Nat_OSuc,X42)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__gt1) ).
fof(fact_self__quotient__aux1,axiom,
! [X149,X143,X84] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> ( X84 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X143),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),X149))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X143),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X149)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).
fof(fact_le__number__of,axiom,
! [X25,X16,X10] :
( ( class_Int_Onumber__ring(X10)
& class_Rings_Olinordered__idom(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X16)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X25)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X16),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__number__of) ).
fof(fact_less__number__of,axiom,
! [X25,X16,X10] :
( ( class_Int_Onumber__ring(X10)
& class_Rings_Olinordered__idom(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X16)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X25)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__number__of) ).
fof(fact_zdvd__antisym__nonneg,axiom,
! [X42,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)),X42))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X97),X42))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X42),X97))
=> X97 = X42 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__antisym__nonneg) ).
fof(fact_list__update__beyond,axiom,
! [X93,X120,X297,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)),X120))
=> hAPP(hAPP(c_List_Olist__update(X94,X297),X120),X93) = X297 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__beyond) ).
fof(fact_le__cube,axiom,
! [X97] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X97),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X97),X97)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__cube) ).
fof(fact_in__set__butlastD,axiom,
! [X290,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),c_List_Obutlast(X10,X290))))
=> hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__butlastD) ).
fof(fact_insert__image,axiom,
! [X2,X13,X154,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(hAPP(c_Set_Oinsert(X13),hAPP(X2,X16)),hAPP(c_Set_Oimage(X10,X13,X2),X154)) = hAPP(c_Set_Oimage(X10,X13,X2),X154) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__image) ).
fof(fact_self__quotient,axiom,
! [X143,X149,X84] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X84,X84),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X149),X143)))
=> ( X84 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> X149 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__quotient) ).
fof(fact_self__remainder,axiom,
! [X143,X149,X84] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X84,X84),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X149),X143)))
=> ( X84 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> X143 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__remainder) ).
fof(fact_wf__exp,axiom,
! [X196,X20,X10] :
( c_Wellfounded_Owf(X10,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X20),X196))
=> c_Wellfounded_Owf(X10,X196) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__exp) ).
fof(fact_of__int__le__iff,axiom,
! [X73,X131,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Oring__1__class_Oof__int(X10),X131)),hAPP(c_Int_Oring__1__class_Oof__int(X10),X73)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X131),X73)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__le__iff) ).
fof(fact_of__nat__le__iff,axiom,
! [X20,X102,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),X102)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),X20)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__le__iff) ).
fof(fact_of__int__less__iff,axiom,
! [X73,X131,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Oring__1__class_Oof__int(X10),X131)),hAPP(c_Int_Oring__1__class_Oof__int(X10),X73)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X131),X73)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__less__iff) ).
fof(fact_of__nat__less__imp__less,axiom,
! [X42,X97,X94] :
( class_Rings_Olinordered__semidom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),X97)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),X42)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__less__imp__less) ).
fof(fact_of__nat__less__iff,axiom,
! [X20,X102,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),X102)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),X20)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__less__iff) ).
fof(fact_nonzero__power__divide,axiom,
! [X42,X84,X92,X94] :
( class_Fields_Ofield(X94)
=> ( X92 != c_Groups_Ozero__class_Ozero(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X84),X92)),X42) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X92),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__power__divide) ).
fof(fact_zless__imp__add1__zle,axiom,
! [X104,X133] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X133),X104))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X133),c_Groups_Oone__class_Oone(tc_Int_Oint))),X104)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).
fof(fact_Min__Un,axiom,
! [X160,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( X160 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),c_Big__Operators_Olinorder__class_OMin(X10,X154)),c_Big__Operators_Olinorder__class_OMin(X10,X160)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min__Un) ).
fof(fact_Max__Un,axiom,
! [X160,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( X160 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),c_Big__Operators_Olinorder__class_OMax(X10,X154)),c_Big__Operators_Olinorder__class_OMax(X10,X160)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max__Un) ).
fof(fact_Inf__fin_Ounion__idem,axiom,
! [X160,X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( X160 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),c_Big__Operators_Olattice__class_OInf__fin(X10,X154)),c_Big__Operators_Olattice__class_OInf__fin(X10,X160)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Ounion__idem) ).
fof(fact_Sup__fin_Ounion__idem,axiom,
! [X160,X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( X160 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),c_Big__Operators_Olattice__class_OSup__fin(X10,X154)),c_Big__Operators_Olattice__class_OSup__fin(X10,X160)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Ounion__idem) ).
fof(fact_code__numeral_Oof__nat__inject,axiom,
! [X25,X16] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X16),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
=> ( hAPP(c_Code__Numeral_Oof__nat,X16) = hAPP(c_Code__Numeral_Oof__nat,X25)
<=> X16 = X25 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Oof__nat__inject) ).
fof(fact_nat__le__eq__zle,axiom,
! [X73,X131] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X131))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73)) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X131)),hAPP(c_Int_Onat,X73)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X131),X73)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__eq__zle) ).
fof(fact_nat__less__eq__zless,axiom,
! [X73,X131] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X131))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X131)),hAPP(c_Int_Onat,X73)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X131),X73)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__eq__zless) ).
fof(fact_nat__mono__iff,axiom,
! [X131,X73] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X131)),hAPP(c_Int_Onat,X73)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X131),X73)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mono__iff) ).
fof(fact_funpow__swap1,axiom,
! [X16,X20,X10,X2] : hAPP(X2,hAPP(hAPP(hAPP(c_Nat_Ocompow(X10,X10),X20),X2),X16)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(X10,X10),X20),X2),hAPP(X2,X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow__swap1) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
! [X92,X97,X84,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X97)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X97)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92)),X97) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
fof(fact_inf__sup__distrib2,axiom,
! [X93,X104,X105,X94] :
( class_Lattices_Odistrib__lattice(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X105),X104)),X93) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X105),X93)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X104),X93)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__distrib2) ).
fof(fact_sup__inf__distrib2,axiom,
! [X93,X104,X105,X94] :
( class_Lattices_Odistrib__lattice(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X105),X104)),X93) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X105),X93)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X104),X93)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__inf__distrib2) ).
fof(fact_min__max_Osup__inf__distrib2,axiom,
! [X93,X104,X105,X94] :
( class_Orderings_Olinorder(X94)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X105),X104)),X93) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X105),X93)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X104),X93)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__inf__distrib2) ).
fof(fact_min__max_Oinf__sup__distrib2,axiom,
! [X93,X104,X105,X94] :
( class_Orderings_Olinorder(X94)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X105),X104)),X93) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X105),X93)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X104),X93)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__sup__distrib2) ).
fof(fact_diff__divide__distrib,axiom,
! [X81,X92,X84,X94] :
( class_Rings_Odivision__ring(X94)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X84),X92)),X81) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X84),X81)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X92),X81)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__divide__distrib) ).
fof(fact_add__divide__distrib,axiom,
! [X81,X92,X84,X94] :
( class_Rings_Odivision__ring(X94)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92)),X81) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X84),X81)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X92),X81)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__divide__distrib) ).
fof(fact_power__divide,axiom,
! [X42,X92,X84,X94] :
( class_Fields_Ofield__inverse__zero(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X84),X92)),X42) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X92),X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__divide) ).
fof(fact_power__mult__distrib,axiom,
! [X42,X92,X84,X94] :
( class_Groups_Ocomm__monoid__mult(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92)),X42) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X92),X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mult__distrib) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
! [X149,X105,X93,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X93),X105)),X149) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),X149)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X105),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
fof(fact_max__diff__distrib__left,axiom,
! [X104,X105,X93,X94] :
( class_Groups_Oordered__ab__group__add(X94)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X93),X105)),X104) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X93),X104)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X105),X104)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__diff__distrib__left) ).
fof(fact_min__diff__distrib__left,axiom,
! [X104,X105,X93,X94] :
( class_Groups_Oordered__ab__group__add(X94)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X93),X105)),X104) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X93),X104)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X105),X104)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__diff__distrib__left) ).
fof(fact_comm__semiring__class_Odistrib,axiom,
! [X81,X92,X84,X94] :
( class_Rings_Ocomm__semiring(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92)),X81) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X81)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X81)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
! [X81,X92,X84,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92)),X81) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X81)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X81)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
fof(fact_max__add__distrib__left,axiom,
! [X104,X105,X93,X94] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X93),X105)),X104) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X93),X104)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X105),X104)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__add__distrib__left) ).
fof(fact_min__add__distrib__left,axiom,
! [X104,X105,X93,X94] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X93),X105)),X104) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X93),X104)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X105),X104)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__add__distrib__left) ).
fof(fact_set__insort,axiom,
! [X290,X16,X2,X10,X13] :
( class_Orderings_Olinorder(X13)
=> hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X13,X2),X16),X290)) = hAPP(hAPP(c_Set_Oinsert(X10),X16),hAPP(c_List_Oset(X10),X290)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__insort) ).
fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
! [X105,X93] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X93))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X105))
=> 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),X93),X105))) ) ),
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,
! [X105,X93] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X93))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X105))
=> 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),X93),X105))) ) ),
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,
! [X105,X93] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X93))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X105))
=> 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),X93),X105))) ) ),
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,
! [X20,X102] :
( 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),X102),X20)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X102))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).
fof(fact_dvd__div__div__eq__mult,axiom,
! [X141,X38,X18,X39,X10] :
( class_Divides_Osemiring__div(X10)
=> ( X39 != c_Groups_Ozero__class_Ozero(X10)
=> ( X18 != c_Groups_Ozero__class_Ozero(X10)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X39),X38))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X18),X141))
=> ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X10),X38),X39) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X10),X141),X18)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X38),X18) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X141) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__div__div__eq__mult) ).
fof(fact_ivl__disj__un_I1_J,axiom,
! [X162,X10] :
( class_Orderings_Olinorder(X10)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X162),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),X162)) = hAPP(c_SetInterval_Oord__class_OatLeast(X10),X162) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I1_J) ).
fof(fact_finite__converse,axiom,
! [X177,X13,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10,X13)),hAPP(c_Relation_Oconverse(X13,X10),X177)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X13,X10)),X177)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__converse) ).
fof(fact_finite__UNIV__card__ge__0,axiom,
! [X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Orderings_Otop__class_Otop(tc_fun(X10,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(X10),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__card__ge__0) ).
fof(fact_set__remove1__eq,axiom,
! [X16,X290,X10] :
( hBOOL(hAPP(c_List_Odistinct(X10),X290))
=> hAPP(c_List_Oset(X10),c_List_Oremove1(X10,X16,X290)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),X290)),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__remove1__eq) ).
fof(fact_Int__Union,axiom,
! [X160,X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X160)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X160),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Union) ).
fof(fact_Un__Inter,axiom,
! [X160,X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X160)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X160),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Inter) ).
fof(fact_length__insort,axiom,
! [X290,X16,X2,X10,X13] :
( class_Orderings_Olinorder(X13)
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X13,X2),X16),X290)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__insort) ).
fof(fact_nat__less__iff,axiom,
! [X102,X131] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X131))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X131)),X102))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X131),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X102))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__iff) ).
fof(fact_remove1__insort,axiom,
! [X290,X16,X10] :
( class_Orderings_Olinorder(X10)
=> c_List_Oremove1(X10,X16,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X10,c_COMBI(X10)),X16),X290)) = X290 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1__insort) ).
fof(fact_Powp__def,axiom,
! [X160,X154,X10] :
( hBOOL(hAPP(c_Predicate_OPowp(X10,X154),X160))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X160))
=> hBOOL(hAPP(X154,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Powp__def) ).
fof(fact_restrict__map__to__empty,axiom,
! [X16,X102,X10,X13] : hAPP(c_Map_Orestrict__map(X13,X10,X102,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool))),X16) = c_Option_Ooption_ONone(X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__map__to__empty) ).
fof(fact_split__curry,axiom,
! [X2,X125,X13,X10] : hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,X125),c_Product__Type_Ocurry(X10,X13,X125,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__curry) ).
fof(fact_eq__number__of__eq,axiom,
! [X25,X16,X10] :
( class_Int_Onumber__ring(X10)
=> ( hAPP(c_Int_Onumber__class_Onumber__of(X10),X16) = hAPP(c_Int_Onumber__class_Onumber__of(X10),X25)
<=> c_Int_Oiszero(X10,hAPP(c_Int_Onumber__class_Onumber__of(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__number__of__eq) ).
fof(fact_append__eq__conv__conj,axiom,
! [X299,X289,X290,X10] :
( hAPP(hAPP(c_List_Oappend(X10),X290),X289) = X299
<=> ( X290 = hAPP(hAPP(c_List_Otake(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290)),X299)
& X289 = hAPP(hAPP(c_List_Odrop(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290)),X299) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__eq__conv__conj) ).
fof(fact_zdiv__zminus2__eq__if,axiom,
! [X84,X92] :
( X92 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X92) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X92)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),X92)) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X92) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X92)) = 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),X84),X92))),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,
! [X39,X10] : hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X39)) = hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__conv) ).
fof(fact_insert__is__Un,axiom,
! [X154,X39,X10] : hAPP(hAPP(c_Set_Oinsert(X10),X39),X154) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),X154),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__is__Un) ).
fof(fact_evalc__elim__cases_I2_J,axiom,
! [X53,X54,X39,X48] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(X48,X39)),X54),X53))
=> X53 = hAPP(hAPP(hAPP(c_Natural_Oupdate,X54),X48),hAPP(X39,X54)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I2_J) ).
fof(fact_less__imp__diff__less,axiom,
! [X42,X103,X119] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X119),X103))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X119),X42)),X103)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).
fof(fact_add__diff__assoc2,axiom,
! [X120,X119,X103] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X103),X119))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X119),X103)),X120) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X119),X120)),X103) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__assoc2) ).
fof(fact_diff__add__assoc2,axiom,
! [X120,X119,X103] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X103),X119))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X119),X120)),X103) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X119),X103)),X120) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__assoc2) ).
fof(fact_Int__absorb2,axiom,
! [X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) = X154 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb2) ).
fof(fact_Int__absorb1,axiom,
! [X154,X160,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),X154))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) = X160 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb1) ).
fof(fact_subset__Un__eq,axiom,
! [X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
<=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160) = X160 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__Un__eq) ).
fof(fact_Un__absorb1,axiom,
! [X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160) = X160 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb1) ).
fof(fact_Un__absorb2,axiom,
! [X154,X160,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),X154))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160) = X154 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb2) ).
fof(fact_zdvd__zmod,axiom,
! [X42,X97,X214] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X214),X97))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X214),X42))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X214),c_Divides_Odiv__class_Omod(tc_Int_Oint,X97,X42))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__zmod) ).
fof(fact_Collect__neg__eq,axiom,
! [X19,X10] : hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10),c_fNot),X19)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_OCollect(X10),X19)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
fof(fact_Sumr_Osimps,axiom,
! [X16,X2,X125,X10,X13] : hAPP(c_Sum__Type_OSumr(X13,X10,X125,X2),hAPP(c_Sum__Type_OInr(X13,X125),X16)) = hAPP(X2,X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sumr_Osimps) ).
fof(fact_Suml_Osimps,axiom,
! [X16,X2,X125,X10,X13] : hAPP(c_Sum__Type_OSuml(X13,X10,X125,X2),hAPP(c_Sum__Type_OInl(X13,X125),X16)) = hAPP(X2,X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suml_Osimps) ).
fof(fact_drop__all,axiom,
! [X42,X297,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)),X42))
=> hAPP(hAPP(c_List_Odrop(X94),X42),X297) = c_List_Olist_ONil(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__all) ).
fof(fact_drop__eq__Nil,axiom,
! [X290,X20,X10] :
( hAPP(hAPP(c_List_Odrop(X10),X20),X290) = c_List_Olist_ONil(X10)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290)),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__eq__Nil) ).
fof(fact_insert__iff,axiom,
! [X154,X38,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X39),hAPP(hAPP(c_Set_Oinsert(X10),X38),X154)))
<=> ( X39 = X38
| hBOOL(hAPP(hAPP(c_member(X10),X39),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__iff) ).
fof(fact_insertE,axiom,
! [X154,X38,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X39),hAPP(hAPP(c_Set_Oinsert(X10),X38),X154)))
=> ( X39 != X38
=> hBOOL(hAPP(hAPP(c_member(X10),X39),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertE) ).
fof(fact_take__all,axiom,
! [X42,X297,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)),X42))
=> hAPP(hAPP(c_List_Otake(X94),X42),X297) = X297 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__all) ).
fof(fact_ivl__diff,axiom,
! [X102,X20,X113,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X113),X20))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X113),X102)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X113),X20)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X20),X102) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__diff) ).
fof(fact_accp_Osimps,axiom,
! [X39,X177,X10] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X10,X177),X39))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(X177,X3),X39))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(X10,X177),X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp_Osimps) ).
fof(fact_accp_Oequations,axiom,
! [X39,X177,X10] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X10,X177),X39))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(X177,X3),X39))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(X10,X177),X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp_Oequations) ).
fof(fact_Times__empty,axiom,
! [X160,X154,X13,X10] :
( hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X154),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),X160)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X13),tc_HOL_Obool))
<=> ( X154 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
| X160 = c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__empty) ).
fof(fact_ivl__disj__un_I13_J,axiom,
! [X165,X162,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X162),X165))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X162,X165)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),X165)) = hAPP(c_SetInterval_Oord__class_OatLeast(X10),X162) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I13_J) ).
fof(fact_ivl__disj__un_I11_J,axiom,
! [X165,X162,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X162),X165))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X162,X165)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),X165)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),X162) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I11_J) ).
fof(fact_ivl__disj__un_I12_J,axiom,
! [X165,X162,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X162),X165))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X162,X165)),hAPP(c_SetInterval_Oord__class_OatLeast(X10),X165)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),X162) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I12_J) ).
fof(fact_Sup__set__fold,axiom,
! [X290,X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> c_Complete__Lattice_OSup__class_OSup(X10,hAPP(c_List_Oset(X10),X290)) = hAPP(c_List_Ofoldl(X10,X10,c_Lattices_Osemilattice__sup__class_Osup(X10),c_Orderings_Obot__class_Obot(X10)),X290) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__set__fold) ).
fof(fact_Inf__set__fold,axiom,
! [X290,X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> c_Complete__Lattice_OInf__class_OInf(X10,hAPP(c_List_Oset(X10),X290)) = hAPP(c_List_Ofoldl(X10,X10,c_Lattices_Osemilattice__inf__class_Oinf(X10),c_Orderings_Otop__class_Otop(X10)),X290) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__set__fold) ).
fof(fact_card__atLeastAtMost__int,axiom,
! [X165,X162] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X162,X165)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X165),X162)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__atLeastAtMost__int) ).
fof(fact_finite__imageI,axiom,
! [X204,X13,X225,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X225))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X13),hAPP(c_Set_Oimage(X10,X13,X204),X225))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageI) ).
fof(fact_dvd_OatMost__iff,axiom,
! [X101,X113] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X113),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X101)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X113),X101)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatMost__iff) ).
fof(fact_dvd_OatLeast__iff,axiom,
! [X101,X113] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X113),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X101)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X101),X113)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeast__iff) ).
fof(fact_Sup__binary,axiom,
! [X38,X39,X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> c_Complete__Lattice_OSup__class_OSup(X10,hAPP(hAPP(c_Set_Oinsert(X10),X39),hAPP(hAPP(c_Set_Oinsert(X10),X38),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X39),X38) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__binary) ).
fof(fact_Inf__binary,axiom,
! [X38,X39,X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> c_Complete__Lattice_OInf__class_OInf(X10,hAPP(hAPP(c_Set_Oinsert(X10),X39),hAPP(hAPP(c_Set_Oinsert(X10),X38),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X39),X38) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__binary) ).
fof(fact_div__mult__swap,axiom,
! [X84,X92,X81,X94] :
( class_Divides_Osemiring__div(X94)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X81),X92))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),X92),X81)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92)),X81) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__swap) ).
fof(fact_ord_OatMost__iff,axiom,
! [X101,X228,X113,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X113),c_SetInterval_Oord_OatMost(X10,X228,X101)))
<=> hBOOL(hAPP(hAPP(X228,X113),X101)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OatMost__iff) ).
fof(fact_ord_OlessThan__iff,axiom,
! [X101,X229,X113,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X113),c_SetInterval_Oord_OlessThan(X10,X229,X101)))
<=> hBOOL(hAPP(hAPP(X229,X113),X101)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OlessThan__iff) ).
fof(fact_ord_OatLeast__iff,axiom,
! [X101,X228,X113,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X113),c_SetInterval_Oord_OatLeast(X10,X228,X101)))
<=> hBOOL(hAPP(hAPP(X228,X101),X113)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OatLeast__iff) ).
fof(fact_ord_OgreaterThan__iff,axiom,
! [X101,X229,X113,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X113),c_SetInterval_Oord_OgreaterThan(X10,X229,X101)))
<=> hBOOL(hAPP(hAPP(X229,X101),X113)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OgreaterThan__iff) ).
fof(fact_partition__set,axiom,
! [X329,X330,X290,X19,X10] :
( c_List_Opartition(X10,X19,X290) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X330),X329)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),X330)),hAPP(c_List_Oset(X10),X329)) = hAPP(c_List_Oset(X10),X290) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition__set) ).
fof(fact_nth__Cons__number__of,axiom,
! [X297,X93,X94,X144] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Onth(X94),hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)) = X93 )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Onth(X94),hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)) = hAPP(hAPP(c_List_Onth(X94),X297),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),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,
! [X177,X10] : hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X177),c_Transitive__Closure_Ortrancl(X10,X177)) = hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),c_Transitive__Closure_Ortrancl(X10,X177)),X177),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__comp__rtrancl__eq) ).
fof(help_c__COMBS__1,axiom,
! [X196,X17,X19,X10,X125,X13] : hAPP(hAPP(hAPP(c_COMBS(X13,X125,X10),X19),X17),X196) = hAPP(hAPP(X19,X196),hAPP(X17,X196)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBS__1) ).
fof(fact_abs__minus__le__zero,axiom,
! [X84,X94] :
( class_Groups_Oordered__ab__group__add__abs(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),X84))),c_Groups_Ozero__class_Ozero(X94))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__minus__le__zero) ).
fof(fact_Un__insert__right,axiom,
! [X160,X39,X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),X160)) = hAPP(hAPP(c_Set_Oinsert(X10),X39),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__insert__right) ).
fof(fact_sum__squares__eq__zero__iff,axiom,
! [X25,X16,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X16),X16)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X25),X25)) = c_Groups_Ozero__class_Ozero(X10)
<=> ( X16 = c_Groups_Ozero__class_Ozero(X10)
& X25 = c_Groups_Ozero__class_Ozero(X10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
fof(fact_map__add__find__right,axiom,
! [X102,X13,X279,X10,X101,X20] :
( hAPP(X20,X101) = hAPP(c_Option_Ooption_OSome(X10),X279)
=> hAPP(c_Map_Omap__add(X13,X10,X102,X20),X101) = hAPP(c_Option_Ooption_OSome(X10),X279) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__find__right) ).
fof(fact_union__fold__insert,axiom,
! [X160,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160) = hAPP(hAPP(c_Finite__Set_Ofold(X10,tc_fun(X10,tc_HOL_Obool),c_Set_Oinsert(X10)),X160),X154) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_union__fold__insert) ).
fof(fact_eq__special_I3_J,axiom,
! [X16,X10] :
( class_Int_Onumber__ring(X10)
=> ( hAPP(c_Int_Onumber__class_Onumber__of(X10),X16) = c_Groups_Ozero__class_Ozero(X10)
<=> c_Int_Oiszero(X10,hAPP(c_Int_Onumber__class_Onumber__of(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16),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,
! [X25,X10] :
( class_Int_Onumber__ring(X10)
=> ( c_Groups_Ozero__class_Ozero(X10) = hAPP(c_Int_Onumber__class_Onumber__of(X10),X25)
<=> c_Int_Oiszero(X10,hAPP(c_Int_Onumber__class_Onumber__of(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__special_I1_J) ).
fof(fact_wf__lex__prod,axiom,
! [X262,X13,X263,X10] :
( c_Wellfounded_Owf(X10,X263)
=> ( c_Wellfounded_Owf(X13,X262)
=> c_Wellfounded_Owf(tc_prod(X10,X13),c_Wellfounded_Olex__prod(X10,X13,X263,X262)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__lex__prod) ).
fof(fact_distinct__zipI1,axiom,
! [X298,X10,X297,X94] :
( hBOOL(hAPP(c_List_Odistinct(X94),X297))
=> hBOOL(hAPP(c_List_Odistinct(tc_prod(X94,X10)),hAPP(hAPP(c_List_Ozip(X94,X10),X297),X298))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__zipI1) ).
fof(fact_distinct__zipI2,axiom,
! [X297,X10,X298,X94] :
( hBOOL(hAPP(c_List_Odistinct(X94),X298))
=> hBOOL(hAPP(c_List_Odistinct(tc_prod(X10,X94)),hAPP(hAPP(c_List_Ozip(X10,X94),X297),X298))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__zipI2) ).
fof(fact_vimage__Union,axiom,
! [X154,X2,X13,X10] : hAPP(c_Set_Ovimage(X10,X13,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X13,tc_HOL_Obool),X154)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X13,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X154),c_Set_Ovimage(X10,X13,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Union) ).
fof(fact_image__Union,axiom,
! [X216,X2,X10,X13] : hAPP(c_Set_Oimage(X13,X10,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X13,tc_HOL_Obool),X216)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X13,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X216),c_Set_Oimage(X13,X10,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Union) ).
fof(fact_Pow__bottom,axiom,
! [X160,X10] : hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),hAPP(c_Set_OPow(X10),X160))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__bottom) ).
fof(fact_listsum__0,axiom,
! [X290,X13,X10] :
( class_Groups_Omonoid__add(X10)
=> hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(X13,X10),hAPP(c_COMBK(X10,X13),c_Groups_Ozero__class_Ozero(X10))),X290)) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__0) ).
fof(fact_Int__left__absorb,axiom,
! [X160,X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__left__absorb) ).
fof(fact_Un__left__absorb,axiom,
! [X160,X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__left__absorb) ).
fof(fact_Un__Diff__cancel,axiom,
! [X160,X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X160),X154)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff__cancel) ).
fof(fact_rotate1__length01,axiom,
! [X297,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
=> hAPP(c_List_Orotate1(X94),X297) = X297 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate1__length01) ).
fof(fact_fold__image__empty,axiom,
! [X73,X1,X2,X13,X10] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X10,X13,X2),X1),X73),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool))) = X73,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__empty) ).
fof(fact_dvd__diff__nat,axiom,
! [X42,X97,X103] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X103),X97))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X103),X42))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X103),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__diff__nat) ).
fof(fact_mult__eq__if,axiom,
! [X42,X97] :
( ( X97 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X97),X42) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X97 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X97),X42) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__if) ).
fof(fact_zdvd__iff__zmod__eq__0__number__of,axiom,
! [X25,X16] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X16)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25)))
<=> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X16)) = 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,
! [X7,X8,X9,X12,X10,X13] : c_Hoare__Mirabelle_Otriple_Otriple__case(X13,X10,X12,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X13),X9),X8),X7)) = hAPP(hAPP(hAPP(X12,X9),X8),X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triple_Osimps_I2_J) ).
fof(fact_triple_Orecs,axiom,
! [X7,X8,X9,X12,X10,X13] : c_Hoare__Mirabelle_Otriple_Otriple__rec(X13,X10,X12,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X13),X9),X8),X7)) = hAPP(hAPP(hAPP(X12,X9),X8),X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triple_Orecs) ).
fof(fact_RangeP_Oequations,axiom,
! [X52,X177,X13,X10] :
( hBOOL(hAPP(c_Predicate_ORangeP(X10,X13,X177),X52))
<=> ? [X116] : hBOOL(hAPP(hAPP(X177,X116),X52)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeP_Oequations) ).
fof(fact_nat__mult__distrib__neg,axiom,
! [X145,X104] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X104),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X104),X145)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X104))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X145))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__distrib__neg) ).
fof(fact_pair__box_Osize_I2_J,axiom,
! [X92,X84,X10,X94] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(X94,X10)),c_Nitpick_Opair__box_OPairBox(X94,X10,X84,X92)) = 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,
! [X93,X297,X94,X103] :
( ( X103 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
=> c_List_Obutlast(X94,hAPP(hAPP(c_List_Olist__update(X94,X297),X103),X93)) = c_List_Obutlast(X94,X297) )
& ( X103 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
=> c_List_Obutlast(X94,hAPP(hAPP(c_List_Olist__update(X94,X297),X103),X93)) = hAPP(hAPP(c_List_Olist__update(X94,c_List_Obutlast(X94,X297)),X103),X93) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast__list__update) ).
fof(fact_image__insert,axiom,
! [X160,X39,X2,X10,X13] : hAPP(c_Set_Oimage(X13,X10,X2),hAPP(hAPP(c_Set_Oinsert(X13),X39),X160)) = hAPP(hAPP(c_Set_Oinsert(X10),hAPP(X2,X39)),hAPP(c_Set_Oimage(X13,X10,X2),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__insert) ).
fof(fact_finite__subset,axiom,
! [X160,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__subset) ).
fof(fact_rev__finite__subset,axiom,
! [X154,X160,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__finite__subset) ).
fof(fact_neg__le__0__iff__le,axiom,
! [X39,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X39)),c_Groups_Ozero__class_Ozero(X10)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X39)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__le__0__iff__le) ).
fof(fact_neg__less__0__iff__less,axiom,
! [X39,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X39)),c_Groups_Ozero__class_Ozero(X10)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X39)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__0__iff__less) ).
fof(fact_zip__rev,axiom,
! [X298,X10,X297,X94] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X298)
=> hAPP(hAPP(c_List_Ozip(X94,X10),hAPP(c_List_Orev(X94),X297)),hAPP(c_List_Orev(X10),X298)) = hAPP(c_List_Orev(tc_prod(X94,X10)),hAPP(hAPP(c_List_Ozip(X94,X10),X297),X298)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__rev) ).
fof(fact_nat__zero__less__power__iff,axiom,
! [X20,X16] :
( 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),X16),X20)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X16))
| X20 = 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,
! [X18,X38,X39,X10] :
( class_Orderings_Olinorder(X10)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X39,X38)),hAPP(c_SetInterval_Oord__class_OatLeast(X10),X18)) = c_SetInterval_Oord__class_OatLeastAtMost(X10,hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X39),X18),X38) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__atLeastAtMostL2) ).
fof(fact_Int__atLeastAtMostL1,axiom,
! [X141,X38,X39,X10] :
( class_Orderings_Olinorder(X10)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X39,X38)),hAPP(c_SetInterval_Oord__class_OatMost(X10),X141)) = c_SetInterval_Oord__class_OatLeastAtMost(X10,X39,hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X38),X141)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__atLeastAtMostL1) ).
fof(fact_list__update__code_I2_J,axiom,
! [X105,X297,X93,X94] : hAPP(hAPP(c_List_Olist__update(X94,hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X105) = hAPP(hAPP(c_List_Olist_OCons(X94),X105),X297),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__code_I2_J) ).
fof(help_c__COMBC__1,axiom,
! [X196,X17,X19,X10,X125,X13] : hAPP(hAPP(hAPP(c_COMBC(X13,X125,X10),X19),X17),X196) = hAPP(hAPP(X19,X196),X17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBC__1) ).
fof(help_c__COMBB__1,axiom,
! [X196,X17,X19,X125,X10,X13] : hAPP(hAPP(hAPP(c_COMBB(X13,X10,X125),X19),X17),X196) = hAPP(X19,hAPP(X17,X196)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_option_Osimps_I5_J,axiom,
! [X39,X37,X12,X13,X10] : hAPP(c_Option_Ooption_Ooption__case(X10,X13,X12,X37),hAPP(c_Option_Ooption_OSome(X13),X39)) = hAPP(X37,X39),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Osimps_I5_J) ).
fof(fact_vimage__Compl,axiom,
! [X154,X2,X13,X10] : hAPP(c_Set_Ovimage(X10,X13,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X13,tc_HOL_Obool)),X154)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X10,X13,X2),X154)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Compl) ).
fof(fact_mod__mult__self3,axiom,
! [X97,X42,X103] : 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),X103),X42)),X97),X42) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X97,X42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self3) ).
fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
! [X105,X93] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X93))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X105))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X93)),hAPP(c_Int_Onat,X105)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X93),X105)) ) ),
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,
! [X105,X93] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X93))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X105))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X93)),hAPP(c_Int_Onat,X105)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X93),X105)) ) ),
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,
! [X105,X93] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X93))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X105))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X93)),hAPP(c_Int_Onat,X105)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X93),X105)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J) ).
fof(fact_nat__add__distrib,axiom,
! [X145,X104] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X104))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X145))
=> hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X104),X145)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X104)),hAPP(c_Int_Onat,X145)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__distrib) ).
fof(fact_length__zip,axiom,
! [X298,X297,X10,X94] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(X94,X10))),hAPP(hAPP(c_List_Ozip(X94,X10),X297),X298)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X298)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__zip) ).
fof(fact_Union__image__eq,axiom,
! [X154,X160,X13,X10] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),hAPP(c_Set_Oimage(X13,tc_fun(X10,tc_HOL_Obool),X160),X154)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X154),X160),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__image__eq) ).
fof(fact_Inter__image__eq,axiom,
! [X154,X160,X13,X10] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),hAPP(c_Set_Oimage(X13,tc_fun(X10,tc_HOL_Obool),X160),X154)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X154),X160),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__image__eq) ).
fof(fact_INTER__eq__Inter__image,axiom,
! [X160,X154,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X154),X160) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),hAPP(c_Set_Oimage(X13,tc_fun(X10,tc_HOL_Obool),X160),X154)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INTER__eq__Inter__image) ).
fof(fact_UNION__eq__Union__image,axiom,
! [X160,X154,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X154),X160) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),hAPP(c_Set_Oimage(X13,tc_fun(X10,tc_HOL_Obool),X160),X154)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNION__eq__Union__image) ).
fof(fact_of__nat__aux_Osimps_I2_J,axiom,
! [X113,X20,X114,X10] :
( class_Rings_Osemiring__1(X10)
=> c_Nat_Osemiring__1__class_Oof__nat__aux(X10,X114,hAPP(c_Nat_OSuc,X20),X113) = c_Nat_Osemiring__1__class_Oof__nat__aux(X10,X114,X20,hAPP(X114,X113)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__aux_Osimps_I2_J) ).
fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
! [X105,X93] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X93))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X105))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X93),hAPP(c_Int_Onat,X105)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X93,X105)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__functions_I2_J) ).
fof(fact_nat__mod__distrib,axiom,
! [X105,X93] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X93))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X105))
=> hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X93,X105)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X93),hAPP(c_Int_Onat,X105)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mod__distrib) ).
fof(fact_zmod__zdiv__equality_H,axiom,
! [X42,X97] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X97,X42) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X97),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X97),X42)),X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zdiv__equality_H) ).
fof(fact_Divides_Omod__div__equality_H,axiom,
! [X42,X97] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X97,X42) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X97),X42)),X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Omod__div__equality_H) ).
fof(fact_one__le__power,axiom,
! [X42,X84,X94] :
( class_Rings_Olinordered__semidom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Oone__class_Oone(X94)),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Oone__class_Oone(X94)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__le__power) ).
fof(fact_zero__le__power,axiom,
! [X42,X84,X94] :
( class_Rings_Olinordered__semidom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__power) ).
fof(fact_zero__less__power,axiom,
! [X42,X84,X94] :
( class_Rings_Olinordered__semidom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__power) ).
fof(fact_image__constant,axiom,
! [X18,X13,X154,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Set_Oimage(X10,X13,hAPP(c_COMBK(X13,X10),X18)),X154) = hAPP(hAPP(c_Set_Oinsert(X13),X18),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__constant) ).
fof(fact_zless__nat__conj,axiom,
! [X73,X131] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X131)),hAPP(c_Int_Onat,X73)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X131),X73)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__nat__conj) ).
fof(fact_UNIV__Times__UNIV,axiom,
! [X13,X10] : hAPP(hAPP(c_Product__Type_OSigma(X10,X13),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__Times__UNIV) ).
fof(fact_zless__add1__eq,axiom,
! [X73,X131] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X131),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X73),c_Groups_Oone__class_Oone(tc_Int_Oint))))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X131),X73))
| X131 = X73 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__add1__eq) ).
fof(fact_minus__le__self__iff,axiom,
! [X39,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X39)),X39))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X39)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__le__self__iff) ).
fof(fact_neg__less__nonneg,axiom,
! [X39,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X39)),X39))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X39)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).
fof(fact_funpow__mult,axiom,
! [X2,X102,X20,X10] : hAPP(hAPP(c_Nat_Ocompow(X10,X10),X20),hAPP(hAPP(c_Nat_Ocompow(X10,X10),X102),X2)) = hAPP(hAPP(c_Nat_Ocompow(X10,X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X102),X20)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow__mult) ).
fof(fact_zdvd__int,axiom,
! [X25,X16] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X16),X25))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X16)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__int) ).
fof(fact_transfer__int__nat__relations_I4_J,axiom,
! [X25,X16] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X16)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X16),X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__relations_I4_J) ).
fof(fact_less__eq__number__of__int__code,axiom,
! [X162,X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X101)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X162)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X101),X162)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__number__of__int__code) ).
fof(fact_transfer__int__nat__relations_I3_J,axiom,
! [X25,X16] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X16)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X16),X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__relations_I3_J) ).
fof(fact_zle__int,axiom,
! [X20,X102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X102)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__int) ).
fof(fact_less__number__of__int__code,axiom,
! [X162,X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X101)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X162)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),X162)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__number__of__int__code) ).
fof(fact_transfer__int__nat__relations_I2_J,axiom,
! [X25,X16] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X16)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16),X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__relations_I2_J) ).
fof(fact_zless__int,axiom,
! [X20,X102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X102)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__int) ).
fof(fact_zero__less__diff,axiom,
! [X102,X20] :
( 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),X20),X102)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__diff) ).
fof(fact_zle__add1__eq__le,axiom,
! [X73,X131] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X131),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X73),c_Groups_Oone__class_Oone(tc_Int_Oint))))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X131),X73)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).
fof(fact_zle__diff1__eq,axiom,
! [X73,X131] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X131),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X73),c_Groups_Oone__class_Oone(tc_Int_Oint))))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X131),X73)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__diff1__eq) ).
fof(fact_minus__number__of__mult,axiom,
! [X104,X133,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),X133))),X104) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X133))),X104) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__number__of__mult) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
! [X97,X84,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X97)),X97) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),c_Groups_Oone__class_Oone(X94))),X97) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
fof(fact_list__update__same__conv,axiom,
! [X16,X290,X10,X113] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X113),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290)))
=> ( hAPP(hAPP(c_List_Olist__update(X10,X290),X113),X16) = X290
<=> hAPP(hAPP(c_List_Onth(X10),X290),X113) = X16 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__same__conv) ).
fof(fact_evaln__elim__cases_I2_J,axiom,
! [X53,X20,X54,X39,X48] :
( c_Natural_Oevaln(c_Com_Ocom_OAss(X48,X39),X54,X20,X53)
=> X53 = hAPP(hAPP(hAPP(c_Natural_Oupdate,X54),X48),hAPP(X39,X54)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I2_J) ).
fof(fact_negative__zle,axiom,
! [X97,X42] : 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),X42))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X97))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__zle) ).
fof(fact_zero__le__zpower__abs,axiom,
! [X42,X93] : 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),X93)),X42))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__zpower__abs) ).
fof(fact_min__diff,axiom,
! [X42,X120,X97] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X120)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X42),X120)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X97),X42)),X120),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__diff) ).
fof(fact_zdiff__zmult__distrib,axiom,
! [X133,X135,X136] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X136),X135)),X133) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X136),X133)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X135),X133)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib) ).
fof(fact_zadd__zmult__distrib,axiom,
! [X133,X135,X136] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X136),X135)),X133) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X136),X133)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X135),X133)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).
fof(fact_diff__mult__distrib,axiom,
! [X103,X42,X97] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42)),X103) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X97),X103)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),X103)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).
fof(fact_add__mult__distrib,axiom,
! [X103,X42,X97] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X42)),X103) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X97),X103)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),X103)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib) ).
fof(fact_nth_Osimps,axiom,
! [X20,X290,X16,X10] : hAPP(hAPP(c_List_Onth(X10),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290)),X20) = c_Nat_Onat_Onat__case(X10,X16,hAPP(c_List_Onth(X10),X290),X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth_Osimps) ).
fof(fact_Plus__eq__empty__conv,axiom,
! [X160,X154,X13,X10] :
( c_Sum__Type_OPlus(X10,X13,X154,X160) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X10,X13),tc_HOL_Obool))
<=> ( X154 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
& X160 = c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Plus__eq__empty__conv) ).
fof(fact_dvd_OatLeastAtMost__singleton__iff,axiom,
! [X18,X38,X39] :
( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X39,X38) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X18),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
<=> ( X39 = X38
& X38 = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastAtMost__singleton__iff) ).
fof(fact_Union__insert,axiom,
! [X160,X39,X10] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X10,tc_HOL_Obool)),X39),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X39),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__insert) ).
fof(fact_Inter__insert,axiom,
! [X160,X39,X10] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X10,tc_HOL_Obool)),X39),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X39),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__insert) ).
fof(fact_zmod__eq__dvd__iff,axiom,
! [X25,X20,X16] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X16,X20) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X20)
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X20),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X16),X25))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__eq__dvd__iff) ).
fof(fact_wf__no__loop,axiom,
! [X196,X10] :
( hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X196),X196) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool))
=> c_Wellfounded_Owf(X10,X196) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__no__loop) ).
fof(fact_add__eq__if,axiom,
! [X42,X97] :
( ( X97 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X42) = X42 )
& ( X97 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X42) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__if) ).
fof(fact_map__upd__nonempty,axiom,
! [X16,X101,X53,X13,X10] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),X53),X101),hAPP(c_Option_Ooption_OSome(X13),X16)) != hAPP(c_COMBK(tc_Option_Ooption(X13),X10),c_Option_Ooption_ONone(X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upd__nonempty) ).
fof(fact_setsum__constant,axiom,
! [X154,X25,X13,X10] :
( class_Rings_Osemiring__1(X10)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X10),hAPP(c_COMBK(X10,X13),X25)),X154) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),hAPP(c_Finite__Set_Ocard(X13),X154))),X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__constant) ).
fof(fact_of__int__le__0__iff,axiom,
! [X73,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Oring__1__class_Oof__int(X10),X73)),c_Groups_Ozero__class_Ozero(X10)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X73),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,
! [X73,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Oring__1__class_Oof__int(X10),X73)),c_Groups_Ozero__class_Ozero(X10)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X73),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,
! [X81,X92,X84,X94] :
( class_Divides_Osemiring__div(X94)
=> c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),c_Divides_Odiv__class_Omod(X94,X92,X81)),X81) = c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92),X81) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__simps_I2_J) ).
fof(fact_mod__diff__right__eq,axiom,
! [X81,X92,X84,X94] :
( class_Divides_Oring__div(X94)
=> c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X84),X92),X81) = c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X84),c_Divides_Odiv__class_Omod(X94,X92,X81)),X81) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__diff__right__eq) ).
fof(fact_mod__mult__right__eq,axiom,
! [X81,X92,X84,X94] :
( class_Divides_Osemiring__div(X94)
=> c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92),X81) = c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),c_Divides_Odiv__class_Omod(X94,X92,X81)),X81) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__right__eq) ).
fof(fact_mod__add__right__eq,axiom,
! [X81,X92,X84,X94] :
( class_Divides_Osemiring__div(X94)
=> c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92),X81) = c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),c_Divides_Odiv__class_Omod(X94,X92,X81)),X81) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__right__eq) ).
fof(fact_predicate1D,axiom,
! [X16,X17,X19,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X19),X17))
=> ( hBOOL(hAPP(X19,X16))
=> hBOOL(hAPP(X17,X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate1D) ).
fof(fact_rev__predicate1D,axiom,
! [X17,X10,X16,X19] :
( hBOOL(hAPP(X19,X16))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X19),X17))
=> hBOOL(hAPP(X17,X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate1D) ).
fof(fact_nat__diff__distrib,axiom,
! [X104,X145] :
( 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__eq(tc_Int_Oint),X145),X104))
=> hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X104),X145)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X104)),hAPP(c_Int_Onat,X145)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__distrib) ).
fof(fact_ivl__disj__un_I14_J,axiom,
! [X165,X162,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X162),X165))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X162),X165)),hAPP(c_SetInterval_Oord__class_OatLeast(X10),X165)) = hAPP(c_SetInterval_Oord__class_OatLeast(X10),X162) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I14_J) ).
fof(fact_le__special_I3_J,axiom,
! [X16,X10] :
( ( class_Int_Onumber__ring(X10)
& class_Rings_Olinordered__idom(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X16)),c_Groups_Ozero__class_Ozero(X10)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X16),c_Int_OPls)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__special_I3_J) ).
fof(fact_less__special_I3_J,axiom,
! [X16,X10] :
( ( class_Int_Onumber__ring(X10)
& class_Rings_Olinordered__idom(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X16)),c_Groups_Ozero__class_Ozero(X10)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16),c_Int_OPls)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__special_I3_J) ).
fof(fact_domIff,axiom,
! [X102,X13,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X39),c_Map_Odom(X10,X13,X102)))
<=> hAPP(X102,X39) != c_Option_Ooption_ONone(X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_domIff) ).
fof(fact_map__fst__zip,axiom,
! [X289,X13,X290,X10] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13)),X289)
=> hAPP(hAPP(c_List_Omap(tc_prod(X10,X13),X10),c_Product__Type_Ofst(X10,X13)),hAPP(hAPP(c_List_Ozip(X10,X13),X290),X289)) = X290 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__fst__zip) ).
fof(fact_map__snd__zip,axiom,
! [X289,X13,X290,X10] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13)),X289)
=> hAPP(hAPP(c_List_Omap(tc_prod(X10,X13),X13),c_Product__Type_Osnd(X10,X13)),hAPP(hAPP(c_List_Ozip(X10,X13),X290),X289)) = X289 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__snd__zip) ).
fof(fact_div__add__self1,axiom,
! [X84,X92,X94] :
( class_Divides_Osemiring__div(X94)
=> ( X92 != c_Groups_Ozero__class_Ozero(X94)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X92),X84)),X92) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),X84),X92)),c_Groups_Oone__class_Oone(X94)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__add__self1) ).
fof(fact_div__add__self2,axiom,
! [X84,X92,X94] :
( class_Divides_Osemiring__div(X94)
=> ( X92 != c_Groups_Ozero__class_Ozero(X94)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92)),X92) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),X84),X92)),c_Groups_Oone__class_Oone(X94)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__add__self2) ).
fof(fact_mod__mult__mult2,axiom,
! [X92,X81,X84,X94] :
( class_Divides_Osemiring__div(X94)
=> c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X81),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X81)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),c_Divides_Odiv__class_Omod(X94,X84,X92)),X81) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__mult2) ).
fof(fact_nat__abs__mult__distrib,axiom,
! [X104,X133] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X133),X104))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X133))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X104))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__abs__mult__distrib) ).
fof(fact_nat__mult__div__cancel1,axiom,
! [X42,X97,X103] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X103))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X103),X97)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X103),X42)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X97),X42) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__div__cancel1) ).
fof(fact_zdiv__zmult2__eq,axiom,
! [X92,X84,X81] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X81))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X92),X81)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),X92)),X81) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zmult2__eq) ).
fof(fact_dom__map__of__conv__image__fst,axiom,
! [X285,X13,X10] : c_Map_Odom(X10,X13,c_Map_Omap__of(X10,X13,X285)) = hAPP(c_Set_Oimage(tc_prod(X10,X13),X10,c_Product__Type_Ofst(X10,X13)),hAPP(c_List_Oset(tc_prod(X10,X13)),X285)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__map__of__conv__image__fst) ).
fof(fact_split__def,axiom,
! [X166,X18,X10,X125,X13] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X13,X125,X10),X18),X166) = hAPP(hAPP(X18,hAPP(c_Product__Type_Ofst(X13,X125),X166)),hAPP(c_Product__Type_Osnd(X13,X125),X166)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__def) ).
fof(fact_split__beta,axiom,
! [X73,X19,X10,X125,X13] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X13,X125,X10),X19),X73) = hAPP(hAPP(X19,hAPP(c_Product__Type_Ofst(X13,X125),X73)),hAPP(c_Product__Type_Osnd(X13,X125),X73)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__beta) ).
fof(fact_prod__case__beta,axiom,
! [X166,X2,X10,X125,X13] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X13,X125,X10),X2),X166) = hAPP(hAPP(X2,hAPP(c_Product__Type_Ofst(X13,X125),X166)),hAPP(c_Product__Type_Osnd(X13,X125),X166)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod__case__beta) ).
fof(fact_append1__eq__conv,axiom,
! [X25,X289,X16,X290,X10] :
( hAPP(hAPP(c_List_Oappend(X10),X290),hAPP(hAPP(c_List_Olist_OCons(X10),X16),c_List_Olist_ONil(X10))) = hAPP(hAPP(c_List_Oappend(X10),X289),hAPP(hAPP(c_List_Olist_OCons(X10),X25),c_List_Olist_ONil(X10)))
<=> ( X290 = X289
& X16 = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append1__eq__conv) ).
fof(fact_dvd__reduce,axiom,
! [X20,X101] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X101),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X101)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X101),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__reduce) ).
fof(fact_hd__drop__conv__nth,axiom,
! [X42,X94,X297] :
( X297 != c_List_Olist_ONil(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)))
=> hAPP(c_List_Ohd(X94),hAPP(hAPP(c_List_Odrop(X94),X42),X297)) = hAPP(hAPP(c_List_Onth(X94),X297),X42) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__drop__conv__nth) ).
fof(fact_abs__add__abs,axiom,
! [X92,X84,X94] :
( class_Groups_Oordered__ab__group__add__abs(X94)
=> hAPP(c_Groups_Oabs__class_Oabs(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),X84)),hAPP(c_Groups_Oabs__class_Oabs(X94),X92))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),X84)),hAPP(c_Groups_Oabs__class_Oabs(X94),X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__add__abs) ).
fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
! [X39,X154,X225,X2,X10] :
( c_Finite__Set_Ofolding__one__idem(X10,X2,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(X225,hAPP(hAPP(c_Set_Oinsert(X10),X39),X154)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,X2),X39),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oeq__fold__idem_H) ).
fof(fact_inf__le1,axiom,
! [X105,X93,X94] :
( class_Lattices_Osemilattice__inf(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),X105)),X93)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__le1) ).
fof(fact_inf__sup__ord_I1_J,axiom,
! [X105,X93,X94] :
( class_Lattices_Olattice(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),X105)),X93)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I1_J) ).
fof(fact_inf__le2,axiom,
! [X105,X93,X94] :
( class_Lattices_Osemilattice__inf(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),X105)),X105)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__le2) ).
fof(fact_inf__sup__ord_I2_J,axiom,
! [X105,X93,X94] :
( class_Lattices_Olattice(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),X105)),X105)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I2_J) ).
fof(fact_min__max_Oinf__le1,axiom,
! [X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X93),X105)),X93)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__le1) ).
fof(fact_min__max_Oinf__le2,axiom,
! [X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X93),X105)),X105)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__le2) ).
fof(fact_expand__Suc,axiom,
! [X144] :
( 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),X144)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_expand__Suc) ).
fof(fact_evalc__evaln,axiom,
! [X44,X45,X81] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X81),X45),X44))
=> ? [X83] : c_Natural_Oevaln(X81,X45,X83,X44) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__evaln) ).
fof(fact_eval__eq,axiom,
! [X53,X54,X18] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X18),X54),X53))
<=> ? [X83] : c_Natural_Oevaln(X18,X54,X83,X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eval__eq) ).
fof(fact_ivl__disj__un_I10_J,axiom,
! [X165,X162,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X162),X165))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X10),X162)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X162,X165)) = hAPP(c_SetInterval_Oord__class_OatMost(X10),X165) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I10_J) ).
fof(fact_ivl__disj__un_I9_J,axiom,
! [X165,X162,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X162),X165))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X10),X162)),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X162,X165)) = hAPP(c_SetInterval_Oord__class_OatMost(X10),X165) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I9_J) ).
fof(fact_ivl__disj__un_I7_J,axiom,
! [X165,X162,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X162),X165))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X10),X162)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X162,X165)) = hAPP(c_SetInterval_Oord__class_OlessThan(X10),X165) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I7_J) ).
fof(fact_minus__dvd__iff,axiom,
! [X25,X16,X10] :
( class_Rings_Ocomm__ring__1(X10)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X16)),X25))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X16),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__dvd__iff) ).
fof(fact_abs__dvd__iff,axiom,
! [X101,X102,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),hAPP(c_Groups_Oabs__class_Oabs(X10),X102)),X101))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X102),X101)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__dvd__iff) ).
fof(fact_abs__le__D1,axiom,
! [X92,X84,X94] :
( class_Groups_Oordered__ab__group__add__abs(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),X84)),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X92)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__le__D1) ).
fof(fact_inf__sup__distrib1,axiom,
! [X104,X105,X93,X94] :
( class_Lattices_Odistrib__lattice(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X105),X104)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),X105)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),X104)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__distrib1) ).
fof(fact_sup__inf__distrib1,axiom,
! [X104,X105,X93,X94] :
( class_Lattices_Odistrib__lattice(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X105),X104)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),X105)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),X104)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__inf__distrib1) ).
fof(fact_min__max_Osup__inf__distrib1,axiom,
! [X104,X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X93),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X105),X104)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X93),X105)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X93),X104)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__inf__distrib1) ).
fof(fact_min__max_Oinf__sup__distrib1,axiom,
! [X104,X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X93),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X105),X104)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X93),X105)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X93),X104)) ),
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,
! [X104,X105,X93,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X93),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X105),X104)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X93),X105)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X93),X104)) ),
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,
! [X138,X140,X139,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X139),X140)),X138) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X139),X138)),X140) ),
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,
! [X81,X92,X84,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92)),X81) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X81)),X92) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(fact_UNIV__option__conv,axiom,
! [X10] : c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X10),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(X10)),c_Option_Ooption_ONone(X10)),hAPP(c_Set_Oimage(X10,tc_Option_Ooption(X10),c_Option_Ooption_OSome(X10)),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__option__conv) ).
fof(fact_id__o,axiom,
! [X1,X10,X13] : hAPP(c_Fun_Ocomp(X13,X13,X10,c_Fun_Oid(X13)),X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__o) ).
fof(fact_length__pos__if__in__set,axiom,
! [X290,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
=> 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(X10)),X290))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__pos__if__in__set) ).
fof(fact_single__valued__rel__pow,axiom,
! [X20,X196,X10] :
( c_Relation_Osingle__valued(X10,X10,X196)
=> c_Relation_Osingle__valued(X10,X10,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X20),X196)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__rel__pow) ).
fof(fact_Random__Sequence_Osingle__def,axiom,
! [X202,X203,X16,X10] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(X10),X16),X203),X202) = 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(X10)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(X10),X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Random__Sequence_Osingle__def) ).
fof(fact_DomainP_Oequations,axiom,
! [X51,X177,X13,X10] :
( hBOOL(hAPP(c_Predicate_ODomainP(X10,X13,X177),X51))
<=> ? [X147] : hBOOL(hAPP(hAPP(X177,X51),X147)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainP_Oequations) ).
fof(fact_inj__eq,axiom,
! [X25,X16,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> ( hAPP(X2,X16) = hAPP(X2,X25)
<=> X16 = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__eq) ).
fof(fact_injD,axiom,
! [X25,X16,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> ( hAPP(X2,X16) = hAPP(X2,X25)
=> X16 = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_injD) ).
fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
! [X39,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(hAPP(c_Set_Oinsert(X10),X39),X154)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omin(X10)),X39),X154) ) ),
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,
! [X39,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_Set_Oinsert(X10),X39),X154)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omax(X10)),X39),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oeq__fold__idem_H) ).
fof(fact_foldl__Nil,axiom,
! [X39,X2,X13,X10] : hAPP(c_List_Ofoldl(X10,X13,X2,X39),c_List_Olist_ONil(X13)) = X39,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__Nil) ).
fof(fact_list_Osimps_I4_J,axiom,
! [X37,X12,X13,X10] : hAPP(c_List_Olist_Olist__case(X10,X13,X12,X37),c_List_Olist_ONil(X13)) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I4_J) ).
fof(fact_o__id,axiom,
! [X2,X13,X10] : hAPP(c_Fun_Ocomp(X10,X13,X10,X2),c_Fun_Oid(X10)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__id) ).
fof(fact_option_Osimps_I4_J,axiom,
! [X37,X12,X13,X10] : hAPP(c_Option_Ooption_Ooption__case(X10,X13,X12,X37),c_Option_Ooption_ONone(X13)) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Osimps_I4_J) ).
fof(fact_add__nonneg__eq__0__iff,axiom,
! [X25,X16,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X16))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X25))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X16),X25) = c_Groups_Ozero__class_Ozero(X10)
<=> ( X16 = c_Groups_Ozero__class_Ozero(X10)
& X25 = c_Groups_Ozero__class_Ozero(X10) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
fof(conj_0,conjecture,
c_Hoare__Mirabelle_Otriple__valid(t_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_diff__add__assoc,axiom,
! [X120,X119,X103] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X103),X119))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X120),X119)),X103) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X120),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X119),X103)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__assoc) ).
fof(fact_diff__diff__right,axiom,
! [X120,X119,X103] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X103),X119))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X120),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X119),X103)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X120),X103)),X119) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__right) ).
fof(fact_add__diff__assoc,axiom,
! [X120,X119,X103] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X103),X119))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X120),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X119),X103)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X120),X119)),X103) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__assoc) ).
fof(fact_compl__mono,axiom,
! [X105,X93,X94] :
( class_Lattices_Oboolean__algebra(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X105))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X105)),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X93))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__mono) ).
fof(fact_le__imp__neg__le,axiom,
! [X92,X84,X94] :
( class_Groups_Oordered__ab__group__add(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X92)),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X84))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__neg__le) ).
fof(fact_one__less__nat__eq,axiom,
! [X73] :
( 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,X73)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X73)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__nat__eq) ).
fof(fact_mod__less__eq__dividend,axiom,
! [X42,X97] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X97,X42)),X97)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__less__eq__dividend) ).
fof(fact_greaterThan__Suc,axiom,
! [X101] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X101)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X101)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X101)),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,
! [X149,X167,X93,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),X167)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),X149)) = hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X167),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
fof(fact_power__add,axiom,
! [X42,X97,X84,X94] :
( class_Groups_Omonoid__mult(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X42)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X97)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__add) ).
fof(fact_fold1__eq__fold__idem,axiom,
! [X39,X154,X10] :
( class_Lattices_Oab__semigroup__idem__mult(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),hAPP(hAPP(c_Set_Oinsert(X10),X39),X154)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Groups_Otimes__class_Otimes(X10)),X39),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__eq__fold__idem) ).
fof(fact_add__scale__eq__noteq,axiom,
! [X112,X81,X92,X84,X143,X94] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X94)
=> ( X143 != c_Groups_Ozero__class_Ozero(X94)
=> ( ( X84 = X92
& X81 != X112 )
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X143),X81)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X92),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X143),X112)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).
fof(fact_some__eq__trivial,axiom,
! [X16,X10] : c_Hilbert__Choice_OEps(X10,hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X16)) = X16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_some__eq__trivial) ).
fof(fact_the__eq__trivial,axiom,
! [X39,X10] : c_HOL_OThe(X10,hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X39)) = X39,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__eq__trivial) ).
fof(fact_diff__less__Suc,axiom,
! [X42,X97] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42)),hAPP(c_Nat_OSuc,X97))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__Suc) ).
fof(fact_less__add__Suc1,axiom,
! [X97,X120] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X120),X97)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
fof(fact_less__add__Suc2,axiom,
! [X97,X120] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X120)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
fof(fact_ivl__disj__int_I16_J,axiom,
! [X165,X102,X162,X10] :
( class_Orderings_Oorder(X10)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X162,X102)),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X102,X165)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I16_J) ).
fof(fact_ivl__disj__int_I12_J,axiom,
! [X165,X102,X162,X10] :
( class_Orderings_Oorder(X10)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X162,X102)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X102,X165)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I12_J) ).
fof(fact_ivl__disj__int_I14_J,axiom,
! [X165,X102,X162,X10] :
( class_Orderings_Oorder(X10)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X162,X102)),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X102,X165)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I14_J) ).
fof(fact_ivl__disj__int_I10_J,axiom,
! [X165,X102,X162,X10] :
( class_Orderings_Oorder(X10)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X162,X102)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X102,X165)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I10_J) ).
fof(fact_ivl__disj__int_I13_J,axiom,
! [X165,X102,X162,X10] :
( class_Orderings_Oorder(X10)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X162,X102)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X102,X165)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I13_J) ).
fof(fact_empty__subsetI,axiom,
! [X154,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),X154)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__subsetI) ).
fof(fact_equiv__comp__eq,axiom,
! [X177,X154,X10] :
( c_Equiv__Relations_Oequiv(X10,X154,X177)
=> hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),hAPP(c_Relation_Oconverse(X10,X10),X177)),X177) = X177 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__comp__eq) ).
fof(fact_evaln__evalc,axiom,
! [X44,X42,X45,X81] :
( c_Natural_Oevaln(X81,X45,X42,X44)
=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(X81),X45),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__evalc) ).
fof(fact_evaln_Oequations_I2_J,axiom,
! [X72,X50,X52,X51] : c_Natural_Oevaln(c_Com_Ocom_OAss(X51,X52),X50,X72,hAPP(hAPP(hAPP(c_Natural_Oupdate,X50),X51),hAPP(X52,X50))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I2_J) ).
fof(fact_evaln_OAssign,axiom,
! [X20,X54,X39,X48] : c_Natural_Oevaln(c_Com_Ocom_OAss(X48,X39),X54,X20,hAPP(hAPP(hAPP(c_Natural_Oupdate,X54),X48),hAPP(X39,X54))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OAssign) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
! [X105,X93] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X93))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X105))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(X93,X105))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).
fof(fact_subset__insertI,axiom,
! [X39,X160,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),hAPP(hAPP(c_Set_Oinsert(X10),X39),X160))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI) ).
fof(fact_zdiff__zmod__right,axiom,
! [X97,X105,X93] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X93),c_Divides_Odiv__class_Omod(tc_Int_Oint,X105,X97)),X97) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X93),X105),X97),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmod__right) ).
fof(fact_zmod__simps_I3_J,axiom,
! [X81,X92,X84] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),c_Divides_Odiv__class_Omod(tc_Int_Oint,X92,X81)),X81) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),X92),X81),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__simps_I3_J) ).
fof(fact_zmod__zmult1__eq,axiom,
! [X81,X92,X84] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),X92),X81) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X84),c_Divides_Odiv__class_Omod(tc_Int_Oint,X92,X81)),X81),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zmult1__eq) ).
fof(fact_ivl__disj__un_I8_J,axiom,
! [X165,X162,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X162),X165))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X10),X162)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X162),X165)) = hAPP(c_SetInterval_Oord__class_OlessThan(X10),X165) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I8_J) ).
fof(fact_atLeastAtMostSuc__conv,axiom,
! [X20,X102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),hAPP(c_Nat_OSuc,X20)))
=> c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X102,hAPP(c_Nat_OSuc,X20)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X102,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMostSuc__conv) ).
fof(fact_finite__option__UNIV,axiom,
! [X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X10)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X10),tc_HOL_Obool))))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__option__UNIV) ).
fof(fact_less__imp__of__nat__less,axiom,
! [X42,X97,X94] :
( class_Rings_Olinordered__semidom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),X97)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),X42))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__of__nat__less) ).
fof(fact_Int__atLeastAtMostR2,axiom,
! [X141,X18,X39,X10] :
( class_Orderings_Olinorder(X10)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X10),X39)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X18,X141)) = c_SetInterval_Oord__class_OatLeastAtMost(X10,hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X39),X18),X141) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__atLeastAtMostR2) ).
fof(fact_Int__atLeastAtMostR1,axiom,
! [X141,X18,X38,X10] :
( class_Orderings_Olinorder(X10)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X10),X38)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X18,X141)) = c_SetInterval_Oord__class_OatLeastAtMost(X10,X18,hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X38),X141)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__atLeastAtMostR1) ).
fof(fact_zless__nat__eq__int__zless,axiom,
! [X73,X102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),hAPP(c_Int_Onat,X73)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X102)),X73)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__nat__eq__int__zless) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
! [X105,X93] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X93))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X105))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X93)),hAPP(c_Int_Onat,X105)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(X93,X105)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J) ).
fof(fact_drop__take,axiom,
! [X297,X97,X42,X94] : hAPP(hAPP(c_List_Odrop(X94),X42),hAPP(hAPP(c_List_Otake(X94),X97),X297)) = hAPP(hAPP(c_List_Otake(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42)),hAPP(hAPP(c_List_Odrop(X94),X42),X297)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__take) ).
fof(fact_rel__comp__empty2,axiom,
! [X196,X13,X125,X10] : hAPP(hAPP(c_Relation_Orel__comp(X10,X125,X13),X196),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X125,X13),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__empty2) ).
fof(fact_curry__split,axiom,
! [X2,X125,X13,X10] : c_Product__Type_Ocurry(X10,X13,X125,hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,X125),X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curry__split) ).
fof(fact_mod__pos__pos__1__number__of,axiom,
! [X133] :
( 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),X133)))
=> 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),X133)) = 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),X133))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__pos__1__number__of) ).
fof(fact_mod__mult__distrib,axiom,
! [X103,X42,X97] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X97,X42)),X103) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X97),X103),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),X103)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__distrib) ).
fof(fact_dvd__power,axiom,
! [X93,X42,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X42))
| X93 = c_Groups_Oone__class_Oone(X94) )
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X93),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),X42))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__power) ).
fof(fact_dvd__mult2,axiom,
! [X81,X92,X84,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X84),X92))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X84),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X81))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult2) ).
fof(fact_dvd__mult,axiom,
! [X92,X81,X84,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X84),X81))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X84),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X81))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult) ).
fof(fact_le__supI1,axiom,
! [X92,X84,X93,X94] :
( class_Lattices_Osemilattice__sup(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X84),X92))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__supI1) ).
fof(fact_le__supI2,axiom,
! [X84,X92,X93,X94] :
( class_Lattices_Osemilattice__sup(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X84),X92))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__supI2) ).
fof(fact_min__max_Ole__supI1,axiom,
! [X92,X84,X93,X94] :
( class_Orderings_Olinorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X84),X92))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__supI1) ).
fof(fact_min__max_Ole__supI2,axiom,
! [X84,X92,X93,X94] :
( class_Orderings_Olinorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X84),X92))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__supI2) ).
fof(fact_less__supI1,axiom,
! [X92,X84,X93,X94] :
( class_Lattices_Osemilattice__sup(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X84),X92))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__supI1) ).
fof(fact_less__supI2,axiom,
! [X84,X92,X93,X94] :
( class_Lattices_Osemilattice__sup(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X84),X92))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__supI2) ).
fof(fact_min__max_Oless__supI1,axiom,
! [X92,X84,X93,X94] :
( class_Orderings_Olinorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X84),X92))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oless__supI1) ).
fof(fact_min__max_Oless__supI2,axiom,
! [X84,X92,X93,X94] :
( class_Orderings_Olinorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X84),X92))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oless__supI2) ).
fof(fact_negative__zle__0,axiom,
! [X42] : 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),X42))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__zle__0) ).
fof(fact_transpose__empty,axiom,
! [X290,X10] :
( c_List_Otranspose(X10,X290) = c_List_Olist_ONil(tc_List_Olist(X10))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X3),hAPP(c_List_Oset(tc_List_Olist(X10)),X290)))
=> X3 = c_List_Olist_ONil(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__empty) ).
fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
! [X101,X2,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> ( hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X10)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X101)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X101)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__lb__Suc0__0__upt) ).
fof(fact_UN__empty2,axiom,
! [X154,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13,tc_fun(X10,tc_HOL_Obool)),X154),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__empty2) ).
fof(fact_less__trans__Suc,axiom,
! [X103,X119,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),X119))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X119),X103))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X120)),X103)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
fof(fact_div__pos__pos__1__number__of,axiom,
! [X133] :
( 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),X133)))
=> 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),X133)) = 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),X133))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__pos__pos__1__number__of) ).
fof(fact_pos__mod__sign,axiom,
! [X84,X92] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X92))
=> 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,X84,X92))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__mod__sign) ).
fof(fact_greaterThanLessThan__upto,axiom,
! [X163,X113] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X113,X163) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X113),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X163),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,
! [X290,X16,X2,X10,X13] : hAPP(hAPP(c_List_Omap(X13,X10),X2),hAPP(hAPP(c_List_Olist_OCons(X13),X16),X290)) = hAPP(hAPP(c_List_Olist_OCons(X10),hAPP(X2,X16)),hAPP(hAPP(c_List_Omap(X13,X10),X2),X290)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map_Osimps_I2_J) ).
fof(fact_power__one__over,axiom,
! [X42,X84,X94] :
( class_Fields_Ofield__inverse__zero(X94)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),c_Groups_Oone__class_Oone(X94)),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42)) = hAPP(hAPP(c_Power_Opower__class_Opower(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),c_Groups_Oone__class_Oone(X94)),X84)),X42) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one__over) ).
fof(fact_le__imp__0__less,axiom,
! [X104] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X104))
=> 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)),X104))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__0__less) ).
fof(fact_insertI2,axiom,
! [X38,X160,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X39),X160))
=> hBOOL(hAPP(hAPP(c_member(X10),X39),hAPP(hAPP(c_Set_Oinsert(X10),X38),X160))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI2) ).
fof(fact_le__minus__iff,axiom,
! [X38,X39,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X38)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X38),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X39))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__minus__iff) ).
fof(fact_less__minus__iff,axiom,
! [X38,X39,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X38)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X38),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X39))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__minus__iff) ).
fof(fact_last__list__update,axiom,
! [X93,X103,X94,X297] :
( X297 != c_List_Olist_ONil(X94)
=> ( ( X103 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
=> c_List_Olast(X94,hAPP(hAPP(c_List_Olist__update(X94,X297),X103),X93)) = X93 )
& ( X103 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
=> c_List_Olast(X94,hAPP(hAPP(c_List_Olist__update(X94,X297),X103),X93)) = c_List_Olast(X94,X297) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__list__update) ).
fof(fact_sgn__less,axiom,
! [X39,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Osgn__class_Osgn(X10,X39)),c_Groups_Ozero__class_Ozero(X10)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),c_Groups_Ozero__class_Ozero(X10))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__less) ).
fof(fact_take__butlast,axiom,
! [X297,X94,X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)))
=> hAPP(hAPP(c_List_Otake(X94),X42),c_List_Obutlast(X94,X297)) = hAPP(hAPP(c_List_Otake(X94),X42),X297) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__butlast) ).
fof(fact_last__drop,axiom,
! [X297,X94,X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)))
=> c_List_Olast(X94,hAPP(hAPP(c_List_Odrop(X94),X42),X297)) = c_List_Olast(X94,X297) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__drop) ).
fof(fact_prod_Osimps_I2_J,axiom,
! [X38,X39,X12,X10,X125,X13] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X13,X125,X10),X12),hAPP(hAPP(c_Product__Type_OPair(X13,X125),X39),X38)) = hAPP(hAPP(X12,X39),X38),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod_Osimps_I2_J) ).
fof(fact_split__conv,axiom,
! [X38,X39,X2,X10,X125,X13] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X13,X125,X10),X2),hAPP(hAPP(c_Product__Type_OPair(X13,X125),X39),X38)) = hAPP(hAPP(X2,X39),X38),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__conv) ).
fof(fact_min__max_OSup__fin_Oin__idem,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X16),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X154)) = c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X154) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oin__idem) ).
fof(fact_min__max_OInf__fin_Oin__idem,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X16),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X154)) = c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X154) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oin__idem) ).
fof(fact_atLeastLessThan__eq__iff,axiom,
! [X141,X18,X38,X39,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),X38))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),X141))
=> ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X39),X38) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X18),X141)
<=> ( X39 = X18
& X38 = X141 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__eq__iff) ).
fof(fact_atLeastLessThan__inj_I1_J,axiom,
! [X141,X18,X38,X39,X10] :
( class_Orderings_Olinorder(X10)
=> ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X39),X38) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X18),X141)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),X38))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),X141))
=> X39 = X18 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I1_J) ).
fof(fact_atLeastLessThan__inj_I2_J,axiom,
! [X141,X18,X38,X39,X10] :
( class_Orderings_Olinorder(X10)
=> ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X39),X38) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X18),X141)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),X38))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),X141))
=> X38 = X141 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I2_J) ).
fof(fact_posDivAlg__correct,axiom,
! [X92,X84] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X92))
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(X84,X92),c_Divides_OposDivAlg(X84,X92))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg__correct) ).
fof(fact_nth__list__update__neq,axiom,
! [X93,X297,X94,X119,X120] :
( X120 != X119
=> hAPP(hAPP(c_List_Onth(X94),hAPP(hAPP(c_List_Olist__update(X94,X297),X120),X93)),X119) = hAPP(hAPP(c_List_Onth(X94),X297),X119) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__list__update__neq) ).
fof(fact_ivl__disj__int_I9_J,axiom,
! [X165,X102,X162,X10] :
( class_Orderings_Oorder(X10)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X162,X102)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X102),X165)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I9_J) ).
fof(fact_converse__inv__image,axiom,
! [X2,X196,X13,X10] : hAPP(c_Relation_Oconverse(X10,X10),hAPP(hAPP(c_Relation_Oinv__image(X13,X10),X196),X2)) = hAPP(hAPP(c_Relation_Oinv__image(X13,X10),hAPP(c_Relation_Oconverse(X13,X13),X196)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__inv__image) ).
fof(fact_Min_Oeq__fold__idem_H,axiom,
! [X39,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> c_Big__Operators_Olinorder__class_OMin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X39),X154)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omin(X10)),X39),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oeq__fold__idem_H) ).
fof(fact_Max_Oeq__fold__idem_H,axiom,
! [X39,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> c_Big__Operators_Olinorder__class_OMax(X10,hAPP(hAPP(c_Set_Oinsert(X10),X39),X154)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omax(X10)),X39),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oeq__fold__idem_H) ).
fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
! [X39,X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X39),X154)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__inf__class_Oinf(X10)),X39),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oeq__fold__idem_H) ).
fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
! [X39,X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X39),X154)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__sup__class_Osup(X10)),X39),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oeq__fold__idem_H) ).
fof(fact_log_Osimps,axiom,
! [X120,X92] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X92),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X120),X92)) )
=> c_Random_Olog(X92,X120) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
& ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X92),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X120),X92)) )
=> c_Random_Olog(X92,X120) = 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(X92,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X120),X92))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_log_Osimps) ).
fof(fact_Ints__minus,axiom,
! [X39,X10] :
( class_Rings_Oring__1(X10)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),c_Int_Oring__1__class_OInts(X10)))
=> hBOOL(hAPP(hAPP(c_member(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X39)),c_Int_Oring__1__class_OInts(X10))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__minus) ).
fof(fact_bot__empty__eq,axiom,
! [X16,X10] :
( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),X16))
<=> hBOOL(hAPP(hAPP(c_member(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__empty__eq) ).
fof(fact_abs__div__pos,axiom,
! [X93,X105,X94] :
( class_Fields_Olinordered__field__inverse__zero(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X105))
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),X93)),X105) = hAPP(c_Groups_Oabs__class_Oabs(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X93),X105)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__div__pos) ).
fof(fact_abs__mult__pos,axiom,
! [X105,X93,X94] :
( class_Rings_Olinordered__idom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X93))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),X105)),X93) = hAPP(c_Groups_Oabs__class_Oabs(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X105),X93)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult__pos) ).
fof(fact_Pow__empty,axiom,
! [X10] : hAPP(c_Set_OPow(X10),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__empty) ).
fof(fact_setsum__shift__lb__Suc0__0,axiom,
! [X101,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)),X101)) = 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),X101)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__lb__Suc0__0) ).
fof(fact_inf__apply,axiom,
! [X16,X1,X2,X13,X10] :
( class_Lattices_Olattice(X10)
=> hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13,X10)),X2),X1),X16) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),hAPP(X2,X16)),hAPP(X1,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__apply) ).
fof(fact_inf__fun__def,axiom,
! [X16,X1,X2,X13,X10] :
( class_Lattices_Olattice(X10)
=> hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13,X10)),X2),X1),X16) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),hAPP(X2,X16)),hAPP(X1,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__fun__def) ).
fof(fact_sup__fun__def,axiom,
! [X16,X1,X2,X13,X10] :
( class_Lattices_Olattice(X10)
=> hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13,X10)),X2),X1),X16) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),hAPP(X2,X16)),hAPP(X1,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__fun__def) ).
fof(fact_sup__apply,axiom,
! [X16,X1,X2,X13,X10] :
( class_Lattices_Olattice(X10)
=> hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13,X10)),X2),X1),X16) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),hAPP(X2,X16)),hAPP(X1,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__apply) ).
fof(fact_fun__diff__def,axiom,
! [X16,X160,X154,X13,X10] :
( class_Groups_Ominus(X10)
=> hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13,X10)),X154),X160),X16) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),hAPP(X154,X16)),hAPP(X160,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__diff__def) ).
fof(fact_minus__apply,axiom,
! [X16,X160,X154,X13,X10] :
( class_Groups_Ominus(X10)
=> hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13,X10)),X154),X160),X16) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),hAPP(X154,X16)),hAPP(X160,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__apply) ).
fof(fact_negDivAlg__correct,axiom,
! [X92,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),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X92))
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(X84,X92),c_Divides_OnegDivAlg(X84,X92))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg__correct) ).
fof(fact_neg__mod__bound,axiom,
! [X84,X92] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X92),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X92),c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X92))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__mod__bound) ).
fof(fact_folding_Oempty,axiom,
! [X225,X2,X13,X10] :
( c_Finite__Set_Ofolding(X10,X13,X2,X225)
=> hAPP(X225,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) = c_Fun_Oid(X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Oempty) ).
fof(fact_less__eq__code__numeral__def,axiom,
! [X102,X20] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X20),X102))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X20)),hAPP(c_Code__Numeral_Onat__of,X102))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__code__numeral__def) ).
fof(fact_less__eq__code__numeral__code,axiom,
! [X102,X20] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X20)),hAPP(c_Code__Numeral_Oof__nat,X102)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20),X102)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__code__numeral__code) ).
fof(fact_Suc__le__mono,axiom,
! [X102,X20] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)),hAPP(c_Nat_OSuc,X102)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20),X102)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
fof(fact_less__code__numeral__def,axiom,
! [X102,X20] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X20),X102))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X20)),hAPP(c_Code__Numeral_Onat__of,X102))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__code__numeral__def) ).
fof(fact_less__code__numeral__code,axiom,
! [X102,X20] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X20)),hAPP(c_Code__Numeral_Oof__nat,X102)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X102)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__code__numeral__code) ).
fof(fact_Suc__less__eq,axiom,
! [X20,X102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X102)),hAPP(c_Nat_OSuc,X20)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
fof(fact_Suc__less__SucD,axiom,
! [X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X97)),hAPP(c_Nat_OSuc,X42)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
fof(fact_nth__take,axiom,
! [X297,X94,X42,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),X42))
=> hAPP(hAPP(c_List_Onth(X94),hAPP(hAPP(c_List_Otake(X94),X42),X297)),X120) = hAPP(hAPP(c_List_Onth(X94),X297),X120) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__take) ).
fof(fact_Diff__disjoint,axiom,
! [X160,X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X160),X154)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__disjoint) ).
fof(fact_rev__eq__Cons__iff,axiom,
! [X289,X25,X290,X10] :
( hAPP(c_List_Orev(X10),X290) = hAPP(hAPP(c_List_Olist_OCons(X10),X25),X289)
<=> X290 = hAPP(hAPP(c_List_Oappend(X10),hAPP(c_List_Orev(X10),X289)),hAPP(hAPP(c_List_Olist_OCons(X10),X25),c_List_Olist_ONil(X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__eq__Cons__iff) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
! [X42,X93] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X93))
=> 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),X93),X42))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
fof(fact_diff__le__self,axiom,
! [X42,X97] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42)),X97)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__self) ).
fof(fact_div__le__dividend,axiom,
! [X42,X97] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X97),X42)),X97)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__le__dividend) ).
fof(fact_ivl__disj__un_I2_J,axiom,
! [X165,X10] :
( class_Orderings_Olinorder(X10)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X10),X165)),hAPP(hAPP(c_Set_Oinsert(X10),X165),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(X10),X165) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I2_J) ).
fof(fact_Min__le,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Big__Operators_Olinorder__class_OMin(X10,X154)),X16)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min__le) ).
fof(fact_zpower__zadd__distrib,axiom,
! [X104,X105,X93] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X93),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X105),X104)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X93),X105)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X93),X104)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__zadd__distrib) ).
fof(fact_zdiff__zmult__distrib2,axiom,
! [X135,X136,X133] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X133),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X136),X135)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X133),X136)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X133),X135)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib2) ).
fof(fact_zadd__zmult__distrib2,axiom,
! [X135,X136,X133] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X133),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X136),X135)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X133),X136)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X133),X135)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).
fof(fact_diff__mult__distrib2,axiom,
! [X42,X97,X103] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X103),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X103),X97)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X103),X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).
fof(fact_add__mult__distrib2,axiom,
! [X42,X97,X103] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X103),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X42)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X103),X97)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X103),X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).
fof(fact_diff__commute,axiom,
! [X103,X119,X120] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X120),X119)),X103) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X120),X103)),X119),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__commute) ).
fof(fact_neg__0__le__iff__le,axiom,
! [X39,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X39)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),c_Groups_Ozero__class_Ozero(X10))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__le__iff__le) ).
fof(fact_neg__0__less__iff__less,axiom,
! [X39,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X39)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),c_Groups_Ozero__class_Ozero(X10))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__less__iff__less) ).
fof(fact_WT_Oequations_I8_J,axiom,
! [X50,X51,X52] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(X52,X51,X50)))
<=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X51))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I8_J) ).
fof(fact_WTs__elim__cases_I8_J,axiom,
! [X39,X19,X48] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(X48,X19,X39)))
=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X19))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WTs__elim__cases_I8_J) ).
fof(fact_dvd__trans,axiom,
! [X81,X92,X84,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X84),X92))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X92),X81))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X84),X81)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__trans) ).
fof(fact_order__trans,axiom,
! [X104,X105,X93,X94] :
( class_Orderings_Opreorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X105))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X105),X104))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X104)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__trans) ).
fof(fact_xt1_I6_J,axiom,
! [X104,X93,X105,X94] :
( class_Orderings_Oorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X105),X93))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X104),X105))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X104),X93)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
fof(fact_order__less__le__trans,axiom,
! [X104,X105,X93,X94] :
( class_Orderings_Opreorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X105))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X105),X104))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X104)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
fof(fact_order__le__less__trans,axiom,
! [X104,X105,X93,X94] :
( class_Orderings_Opreorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X105))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X105),X104))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X104)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
fof(fact_order__less__trans,axiom,
! [X104,X105,X93,X94] :
( class_Orderings_Opreorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X105))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X105),X104))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X104)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__trans) ).
fof(fact_xt1_I7_J,axiom,
! [X104,X93,X105,X94] :
( class_Orderings_Oorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X105),X93))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X104),X105))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X104),X93)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
fof(fact_xt1_I8_J,axiom,
! [X104,X93,X105,X94] :
( class_Orderings_Oorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X105),X93))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X104),X105))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X104),X93)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
fof(fact_xt1_I10_J,axiom,
! [X104,X93,X105,X94] :
( class_Orderings_Oorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X105),X93))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X104),X105))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X104),X93)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
fof(fact_divmod__int__rel__0,axiom,
! [X92] :
( X92 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X92),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,
! [X92,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)),X92))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X92) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X84,X92)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__pos) ).
fof(fact_diff__eq__diff__less__eq,axiom,
! [X141,X18,X38,X39,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X39),X38) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X18),X141)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),X38))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X18),X141)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__less__eq) ).
fof(fact_diff__eq__diff__less,axiom,
! [X141,X18,X38,X39,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X39),X38) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X18),X141)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),X38))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),X141)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__less) ).
fof(fact_eq__diff__iff,axiom,
! [X20,X102,X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X101),X102))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X101),X20))
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X102),X101) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20),X101)
<=> X102 = X20 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__diff__iff) ).
fof(fact_uminus__dvd__conv_I1_J,axiom,
! [X53,X141] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X141),X53))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X141)),X53)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_uminus__dvd__conv_I1_J) ).
fof(fact_Sigma__empty2,axiom,
! [X154,X13,X10] : hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X154),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X13),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,
! [X84,X97,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X97),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X97)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),c_Groups_Oone__class_Oone(X94))),X97) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(fact_div__pos__pos,axiom,
! [X92,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)),X92))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),X92) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X84,X92)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__pos__pos) ).
fof(fact_ivl__disj__int_I15_J,axiom,
! [X165,X102,X162,X10] :
( class_Orderings_Oorder(X10)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X162),X102)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X102,X165)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I15_J) ).
fof(fact_of__int__0__le__iff,axiom,
! [X73,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Oring__1__class_Oof__int(X10),X73)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__0__le__iff) ).
fof(fact_of__int__0__less__iff,axiom,
! [X73,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Oring__1__class_Oof__int(X10),X73)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__0__less__iff) ).
fof(fact_of__nat__0__less__iff,axiom,
! [X20,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),X20)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__0__less__iff) ).
fof(fact_com_Osize_I5_J,axiom,
! [X55,X56,X29] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X29,X56,X55)) = 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(X56)),c_Com_Ocom_Ocom__size(X55))),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,
! [X39,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Groups_Oabs__class_Oabs(X10),X39)),c_Groups_Ozero__class_Ozero(X10)))
<=> X39 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__le__zero__iff) ).
fof(fact_dvd__imp__le__int,axiom,
! [X112,X120] :
( X120 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X112),X120))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X112)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X120))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__imp__le__int) ).
fof(fact_mod__neg__pos,axiom,
! [X92,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),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X92))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X92) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X84,X92)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__neg__pos) ).
fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X16),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X154)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oinsert__idem) ).
fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X16),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X154)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oinsert__idem) ).
fof(fact_dvd__div__mult__self,axiom,
! [X92,X84,X94] :
( class_Divides_Osemiring__div(X94)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X84),X92))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),X92),X84)),X84) = X92 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__div__mult__self) ).
fof(fact_of__nat__diff,axiom,
! [X97,X42,X94] :
( class_Rings_Oring__1(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),X97))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),X97)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__diff) ).
fof(fact_div__neg__pos,axiom,
! [X92,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),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X92))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),X92) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X84,X92)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__neg__pos) ).
fof(fact_finite__insert,axiom,
! [X154,X39,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(hAPP(c_Set_Oinsert(X10),X39),X154)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__insert) ).
fof(fact_inf__Inf__fold__inf,axiom,
! [X160,X154,X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X160),c_Complete__Lattice_OInf__class_OInf(X10,X154)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__inf__class_Oinf(X10)),X160),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Inf__fold__inf) ).
fof(fact_sup__Sup__fold__sup,axiom,
! [X160,X154,X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X160),c_Complete__Lattice_OSup__class_OSup(X10,X154)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__sup__class_Osup(X10)),X160),X154) ) ),
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,
! [X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X154)),X154) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__disjoint2) ).
fof(fact_Compl__partition2,axiom,
! [X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X154)),X154) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__partition2) ).
fof(fact_UNIV__Plus__UNIV,axiom,
! [X13,X10] : c_Sum__Type_OPlus(X10,X13,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X10,X13),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__Plus__UNIV) ).
fof(fact_ivl__disj__int_I7_J,axiom,
! [X165,X162,X10] :
( class_Orderings_Oorder(X10)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X162,X165)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),X165)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I7_J) ).
fof(fact_ivl__disj__int_I5_J,axiom,
! [X165,X162,X10] :
( class_Orderings_Oorder(X10)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X162,X165)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),X165)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I5_J) ).
fof(fact_ivl__disj__int_I6_J,axiom,
! [X165,X162,X10] :
( class_Orderings_Oorder(X10)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X162,X165)),hAPP(c_SetInterval_Oord__class_OatLeast(X10),X165)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I6_J) ).
fof(fact_le__special_I1_J,axiom,
! [X25,X10] :
( ( class_Int_Onumber__ring(X10)
& class_Rings_Olinordered__idom(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X25)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__special_I1_J) ).
fof(fact_less__special_I1_J,axiom,
! [X25,X10] :
( ( class_Int_Onumber__ring(X10)
& class_Rings_Olinordered__idom(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X25)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__special_I1_J) ).
fof(fact_finite__Domain,axiom,
! [X177,X13,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10,X13)),X177))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Relation_ODomain(X10,X13),X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Domain) ).
fof(fact_finite__Range,axiom,
! [X177,X13,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10,X13)),X177))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X13),hAPP(c_Relation_ORange(X10,X13),X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Range) ).
fof(fact_fold1Set__nonempty,axiom,
! [X16,X154,X2,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X10,X2,X154),X16))
=> X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1Set__nonempty) ).
fof(fact_Nitpick_Oint__gcd__def,axiom,
! [X105,X93] : hAPP(hAPP(c_Nitpick_Oint__gcd,X93),X105) = 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),X93)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X105)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Oint__gcd__def) ).
fof(fact_drop__map,axiom,
! [X290,X2,X13,X20,X10] : hAPP(hAPP(c_List_Odrop(X10),X20),hAPP(hAPP(c_List_Omap(X13,X10),X2),X290)) = hAPP(hAPP(c_List_Omap(X13,X10),X2),hAPP(hAPP(c_List_Odrop(X13),X20),X290)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__map) ).
fof(fact_take__map,axiom,
! [X290,X2,X13,X20,X10] : hAPP(hAPP(c_List_Otake(X10),X20),hAPP(hAPP(c_List_Omap(X13,X10),X2),X290)) = hAPP(hAPP(c_List_Omap(X13,X10),X2),hAPP(hAPP(c_List_Otake(X13),X20),X290)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__map) ).
fof(fact_filter__append,axiom,
! [X289,X290,X19,X10] : hAPP(c_List_Ofilter(X10,X19),hAPP(hAPP(c_List_Oappend(X10),X290),X289)) = hAPP(hAPP(c_List_Oappend(X10),hAPP(c_List_Ofilter(X10,X19),X290)),hAPP(c_List_Ofilter(X10,X19),X289)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__append) ).
fof(fact_wf__acc__iff,axiom,
! [X177,X10] :
( c_Wellfounded_Owf(X10,X177)
<=> ! [X3] : hBOOL(hAPP(hAPP(c_member(X10),X3),c_Wellfounded_Oacc(X10,X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__acc__iff) ).
fof(fact_minus__Min__eq__Max,axiom,
! [X216,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X216))
=> ( X216 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(c_Groups_Ouminus__class_Ouminus(X10),c_Big__Operators_Olinorder__class_OMin(X10,X216)) = c_Big__Operators_Olinorder__class_OMax(X10,hAPP(c_Set_Oimage(X10,X10,c_Groups_Ouminus__class_Ouminus(X10)),X216)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__Min__eq__Max) ).
fof(fact_minus__Max__eq__Min,axiom,
! [X216,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X216))
=> ( X216 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(c_Groups_Ouminus__class_Ouminus(X10),c_Big__Operators_Olinorder__class_OMax(X10,X216)) = c_Big__Operators_Olinorder__class_OMin(X10,hAPP(c_Set_Oimage(X10,X10,c_Groups_Ouminus__class_Ouminus(X10)),X216)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__Max__eq__Min) ).
fof(fact_finite__UnionD,axiom,
! [X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X154)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X10,tc_HOL_Obool)),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UnionD) ).
fof(fact_Suc__times__mod__eq,axiom,
! [X97,X103] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X103))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X103),X97)),X103) = 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,
! [X39,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),c_Groups_Osgn__class_Osgn(X10,X39)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X39)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__greater) ).
fof(fact_dvd__neg__div,axiom,
! [X93,X105,X94] :
( class_Divides_Oring__div(X94)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X105),X93))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X93)),X105) = hAPP(c_Groups_Ouminus__class_Ouminus(X94),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),X93),X105)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__neg__div) ).
fof(fact_mod__mult__mult1,axiom,
! [X92,X84,X81,X94] :
( class_Divides_Osemiring__div(X94)
=> c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),X84),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),X92)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),c_Divides_Odiv__class_Omod(X94,X84,X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__mult1) ).
fof(fact_INT__constant,axiom,
! [X18,X13,X10,X154] :
( ( X154 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X154),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),X18)) = c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)) )
& ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X154),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),X18)) = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__constant) ).
fof(fact_UN__constant,axiom,
! [X18,X13,X10,X154] :
( ( X154 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X154),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),X18)) = c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool)) )
& ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X13,tc_HOL_Obool)),X154),hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X10),X18)) = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__constant) ).
fof(fact_Random__Sequence_Oempty__def,axiom,
! [X202,X203,X10] : c_Random__Sequence_Oempty(X10,X203,X202) = 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(X10)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Random__Sequence_Oempty__def) ).
fof(fact_div__mult__mult1__if,axiom,
! [X92,X84,X81,X94] :
( class_Divides_Osemiring__div(X94)
=> ( ( X81 = c_Groups_Ozero__class_Ozero(X94)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),X84)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),X92)) = c_Groups_Ozero__class_Ozero(X94) )
& ( X81 != c_Groups_Ozero__class_Ozero(X94)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),X84)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),X92)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),X84),X92) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__mult1__if) ).
fof(fact_mult__divide__mult__cancel__left,axiom,
! [X92,X84,X81,X94] :
( class_Fields_Ofield__inverse__zero(X94)
=> ( X81 != c_Groups_Ozero__class_Ozero(X94)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),X84)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),X92)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X84),X92) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__left) ).
fof(fact_mult__divide__mult__cancel__right,axiom,
! [X92,X84,X81,X94] :
( class_Fields_Ofield__inverse__zero(X94)
=> ( X81 != c_Groups_Ozero__class_Ozero(X94)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X81)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X81)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X84),X92) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__right) ).
fof(fact_div__mult__mult1,axiom,
! [X92,X84,X81,X94] :
( class_Divides_Osemiring__div(X94)
=> ( X81 != c_Groups_Ozero__class_Ozero(X94)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),X84)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),X92)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),X84),X92) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__mult1) ).
fof(fact_div__mult__mult2,axiom,
! [X92,X84,X81,X94] :
( class_Divides_Osemiring__div(X94)
=> ( X81 != c_Groups_Ozero__class_Ozero(X94)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X81)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X81)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),X84),X92) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__mult2) ).
fof(fact_nat__rec__Suc,axiom,
! [X110,X37,X12,X10] : hAPP(c_Nat_Onat_Onat__rec(X10,X12,X37),hAPP(c_Nat_OSuc,X110)) = hAPP(hAPP(X37,X110),hAPP(c_Nat_Onat_Onat__rec(X10,X12,X37),X110)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__rec__Suc) ).
fof(fact_trans__le__add1,axiom,
! [X97,X119,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X120),X119))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X120),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X119),X97))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add1) ).
fof(fact_termination__basic__simps_I3_J,axiom,
! [X104,X105,X93] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X93),X105))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X93),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X105),X104))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
fof(fact_trans__le__add2,axiom,
! [X97,X119,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X120),X119))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X120),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X119))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add2) ).
fof(fact_termination__basic__simps_I4_J,axiom,
! [X105,X104,X93] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X93),X104))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X93),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X105),X104))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
fof(fact_termination__basic__simps_I1_J,axiom,
! [X104,X105,X93] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X93),X105))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X93),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X105),X104))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
fof(fact_trans__less__add1,axiom,
! [X97,X119,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),X119))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X119),X97))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add1) ).
fof(fact_termination__basic__simps_I2_J,axiom,
! [X105,X104,X93] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X93),X104))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X93),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X105),X104))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
fof(fact_trans__less__add2,axiom,
! [X97,X119,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),X119))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X119))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add2) ).
fof(fact_mod__mult__self2,axiom,
! [X81,X92,X84,X94] :
( class_Divides_Osemiring__div(X94)
=> c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X81)),X92) = c_Divides_Odiv__class_Omod(X94,X84,X92) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self2) ).
fof(fact_mod__mult__self1,axiom,
! [X92,X81,X84,X94] :
( class_Divides_Osemiring__div(X94)
=> c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X81),X92)),X92) = c_Divides_Odiv__class_Omod(X94,X84,X92) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self1) ).
fof(fact_less__Suc__eq__0__disj,axiom,
! [X20,X102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),hAPP(c_Nat_OSuc,X20)))
<=> ( X102 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [X123] :
( X102 = hAPP(c_Nat_OSuc,X123)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X123),X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
fof(fact_rotate1__hd__tl,axiom,
! [X94,X297] :
( X297 != c_List_Olist_ONil(X94)
=> hAPP(c_List_Orotate1(X94),X297) = hAPP(hAPP(c_List_Oappend(X94),hAPP(c_List_Otl(X94),X297)),hAPP(hAPP(c_List_Olist_OCons(X94),hAPP(c_List_Ohd(X94),X297)),c_List_Olist_ONil(X94))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate1__hd__tl) ).
fof(fact_fun__upd__apply,axiom,
! [X25,X2,X13,X10,X16,X73] :
( ( X73 = X16
=> hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,X13),X2),X16),X25),X73) = X25 )
& ( X73 != X16
=> hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,X13),X2),X16),X25),X73) = hAPP(X2,X73) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__apply) ).
fof(fact_fun__upd__other,axiom,
! [X25,X2,X13,X10,X16,X73] :
( X73 != X16
=> hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,X13),X2),X16),X25),X73) = hAPP(X2,X73) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__other) ).
fof(fact_fun__upd__def,axiom,
! [X38,X2,X13,X10,X39,X16] :
( ( X16 = X39
=> hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,X13),X2),X39),X38),X16) = X38 )
& ( X16 != X39
=> hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,X13),X2),X39),X38),X16) = hAPP(X2,X16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__def) ).
fof(fact_setsum__set__upto__conv__listsum__int,axiom,
! [X163,X113,X2,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X10),X2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X113,X163))) = hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X10),X2),c_List_Oupto(X113,X163))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__set__upto__conv__listsum__int) ).
fof(fact_interv__listsum__conv__setsum__set__int,axiom,
! [X162,X101,X2,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X10),X2),c_List_Oupto(X101,X162))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X10),X2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X101,X162))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_interv__listsum__conv__setsum__set__int) ).
fof(fact_inf__assoc,axiom,
! [X104,X105,X93,X94] :
( class_Lattices_Osemilattice__inf(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),X105)),X104) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X105),X104)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__assoc) ).
fof(fact_inf_Oassoc,axiom,
! [X81,X92,X84,X94] :
( class_Lattices_Osemilattice__inf(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X84),X92)),X81) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X84),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X92),X81)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oassoc) ).
fof(fact_inf__sup__aci_I2_J,axiom,
! [X104,X105,X93,X94] :
( class_Lattices_Olattice(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),X105)),X104) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X105),X104)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I2_J) ).
fof(fact_sup_Oassoc,axiom,
! [X81,X92,X84,X94] :
( class_Lattices_Osemilattice__sup(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X84),X92)),X81) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X84),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X92),X81)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oassoc) ).
fof(fact_sup__assoc,axiom,
! [X104,X105,X93,X94] :
( class_Lattices_Osemilattice__sup(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),X105)),X104) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X105),X104)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__assoc) ).
fof(fact_inf__sup__aci_I6_J,axiom,
! [X104,X105,X93,X94] :
( class_Lattices_Olattice(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),X105)),X104) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X105),X104)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I6_J) ).
fof(fact_min__max_Osup__assoc,axiom,
! [X104,X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X93),X105)),X104) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X93),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X105),X104)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__assoc) ).
fof(fact_min__max_Osup_Oassoc,axiom,
! [X81,X92,X84,X94] :
( class_Orderings_Olinorder(X94)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X84),X92)),X81) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X84),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X92),X81)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup_Oassoc) ).
fof(fact_min__max_Oinf_Oassoc,axiom,
! [X81,X92,X84,X94] :
( class_Orderings_Olinorder(X94)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X84),X92)),X81) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X84),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X92),X81)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf_Oassoc) ).
fof(fact_min__max_Oinf__assoc,axiom,
! [X104,X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X93),X105)),X104) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X93),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X105),X104)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__assoc) ).
fof(fact_power__commutes,axiom,
! [X42,X84,X94] :
( class_Groups_Omonoid__mult(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42)),X84) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__commutes) ).
fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
! [X81,X92,X84,X94] :
( class_Groups_Oab__semigroup__mult(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92)),X81) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X81)) ),
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,
! [X138,X140,X139,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X139),X140)),X138) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X139),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X140),X138)) ),
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,
! [X81,X92,X84,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92)),X81) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X92),X81)) ),
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,
! [X81,X92,X84,X94] :
( class_Groups_Oab__semigroup__add(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92)),X81) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X92),X81)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(fact_times__divide__eq__right,axiom,
! [X81,X92,X84,X94] :
( class_Rings_Odivision__ring(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X92),X81)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92)),X81) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__divide__eq__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
! [X137,X138,X139,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X139),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X138),X137)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X139),X138)),X137) ),
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,
! [X112,X81,X84,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X81),X112)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X81)),X112) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_last__conv__nth,axiom,
! [X94,X297] :
( X297 != c_List_Olist_ONil(X94)
=> c_List_Olast(X94,X297) = hAPP(hAPP(c_List_Onth(X94),X297),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)),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,
! [X131,X10] :
( class_Int_Onumber__ring(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X131))
=> hBOOL(hAPP(hAPP(c_member(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),c_Nat_Osemiring__1__class_ONats(X10))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nats__number__of) ).
fof(fact_card__Pow,axiom,
! [X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(c_Finite__Set_Ocard(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_OPow(X10),X154)) = 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(X10),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Pow) ).
fof(fact_atLeast__Suc,axiom,
! [X101] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X101)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),X101)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X101),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,
! [X160,X154,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Compl) ).
fof(fact_Diff__eq,axiom,
! [X160,X154,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X160)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__eq) ).
fof(fact_zero__less__two,axiom,
! [X94] :
( class_Rings_Olinordered__semidom(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),c_Groups_Oone__class_Oone(X94)),c_Groups_Oone__class_Oone(X94)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__two) ).
fof(fact_card__greaterThanLessThan__int,axiom,
! [X165,X162] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X162,X165)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X165),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X162),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,
! [X39,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X39),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X154)) = X39 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__Inf__absorb) ).
fof(fact_min__max_Oinf__Sup__absorb,axiom,
! [X39,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X39),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X154)) = X39 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__Sup__absorb) ).
fof(fact_le__minus__self__iff,axiom,
! [X39,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X39)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),c_Groups_Ozero__class_Ozero(X10))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__minus__self__iff) ).
fof(fact_less__minus__self__iff,axiom,
! [X39,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X39)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),c_Groups_Ozero__class_Ozero(X10))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__minus__self__iff) ).
fof(fact_Diff__triv,axiom,
! [X160,X154,X10] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160) = X154 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__triv) ).
fof(fact_insort__not__Nil,axiom,
! [X290,X39,X2,X10,X13] :
( class_Orderings_Olinorder(X13)
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X13,X2),X39),X290) != c_List_Olist_ONil(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__not__Nil) ).
fof(fact_setprod__constant,axiom,
! [X25,X154,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),hAPP(c_COMBK(X13,X10),X25)),X154) = hAPP(hAPP(c_Power_Opower__class_Opower(X13),X25),hAPP(c_Finite__Set_Ocard(X10),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__constant) ).
fof(fact_fold1__insert__idem,axiom,
! [X16,X154,X10] :
( class_Lattices_Oab__semigroup__idem__mult(X10)
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X16),hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),X154)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__insert__idem) ).
fof(fact_ivl__disj__int_I11_J,axiom,
! [X165,X102,X162,X10] :
( class_Orderings_Oorder(X10)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X162),X102)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X102),X165)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I11_J) ).
fof(fact_diff__Suc,axiom,
! [X20,X102] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X102),hAPP(c_Nat_OSuc,X20)) = 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),X102),X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc) ).
fof(fact_append__assoc,axiom,
! [X296,X298,X297,X94] : hAPP(hAPP(c_List_Oappend(X94),hAPP(hAPP(c_List_Oappend(X94),X297),X298)),X296) = hAPP(hAPP(c_List_Oappend(X94),X297),hAPP(hAPP(c_List_Oappend(X94),X298),X296)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__assoc) ).
fof(fact_append__Cons,axiom,
! [X298,X297,X93,X94] : hAPP(hAPP(c_List_Oappend(X94),hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)),X298) = hAPP(hAPP(c_List_Olist_OCons(X94),X93),hAPP(hAPP(c_List_Oappend(X94),X297),X298)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__Cons) ).
fof(fact_zdvd__imp__le,axiom,
! [X42,X104] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X104),X42))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X42))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X104),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__imp__le) ).
fof(fact_dvd__imp__le,axiom,
! [X42,X103] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X103),X42))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X42))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X103),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__imp__le) ).
fof(fact_take__Suc,axiom,
! [X42,X94,X297] :
( X297 != c_List_Olist_ONil(X94)
=> hAPP(hAPP(c_List_Otake(X94),hAPP(c_Nat_OSuc,X42)),X297) = hAPP(hAPP(c_List_Olist_OCons(X94),hAPP(c_List_Ohd(X94),X297)),hAPP(hAPP(c_List_Otake(X94),X42),hAPP(c_List_Otl(X94),X297))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Suc) ).
fof(fact_image__atLeastZeroLessThan__int,axiom,
! [X165] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X165))
=> hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X165) = 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,X165))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__atLeastZeroLessThan__int) ).
fof(fact_nth__Cons_H,axiom,
! [X297,X93,X94,X42] :
( ( X42 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Onth(X94),hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)),X42) = X93 )
& ( X42 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Onth(X94),hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)),X42) = hAPP(hAPP(c_List_Onth(X94),X297),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X42),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,
! [X18,X13,X10,X154] :
( ( X154 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(X10,X13,hAPP(c_COMBK(X13,X10),X18)),X154) = c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool)) )
& ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(X10,X13,hAPP(c_COMBK(X13,X10),X18)),X154) = hAPP(hAPP(c_Set_Oinsert(X13),X18),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__constant__conv) ).
fof(fact_WT_Oequations_I5_J,axiom,
! [X52,X51,X50] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X50,X51,X52)))
<=> ( hBOOL(hAPP(c_Com_OWT,X51))
& hBOOL(hAPP(c_Com_OWT,X52)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I5_J) ).
fof(fact_WT_Oequations_I3_J,axiom,
! [X51,X50,X52] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X52,X50,X51)))
<=> hBOOL(hAPP(c_Com_OWT,X51)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I3_J) ).
fof(fact_WTs__elim__cases_I3_J,axiom,
! [X18,X39,X78] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X78,X39,X18)))
=> hBOOL(hAPP(c_Com_OWT,X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WTs__elim__cases_I3_J) ).
fof(fact_listsum__distinct__conv__setsum__set,axiom,
! [X2,X290,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( hBOOL(hAPP(c_List_Odistinct(X10),X290))
=> hAPP(c_List_Omonoid__add__class_Olistsum(X13),hAPP(hAPP(c_List_Omap(X10,X13),X2),X290)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),hAPP(c_List_Oset(X10),X290)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__distinct__conv__setsum__set) ).
fof(fact_power__mult,axiom,
! [X42,X97,X84,X94] :
( class_Groups_Omonoid__mult(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X97),X42)) = hAPP(hAPP(c_Power_Opower__class_Opower(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X97)),X42) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mult) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
! [X149,X167,X93,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),X167)),X149) = hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X167),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
fof(fact_mod__minus__eq,axiom,
! [X92,X84,X94] :
( class_Divides_Oring__div(X94)
=> c_Divides_Odiv__class_Omod(X94,hAPP(c_Groups_Ouminus__class_Ouminus(X94),X84),X92) = c_Divides_Odiv__class_Omod(X94,hAPP(c_Groups_Ouminus__class_Ouminus(X94),c_Divides_Odiv__class_Omod(X94,X84,X92)),X92) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__minus__eq) ).
fof(fact_tl__take,axiom,
! [X297,X42,X94] : hAPP(c_List_Otl(X94),hAPP(hAPP(c_List_Otake(X94),X42),X297)) = hAPP(hAPP(c_List_Otake(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X42),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(X94),X297)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl__take) ).
fof(fact_abs__power__minus,axiom,
! [X42,X84,X94] :
( class_Rings_Olinordered__idom(X94)
=> hAPP(c_Groups_Oabs__class_Oabs(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X84)),X42)) = hAPP(c_Groups_Oabs__class_Oabs(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__power__minus) ).
fof(fact_fun__upd__same,axiom,
! [X25,X16,X2,X10,X13] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X13,X10),X2),X16),X25),X16) = X25,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__same) ).
fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
! [X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))))
=> ( hAPP(c_Finite__Set_Ocard(X10),X154) = hAPP(c_Finite__Set_Ocard(X10),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> X154 = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__eq__UNIV__imp__eq__UNIV) ).
fof(fact_drop__Cons_H,axiom,
! [X297,X93,X94,X42] :
( ( X42 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Odrop(X94),X42),hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)) = hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297) )
& ( X42 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Odrop(X94),X42),hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)) = hAPP(hAPP(c_List_Odrop(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X42),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X297) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__Cons_H) ).
fof(fact_neg__zminus__int,axiom,
! [X42] : 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,X42))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__zminus__int) ).
fof(fact_insert__code,axiom,
! [X16,X154,X25,X10] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X10),X25),X154),X16))
<=> ( X25 = X16
| hBOOL(hAPP(X154,X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__code) ).
fof(fact_dvd__minus__iff,axiom,
! [X25,X16,X10] :
( class_Rings_Ocomm__ring__1(X10)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X16),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X25)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X16),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__minus__iff) ).
fof(fact_dvd__abs__iff,axiom,
! [X101,X102,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X102),hAPP(c_Groups_Oabs__class_Oabs(X10),X101)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X102),X101)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__abs__iff) ).
fof(fact_atMost__iff,axiom,
! [X101,X113,X10] :
( class_Orderings_Oord(X10)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X113),hAPP(c_SetInterval_Oord__class_OatMost(X10),X101)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X113),X101)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atMost__iff) ).
fof(fact_atLeast__iff,axiom,
! [X101,X113,X10] :
( class_Orderings_Oord(X10)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X113),hAPP(c_SetInterval_Oord__class_OatLeast(X10),X101)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X101),X113)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__iff) ).
fof(fact_lessThan__iff,axiom,
! [X101,X113,X10] :
( class_Orderings_Oord(X10)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X113),hAPP(c_SetInterval_Oord__class_OlessThan(X10),X101)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X113),X101)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__iff) ).
fof(fact_greaterThan__iff,axiom,
! [X101,X113,X10] :
( class_Orderings_Oord(X10)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X113),hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),X101)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X101),X113)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__iff) ).
fof(fact_image__uminus__greaterThanAtMost,axiom,
! [X25,X16,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> hAPP(c_Set_Oimage(X10,X10,c_Groups_Ouminus__class_Ouminus(X10)),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X16,X25)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,hAPP(c_Groups_Ouminus__class_Ouminus(X10),X25)),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__greaterThanAtMost) ).
fof(fact_folding__one__idem_Oin__idem,axiom,
! [X16,X154,X225,X2,X10] :
( c_Finite__Set_Ofolding__one__idem(X10,X2,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(hAPP(X2,X16),hAPP(X225,X154)) = hAPP(X225,X154) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oin__idem) ).
fof(fact_Max__ge,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),c_Big__Operators_Olinorder__class_OMax(X10,X154))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max__ge) ).
fof(fact_listsum__setsum__nth,axiom,
! [X290,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> hAPP(c_List_Omonoid__add__class_Olistsum(X10),X290) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),hAPP(c_List_Onth(X10),X290)),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(X10)),X290))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__setsum__nth) ).
fof(fact_zdiff__int,axiom,
! [X97,X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),X97))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X97)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X42)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__int) ).
fof(fact_abs__div,axiom,
! [X93,X105] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X105),X93))
=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X93),X105)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X93)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X105)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__div) ).
fof(fact_odd__nonzero,axiom,
! [X104] : 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)),X104)),X104) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__nonzero) ).
fof(fact_Field__def,axiom,
! [X177,X10] : hAPP(c_Relation_OField(X10),X177) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X10,X10),X177)),hAPP(c_Relation_ORange(X10,X10),X177)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__def) ).
fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
! [X20,X102] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X102,X20) = 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),X102),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__functions_I2_J) ).
fof(fact_div__mult__self1__is__m,axiom,
! [X97,X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X42))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),X97)),X42) = X97 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self1__is__m) ).
fof(fact_div__mult__self__is__m,axiom,
! [X97,X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X42))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X97),X42)),X42) = X97 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self__is__m) ).
fof(fact_zmod__zminus2__eq__if,axiom,
! [X92,X84] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X92) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X92)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X92) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X92)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X92)),X92) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus2__eq__if) ).
fof(fact_subset__UNIV,axiom,
! [X154,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__UNIV) ).
fof(fact_dvd_Oorder__trans,axiom,
! [X104,X105,X93] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X93),X105))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X105),X104))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X93),X104)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oorder__trans) ).
fof(fact_zle__trans,axiom,
! [X103,X119,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X120),X119))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X119),X103))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X120),X103)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__trans) ).
fof(fact_le__trans,axiom,
! [X103,X119,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X120),X119))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X119),X103))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X120),X103)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__trans) ).
fof(fact_mod__mod__cancel,axiom,
! [X84,X92,X81,X94] :
( class_Divides_Osemiring__div(X94)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X81),X92))
=> c_Divides_Odiv__class_Omod(X94,c_Divides_Odiv__class_Omod(X94,X84,X92),X81) = c_Divides_Odiv__class_Omod(X94,X84,X81) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mod__cancel) ).
fof(fact_evaln__elim__cases_I1_J,axiom,
! [X44,X42,X45] :
( c_Natural_Oevaln(c_Com_Ocom_OSKIP,X45,X42,X44)
=> X44 = X45 ),
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,
! [X97,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X97),X97) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),c_Groups_Oone__class_Oone(X94)),c_Groups_Oone__class_Oone(X94))),X97) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(fact_less__add__eq__less,axiom,
! [X42,X97,X121,X103] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X103),X121))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X121) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X103),X42)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
fof(fact_dvd__div__neg,axiom,
! [X93,X105,X94] :
( class_Divides_Oring__div(X94)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X105),X93))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),X93),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X105)) = hAPP(c_Groups_Ouminus__class_Ouminus(X94),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),X93),X105)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__div__neg) ).
fof(fact_Suc__leD,axiom,
! [X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X97)),X42))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leD) ).
fof(fact_less__eq__Suc__le,axiom,
! [X102,X20] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X102))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)),X102)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
fof(fact_Suc__le__eq,axiom,
! [X20,X102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X102)),X20))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__eq) ).
fof(fact_Suc__le__lessD,axiom,
! [X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X97)),X42))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
fof(fact_Suc__lessD,axiom,
! [X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X97)),X42))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessD) ).
fof(fact_drop__drop,axiom,
! [X297,X97,X42,X94] : hAPP(hAPP(c_List_Odrop(X94),X42),hAPP(hAPP(c_List_Odrop(X94),X97),X297)) = hAPP(hAPP(c_List_Odrop(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),X97)),X297),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__drop) ).
fof(fact_take__take,axiom,
! [X297,X97,X42,X94] : hAPP(hAPP(c_List_Otake(X94),X42),hAPP(hAPP(c_List_Otake(X94),X97),X297)) = hAPP(hAPP(c_List_Otake(X94),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X42),X97)),X297),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__take) ).
fof(fact_Inf__lower,axiom,
! [X154,X16,X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Complete__Lattice_OInf__class_OInf(X10,X154)),X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__lower) ).
fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
! [X19] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
=> hBOOL(hAPP(X19,X3)) )
<=> ! [X3] : hBOOL(hAPP(X19,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,
! [X105,X93] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X93))
=> hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X93),X105)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X93)),hAPP(c_Int_Onat,X105)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__div__distrib) ).
fof(fact_nat__mult__distrib,axiom,
! [X145,X104] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X104))
=> hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X104),X145)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X104)),hAPP(c_Int_Onat,X145)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__distrib) ).
fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
! [X20,X102] :
( c_Nat__Transfer_Ois__nat(X102)
=> ( c_Nat__Transfer_Ois__nat(X20)
=> c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X102,X20) = 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,X102),hAPP(c_Int_Onat,X20))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__int__nat__set__functions) ).
fof(fact_transpose_Opsimps_I1_J,axiom,
! [X10] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X10)),c_List_Otranspose__rel(X10)),c_List_Olist_ONil(tc_List_Olist(X10))))
=> c_List_Otranspose(X10,c_List_Olist_ONil(tc_List_Olist(X10))) = c_List_Olist_ONil(tc_List_Olist(X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose_Opsimps_I1_J) ).
fof(fact_mod__mult__distrib2,axiom,
! [X42,X97,X103] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X103),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X97,X42)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X103),X97),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X103),X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__distrib2) ).
fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
! [X160,X154] :
( X154 = X160
<=> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X154) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X160) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I3_J) ).
fof(fact_set__append,axiom,
! [X289,X290,X10] : hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Oappend(X10),X290),X289)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),X290)),hAPP(c_List_Oset(X10),X289)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__append) ).
fof(fact_Suc__mono,axiom,
! [X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X97)),hAPP(c_Nat_OSuc,X42))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mono) ).
fof(fact_power__inject__exp,axiom,
! [X20,X102,X39,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Oone__class_Oone(X10)),X39))
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X10),X39),X102) = hAPP(hAPP(c_Power_Opower__class_Opower(X10),X39),X20)
<=> X102 = X20 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__inject__exp) ).
fof(fact_listset_Osimps_I2_J,axiom,
! [X311,X154,X10] : c_List_Olistset(X10,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X10,tc_HOL_Obool)),X154),X311)) = c_List_Oset__Cons(X10,X154,c_List_Olistset(X10,X311)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listset_Osimps_I2_J) ).
fof(fact_Sup__fold__sup,axiom,
! [X154,X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> c_Complete__Lattice_OSup__class_OSup(X10,X154) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__sup__class_Osup(X10)),c_Orderings_Obot__class_Obot(X10)),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fold__sup) ).
fof(fact_Inf__fold__inf,axiom,
! [X154,X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> c_Complete__Lattice_OInf__class_OInf(X10,X154) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__inf__class_Oinf(X10)),c_Orderings_Otop__class_Otop(X10)),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fold__inf) ).
fof(fact_power__eq__if,axiom,
! [X167,X97] :
( ( X97 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X167),X97) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X97 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X167),X97) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X167),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X167),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__if) ).
fof(fact_image__uminus__atLeastAtMost,axiom,
! [X25,X16,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> hAPP(c_Set_Oimage(X10,X10,c_Groups_Ouminus__class_Ouminus(X10)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X16,X25)) = c_SetInterval_Oord__class_OatLeastAtMost(X10,hAPP(c_Groups_Ouminus__class_Ouminus(X10),X25),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__atLeastAtMost) ).
fof(fact_image__uminus__greaterThanLessThan,axiom,
! [X25,X16,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> hAPP(c_Set_Oimage(X10,X10,c_Groups_Ouminus__class_Ouminus(X10)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X16,X25)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X10,hAPP(c_Groups_Ouminus__class_Ouminus(X10),X25),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__greaterThanLessThan) ).
fof(fact_lessThan__Suc__eq__insert__0,axiom,
! [X20] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)) = 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),X20))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__Suc__eq__insert__0) ).
fof(fact_div__mod__code__numeral__def,axiom,
! [X97,X42] : c_Code__Numeral_Odiv__mod__code__numeral(X42,X97) = 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),X42),X97)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X42,X97)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mod__code__numeral__def) ).
fof(fact_divmod__int__mod__div,axiom,
! [X149,X167] : c_Divides_Odivmod__int(X167,X149) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X167),X149)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X167,X149)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__mod__div) ).
fof(fact_zminus__zmod,axiom,
! [X97,X93] : 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,X93,X97)),X97) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X93),X97),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zmod) ).
fof(fact_transfer__nat__int__relations_I1_J,axiom,
! [X25,X16] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25))
=> ( hAPP(c_Int_Onat,X16) = hAPP(c_Int_Onat,X25)
<=> X16 = X25 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I1_J) ).
fof(fact_eq__nat__nat__iff,axiom,
! [X146,X73] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X146))
=> ( hAPP(c_Int_Onat,X73) = hAPP(c_Int_Onat,X146)
<=> X73 = X146 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__nat__nat__iff) ).
fof(fact_zless__iff__Suc__zadd,axiom,
! [X73,X131] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X131),X73))
<=> ? [X83] : X73 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X131),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X83))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__iff__Suc__zadd) ).
fof(fact_div__mod__equality_H,axiom,
! [X42,X97] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X97),X42)),X42) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X97,X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mod__equality_H) ).
fof(fact_le__add__diff__inverse2,axiom,
! [X97,X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),X97))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42)),X42) = X97 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff__inverse2) ).
fof(fact_zero__less__int__conv,axiom,
! [X20] :
( 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),X20)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__int__conv) ).
fof(fact_int__eq__iff__number__of,axiom,
! [X168,X102] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X102) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X168)
<=> ( X102 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X168))
& 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),X168))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__eq__iff__number__of) ).
fof(fact_ranI,axiom,
! [X13,X38,X10,X39,X102] :
( hAPP(X102,X39) = hAPP(c_Option_Ooption_OSome(X10),X38)
=> hBOOL(hAPP(hAPP(c_member(X10),X38),c_Map_Oran(X13,X10,X102))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ranI) ).
fof(fact_domI,axiom,
! [X13,X38,X10,X39,X102] :
( hAPP(X102,X39) = hAPP(c_Option_Ooption_OSome(X10),X38)
=> hBOOL(hAPP(hAPP(c_member(X13),X39),c_Map_Odom(X13,X10,X102))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_domI) ).
fof(fact_finite__Pow__iff,axiom,
! [X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_OPow(X10),X154)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Pow__iff) ).
fof(fact_DomainP_Ointros,axiom,
! [X13,X10,X38,X39,X177] :
( hBOOL(hAPP(hAPP(X177,X39),X38))
=> hBOOL(hAPP(c_Predicate_ODomainP(X10,X13,X177),X39)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainP_Ointros) ).
fof(fact_RangeP_Ointros,axiom,
! [X13,X10,X38,X39,X177] :
( hBOOL(hAPP(hAPP(X177,X39),X38))
=> hBOOL(hAPP(c_Predicate_ORangeP(X10,X13,X177),X38)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeP_Ointros) ).
fof(fact_length__greater__0__conv,axiom,
! [X290,X10] :
( 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(X10)),X290)))
<=> X290 != c_List_Olist_ONil(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__greater__0__conv) ).
fof(fact_ivl__disj__int_I8_J,axiom,
! [X165,X162,X10] :
( class_Orderings_Oorder(X10)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X162),X165)),hAPP(c_SetInterval_Oord__class_OatLeast(X10),X165)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I8_J) ).
fof(fact_le__less__Suc__eq,axiom,
! [X20,X102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),hAPP(c_Nat_OSuc,X102)))
<=> X20 = X102 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
fof(fact_mod__pos__pos__trivial,axiom,
! [X92,X84] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),X92))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X92) = X84 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__pos__trivial) ).
fof(fact_atMost__Int__atLeast,axiom,
! [X20,X10] :
( class_Orderings_Oorder(X10)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X10),X20)),hAPP(c_SetInterval_Oord__class_OatLeast(X10),X20)) = hAPP(hAPP(c_Set_Oinsert(X10),X20),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atMost__Int__atLeast) ).
fof(fact_length__append,axiom,
! [X298,X297,X94] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),hAPP(hAPP(c_List_Oappend(X94),X297),X298)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X298)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__append) ).
fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
! [X160,X154] :
( c_Nat__Transfer_Onat__set(X154)
=> ( c_Nat__Transfer_Onat__set(X160)
=> ( X154 = X160
<=> hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X154) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X160) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I3_J) ).
fof(fact_triple_Oinject,axiom,
! [X4,X5,X6,X7,X8,X9,X10] :
( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X10),X9),X8),X7) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X10),X6),X5),X4)
<=> ( X9 = X6
& X8 = X5
& X7 = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triple_Oinject) ).
fof(fact_setprod__zero,axiom,
! [X2,X154,X10,X13] :
( class_Rings_Ocomm__semiring__1(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
& hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X13) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),X154) = c_Groups_Ozero__class_Ozero(X13) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__zero) ).
fof(fact_nat__mult__div__cancel__disj,axiom,
! [X42,X97,X103] :
( ( X103 = 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),X103),X97)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X103),X42)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X103 != 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),X103),X97)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X103),X42)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X97),X42) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__div__cancel__disj) ).
fof(fact_Pow__top,axiom,
! [X154,X10] : hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(c_Set_OPow(X10),X154))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__top) ).
fof(fact_rev_Osimps_I2_J,axiom,
! [X297,X93,X94] : hAPP(c_List_Orev(X94),hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)) = hAPP(hAPP(c_List_Oappend(X94),hAPP(c_List_Orev(X94),X297)),hAPP(hAPP(c_List_Olist_OCons(X94),X93),c_List_Olist_ONil(X94))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev_Osimps_I2_J) ).
fof(fact_div__pos__pos__trivial,axiom,
! [X92,X84] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),X92))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),X92) = 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,
! [X101,X113] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X113),X101) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
<=> ( X101 = 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)),X113))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X113),X101)) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X113),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),X113)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__eq__0__iff) ).
fof(fact_Inf__le__Sup,axiom,
! [X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Big__Operators_Olattice__class_OInf__fin(X10,X154)),c_Big__Operators_Olattice__class_OSup__fin(X10,X154))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__le__Sup) ).
fof(fact_equivp__transp,axiom,
! [X73,X25,X16,X196,X10] :
( c_Equiv__Relations_Oequivp(X10,X196)
=> ( hBOOL(hAPP(hAPP(X196,X16),X25))
=> ( hBOOL(hAPP(hAPP(X196,X25),X73))
=> hBOOL(hAPP(hAPP(X196,X16),X73)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivp__transp) ).
fof(fact_folding__one__idem_Oinsert__idem,axiom,
! [X16,X154,X225,X2,X10] :
( c_Finite__Set_Ofolding__one__idem(X10,X2,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(X225,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(X2,X16),hAPP(X225,X154)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oinsert__idem) ).
fof(fact_mod__minus__cong,axiom,
! [X95,X92,X84,X94] :
( class_Divides_Oring__div(X94)
=> ( c_Divides_Odiv__class_Omod(X94,X84,X92) = c_Divides_Odiv__class_Omod(X94,X95,X92)
=> c_Divides_Odiv__class_Omod(X94,hAPP(c_Groups_Ouminus__class_Ouminus(X94),X84),X92) = c_Divides_Odiv__class_Omod(X94,hAPP(c_Groups_Ouminus__class_Ouminus(X94),X95),X92) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__minus__cong) ).
fof(fact_Union__def,axiom,
! [X216,X10] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X216) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X216),c_COMBI(tc_fun(X10,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__def) ).
fof(fact_Inter__def,axiom,
! [X216,X10] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X216) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X216),c_COMBI(tc_fun(X10,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__def) ).
fof(fact_zabs__less__one__iff,axiom,
! [X73] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X73)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> X73 = 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,
! [X20] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
<=> X20 = 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,
! [X102,X13,X10] : c_Map_Omap__add(X10,X13,hAPP(c_COMBK(tc_Option_Ooption(X13),X10),c_Option_Ooption_ONone(X13)),X102) = X102,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__map__add) ).
fof(fact_map__add__empty,axiom,
! [X102,X13,X10] : c_Map_Omap__add(X10,X13,X102,hAPP(c_COMBK(tc_Option_Ooption(X13),X10),c_Option_Ooption_ONone(X13))) = X102,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__add__empty) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
! [X42,X93] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X93))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X93)),X42) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X93),X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J) ).
fof(fact_nat__power__eq,axiom,
! [X42,X104] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X104))
=> hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X104),X42)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X104)),X42) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__power__eq) ).
fof(fact_diff__cancel,axiom,
! [X42,X97,X103] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X103),X97)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X103),X42)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__cancel) ).
fof(fact_diff__cancel2,axiom,
! [X42,X103,X97] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X103)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),X103)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__cancel2) ).
fof(fact_zpower__zpower,axiom,
! [X104,X105,X93] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X93),X105)),X104) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X93),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X105),X104)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__zpower) ).
fof(fact_diff__diff__left,axiom,
! [X103,X119,X120] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X120),X119)),X103) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X120),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X119),X103)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__left) ).
fof(fact_zmult__assoc,axiom,
! [X134,X135,X136] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X136),X135)),X134) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X136),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X135),X134)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__assoc) ).
fof(fact_nat__mult__assoc,axiom,
! [X103,X42,X97] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X97),X42)),X103) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X97),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),X103)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).
fof(fact_zadd__assoc,axiom,
! [X134,X135,X136] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X136),X135)),X134) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X136),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X135),X134)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__assoc) ).
fof(fact_nat__add__assoc,axiom,
! [X103,X42,X97] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X42)),X103) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),X103)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
fof(fact_div__mult2__eq,axiom,
! [X81,X92,X84] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X84),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X92),X81)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X84),X92)),X81),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult2__eq) ).
fof(fact_ball__empty,axiom,
! [X19,X10,X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))
=> hBOOL(hAPP(X19,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ball__empty) ).
fof(fact_ivl__disj__int_I4_J,axiom,
! [X165,X162,X10] :
( class_Orderings_Oorder(X10)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X10),X162)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X162,X165)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I4_J) ).
fof(fact_ivl__disj__int_I3_J,axiom,
! [X165,X162,X10] :
( class_Orderings_Oorder(X10)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X10),X162)),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X162,X165)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I3_J) ).
fof(fact_ivl__disj__int_I1_J,axiom,
! [X165,X162,X10] :
( class_Orderings_Oorder(X10)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X10),X162)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X162,X165)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I1_J) ).
fof(fact_mod__neg__neg__trivial,axiom,
! [X92,X84] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X84),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X92),X84))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X92) = X84 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__neg__neg__trivial) ).
fof(fact_set__map,axiom,
! [X290,X2,X13,X10] : hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Omap(X13,X10),X2),X290)) = hAPP(c_Set_Oimage(X13,X10,X2),hAPP(c_List_Oset(X13),X290)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__map) ).
fof(fact_append__take__drop__id,axiom,
! [X297,X42,X94] : hAPP(hAPP(c_List_Oappend(X94),hAPP(hAPP(c_List_Otake(X94),X42),X297)),hAPP(hAPP(c_List_Odrop(X94),X42),X297)) = X297,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__take__drop__id) ).
fof(fact_mod__Suc__eq__Suc__mod,axiom,
! [X42,X97] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X97),X42) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X97,X42)),X42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__Suc__eq__Suc__mod) ).
fof(fact_com_Osize_I4_J,axiom,
! [X68,X69] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X69,X68)) = 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(X69)),c_Com_Ocom_Ocom__size(X68))),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,
! [X168] :
( 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),X168)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X168)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__0__number__of) ).
fof(fact_WT_OCall,axiom,
! [X39,X48,X49] :
( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X49)))
=> hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(X48,X49,X39))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_OCall) ).
fof(fact_div__neg__neg__trivial,axiom,
! [X92,X84] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X84),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X92),X84))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),X92) = 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,
! [X297,X93,X42,X94] : hAPP(hAPP(c_List_Otake(X94),hAPP(c_Nat_OSuc,X42)),hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)) = hAPP(hAPP(c_List_Olist_OCons(X94),X93),hAPP(hAPP(c_List_Otake(X94),X42),X297)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Suc__Cons) ).
fof(fact_map__eq__imp__length__eq,axiom,
! [X289,X1,X125,X290,X2,X10,X13] :
( hAPP(hAPP(c_List_Omap(X13,X10),X2),X290) = hAPP(hAPP(c_List_Omap(X125,X10),X1),X289)
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13)),X290) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X125)),X289) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__eq__imp__length__eq) ).
fof(fact_transfer__int__nat__set__return__embed,axiom,
! [X154] : 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)),X154)) = X154,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__set__return__embed) ).
fof(fact_fst__eqD,axiom,
! [X84,X105,X93,X10,X94] :
( hAPP(c_Product__Type_Ofst(X94,X10),hAPP(hAPP(c_Product__Type_OPair(X94,X10),X93),X105)) = X84
=> X93 = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__eqD) ).
fof(fact_snd__eqD,axiom,
! [X84,X105,X93,X94,X10] :
( hAPP(c_Product__Type_Osnd(X10,X94),hAPP(hAPP(c_Product__Type_OPair(X10,X94),X93),X105)) = X84
=> X105 = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__eqD) ).
fof(fact_transfer__nat__int__set__return__embed,axiom,
! [X154] :
( c_Nat__Transfer_Onat__set(X154)
=> 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),X154)) = X154 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__set__return__embed) ).
fof(fact_finite__Field,axiom,
! [X177,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10,X10)),X177))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Relation_OField(X10),X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Field) ).
fof(fact_image__uminus__atLeastLessThan,axiom,
! [X25,X16,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> hAPP(c_Set_Oimage(X10,X10,c_Groups_Ouminus__class_Ouminus(X10)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X16),X25)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X10,hAPP(c_Groups_Ouminus__class_Ouminus(X10),X25),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__atLeastLessThan) ).
fof(fact_Suc__lessI,axiom,
! [X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42))
=> ( hAPP(c_Nat_OSuc,X97) != X42
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X97)),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessI) ).
fof(fact_finite__nat__set__iff__bounded__le,axiom,
! [X226] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X226))
<=> ? [X122] :
! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X226))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X122)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).
fof(fact_finite__nat__set__iff__bounded,axiom,
! [X226] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X226))
<=> ? [X122] :
! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X226))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X122)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).
fof(fact_diff__number__of__eq,axiom,
! [X133,X144,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),X144)),hAPP(c_Int_Onumber__class_Onumber__of(X94),X133)) = hAPP(c_Int_Onumber__class_Onumber__of(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X144),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X133))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__number__of__eq) ).
fof(fact_zero__less__nat__eq,axiom,
! [X73] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X73)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__nat__eq) ).
fof(fact_butlast__snoc,axiom,
! [X93,X297,X94] : c_List_Obutlast(X94,hAPP(hAPP(c_List_Oappend(X94),X297),hAPP(hAPP(c_List_Olist_OCons(X94),X93),c_List_Olist_ONil(X94)))) = X297,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast__snoc) ).
fof(fact_last__snoc,axiom,
! [X93,X297,X94] : c_List_Olast(X94,hAPP(hAPP(c_List_Oappend(X94),X297),hAPP(hAPP(c_List_Olist_OCons(X94),X93),c_List_Olist_ONil(X94)))) = X93,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__snoc) ).
fof(fact_rtrancl__idemp__self__comp,axiom,
! [X196,X10] : hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),c_Transitive__Closure_Ortrancl(X10,X196)),c_Transitive__Closure_Ortrancl(X10,X196)) = c_Transitive__Closure_Ortrancl(X10,X196),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__idemp__self__comp) ).
fof(fact_fst__def,axiom,
! [X166,X13,X10] : hAPP(c_Product__Type_Ofst(X10,X13),X166) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,X10),c_COMBK(X10,X13)),X166),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__def) ).
fof(fact_finite__acyclic__wf__converse,axiom,
! [X177,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10,X10)),X177))
=> ( c_Wellfounded_Oacyclic(X10,X177)
=> c_Wellfounded_Owf(X10,hAPP(c_Relation_Oconverse(X10,X10),X177)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__acyclic__wf__converse) ).
fof(fact_order__eq__iff,axiom,
! [X25,X16,X10] :
( class_Orderings_Oorder(X10)
=> ( X16 = X25
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X25))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X25),X16)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__iff) ).
fof(fact_order__antisym__conv,axiom,
! [X16,X25,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X25),X16))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X25))
<=> X16 = X25 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
fof(fact_order__antisym,axiom,
! [X105,X93,X94] :
( class_Orderings_Oorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X105))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X105),X93))
=> X93 = X105 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym) ).
fof(fact_xt1_I5_J,axiom,
! [X93,X105,X94] :
( class_Orderings_Oorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X105),X93))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X105))
=> X93 = X105 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
fof(fact_le__mod__geq,axiom,
! [X97,X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),X97))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X97,X42) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42),X42) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__mod__geq) ).
fof(fact_dvd_OatLeastAtMost__singleton_H,axiom,
! [X38,X39] :
( X39 = X38
=> c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X39,X38) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X39),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,
! [X53,X141] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X141),X53))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X141),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X53))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_uminus__dvd__conv_I2_J) ).
fof(fact_Suc__diff__le,axiom,
! [X97,X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),X97))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X97)),X42) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__le) ).
fof(fact_abs__ge__minus__self,axiom,
! [X84,X94] :
( class_Groups_Oordered__ab__group__add__abs(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X84)),hAPP(c_Groups_Oabs__class_Oabs(X94),X84))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__ge__minus__self) ).
fof(fact_zero__le__square,axiom,
! [X84,X94] :
( class_Rings_Olinordered__ring(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X84))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__square) ).
fof(fact_less__add__one,axiom,
! [X84,X94] :
( class_Rings_Olinordered__semidom(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),c_Groups_Oone__class_Oone(X94)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__one) ).
fof(fact_zero__less__abs__iff,axiom,
! [X39,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Groups_Oabs__class_Oabs(X10),X39)))
<=> X39 != c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__abs__iff) ).
fof(fact_accp__downward,axiom,
! [X39,X38,X177,X10] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X10,X177),X38))
=> ( hBOOL(hAPP(hAPP(X177,X39),X38))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(X10,X177),X39)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__downward) ).
fof(fact_hd__in__set,axiom,
! [X10,X290] :
( X290 != c_List_Olist_ONil(X10)
=> hBOOL(hAPP(hAPP(c_member(X10),hAPP(c_List_Ohd(X10),X290)),hAPP(c_List_Oset(X10),X290))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__in__set) ).
fof(fact_dvd_OatLeastAtMost__singleton,axiom,
! [X39] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X39,X39) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X39),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,
! [X149,X93,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),X149)),X93) = hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),hAPP(c_Nat_OSuc,X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).
fof(fact_power__Suc2,axiom,
! [X42,X84,X94] :
( class_Groups_Omonoid__mult(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),hAPP(c_Nat_OSuc,X42)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42)),X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc2) ).
fof(fact_com__det,axiom,
! [X80,X44,X45,X81] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X81),X45),X44))
=> ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X81),X45),X80))
=> X80 = X44 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com__det) ).
fof(fact_map__upd__triv,axiom,
! [X13,X16,X10,X101,X53] :
( hAPP(X53,X101) = hAPP(c_Option_Ooption_OSome(X10),X16)
=> hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X13,tc_Option_Ooption(X10)),X53),X101),hAPP(c_Option_Ooption_OSome(X10),X16)) = X53 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__upd__triv) ).
fof(fact_semigroup_Oassoc,axiom,
! [X18,X38,X39,X2,X10] :
( c_Groups_Osemigroup(X10,X2)
=> hAPP(hAPP(X2,hAPP(hAPP(X2,X39),X38)),X18) = hAPP(hAPP(X2,X39),hAPP(hAPP(X2,X38),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semigroup_Oassoc) ).
fof(fact_list_Osize_I4_J,axiom,
! [X302,X84,X94] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),hAPP(hAPP(c_List_Olist_OCons(X94),X84),X302)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X302)),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,
! [X19] :
( ? [X3] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
& hBOOL(hAPP(X19,X3)) )
<=> ? [X3] : hBOOL(hAPP(X19,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,
! [X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X97)),X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leI) ).
fof(fact_Inf__fin_Oin__idem,axiom,
! [X16,X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X16),c_Big__Operators_Olattice__class_OInf__fin(X10,X154)) = c_Big__Operators_Olattice__class_OInf__fin(X10,X154) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oin__idem) ).
fof(fact_Sup__fin_Oin__idem,axiom,
! [X16,X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X16),c_Big__Operators_Olattice__class_OSup__fin(X10,X154)) = c_Big__Operators_Olattice__class_OSup__fin(X10,X154) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oin__idem) ).
fof(fact_Max_Oin__idem,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X16),c_Big__Operators_Olinorder__class_OMax(X10,X154)) = c_Big__Operators_Olinorder__class_OMax(X10,X154) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oin__idem) ).
fof(fact_Min_Oin__idem,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X16),c_Big__Operators_Olinorder__class_OMin(X10,X154)) = c_Big__Operators_Olinorder__class_OMin(X10,X154) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oin__idem) ).
fof(fact_Sup__upper,axiom,
! [X154,X16,X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),c_Complete__Lattice_OSup__class_OSup(X10,X154))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__upper) ).
fof(fact_ivl__disj__int_I2_J,axiom,
! [X165,X162,X10] :
( class_Orderings_Oorder(X10)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X10),X162)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X162),X165)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I2_J) ).
fof(fact_card__gt__0__iff,axiom,
! [X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X10),X154)))
<=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__gt__0__iff) ).
fof(fact_nth__Cons__Suc,axiom,
! [X42,X297,X93,X94] : hAPP(hAPP(c_List_Onth(X94),hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)),hAPP(c_Nat_OSuc,X42)) = hAPP(hAPP(c_List_Onth(X94),X297),X42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__Cons__Suc) ).
fof(fact_map__tl,axiom,
! [X290,X2,X10,X13] : hAPP(hAPP(c_List_Omap(X13,X10),X2),hAPP(c_List_Otl(X13),X290)) = hAPP(c_List_Otl(X10),hAPP(hAPP(c_List_Omap(X13,X10),X2),X290)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__tl) ).
fof(fact_rev__map,axiom,
! [X290,X2,X13,X10] : hAPP(c_List_Orev(X10),hAPP(hAPP(c_List_Omap(X13,X10),X2),X290)) = hAPP(hAPP(c_List_Omap(X13,X10),X2),hAPP(c_List_Orev(X13),X290)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__map) ).
fof(fact_zdvd__antisym__abs,axiom,
! [X92,X84] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X84),X92))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X92),X84))
=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X84) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X92) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__antisym__abs) ).
fof(fact_dvd__mult__div__cancel,axiom,
! [X92,X84,X94] :
( class_Divides_Osemiring__div(X94)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X84),X92))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),X92),X84)) = X92 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__div__cancel) ).
fof(fact_ex__nat,axiom,
! [X19] :
( ? [X147] : hBOOL(hAPP(X19,X147))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
& hBOOL(hAPP(X19,hAPP(c_Int_Onat,X3))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__nat) ).
fof(fact_card__ge__0__finite,axiom,
! [X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X10),X154)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__ge__0__finite) ).
fof(fact_Suc__pred,axiom,
! [X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X42))
=> hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X42),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X42 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__pred) ).
fof(fact_singleton__inject,axiom,
! [X38,X39,X10] :
( hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(X10),X38),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))
=> X39 = X38 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__inject) ).
fof(fact_of__nat__inverse,axiom,
! [X25] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25),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,X25)) = X25 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__inverse) ).
fof(fact_divide__eq__eq__number__of,axiom,
! [X131,X18,X38,X10] :
( ( class_Fields_Ofield__inverse__zero(X10)
& class_Int_Onumber(X10) )
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),X18) = hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)
<=> ( ( X18 != c_Groups_Ozero__class_Ozero(X10)
=> X38 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),X18) )
& ( X18 = c_Groups_Ozero__class_Ozero(X10)
=> hAPP(c_Int_Onumber__class_Onumber__of(X10),X131) = c_Groups_Ozero__class_Ozero(X10) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__eq__eq__number__of) ).
fof(fact_eq__divide__eq__number__of,axiom,
! [X18,X38,X131,X10] :
( ( class_Fields_Ofield__inverse__zero(X10)
& class_Int_Onumber(X10) )
=> ( hAPP(c_Int_Onumber__class_Onumber__of(X10),X131) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),X18)
<=> ( ( X18 != c_Groups_Ozero__class_Ozero(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),X18) = X38 )
& ( X18 = c_Groups_Ozero__class_Ozero(X10)
=> hAPP(c_Int_Onumber__class_Onumber__of(X10),X131) = c_Groups_Ozero__class_Ozero(X10) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__divide__eq__number__of) ).
fof(fact_le__Suc__eq,axiom,
! [X20,X102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),hAPP(c_Nat_OSuc,X20)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20))
| X102 = hAPP(c_Nat_OSuc,X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
fof(fact_append__butlast__last__id,axiom,
! [X94,X297] :
( X297 != c_List_Olist_ONil(X94)
=> hAPP(hAPP(c_List_Oappend(X94),c_List_Obutlast(X94,X297)),hAPP(hAPP(c_List_Olist_OCons(X94),c_List_Olast(X94,X297)),c_List_Olist_ONil(X94))) = X297 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__butlast__last__id) ).
fof(fact_WT_OIf,axiom,
! [X38,X75,X76] :
( hBOOL(hAPP(c_Com_OWT,X76))
=> ( hBOOL(hAPP(c_Com_OWT,X75))
=> hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X38,X76,X75))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_OIf) ).
fof(fact_pair__collapse,axiom,
! [X167,X10,X94] : hAPP(hAPP(c_Product__Type_OPair(X94,X10),hAPP(c_Product__Type_Ofst(X94,X10),X167)),hAPP(c_Product__Type_Osnd(X94,X10),X167)) = X167,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__collapse) ).
fof(fact_surjective__pairing,axiom,
! [X10,X94,X44] : X44 = hAPP(hAPP(c_Product__Type_OPair(X94,X10),hAPP(c_Product__Type_Ofst(X94,X10),X44)),hAPP(c_Product__Type_Osnd(X94,X10),X44)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surjective__pairing) ).
fof(fact_insort__key_Osimps_I1_J,axiom,
! [X16,X2,X10,X13] :
( class_Orderings_Olinorder(X13)
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X13,X2),X16),c_List_Olist_ONil(X10)) = hAPP(hAPP(c_List_Olist_OCons(X10),X16),c_List_Olist_ONil(X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__key_Osimps_I1_J) ).
fof(fact_fun__upd__idem__iff,axiom,
! [X25,X16,X2,X13,X10] :
( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,X13),X2),X16),X25) = X2
<=> hAPP(X2,X16) = X25 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__idem__iff) ).
fof(fact_distinct__takeWhile,axiom,
! [X19,X290,X10] :
( hBOOL(hAPP(c_List_Odistinct(X10),X290))
=> hBOOL(hAPP(c_List_Odistinct(X10),c_List_OtakeWhile(X10,X19,X290))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__takeWhile) ).
fof(fact_distinct__sublistI,axiom,
! [X241,X290,X10] :
( hBOOL(hAPP(c_List_Odistinct(X10),X290))
=> hBOOL(hAPP(c_List_Odistinct(X10),c_List_Osublist(X10,X290,X241))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__sublistI) ).
fof(fact_distinct__remove1,axiom,
! [X93,X297,X94] :
( hBOOL(hAPP(c_List_Odistinct(X94),X297))
=> hBOOL(hAPP(c_List_Odistinct(X94),c_List_Oremove1(X94,X93,X297))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__remove1) ).
fof(fact_remove1__commute,axiom,
! [X296,X105,X93,X94] : c_List_Oremove1(X94,X93,c_List_Oremove1(X94,X105,X296)) = c_List_Oremove1(X94,X105,c_List_Oremove1(X94,X93,X296)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1__commute) ).
fof(fact_fun__left__comm_Ofun__left__comm,axiom,
! [X73,X25,X16,X2,X13,X10] :
( c_Finite__Set_Ofun__left__comm(X10,X13,X2)
=> hAPP(hAPP(X2,X16),hAPP(hAPP(X2,X25),X73)) = hAPP(hAPP(X2,X25),hAPP(hAPP(X2,X16),X73)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__left__comm) ).
fof(fact_inf__Sup__absorb,axiom,
! [X39,X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X39),c_Big__Operators_Olattice__class_OSup__fin(X10,X154)) = X39 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Sup__absorb) ).
fof(fact_sup__Inf__absorb,axiom,
! [X39,X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X39),c_Big__Operators_Olattice__class_OInf__fin(X10,X154)) = X39 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Inf__absorb) ).
fof(fact_wfP__empty,axiom,
! [X10] : c_Wellfounded_OwfP(X10,hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X10),hAPP(c_COMBK(tc_HOL_Obool,X10),c_fFalse))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__empty) ).
fof(fact_dvd__triv__left,axiom,
! [X92,X84,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X84),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__triv__left) ).
fof(fact_dvd__triv__right,axiom,
! [X92,X84,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X84),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X84))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__triv__right) ).
fof(fact_sup__ge1,axiom,
! [X105,X93,X94] :
( class_Lattices_Osemilattice__sup(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),X105))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__ge1) ).
fof(fact_inf__sup__ord_I3_J,axiom,
! [X105,X93,X94] :
( class_Lattices_Olattice(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),X105))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I3_J) ).
fof(fact_sup__ge2,axiom,
! [X93,X105,X94] :
( class_Lattices_Osemilattice__sup(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X105),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),X105))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__ge2) ).
fof(fact_inf__sup__ord_I4_J,axiom,
! [X93,X105,X94] :
( class_Lattices_Olattice(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X105),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),X105))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I4_J) ).
fof(fact_le__maxI1,axiom,
! [X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X93),X105))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__maxI1) ).
fof(fact_le__maxI2,axiom,
! [X93,X105,X94] :
( class_Orderings_Olinorder(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X105),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X93),X105))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__maxI2) ).
fof(fact_mem__Collect__eq,axiom,
! [X19,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X39),hAPP(c_Set_OCollect(X10),X19)))
<=> hBOOL(hAPP(X19,X39)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__Collect__eq) ).
fof(fact_CollectD,axiom,
! [X19,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X39),hAPP(c_Set_OCollect(X10),X19)))
=> hBOOL(hAPP(X19,X39)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_CollectD) ).
fof(fact_CollectE,axiom,
! [X19,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X39),hAPP(c_Set_OCollect(X10),X19)))
=> hBOOL(hAPP(X19,X39)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_CollectE) ).
fof(fact_Suc__nat__eq__nat__zadd1,axiom,
! [X104] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X104))
=> hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,X104)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X104)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__nat__eq__nat__zadd1) ).
fof(fact_remove1_Osimps_I2_J,axiom,
! [X297,X94,X105,X93] :
( ( X93 = X105
=> c_List_Oremove1(X94,X93,hAPP(hAPP(c_List_Olist_OCons(X94),X105),X297)) = X297 )
& ( X93 != X105
=> c_List_Oremove1(X94,X93,hAPP(hAPP(c_List_Olist_OCons(X94),X105),X297)) = hAPP(hAPP(c_List_Olist_OCons(X94),X105),c_List_Oremove1(X94,X93,X297)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1_Osimps_I2_J) ).
fof(fact_dvd__div__eq__mult,axiom,
! [X18,X38,X39,X10] :
( class_Divides_Osemiring__div(X10)
=> ( X39 != c_Groups_Ozero__class_Ozero(X10)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X39),X38))
=> ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X10),X38),X39) = X18
<=> X38 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X39) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__div__eq__mult) ).
fof(fact_less__Suc__eq,axiom,
! [X20,X102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),hAPP(c_Nat_OSuc,X20)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X20))
| X102 = X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
fof(fact_Image__Id__on,axiom,
! [X160,X154,X10] : hAPP(c_Relation_OImage(X10,X10,c_Relation_OId__on(X10,X154)),X160) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Id__on) ).
fof(fact_inf__left__commute,axiom,
! [X104,X105,X93,X94] :
( class_Lattices_Osemilattice__inf(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X105),X104)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X105),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),X104)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__left__commute) ).
fof(fact_inf_Oleft__commute,axiom,
! [X81,X84,X92,X94] :
( class_Lattices_Osemilattice__inf(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X92),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X84),X81)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X84),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X92),X81)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oleft__commute) ).
fof(fact_inf__sup__aci_I3_J,axiom,
! [X104,X105,X93,X94] :
( class_Lattices_Olattice(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X105),X104)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X105),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),X104)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I3_J) ).
fof(fact_sup_Oleft__commute,axiom,
! [X81,X84,X92,X94] :
( class_Lattices_Osemilattice__sup(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X92),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X84),X81)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X84),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X92),X81)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oleft__commute) ).
fof(fact_sup__left__commute,axiom,
! [X104,X105,X93,X94] :
( class_Lattices_Osemilattice__sup(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X105),X104)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X105),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),X104)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__left__commute) ).
fof(fact_inf__sup__aci_I7_J,axiom,
! [X104,X105,X93,X94] :
( class_Lattices_Olattice(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X105),X104)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X105),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),X104)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I7_J) ).
fof(fact_min__max_Osup__left__commute,axiom,
! [X104,X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X93),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X105),X104)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X105),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X93),X104)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__left__commute) ).
fof(fact_min__max_Osup_Oleft__commute,axiom,
! [X81,X84,X92,X94] :
( class_Orderings_Olinorder(X94)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X92),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X84),X81)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X84),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X92),X81)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup_Oleft__commute) ).
fof(fact_min__max_Oinf_Oleft__commute,axiom,
! [X81,X84,X92,X94] :
( class_Orderings_Olinorder(X94)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X92),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X84),X81)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X84),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X92),X81)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf_Oleft__commute) ).
fof(fact_min__max_Oinf__left__commute,axiom,
! [X104,X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X93),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X105),X104)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X105),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X93),X104)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__left__commute) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
! [X137,X138,X139,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X139),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X138),X137)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X138),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X139),X137)) ),
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,
! [X112,X81,X84,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X81),X112)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X81),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X112)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_add__minus__cancel,axiom,
! [X92,X84,X94] :
( class_Groups_Ogroup__add(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X84)),X92)) = X92 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__minus__cancel) ).
fof(fact_nat__mult__eq__cancel1,axiom,
! [X20,X102,X101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X101))
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X101),X102) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X101),X20)
<=> X102 = X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).
fof(fact_less__Suc__eq__le,axiom,
! [X20,X102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),hAPP(c_Nat_OSuc,X20)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
fof(fact_one__div__nat__number__of,axiom,
! [X170] : 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),X170)) = 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),X170))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__div__nat__number__of) ).
fof(fact_split__nat,axiom,
! [X113,X19] :
( hBOOL(hAPP(X19,hAPP(c_Int_Onat,X113)))
<=> ( ! [X83] :
( X113 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X83)
=> hBOOL(hAPP(X19,X83)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X113),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__nat) ).
fof(fact_distinct__drop,axiom,
! [X120,X297,X94] :
( hBOOL(hAPP(c_List_Odistinct(X94),X297))
=> hBOOL(hAPP(c_List_Odistinct(X94),hAPP(hAPP(c_List_Odrop(X94),X120),X297))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__drop) ).
fof(fact_distinct__take,axiom,
! [X120,X297,X94] :
( hBOOL(hAPP(c_List_Odistinct(X94),X297))
=> hBOOL(hAPP(c_List_Odistinct(X94),hAPP(hAPP(c_List_Otake(X94),X120),X297))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__take) ).
fof(fact_finite_OinsertI,axiom,
! [X39,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(hAPP(c_Set_Oinsert(X10),X39),X154))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_OinsertI) ).
fof(fact_image__Suc__atLeastAtMost,axiom,
! [X163,X113] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X113,X163)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X113),hAPP(c_Nat_OSuc,X163)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Suc__atLeastAtMost) ).
fof(fact_INT__empty,axiom,
! [X160,X10,X13] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool))),X160) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__empty) ).
fof(fact_minus__numeral__code_I6_J,axiom,
! [X133,X144] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X144),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X133))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__numeral__code_I6_J) ).
fof(fact_Compl__eq__Diff__UNIV,axiom,
! [X154,X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X154) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),X154),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__eq__Diff__UNIV) ).
fof(fact_map__butlast,axiom,
! [X290,X2,X10,X13] : hAPP(hAPP(c_List_Omap(X13,X10),X2),c_List_Obutlast(X13,X290)) = c_List_Obutlast(X10,hAPP(hAPP(c_List_Omap(X13,X10),X2),X290)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__butlast) ).
fof(fact_Min__in,axiom,
! [X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_member(X10),c_Big__Operators_Olinorder__class_OMin(X10,X154)),X154)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min__in) ).
fof(fact_Max__in,axiom,
! [X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_member(X10),c_Big__Operators_Olinorder__class_OMax(X10,X154)),X154)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max__in) ).
fof(fact_all__nat,axiom,
! [X19] :
( ! [X147] : hBOOL(hAPP(X19,X147))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
=> hBOOL(hAPP(X19,hAPP(c_Int_Onat,X3))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__nat) ).
fof(fact_insertI1,axiom,
! [X160,X39,X10] : hBOOL(hAPP(hAPP(c_member(X10),X39),hAPP(hAPP(c_Set_Oinsert(X10),X39),X160))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI1) ).
fof(fact_mod__Suc,axiom,
! [X42,X97] :
( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X97,X42)) = X42
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X97),X42) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X97,X42)) != X42
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X97),X42) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X97,X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__Suc) ).
fof(fact_insert__commute,axiom,
! [X154,X25,X16,X10] : hAPP(hAPP(c_Set_Oinsert(X10),X16),hAPP(hAPP(c_Set_Oinsert(X10),X25),X154)) = hAPP(hAPP(c_Set_Oinsert(X10),X25),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__commute) ).
fof(fact_folding__one_Osingleton,axiom,
! [X16,X225,X2,X10] :
( c_Finite__Set_Ofolding__one(X10,X2,X225)
=> hAPP(X225,hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Osingleton) ).
fof(fact_diff__Suc__eq__diff__pred,axiom,
! [X42,X97] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),hAPP(c_Nat_OSuc,X42)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).
fof(fact_less__imp__add__positive,axiom,
! [X119,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),X119))
=> ? [X124] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X124))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X120),X124) = X119 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__add__positive) ).
fof(fact_fold__empty,axiom,
! [X73,X2,X10,X13] : hAPP(hAPP(c_Finite__Set_Ofold(X13,X10,X2),X73),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool))) = X73,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__empty) ).
fof(fact_length__drop,axiom,
! [X297,X42,X94] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),hAPP(hAPP(c_List_Odrop(X94),X42),X297)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)),X42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__drop) ).
fof(fact_length__take,axiom,
! [X297,X42,X94] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),hAPP(hAPP(c_List_Otake(X94),X42),X297)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)),X42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__take) ).
fof(fact_inj__of__nat,axiom,
! [X10] :
( class_Nat_Osemiring__char__0(X10)
=> c_Fun_Oinj__on(tc_Nat_Onat,X10,c_Nat_Osemiring__1__class_Oof__nat(X10),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,
! [X297,X42,X94] : hAPP(hAPP(c_List_Otake(X94),X42),hAPP(c_List_Otl(X94),X297)) = hAPP(c_List_Otl(X94),hAPP(hAPP(c_List_Otake(X94),hAPP(c_Nat_OSuc,X42)),X297)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__tl) ).
fof(fact_less__imp__Suc__add,axiom,
! [X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42))
=> ? [X124] : X42 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X124)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__Suc__add) ).
fof(fact_less__iff__Suc__add,axiom,
! [X20,X102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X20))
<=> ? [X124] : X20 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X124)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
! [X20] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X20) = 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),X20))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__functions_I1_J) ).
fof(fact_nonzero__abs__divide,axiom,
! [X84,X92,X94] :
( class_Fields_Olinordered__field(X94)
=> ( X92 != c_Groups_Ozero__class_Ozero(X94)
=> hAPP(c_Groups_Oabs__class_Oabs(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X84),X92)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),X84)),hAPP(c_Groups_Oabs__class_Oabs(X94),X92)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__abs__divide) ).
fof(fact_card_Oneutral,axiom,
! [X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ( ? [X3] : hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
=> hAPP(c_Finite__Set_Ocard(X10),X154) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oneutral) ).
fof(fact_Compl__disjoint,axiom,
! [X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X154)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__disjoint) ).
fof(fact_Compl__partition,axiom,
! [X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X154)) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__partition) ).
fof(fact_inj__Inl,axiom,
! [X154,X13,X10] : c_Fun_Oinj__on(X10,tc_sum(X10,X13),c_Sum__Type_OInl(X10,X13),X154),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__Inl) ).
fof(fact_inj__Inr,axiom,
! [X154,X13,X10] : c_Fun_Oinj__on(X10,tc_sum(X13,X10),c_Sum__Type_OInr(X10,X13),X154),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__Inr) ).
fof(fact_inj__on__empty,axiom,
! [X2,X13,X10] : c_Fun_Oinj__on(X10,X13,X2,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__empty) ).
fof(fact_dvd_Oeq__iff,axiom,
! [X25,X16] :
( X16 = X25
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X16),X25))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25),X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oeq__iff) ).
fof(fact_dvd_Oantisym__conv,axiom,
! [X16,X25] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25),X16))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X16),X25))
<=> X16 = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oantisym__conv) ).
fof(fact_dvd__antisym,axiom,
! [X42,X97] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X97),X42))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X42),X97))
=> X97 = X42 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__antisym) ).
fof(fact_dvd_Oantisym,axiom,
! [X105,X93] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X93),X105))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X105),X93))
=> X93 = X105 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oantisym) ).
fof(fact_zle__antisym,axiom,
! [X133,X104] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X104),X133))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X133),X104))
=> X104 = X133 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__antisym) ).
fof(fact_le__antisym,axiom,
! [X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),X42))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),X97))
=> X97 = X42 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__antisym) ).
fof(fact_zmod__minus1,axiom,
! [X92] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X92))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X92) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X92),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__minus1) ).
fof(fact_triple_Oexhaust,axiom,
! [X10,X25] :
~ ! [X26,X27,X28] : X25 != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X10),X26),X27),X28),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triple_Oexhaust) ).
fof(fact_Min__insert,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X16),c_Big__Operators_Olinorder__class_OMin(X10,X154)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min__insert) ).
fof(fact_Max__insert,axiom,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X16),c_Big__Operators_Olinorder__class_OMax(X10,X154)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max__insert) ).
fof(fact_Inf__fin_Oinsert__idem,axiom,
! [X16,X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X16),c_Big__Operators_Olattice__class_OInf__fin(X10,X154)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oinsert__idem) ).
fof(fact_Sup__fin_Oinsert__idem,axiom,
! [X16,X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X16),c_Big__Operators_Olattice__class_OSup__fin(X10,X154)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oinsert__idem) ).
fof(fact_Un__empty,axiom,
! [X160,X154,X10] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
<=> ( X154 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
& X160 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty) ).
fof(fact_listsum__append,axiom,
! [X298,X297,X94] :
( class_Groups_Omonoid__add(X94)
=> hAPP(c_List_Omonoid__add__class_Olistsum(X94),hAPP(hAPP(c_List_Oappend(X94),X297),X298)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(c_List_Omonoid__add__class_Olistsum(X94),X297)),hAPP(c_List_Omonoid__add__class_Olistsum(X94),X298)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__append) ).
fof(fact_abs__divide,axiom,
! [X92,X84,X94] :
( class_Fields_Olinordered__field__inverse__zero(X94)
=> hAPP(c_Groups_Oabs__class_Oabs(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X84),X92)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),X84)),hAPP(c_Groups_Oabs__class_Oabs(X94),X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__divide) ).
fof(fact_abs__mult,axiom,
! [X92,X84,X94] :
( class_Rings_Olinordered__idom(X94)
=> hAPP(c_Groups_Oabs__class_Oabs(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),X84)),hAPP(c_Groups_Oabs__class_Oabs(X94),X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult) ).
fof(fact_compl__inf,axiom,
! [X105,X93,X94] :
( class_Lattices_Oboolean__algebra(X94)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X94),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),X105)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X93)),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X105)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__inf) ).
fof(fact_compl__sup,axiom,
! [X105,X93,X94] :
( class_Lattices_Oboolean__algebra(X94)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X94),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),X105)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X93)),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X105)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__sup) ).
fof(fact_minus__max__eq__min,axiom,
! [X105,X93,X94] :
( class_Groups_Olinordered__ab__group__add(X94)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X94),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X93),X105)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X93)),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X105)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__max__eq__min) ).
fof(fact_minus__min__eq__max,axiom,
! [X105,X93,X94] :
( class_Groups_Olinordered__ab__group__add(X94)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X94),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X93),X105)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X93)),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X105)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__min__eq__max) ).
fof(fact_minus__add__distrib,axiom,
! [X92,X84,X94] :
( class_Groups_Oab__group__add(X94)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X84)),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add__distrib) ).
fof(fact_minus__add,axiom,
! [X92,X84,X94] :
( class_Groups_Ogroup__add(X94)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X92)),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X84)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add) ).
fof(fact_Cantors__paradox,axiom,
! [X154,X10] :
~ ? [X247] : hAPP(c_Set_Oimage(X10,tc_fun(X10,tc_HOL_Obool),X247),X154) = hAPP(c_Set_OPow(X10),X154),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cantors__paradox) ).
fof(fact_equalityD1,axiom,
! [X10,X160,X154] :
( X154 = X160
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD1) ).
fof(fact_equalityD2,axiom,
! [X10,X160,X154] :
( X154 = X160
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD2) ).
fof(fact_last__in__set,axiom,
! [X10,X312] :
( X312 != c_List_Olist_ONil(X10)
=> hBOOL(hAPP(hAPP(c_member(X10),c_List_Olast(X10,X312)),hAPP(c_List_Oset(X10),X312))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__in__set) ).
fof(fact_Suc__mult__cancel1,axiom,
! [X20,X102,X101] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X101)),X102) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X101)),X20)
<=> X102 = X20 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).
fof(fact_Pair__eq,axiom,
! [X118,X96,X38,X39,X13,X10] :
( hAPP(hAPP(c_Product__Type_OPair(X10,X13),X39),X38) = hAPP(hAPP(c_Product__Type_OPair(X10,X13),X96),X118)
<=> ( X39 = X96
& X38 = X118 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__eq) ).
fof(fact_Pair__inject,axiom,
! [X130,X95,X92,X84,X10,X94] :
( hAPP(hAPP(c_Product__Type_OPair(X94,X10),X84),X92) = hAPP(hAPP(c_Product__Type_OPair(X94,X10),X95),X130)
=> ~ ( X84 = X95
=> X92 != X130 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__inject) ).
fof(fact_zmod__zminus1__eq__if,axiom,
! [X92,X84] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X92) = 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),X84),X92) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X92) != 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),X84),X92) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X92),c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X92)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus1__eq__if) ).
fof(fact_subset__refl,axiom,
! [X154,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X154)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__refl) ).
fof(fact_image__Suc__atLeastLessThan,axiom,
! [X163,X113] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X113),X163)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X113)),hAPP(c_Nat_OSuc,X163)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Suc__atLeastLessThan) ).
fof(fact_rev__append,axiom,
! [X298,X297,X94] : hAPP(c_List_Orev(X94),hAPP(hAPP(c_List_Oappend(X94),X297),X298)) = hAPP(hAPP(c_List_Oappend(X94),hAPP(c_List_Orev(X94),X298)),hAPP(c_List_Orev(X94),X297)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__append) ).
fof(fact_rotate__simps,axiom,
! [X297,X93,X10,X94] :
( hAPP(c_List_Orotate1(X94),c_List_Olist_ONil(X94)) = c_List_Olist_ONil(X94)
& hAPP(c_List_Orotate1(X10),hAPP(hAPP(c_List_Olist_OCons(X10),X93),X297)) = hAPP(hAPP(c_List_Oappend(X10),X297),hAPP(hAPP(c_List_Olist_OCons(X10),X93),c_List_Olist_ONil(X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__simps) ).
fof(fact_le__SucI,axiom,
! [X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),X42))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),hAPP(c_Nat_OSuc,X42))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucI) ).
fof(fact_le__imp__less__Suc,axiom,
! [X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),X42))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),hAPP(c_Nat_OSuc,X42))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
fof(fact_less__SucI,axiom,
! [X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),hAPP(c_Nat_OSuc,X42))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucI) ).
fof(fact_greaterThanAtMost__upto,axiom,
! [X163,X113] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X113,X163) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X113),c_Groups_Oone__class_Oone(tc_Int_Oint)),X163)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanAtMost__upto) ).
fof(fact_Ints__double__eq__0__iff,axiom,
! [X39,X10] :
( class_Int_Oring__char__0(X10)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),c_Int_Oring__1__class_OInts(X10)))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X39),X39) = c_Groups_Ozero__class_Ozero(X10)
<=> X39 = c_Groups_Ozero__class_Ozero(X10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__double__eq__0__iff) ).
fof(fact_div__eq__minus1,axiom,
! [X92] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X92))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),X92) = 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,
! [X160,X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X160),X154),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__commute) ).
fof(fact_Un__commute,axiom,
! [X160,X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X160),X154),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__commute) ).
fof(fact_triple_Osize_I1_J,axiom,
! [X7,X8,X9,X11,X10] : c_Hoare__Mirabelle_Otriple_Otriple__size(X10,X11,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X10),X9),X8),X7)) = 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,
! [X103] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X103))
=> ? [X83] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X83))
& X103 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X83) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__imp__eq__int) ).
fof(fact_frac__eq__eq,axiom,
! [X131,X16,X73,X25,X10] :
( class_Fields_Ofield(X10)
=> ( X25 != c_Groups_Ozero__class_Ozero(X10)
=> ( X73 != c_Groups_Ozero__class_Ozero(X10)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X16),X25) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X131),X73)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X16),X73) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X131),X25) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_frac__eq__eq) ).
fof(fact_zmult__div__cancel,axiom,
! [X97,X42] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X42),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X97),X42)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X97),c_Divides_Odiv__class_Omod(tc_Int_Oint,X97,X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__div__cancel) ).
fof(fact_mult__div__cancel,axiom,
! [X97,X42] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X97),X42)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X97,X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__div__cancel) ).
fof(fact_minus__code__numeral__def,axiom,
! [X97,X42] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X42),X97) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X42)),hAPP(c_Code__Numeral_Onat__of,X97))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__code__numeral__def) ).
fof(fact_div__code__numeral__def,axiom,
! [X97,X42] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X42),X97) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X42)),hAPP(c_Code__Numeral_Onat__of,X97))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__code__numeral__def) ).
fof(fact_times__code__numeral__def,axiom,
! [X97,X42] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),X42),X97) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X42)),hAPP(c_Code__Numeral_Onat__of,X97))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__code__numeral__def) ).
fof(fact_plus__code__numeral__def,axiom,
! [X97,X42] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X42),X97) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X42)),hAPP(c_Code__Numeral_Onat__of,X97))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__code__numeral__def) ).
fof(fact_diff__diff__cancel,axiom,
! [X42,X120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X120),X42))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X42),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X42),X120)) = X120 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).
fof(fact_zdvd__mult__div__cancel,axiom,
! [X97,X42] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X42),X97))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X42),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X97),X42)) = X97 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__mult__div__cancel) ).
fof(fact_le__add__diff__inverse,axiom,
! [X97,X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),X97))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42)) = X97 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).
fof(fact_nat__case__Suc,axiom,
! [X110,X37,X12,X10] : c_Nat_Onat_Onat__case(X10,X12,X37,hAPP(c_Nat_OSuc,X110)) = hAPP(X37,X110),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__Suc) ).
fof(fact_listsum__eq__0__nat__iff__nat,axiom,
! [X305] :
( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X305) = 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),X305)))
=> 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,
! [X39,X78,X18] :
( hBOOL(hAPP(c_Com_OWT,X18))
=> hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X78,X39,X18))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_OLocal) ).
fof(fact_xt1_I11_J,axiom,
! [X84,X92,X94] :
( class_Orderings_Oorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X92),X84))
=> ( X84 != X92
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X92),X84)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
fof(fact_order__le__neq__trans,axiom,
! [X92,X84,X94] :
( class_Orderings_Oorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X92))
=> ( X84 != X92
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),X92)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
fof(fact_order__le__imp__less__or__eq,axiom,
! [X105,X93,X94] :
( class_Orderings_Oorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X105))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X105))
| X93 = X105 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
fof(fact_order__neq__le__trans,axiom,
! [X92,X84,X94] :
( class_Orderings_Oorder(X94)
=> ( X84 != X92
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X92))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),X92)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
fof(fact_order__le__less,axiom,
! [X25,X16,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X25))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X16),X25))
| X16 = X25 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less) ).
fof(fact_order__less__le,axiom,
! [X25,X16,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X16),X25))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X25))
& X16 != X25 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le) ).
fof(fact_xt1_I12_J,axiom,
! [X92,X84,X94] :
( class_Orderings_Oorder(X94)
=> ( X84 != X92
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X92),X84))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X92),X84)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
fof(fact_arith__simps_I32_J,axiom,
! [X133,X144,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),X144)),hAPP(c_Int_Onumber__class_Onumber__of(X94),X133)) = hAPP(c_Int_Onumber__class_Onumber__of(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X144),X133)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arith__simps_I32_J) ).
fof(fact_add__number__of__eq,axiom,
! [X133,X144,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),X144)),hAPP(c_Int_Onumber__class_Onumber__of(X94),X133)) = hAPP(c_Int_Onumber__class_Onumber__of(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X144),X133)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__number__of__eq) ).
fof(fact_number__of__diff,axiom,
! [X133,X144,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(c_Int_Onumber__class_Onumber__of(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X144),X133)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),X144)),hAPP(c_Int_Onumber__class_Onumber__of(X94),X133)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__diff) ).
fof(fact_number__of__mult,axiom,
! [X133,X144,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(c_Int_Onumber__class_Onumber__of(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X144),X133)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),X144)),hAPP(c_Int_Onumber__class_Onumber__of(X94),X133)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__mult) ).
fof(fact_number__of__add,axiom,
! [X133,X144,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(c_Int_Onumber__class_Onumber__of(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X144),X133)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),X144)),hAPP(c_Int_Onumber__class_Onumber__of(X94),X133)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__add) ).
fof(fact_of__int__diff,axiom,
! [X104,X133,X94] :
( class_Rings_Oring__1(X94)
=> hAPP(c_Int_Oring__1__class_Oof__int(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X133),X104)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),hAPP(c_Int_Oring__1__class_Oof__int(X94),X133)),hAPP(c_Int_Oring__1__class_Oof__int(X94),X104)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__diff) ).
fof(fact_of__int__mult,axiom,
! [X104,X133,X94] :
( class_Rings_Oring__1(X94)
=> hAPP(c_Int_Oring__1__class_Oof__int(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X133),X104)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(c_Int_Oring__1__class_Oof__int(X94),X133)),hAPP(c_Int_Oring__1__class_Oof__int(X94),X104)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__mult) ).
fof(fact_of__int__add,axiom,
! [X104,X133,X94] :
( class_Rings_Oring__1(X94)
=> hAPP(c_Int_Oring__1__class_Oof__int(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X133),X104)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(c_Int_Oring__1__class_Oof__int(X94),X133)),hAPP(c_Int_Oring__1__class_Oof__int(X94),X104)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__add) ).
fof(fact_of__nat__mult,axiom,
! [X42,X97,X94] :
( class_Rings_Osemiring__1(X94)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X97),X42)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),X97)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__mult) ).
fof(fact_of__nat__add,axiom,
! [X42,X97,X94] :
( class_Rings_Osemiring__1(X94)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X42)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),X97)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__add) ).
fof(fact_minus1__divide,axiom,
! [X93,X94] :
( ( class_Fields_Ofield__inverse__zero(X94)
& class_Int_Onumber__ring(X94) )
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OMin)),X93) = hAPP(c_Groups_Ouminus__class_Ouminus(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),c_Groups_Oone__class_Oone(X94)),X93)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus1__divide) ).
fof(fact_setsum__0,axiom,
! [X154,X13,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X10),hAPP(c_COMBK(X10,X13),c_Groups_Ozero__class_Ozero(X10))),X154) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__0) ).
fof(fact_setprod__1,axiom,
! [X154,X13,X10] :
( class_Groups_Ocomm__monoid__mult(X10)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X13,X10),hAPP(c_COMBK(X10,X13),c_Groups_Oone__class_Oone(X10))),X154) = c_Groups_Oone__class_Oone(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__1) ).
fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
! [X165,X162] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X162),c_Groups_Oone__class_Oone(tc_Int_Oint))),X165) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X162,X165),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastPlusOneLessThan__greaterThanLessThan__int) ).
fof(fact_order__less__imp__le,axiom,
! [X105,X93,X94] :
( class_Orderings_Opreorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X105))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X105)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
fof(fact_negateSnd__eq,axiom,
! [X143,X149] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X149),X143)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X149),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X143)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negateSnd__eq) ).
fof(fact_abs__power__minus__one,axiom,
! [X42,X94] :
( ( class_Int_Onumber__ring(X94)
& class_Rings_Olinordered__idom(X94) )
=> hAPP(c_Groups_Oabs__class_Oabs(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OMin)),X42)) = c_Groups_Oone__class_Oone(X94) ),
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,
! [X160,X154] :
( c_Nat__Transfer_Onat__set(X154)
=> ( c_Nat__Transfer_Onat__set(X160)
=> c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X154),X160)) ) ),
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,
! [X160,X154] :
( c_Nat__Transfer_Onat__set(X154)
=> ( c_Nat__Transfer_Onat__set(X160)
=> c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X154),X160)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J) ).
fof(fact_zle__iff__zadd,axiom,
! [X73,X131] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X131),X73))
<=> ? [X83] : X73 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X131),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X83)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__iff__zadd) ).
fof(fact_filter__remove1,axiom,
! [X290,X16,X17,X10] : hAPP(c_List_Ofilter(X10,X17),c_List_Oremove1(X10,X16,X290)) = c_List_Oremove1(X10,X16,hAPP(c_List_Ofilter(X10,X17),X290)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__remove1) ).
fof(fact_snoc__eq__iff__butlast,axiom,
! [X289,X16,X290,X10] :
( hAPP(hAPP(c_List_Oappend(X10),X290),hAPP(hAPP(c_List_Olist_OCons(X10),X16),c_List_Olist_ONil(X10))) = X289
<=> ( X289 != c_List_Olist_ONil(X10)
& c_List_Obutlast(X10,X289) = X290
& c_List_Olast(X10,X289) = X16 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snoc__eq__iff__butlast) ).
fof(fact_negD,axiom,
! [X93] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X93),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ? [X83] : X93 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X83))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negD) ).
fof(fact_Ints__number__of,axiom,
! [X131,X10] :
( class_Int_Onumber__ring(X10)
=> hBOOL(hAPP(hAPP(c_member(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),c_Int_Oring__1__class_OInts(X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__number__of) ).
fof(fact_Ints__of__int,axiom,
! [X73,X10] :
( class_Rings_Oring__1(X10)
=> hBOOL(hAPP(hAPP(c_member(X10),hAPP(c_Int_Oring__1__class_Oof__int(X10),X73)),c_Int_Oring__1__class_OInts(X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__of__int) ).
fof(fact_Ints__of__nat,axiom,
! [X20,X10] :
( class_Rings_Oring__1(X10)
=> hBOOL(hAPP(hAPP(c_member(X10),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),X20)),c_Int_Oring__1__class_OInts(X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__of__nat) ).
fof(fact_of__nat__in__Nats,axiom,
! [X20,X10] :
( class_Rings_Osemiring__1(X10)
=> hBOOL(hAPP(hAPP(c_member(X10),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),X20)),c_Nat_Osemiring__1__class_ONats(X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__in__Nats) ).
fof(fact_Suc__diff__1,axiom,
! [X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X42))
=> hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X42),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X42 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__1) ).
fof(fact_Suc__pred_H,axiom,
! [X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X42))
=> X42 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X42),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__pred_H) ).
fof(fact_nat__of,axiom,
! [X16] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X16)),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,
! [X92,X84,X94] :
( class_Divides_Osemiring__div(X94)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),c_Divides_Odiv__class_Omod(X94,X84,X92)),X92) = c_Groups_Ozero__class_Ozero(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__div__trivial) ).
fof(fact_negDivAlg__minus1,axiom,
! [X92] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X92) = 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),X92),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,
! [X25,X16] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16))
=> c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X16,X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__function__closures) ).
fof(fact_min__max_OInf__fin_Osingleton,axiom,
! [X16,X10] :
( class_Orderings_Olinorder(X10)
=> c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Osingleton) ).
fof(fact_min__max_OSup__fin_Osingleton,axiom,
! [X16,X10] :
( class_Orderings_Olinorder(X10)
=> c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Osingleton) ).
fof(fact_int__one__le__iff__zero__less,axiom,
! [X73] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X73))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).
fof(fact_Int__empty__left,axiom,
! [X160,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),X160) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__empty__left) ).
fof(fact_Un__UNIV__left,axiom,
! [X160,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),X160) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__UNIV__left) ).
fof(fact_empty__Diff,axiom,
! [X154,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),X154) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__Diff) ).
fof(fact_Sigma__empty1,axiom,
! [X160,X13,X10] : hAPP(hAPP(c_Product__Type_OSigma(X10,X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),X160) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__empty1) ).
fof(fact_le__square,axiom,
! [X97] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X97),X97))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__square) ).
fof(fact_le__add1,axiom,
! [X97,X42] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),X97))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add1) ).
fof(fact_le__add2,axiom,
! [X97,X42] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X42))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add2) ).
fof(fact_divide__eq__eq__number__of1,axiom,
! [X39,X131,X38,X10] :
( ( class_Fields_Ofield__inverse__zero(X10)
& class_Int_Onumber(X10) )
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)) = X39
<=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(X10),X131) != c_Groups_Ozero__class_Ozero(X10)
=> X38 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(X10),X131) = c_Groups_Ozero__class_Ozero(X10)
=> X39 = c_Groups_Ozero__class_Ozero(X10) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__eq__eq__number__of1) ).
fof(fact_eq__divide__eq__number__of1,axiom,
! [X131,X38,X39,X10] :
( ( class_Fields_Ofield__inverse__zero(X10)
& class_Int_Onumber(X10) )
=> ( X39 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131))
<=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(X10),X131) != c_Groups_Ozero__class_Ozero(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)) = X38 )
& ( hAPP(c_Int_Onumber__class_Onumber__of(X10),X131) = c_Groups_Ozero__class_Ozero(X10)
=> X39 = c_Groups_Ozero__class_Ozero(X10) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__divide__eq__number__of1) ).
fof(fact_nat__less__cases,axiom,
! [X19,X20,X102] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X20))
=> hBOOL(hAPP(hAPP(X19,X20),X102)) )
=> ( ( X102 = X20
=> hBOOL(hAPP(hAPP(X19,X20),X102)) )
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X102))
=> hBOOL(hAPP(hAPP(X19,X20),X102)) )
=> hBOOL(hAPP(hAPP(X19,X20),X102)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__cases) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
! [X154] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X154) = 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)),X154)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J) ).
fof(fact_append__eq__appendI,axiom,
! [X317,X298,X296,X315,X297,X94] :
( hAPP(hAPP(c_List_Oappend(X94),X297),X315) = X296
=> ( X298 = hAPP(hAPP(c_List_Oappend(X94),X315),X317)
=> hAPP(hAPP(c_List_Oappend(X94),X297),X298) = hAPP(hAPP(c_List_Oappend(X94),X296),X317) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__eq__appendI) ).
fof(fact_Cons__eq__appendI,axiom,
! [X296,X297,X298,X315,X93,X94] :
( hAPP(hAPP(c_List_Olist_OCons(X94),X93),X315) = X298
=> ( X297 = hAPP(hAPP(c_List_Oappend(X94),X315),X296)
=> hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297) = hAPP(hAPP(c_List_Oappend(X94),X298),X296) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__eq__appendI) ).
fof(fact_zadd__left__commute,axiom,
! [X104,X105,X93] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X93),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X105),X104)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X105),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X93),X104)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
fof(fact_nat__add__left__commute,axiom,
! [X104,X105,X93] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X93),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X105),X104)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X105),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X93),X104)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
fof(fact_atLeastLessThan__upto,axiom,
! [X163,X113] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X113),X163) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X113,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X163),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,
! [X97,X42] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X42),X97)),X97) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X42),X97),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__minus__add__max) ).
fof(fact_dual__max,axiom,
! [X10] :
( class_Orderings_Olinorder(X10)
=> c_Orderings_Oord_Omax(X10,hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X10))) = c_Orderings_Oord__class_Omin(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dual__max) ).
fof(fact_dual__min,axiom,
! [X10] :
( class_Orderings_Olinorder(X10)
=> c_Orderings_Oord_Omin(X10,hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X10))) = c_Orderings_Oord__class_Omax(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dual__min) ).
fof(fact_listsum__foldl,axiom,
! [X10] :
( class_Groups_Omonoid__add(X10)
=> c_List_Omonoid__add__class_Olistsum(X10) = c_List_Ofoldl(X10,X10,c_Groups_Oplus__class_Oplus(X10),c_Groups_Ozero__class_Ozero(X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__foldl) ).
fof(fact_elem__set,axiom,
! [X215,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X16),c_Option_Oset(X10,X215)))
<=> X215 = hAPP(c_Option_Ooption_OSome(X10),X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_elem__set) ).
fof(fact_div__mult__self1__is__id,axiom,
! [X84,X92,X94] :
( class_Divides_Osemiring__div(X94)
=> ( X92 != c_Groups_Ozero__class_Ozero(X94)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X84)),X92) = X84 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self1__is__id) ).
fof(fact_div__mult__self2__is__id,axiom,
! [X84,X92,X94] :
( class_Divides_Osemiring__div(X94)
=> ( X92 != c_Groups_Ozero__class_Ozero(X94)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92)),X92) = X84 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self2__is__id) ).
fof(fact_le__imp__diff__is__add,axiom,
! [X101,X163,X113] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X113),X163))
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X163),X113) = X101
<=> X163 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X101),X113) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__diff__is__add) ).
fof(fact_zmod__zminus2,axiom,
! [X92,X84] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X92)) = 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),X84),X92)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus2) ).
fof(fact_vname_Orecs_I1_J,axiom,
! [X107,X37,X12,X10] : c_Com_Ovname_Ovname__rec(X10,X12,X37,c_Com_Ovname_OGlb(X107)) = hAPP(X12,X107),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vname_Orecs_I1_J) ).
fof(fact_vname_Orecs_I2_J,axiom,
! [X79,X37,X12,X10] : c_Com_Ovname_Ovname__rec(X10,X12,X37,c_Com_Ovname_OLoc(X79)) = hAPP(X37,X79),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vname_Orecs_I2_J) ).
fof(fact_vname_Osimps_I5_J,axiom,
! [X107,X37,X12,X10] : c_Com_Ovname_Ovname__case(X10,X12,X37,c_Com_Ovname_OGlb(X107)) = hAPP(X12,X107),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vname_Osimps_I5_J) ).
fof(fact_vname_Osimps_I6_J,axiom,
! [X79,X37,X12,X10] : c_Com_Ovname_Ovname__case(X10,X12,X37,c_Com_Ovname_OLoc(X79)) = hAPP(X37,X79),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vname_Osimps_I6_J) ).
fof(fact_insert__dom,axiom,
! [X13,X25,X10,X16,X2] :
( hAPP(X2,X16) = hAPP(c_Option_Ooption_OSome(X10),X25)
=> hAPP(hAPP(c_Set_Oinsert(X13),X16),c_Map_Odom(X13,X10,X2)) = c_Map_Odom(X13,X10,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__dom) ).
fof(fact_Nitpick_Owf_H__def,axiom,
! [X177,X10] :
( c_Nitpick_Owf_H(X10,X177)
<=> ( c_Wellfounded_Oacyclic(X10,X177)
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10,X10)),X177))
| 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,
! [X177,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10,X10)),X177))
=> ( c_Wellfounded_Owf(X10,X177)
<=> c_Wellfounded_Oacyclic(X10,X177) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__iff__acyclic__if__finite) ).
fof(fact_finite__acyclic__wf,axiom,
! [X177,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10,X10)),X177))
=> ( c_Wellfounded_Oacyclic(X10,X177)
=> c_Wellfounded_Owf(X10,X177) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__acyclic__wf) ).
fof(fact_inj__on__rev,axiom,
! [X154,X10] : c_Fun_Oinj__on(tc_List_Olist(X10),tc_List_Olist(X10),c_List_Orev(X10),X154),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__rev) ).
fof(fact_distinct__filter,axiom,
! [X19,X290,X10] :
( hBOOL(hAPP(c_List_Odistinct(X10),X290))
=> hBOOL(hAPP(c_List_Odistinct(X10),hAPP(c_List_Ofilter(X10,X19),X290))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__filter) ).
fof(fact_triple_Osize_I2_J,axiom,
! [X7,X8,X9,X10] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(X10)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X10),X9),X8),X7)) = 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,
! [X196,X10] :
( c_Equiv__Relations_Oequivp(X10,X196)
<=> ! [X3,X90] :
( hBOOL(hAPP(hAPP(X196,X3),X90))
<=> hAPP(X196,X3) = hAPP(X196,X90) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivp__def) ).
fof(fact_add__diff__cancel,axiom,
! [X92,X84,X94] :
( class_Groups_Ogroup__add(X94)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92)),X92) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__cancel) ).
fof(fact_diff__add__cancel,axiom,
! [X92,X84,X94] :
( class_Groups_Ogroup__add(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X84),X92)),X92) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__cancel) ).
fof(fact_fst__eq__Domain,axiom,
! [X196,X13,X10] : hAPP(c_Set_Oimage(tc_prod(X10,X13),X10,c_Product__Type_Ofst(X10,X13)),X196) = hAPP(c_Relation_ODomain(X10,X13),X196),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__eq__Domain) ).
fof(fact_snd__eq__Range,axiom,
! [X196,X10,X13] : hAPP(c_Set_Oimage(tc_prod(X13,X10),X10,c_Product__Type_Osnd(X13,X10)),X196) = hAPP(c_Relation_ORange(X13,X10),X196),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__eq__Range) ).
fof(fact_zero__induct,axiom,
! [X101,X19] :
( hBOOL(hAPP(X19,X101))
=> ( ! [X83] :
( hBOOL(hAPP(X19,hAPP(c_Nat_OSuc,X83)))
=> hBOOL(hAPP(X19,X83)) )
=> hBOOL(hAPP(X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__induct) ).
fof(fact_total__on__converse,axiom,
! [X177,X154,X10] :
( c_Relation_Ototal__on(X10,X154,hAPP(c_Relation_Oconverse(X10,X10),X177))
<=> c_Relation_Ototal__on(X10,X154,X177) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__converse) ).
fof(fact_refl__on__converse,axiom,
! [X177,X154,X10] :
( c_Relation_Orefl__on(X10,X154,hAPP(c_Relation_Oconverse(X10,X10),X177))
<=> c_Relation_Orefl__on(X10,X154,X177) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__converse) ).
fof(fact_com_Osize_I11_J,axiom,
! [X8,X29,X79] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(X79,X29,X8)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X8)),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,
! [X154] :
( c_Nat__Transfer_Onat__set(X154)
=> hAPP(c_Finite__Set_Ocard(tc_Int_Oint),X154) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X154)) ),
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,
! [X16,X154] :
( c_Nat__Transfer_Onat__set(X154)
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X16),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J) ).
fof(fact_nat__set__def,axiom,
! [X216] :
( c_Nat__Transfer_Onat__set(X216)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),X216))
=> 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,
! [X10] : c_Relation_Orefl__on(X10,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__empty) ).
fof(fact_card__eq__setsum,axiom,
! [X154,X10] : hAPP(c_Finite__Set_Ocard(X10),X154) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X10),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X154),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__eq__setsum) ).
fof(fact_divmod__nat__rel__unique,axiom,
! [X184,X185,X42,X97] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X97,X42),X185))
=> ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X97,X42),X184))
=> X185 = X184 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__unique) ).
fof(fact_inj__uminus,axiom,
! [X154,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> c_Fun_Oinj__on(X10,X10,c_Groups_Ouminus__class_Ouminus(X10),X154) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__uminus) ).
fof(fact_mod__code__numeral__def,axiom,
! [X97,X42] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X42,X97) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,X42),hAPP(c_Code__Numeral_Onat__of,X97))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__code__numeral__def) ).
fof(fact_nth__Cons__0,axiom,
! [X297,X93,X94] : hAPP(hAPP(c_List_Onth(X94),hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X93,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__Cons__0) ).
fof(fact_image__is__empty,axiom,
! [X154,X2,X10,X13] :
( hAPP(c_Set_Oimage(X13,X10,X2),X154) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
<=> X154 = c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__is__empty) ).
fof(fact_empty__is__image,axiom,
! [X154,X2,X13,X10] :
( c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) = hAPP(c_Set_Oimage(X13,X10,X2),X154)
<=> X154 = c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__is__image) ).
fof(fact_inj__Some,axiom,
! [X154,X10] : c_Fun_Oinj__on(X10,tc_Option_Ooption(X10),c_Option_Ooption_OSome(X10),X154),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__Some) ).
fof(fact_listrelp_ONil,axiom,
! [X177,X10] : c_List_Olistrelp(X10,X177,c_List_Olist_ONil(X10),c_List_Olist_ONil(X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrelp_ONil) ).
fof(fact_listrelp_Oequations_I1_J,axiom,
! [X177,X10] : c_List_Olistrelp(X10,X177,c_List_Olist_ONil(X10),c_List_Olist_ONil(X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrelp_Oequations_I1_J) ).
fof(fact_hd__map,axiom,
! [X2,X13,X10,X290] :
( X290 != c_List_Olist_ONil(X10)
=> hAPP(c_List_Ohd(X13),hAPP(hAPP(c_List_Omap(X10,X13),X2),X290)) = hAPP(X2,hAPP(c_List_Ohd(X10),X290)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__map) ).
fof(fact_of__nat__aux_Osimps_I1_J,axiom,
! [X113,X114,X10] :
( class_Rings_Osemiring__1(X10)
=> c_Nat_Osemiring__1__class_Oof__nat__aux(X10,X114,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X113) = X113 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__aux_Osimps_I1_J) ).
fof(fact_atLeastAtMost__singleton__iff,axiom,
! [X18,X38,X39,X10] :
( class_Orderings_Oorder(X10)
=> ( c_SetInterval_Oord__class_OatLeastAtMost(X10,X39,X38) = hAPP(hAPP(c_Set_Oinsert(X10),X18),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))
<=> ( X39 = X38
& X38 = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMost__singleton__iff) ).
fof(fact_pos__single__def,axiom,
! [X201,X202,X203,X16,X10] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(X10),X16),X203),X202),X201) = c_New__DSequence_Opos__single(X10,X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__single__def) ).
fof(fact_neg__single__def,axiom,
! [X201,X202,X203,X16,X10] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(X10),X16),X203),X202),X201) = c_New__DSequence_Oneg__single(X10,X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__single__def) ).
fof(fact_power__abs,axiom,
! [X42,X84,X94] :
( class_Rings_Olinordered__idom(X94)
=> hAPP(c_Groups_Oabs__class_Oabs(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42)) = hAPP(hAPP(c_Power_Opower__class_Opower(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),X84)),X42) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__abs) ).
fof(fact_minus__divide__left,axiom,
! [X92,X84,X94] :
( class_Rings_Odivision__ring(X94)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X84),X92)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X84)),X92) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__divide__left) ).
fof(fact_minus__mult__left,axiom,
! [X92,X84,X94] :
( class_Rings_Oring(X94)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X84)),X92) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__left) ).
fof(fact_power_Opower_Opower__0,axiom,
! [X39,X172,X173,X10] : hAPP(hAPP(c_Power_Opower_Opower(X10,X173,X172),X39),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X173,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power_Opower_Opower__0) ).
fof(fact_map__filter__simps_I2_J,axiom,
! [X2,X10,X13] : c_List_Omap__filter(X13,X10,X2,c_List_Olist_ONil(X13)) = c_List_Olist_ONil(X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__filter__simps_I2_J) ).
fof(fact_atLeastatMost__empty,axiom,
! [X39,X38,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X38),X39))
=> c_SetInterval_Oord__class_OatLeastAtMost(X10,X39,X38) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastatMost__empty) ).
fof(fact_greaterThanAtMost__empty,axiom,
! [X101,X162,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X162),X101))
=> c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X101,X162) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanAtMost__empty) ).
fof(fact_greaterThanLessThan__empty,axiom,
! [X101,X162,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X162),X101))
=> c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X101,X162) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanLessThan__empty) ).
fof(fact_dvd__1__iff__1,axiom,
! [X102] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X102),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> X102 = 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,
! [X298,X94,X297] :
( X297 != c_List_Olist_ONil(X94)
=> hAPP(c_List_Otl(X94),hAPP(hAPP(c_List_Oappend(X94),X297),X298)) = hAPP(hAPP(c_List_Oappend(X94),hAPP(c_List_Otl(X94),X297)),X298) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl__append2) ).
fof(fact_zmod__zdiv__trivial,axiom,
! [X92,X84] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X92)),X92) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zdiv__trivial) ).
fof(fact_prod__eqI,axiom,
! [X149,X167,X10,X94] :
( hAPP(c_Product__Type_Ofst(X94,X10),X167) = hAPP(c_Product__Type_Ofst(X94,X10),X149)
=> ( hAPP(c_Product__Type_Osnd(X94,X10),X167) = hAPP(c_Product__Type_Osnd(X94,X10),X149)
=> X167 = X149 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod__eqI) ).
fof(fact_Pair__fst__snd__eq,axiom,
! [X13,X10,X53,X54] :
( X54 = X53
<=> ( hAPP(c_Product__Type_Ofst(X10,X13),X54) = hAPP(c_Product__Type_Ofst(X10,X13),X53)
& hAPP(c_Product__Type_Osnd(X10,X13),X54) = hAPP(c_Product__Type_Osnd(X10,X13),X53) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__fst__snd__eq) ).
fof(fact_inj__on__id,axiom,
! [X154,X10] : c_Fun_Oinj__on(X10,X10,c_Fun_Oid(X10),X154),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__id) ).
fof(fact_inj__on__id2,axiom,
! [X154,X10] : c_Fun_Oinj__on(X10,X10,c_COMBI(X10),X154),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__id2) ).
fof(fact_sgn__times,axiom,
! [X92,X84,X94] :
( class_Rings_Olinordered__idom(X94)
=> c_Groups_Osgn__class_Osgn(X94,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),c_Groups_Osgn__class_Osgn(X94,X84)),c_Groups_Osgn__class_Osgn(X94,X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__times) ).
fof(fact_sorted__distinct__set__unique,axiom,
! [X289,X290,X10] :
( class_Orderings_Olinorder(X10)
=> ( c_List_Olinorder__class_Osorted(X10,X290)
=> ( hBOOL(hAPP(c_List_Odistinct(X10),X290))
=> ( c_List_Olinorder__class_Osorted(X10,X289)
=> ( hBOOL(hAPP(c_List_Odistinct(X10),X289))
=> ( hAPP(c_List_Oset(X10),X290) = hAPP(c_List_Oset(X10),X289)
=> X290 = X289 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__distinct__set__unique) ).
fof(fact_drop__Suc__Cons,axiom,
! [X297,X93,X42,X94] : hAPP(hAPP(c_List_Odrop(X94),hAPP(c_Nat_OSuc,X42)),hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)) = hAPP(hAPP(c_List_Odrop(X94),X42),X297),
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,
! [X92,X84,X94] :
( class_Groups_Oordered__ab__group__add__abs(X94)
=> hAPP(c_Groups_Oabs__class_Oabs(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X84),X92)) = hAPP(c_Groups_Oabs__class_Oabs(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X92),X84)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__minus__commute) ).
fof(fact_nat__case__0,axiom,
! [X37,X12,X10] : c_Nat_Onat_Onat__case(X10,X12,X37,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__0) ).
fof(fact_code__numeral_Orecs_I1_J,axiom,
! [X37,X12,X10] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X10,X12,X37,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Orecs_I1_J) ).
fof(fact_code__numeral_Osimps_I4_J,axiom,
! [X37,X12,X10] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X10,X12,X37,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Osimps_I4_J) ).
fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
! [X105,X93] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X93)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X105)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X93),X105)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__functions_I1_J) ).
fof(fact_times__numeral__code_I5_J,axiom,
! [X133,X144] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X144),X133)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__numeral__code_I5_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
! [X105,X93] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X93)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X105)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),X105)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J) ).
fof(fact_zmult__int,axiom,
! [X42,X97] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X97)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X42)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X97),X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__int) ).
fof(fact_plus__numeral__code_I9_J,axiom,
! [X133,X144] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X144),X133)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__numeral__code_I9_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
! [X105,X93] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X93)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X105)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X93),X105)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).
fof(fact_zadd__int,axiom,
! [X42,X97] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X97)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X42)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__int) ).
fof(fact_zminus__zadd__distrib,axiom,
! [X133,X104] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X104),X133)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X104)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X133)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).
fof(fact_zdiv__int,axiom,
! [X92,X84] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X84),X92)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X84)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X92)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__int) ).
fof(fact_int__mult,axiom,
! [X42,X97] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X97),X42)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X97)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__mult) ).
fof(fact_Int__UNIV__left,axiom,
! [X160,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),X160) = X160,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__UNIV__left) ).
fof(fact_Un__empty__left,axiom,
! [X160,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),X160) = X160,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty__left) ).
fof(fact_pos__zmult__eq__1__iff,axiom,
! [X20,X102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X102))
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X102),X20) = c_Groups_Oone__class_Oone(tc_Int_Oint)
<=> ( X102 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& X20 = 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,
! [X39,X2,X10] : hAPP(c_Finite__Set_Ofold1(X10,X2),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = X39,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__singleton) ).
fof(fact_length__list__update,axiom,
! [X93,X120,X297,X94] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),hAPP(hAPP(c_List_Olist__update(X94,X297),X120),X93)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__list__update) ).
fof(fact_length__map,axiom,
! [X290,X2,X13,X10] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),hAPP(hAPP(c_List_Omap(X13,X10),X2),X290)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13)),X290),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__map) ).
fof(fact_evaln_Oequations_I1_J,axiom,
! [X46,X47] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X47,X46,X47),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I1_J) ).
fof(fact_evaln_OSkip,axiom,
! [X42,X45] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X45,X42,X45),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OSkip) ).
fof(fact_of__int__power,axiom,
! [X42,X104,X94] :
( class_Rings_Oring__1(X94)
=> hAPP(c_Int_Oring__1__class_Oof__int(X94),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X104),X42)) = hAPP(hAPP(c_Power_Opower__class_Opower(X94),hAPP(c_Int_Oring__1__class_Oof__int(X94),X104)),X42) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__power) ).
fof(fact_of__nat__power,axiom,
! [X42,X97,X94] :
( class_Rings_Osemiring__1(X94)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X97),X42)) = hAPP(hAPP(c_Power_Opower__class_Opower(X94),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),X97)),X42) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__power) ).
fof(fact_zless__le,axiom,
! [X131,X73] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X73),X131))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X73),X131))
& X73 != X131 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__le) ).
fof(fact_nat__less__le,axiom,
! [X20,X102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X20))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20))
& X102 != X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__le) ).
fof(fact_le__eq__less__or__eq,axiom,
! [X20,X102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X20))
| X102 = X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
fof(fact_le__neq__implies__less,axiom,
! [X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),X42))
=> ( X97 != X42
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
fof(fact_fold1__singleton__def,axiom,
! [X39,X2,X10,X1] :
( X1 = c_Finite__Set_Ofold1(X10,X2)
=> hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = X39 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__singleton__def) ).
fof(fact_length__tl,axiom,
! [X297,X94] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),hAPP(c_List_Otl(X94),X297)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)),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,
! [X73,X16,X2,X13,X10] :
( c_Finite__Set_Ofun__left__comm__idem(X10,X13,X2)
=> hAPP(hAPP(X2,X16),hAPP(hAPP(X2,X16),X73)) = hAPP(hAPP(X2,X16),X73) ),
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,
! [X198] : 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)),X198)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J) ).
fof(fact_finite__atLeastAtMost__int,axiom,
! [X165,X162] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X162,X165))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastAtMost__int) ).
fof(fact_finite__greaterThanAtMost__int,axiom,
! [X165,X162] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X162,X165))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__greaterThanAtMost__int) ).
fof(fact_finite__greaterThanLessThan__int,axiom,
! [X165,X162] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X162,X165))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__greaterThanLessThan__int) ).
fof(fact_finite__atLeastAtMost,axiom,
! [X165,X162] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X162,X165))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastAtMost) ).
fof(fact_finite__greaterThanAtMost,axiom,
! [X165,X162] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X162,X165))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__greaterThanAtMost) ).
fof(fact_finite__greaterThanLessThan,axiom,
! [X165,X162] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X162,X165))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__greaterThanLessThan) ).
fof(fact_less__Suc0,axiom,
! [X20] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc0) ).
fof(fact_inj__Suc,axiom,
! [X226] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X226),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__Suc) ).
fof(fact_less__imp__le__nat,axiom,
! [X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
fof(fact_less__or__eq__imp__le,axiom,
! [X42,X97] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42))
| X97 = X42 )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
fof(fact_termination__basic__simps_I5_J,axiom,
! [X105,X93] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X93),X105))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X93),X105)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
fof(fact_atLeastLessThan__empty,axiom,
! [X39,X38,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X38),X39))
=> hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X39),X38) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__empty) ).
fof(fact_eq__mem,axiom,
! [X25,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_fequal,X25)))
<=> X16 = X25 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__mem) ).
fof(fact_last__map,axiom,
! [X2,X13,X10,X290] :
( X290 != c_List_Olist_ONil(X10)
=> c_List_Olast(X13,hAPP(hAPP(c_List_Omap(X10,X13),X2),X290)) = hAPP(X2,c_List_Olast(X10,X290)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__map) ).
fof(fact_map__of_Osimps_I1_J,axiom,
! [X261,X10,X94] : hAPP(c_Map_Omap__of(X94,X10,c_List_Olist_ONil(tc_prod(X94,X10))),X261) = c_Option_Ooption_ONone(X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of_Osimps_I1_J) ).
fof(fact_map__of__Cons__code_I1_J,axiom,
! [X103,X94,X10] : hAPP(c_Map_Omap__of(X10,X94,c_List_Olist_ONil(tc_prod(X10,X94))),X103) = c_Option_Ooption_ONone(X94),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__of__Cons__code_I1_J) ).
fof(fact_minus__add__cancel,axiom,
! [X92,X84,X94] :
( class_Groups_Ogroup__add(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X84)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92)) = X92 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add__cancel) ).
fof(fact_ex__in__conv,axiom,
! [X154,X10] :
( ? [X3] : hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
<=> X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__in__conv) ).
fof(fact_of__nat__nat,axiom,
! [X104,X94] :
( class_Rings_Oring__1(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X104))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),hAPP(c_Int_Onat,X104)) = hAPP(c_Int_Oring__1__class_Oof__int(X94),X104) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__nat) ).
fof(fact_zmod__zminus__zminus,axiom,
! [X92,X84] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X84),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X92)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X92)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus__zminus) ).
fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
! [X105,X93] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X93),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X105)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X93,X105)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__functions_I2_J) ).
fof(fact_zmod__int,axiom,
! [X92,X84] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X84,X92)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X84),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X92)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__int) ).
fof(fact_distinct__listsum__conv__Setsum,axiom,
! [X290,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> ( hBOOL(hAPP(c_List_Odistinct(X10),X290))
=> hAPP(c_List_Omonoid__add__class_Olistsum(X10),X290) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X10),c_COMBI(X10)),hAPP(c_List_Oset(X10),X290)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__listsum__conv__Setsum) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
! [X149,X93,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X93),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),X149)) = hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),hAPP(c_Nat_OSuc,X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).
fof(fact_power__Suc,axiom,
! [X42,X84,X94] :
( class_Power_Opower(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),hAPP(c_Nat_OSuc,X42)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
! [X149,X93,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),hAPP(c_Nat_OSuc,X149)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X93),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),X149)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).
fof(fact_image__uminus__greaterThan,axiom,
! [X16,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> hAPP(c_Set_Oimage(X10,X10,c_Groups_Ouminus__class_Ouminus(X10)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),X16)) = hAPP(c_SetInterval_Oord__class_OlessThan(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__greaterThan) ).
fof(fact_image__uminus__atLeast,axiom,
! [X16,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> hAPP(c_Set_Oimage(X10,X10,c_Groups_Ouminus__class_Ouminus(X10)),hAPP(c_SetInterval_Oord__class_OatLeast(X10),X16)) = hAPP(c_SetInterval_Oord__class_OatMost(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__atLeast) ).
fof(fact_image__uminus__lessThan,axiom,
! [X16,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> hAPP(c_Set_Oimage(X10,X10,c_Groups_Ouminus__class_Ouminus(X10)),hAPP(c_SetInterval_Oord__class_OlessThan(X10),X16)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__lessThan) ).
fof(fact_image__uminus__atMost,axiom,
! [X16,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> hAPP(c_Set_Oimage(X10,X10,c_Groups_Ouminus__class_Ouminus(X10)),hAPP(c_SetInterval_Oord__class_OatMost(X10),X16)) = hAPP(c_SetInterval_Oord__class_OatLeast(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__atMost) ).
fof(fact_abs__of__nonneg,axiom,
! [X84,X94] :
( class_Groups_Oordered__ab__group__add__abs(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> hAPP(c_Groups_Oabs__class_Oabs(X94),X84) = X84 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__nonneg) ).
fof(fact_abs__of__pos,axiom,
! [X84,X94] :
( class_Groups_Oordered__ab__group__add__abs(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> hAPP(c_Groups_Oabs__class_Oabs(X94),X84) = X84 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__pos) ).
fof(fact_abs__of__nonpos,axiom,
! [X84,X94] :
( class_Groups_Oordered__ab__group__add__abs(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),c_Groups_Ozero__class_Ozero(X94)))
=> hAPP(c_Groups_Oabs__class_Oabs(X94),X84) = hAPP(c_Groups_Ouminus__class_Ouminus(X94),X84) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__nonpos) ).
fof(fact_abs__of__neg,axiom,
! [X84,X94] :
( class_Groups_Oordered__ab__group__add__abs(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),c_Groups_Ozero__class_Ozero(X94)))
=> hAPP(c_Groups_Oabs__class_Oabs(X94),X84) = hAPP(c_Groups_Ouminus__class_Ouminus(X94),X84) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__neg) ).
fof(fact_sgn__1__neg,axiom,
! [X39,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Groups_Osgn__class_Osgn(X10,X39) = hAPP(c_Groups_Ouminus__class_Ouminus(X10),c_Groups_Oone__class_Oone(X10))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),c_Groups_Ozero__class_Ozero(X10))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__1__neg) ).
fof(fact_sgn__neg,axiom,
! [X84,X94] :
( class_Rings_Olinordered__idom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),c_Groups_Ozero__class_Ozero(X94)))
=> c_Groups_Osgn__class_Osgn(X94,X84) = hAPP(c_Groups_Ouminus__class_Ouminus(X94),c_Groups_Oone__class_Oone(X94)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__neg) ).
fof(fact_equivp__symp,axiom,
! [X25,X16,X196,X10] :
( c_Equiv__Relations_Oequivp(X10,X196)
=> ( hBOOL(hAPP(hAPP(X196,X16),X25))
=> hBOOL(hAPP(hAPP(X196,X25),X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivp__symp) ).
fof(fact_dvd__eq__mod__eq__0,axiom,
! [X38,X39,X10] :
( class_Divides_Osemiring__div(X10)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X39),X38))
<=> c_Divides_Odiv__class_Omod(X10,X38,X39) = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__eq__mod__eq__0) ).
fof(fact_dvd__imp__mod__0,axiom,
! [X92,X84,X94] :
( class_Divides_Osemiring__div(X94)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X84),X92))
=> c_Divides_Odiv__class_Omod(X94,X92,X84) = c_Groups_Ozero__class_Ozero(X94) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__imp__mod__0) ).
fof(fact_length__butlast,axiom,
! [X297,X94] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),c_List_Obutlast(X94,X297)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__butlast) ).
fof(fact_lists_ONil,axiom,
! [X154,X10] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),c_List_Olist_ONil(X10)),c_List_Olists(X10,X154))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists_ONil) ).
fof(fact_sgn__pos,axiom,
! [X84,X94] :
( class_Rings_Olinordered__idom(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> c_Groups_Osgn__class_Osgn(X94,X84) = c_Groups_Oone__class_Oone(X94) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__pos) ).
fof(fact_sgn__1__pos,axiom,
! [X39,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Groups_Osgn__class_Osgn(X10,X39) = c_Groups_Oone__class_Oone(X10)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X39)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__1__pos) ).
fof(fact_nonzero__minus__divide__divide,axiom,
! [X84,X92,X94] :
( class_Rings_Odivision__ring(X94)
=> ( X92 != c_Groups_Ozero__class_Ozero(X94)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X84)),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X92)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X84),X92) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__minus__divide__divide) ).
fof(fact_lists__empty,axiom,
! [X10] : c_List_Olists(X10,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X10)),c_List_Olist_ONil(X10)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X10),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__empty) ).
fof(fact_listset_Osimps_I1_J,axiom,
! [X10] : c_List_Olistset(X10,c_List_Olist_ONil(tc_fun(X10,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X10)),c_List_Olist_ONil(X10)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X10),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listset_Osimps_I1_J) ).
fof(fact_CollectI,axiom,
! [X10,X39,X19] :
( hBOOL(hAPP(X19,X39))
=> hBOOL(hAPP(hAPP(c_member(X10),X39),hAPP(c_Set_OCollect(X10),X19))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_CollectI) ).
fof(fact_distinct__rev,axiom,
! [X290,X10] :
( hBOOL(hAPP(c_List_Odistinct(X10),hAPP(c_List_Orev(X10),X290)))
<=> hBOOL(hAPP(c_List_Odistinct(X10),X290)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__rev) ).
fof(fact_distinct1__rotate,axiom,
! [X290,X10] :
( hBOOL(hAPP(c_List_Odistinct(X10),hAPP(c_List_Orotate1(X10),X290)))
<=> hBOOL(hAPP(c_List_Odistinct(X10),X290)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct1__rotate) ).
fof(fact_quotient__empty,axiom,
! [X177,X10] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),X177) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__empty) ).
fof(fact_split__Pair,axiom,
! [X13,X10] : hAPP(c_Product__Type_Oprod_Oprod__case(X10,X13,tc_prod(X10,X13)),c_Product__Type_OPair(X10,X13)) = c_Fun_Oid(tc_prod(X10,X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__Pair) ).
fof(fact_inf__absorb1,axiom,
! [X105,X93,X94] :
( class_Lattices_Osemilattice__inf(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X105))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),X105) = X93 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__absorb1) ).
fof(fact_le__iff__inf,axiom,
! [X25,X16,X10] :
( class_Lattices_Osemilattice__inf(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X25))
<=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X16),X25) = X16 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__inf) ).
fof(fact_inf__absorb2,axiom,
! [X93,X105,X94] :
( class_Lattices_Osemilattice__inf(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X105),X93))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),X105) = X105 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__absorb2) ).
fof(fact_sup__absorb2,axiom,
! [X105,X93,X94] :
( class_Lattices_Osemilattice__sup(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X105))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),X105) = X105 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__absorb2) ).
fof(fact_le__iff__sup,axiom,
! [X25,X16,X10] :
( class_Lattices_Osemilattice__sup(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X25))
<=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X16),X25) = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__sup) ).
fof(fact_sup__absorb1,axiom,
! [X93,X105,X94] :
( class_Lattices_Osemilattice__sup(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X105),X93))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),X105) = X93 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__absorb1) ).
fof(fact_min__max_Ole__iff__sup,axiom,
! [X25,X16,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X25))
<=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X16),X25) = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__iff__sup) ).
fof(fact_min__max_Osup__absorb2,axiom,
! [X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X105))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X93),X105) = X105 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__absorb2) ).
fof(fact_min__max_Osup__absorb1,axiom,
! [X93,X105,X94] :
( class_Orderings_Olinorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X105),X93))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X93),X105) = X93 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__absorb1) ).
fof(fact_min__max_Oinf__absorb1,axiom,
! [X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X105))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X93),X105) = X93 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__absorb1) ).
fof(fact_min__max_Ole__iff__inf,axiom,
! [X25,X16,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X25))
<=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X16),X25) = X16 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__iff__inf) ).
fof(fact_min__max_Oinf__absorb2,axiom,
! [X93,X105,X94] :
( class_Orderings_Olinorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X105),X93))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X93),X105) = X105 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__absorb2) ).
fof(fact_Sup__singleton,axiom,
! [X39,X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> c_Complete__Lattice_OSup__class_OSup(X10,hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = X39 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__singleton) ).
fof(fact_Inf__singleton,axiom,
! [X39,X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> c_Complete__Lattice_OInf__class_OInf(X10,hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = X39 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__singleton) ).
fof(fact_Min_Osingleton,axiom,
! [X16,X10] :
( class_Orderings_Olinorder(X10)
=> c_Big__Operators_Olinorder__class_OMin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Osingleton) ).
fof(fact_Max_Osingleton,axiom,
! [X16,X10] :
( class_Orderings_Olinorder(X10)
=> c_Big__Operators_Olinorder__class_OMax(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Osingleton) ).
fof(fact_Inf__fin_Osingleton,axiom,
! [X16,X10] :
( class_Lattices_Olattice(X10)
=> c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Osingleton) ).
fof(fact_Sup__fin_Osingleton,axiom,
! [X16,X10] :
( class_Lattices_Olattice(X10)
=> c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Osingleton) ).
fof(fact_mult__Suc,axiom,
! [X42,X97] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X97)),X42) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X97),X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Suc) ).
fof(fact_cut,axiom,
! [X210,X211,X213,X10] :
( c_Hoare__Mirabelle_Ohoare__derivs(X10,X213,X211)
=> ( c_Hoare__Mirabelle_Ohoare__derivs(X10,X210,X213)
=> c_Hoare__Mirabelle_Ohoare__derivs(X10,X210,X211) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cut) ).
fof(fact_diff__add__inverse,axiom,
! [X97,X42] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),X97)),X42) = X97,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse) ).
fof(fact_diff__add__inverse2,axiom,
! [X42,X97] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X42)),X42) = X97,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).
fof(fact_Union__quotient,axiom,
! [X177,X154,X10] :
( c_Equiv__Relations_Oequiv(X10,X154,X177)
=> c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X154),X177)) = X154 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__quotient) ).
fof(fact_minus__divide__divide,axiom,
! [X92,X84,X94] :
( class_Fields_Ofield__inverse__zero(X94)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X84)),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X92)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X84),X92) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__divide__divide) ).
fof(fact_abs__mult__self,axiom,
! [X84,X94] :
( class_Rings_Olinordered__idom(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),X84)),hAPP(c_Groups_Oabs__class_Oabs(X94),X84)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult__self) ).
fof(fact_minus__mult__minus,axiom,
! [X92,X84,X94] :
( class_Rings_Oring(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X84)),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X92)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__minus) ).
fof(fact_minus__mult__commute,axiom,
! [X92,X84,X94] :
( class_Rings_Oring(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X84)),X92) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__commute) ).
fof(fact_wfP__accp__iff,axiom,
! [X177,X10] :
( c_Wellfounded_OwfP(X10,X177)
<=> ! [X147] : hBOOL(hAPP(c_Wellfounded_Oaccp(X10,X177),X147)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__accp__iff) ).
fof(fact_nonzero__minus__divide__right,axiom,
! [X84,X92,X94] :
( class_Rings_Odivision__ring(X94)
=> ( X92 != c_Groups_Ozero__class_Ozero(X94)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X84),X92)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X84),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X92)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__minus__divide__right) ).
fof(fact_quotient__is__empty2,axiom,
! [X177,X154,X10] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X154),X177)
<=> X154 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__is__empty2) ).
fof(fact_quotient__is__empty,axiom,
! [X177,X154,X10] :
( hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X154),X177) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool))
<=> X154 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__is__empty) ).
fof(fact_card__greaterThanAtMost__int,axiom,
! [X165,X162] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X162,X165)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X165),X162)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__greaterThanAtMost__int) ).
fof(fact_linorder__neq__iff,axiom,
! [X25,X16,X10] :
( class_Orderings_Olinorder(X10)
=> ( X16 != X25
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X16),X25))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X25),X16)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
fof(fact_linorder__less__linear,axiom,
! [X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X105))
| X93 = X105
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X105),X93)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
fof(fact_mod__mod__trivial,axiom,
! [X92,X84,X94] :
( class_Divides_Osemiring__div(X94)
=> c_Divides_Odiv__class_Omod(X94,c_Divides_Odiv__class_Omod(X94,X84,X92),X92) = c_Divides_Odiv__class_Omod(X94,X84,X92) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mod__trivial) ).
fof(fact_Int__empty__right,axiom,
! [X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__empty__right) ).
fof(fact_Un__UNIV__right,axiom,
! [X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__UNIV__right) ).
fof(fact_Diff__UNIV,axiom,
! [X154,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__UNIV) ).
fof(fact_Domain__empty,axiom,
! [X13,X10] : hAPP(c_Relation_ODomain(X10,X13),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X13),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__empty) ).
fof(fact_Range__empty,axiom,
! [X10,X13] : hAPP(c_Relation_ORange(X13,X10),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X13,X10),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__empty) ).
fof(fact_fun__upd__triv,axiom,
! [X16,X2,X13,X10] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,X13),X2),X16),hAPP(X2,X16)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__triv) ).
fof(fact_fst__conv,axiom,
! [X92,X84,X10,X94] : hAPP(c_Product__Type_Ofst(X94,X10),hAPP(hAPP(c_Product__Type_OPair(X94,X10),X84),X92)) = X84,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__conv) ).
fof(fact_snd__conv,axiom,
! [X92,X84,X94,X10] : hAPP(c_Product__Type_Osnd(X10,X94),hAPP(hAPP(c_Product__Type_OPair(X10,X94),X84),X92)) = X92,
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,
! [X20,X102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20))
<=> ? [X124] : X20 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X124) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__add) ).
fof(fact_insert__absorb,axiom,
! [X154,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(c_Set_Oinsert(X10),X39),X154) = X154 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb) ).
fof(fact_the__elem__eq,axiom,
! [X16,X10] : c_Set_Othe__elem(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = X16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__elem__eq) ).
fof(fact_linorder__linear,axiom,
! [X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X105))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X105),X93)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__linear) ).
fof(fact_linorder__le__less__linear,axiom,
! [X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X105))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X105),X93)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
fof(fact_fun__upd__idem,axiom,
! [X10,X13,X25,X16,X2] :
( hAPP(X2,X16) = X25
=> hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X13,X10),X2),X16),X25) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__idem) ).
fof(fact_listsum__simps_I2_J,axiom,
! [X297,X93,X94] :
( class_Groups_Omonoid__add(X94)
=> hAPP(c_List_Omonoid__add__class_Olistsum(X94),hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X93),hAPP(c_List_Omonoid__add__class_Olistsum(X94),X297)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__simps_I2_J) ).
fof(fact_minus__divide__right,axiom,
! [X92,X84,X94] :
( class_Fields_Ofield__inverse__zero(X94)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X84),X92)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X84),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__divide__right) ).
fof(fact_minus__mult__right,axiom,
! [X92,X84,X94] :
( class_Rings_Oring(X94)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__right) ).
fof(fact_option_Osize_I2_J,axiom,
! [X39,X11,X10] : c_Option_Ooption_Ooption__size(X10,X11,hAPP(c_Option_Ooption_OSome(X10),X39)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X11,X39)),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,
! [X19,X10] : c_List_Opartition(X10,X19,c_List_Olist_ONil(X10)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_ONil(X10)),c_List_Olist_ONil(X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition_Osimps_I1_J) ).
fof(fact_take__1__Cons,axiom,
! [X297,X93,X94] : hAPP(hAPP(c_List_Otake(X94),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)) = hAPP(hAPP(c_List_Olist_OCons(X94),X93),c_List_Olist_ONil(X94)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__1__Cons) ).
fof(fact_wf__inv__image,axiom,
! [X2,X13,X177,X10] :
( c_Wellfounded_Owf(X10,X177)
=> c_Wellfounded_Owf(X13,hAPP(hAPP(c_Relation_Oinv__image(X10,X13),X177),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__inv__image) ).
fof(fact_rp__inv__image__rp,axiom,
! [X2,X13,X19,X10] :
( c_FunDef_Oreduction__pair(X10,X19)
=> c_FunDef_Oreduction__pair(X13,hAPP(hAPP(c_FunDef_Orp__inv__image(X10,X13),X19),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rp__inv__image__rp) ).
fof(fact_dvd__0__left,axiom,
! [X84,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),c_Groups_Ozero__class_Ozero(X94)),X84))
=> X84 = c_Groups_Ozero__class_Ozero(X94) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__0__left) ).
fof(fact_mod__add__self1,axiom,
! [X84,X92,X94] :
( class_Divides_Osemiring__div(X94)
=> c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X92),X84),X92) = c_Divides_Odiv__class_Omod(X94,X84,X92) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__self1) ).
fof(fact_mod__add__self2,axiom,
! [X92,X84,X94] :
( class_Divides_Osemiring__div(X94)
=> c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92),X92) = c_Divides_Odiv__class_Omod(X94,X84,X92) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__self2) ).
fof(fact_nth__via__drop,axiom,
! [X298,X105,X297,X42,X94] :
( hAPP(hAPP(c_List_Odrop(X94),X42),X297) = hAPP(hAPP(c_List_Olist_OCons(X94),X105),X298)
=> hAPP(hAPP(c_List_Onth(X94),X297),X42) = X105 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__via__drop) ).
fof(fact_max__Suc__Suc,axiom,
! [X42,X97] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X97)),hAPP(c_Nat_OSuc,X42)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X97),X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__Suc__Suc) ).
fof(fact_min__Suc__Suc,axiom,
! [X42,X97] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X97)),hAPP(c_Nat_OSuc,X42)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X97),X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__Suc__Suc) ).
fof(fact_times__code__numeral__code,axiom,
! [X97,X42] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X42)),hAPP(c_Code__Numeral_Oof__nat,X97)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),X97)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__code__numeral__code) ).
fof(fact_plus__code__numeral__code,axiom,
! [X97,X42] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X42)),hAPP(c_Code__Numeral_Oof__nat,X97)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),X97)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__code__numeral__code) ).
fof(fact_zpower__int,axiom,
! [X42,X97] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X97)),X42) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X97),X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__int) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
! [X42,X93] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X93)),X42) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X93),X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J) ).
fof(fact_zmult__zminus,axiom,
! [X133,X104] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X104)),X133) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X104),X133)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__zminus) ).
fof(fact_int__power,axiom,
! [X42,X97] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X97),X42)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X97)),X42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__power) ).
fof(fact_abs__ge__zero,axiom,
! [X84,X94] :
( class_Groups_Oordered__ab__group__add__abs(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(c_Groups_Oabs__class_Oabs(X94),X84))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__ge__zero) ).
fof(fact_of__nat__0__le__iff,axiom,
! [X42,X94] :
( class_Rings_Olinordered__semidom(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),X42))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__0__le__iff) ).
fof(fact_zero__le__imp__of__nat,axiom,
! [X97,X94] :
( class_Rings_Olinordered__semidom(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),X97))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__imp__of__nat) ).
fof(fact_inf__left__idem,axiom,
! [X105,X93,X94] :
( class_Lattices_Osemilattice__inf(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),X105)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),X105) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__left__idem) ).
fof(fact_inf_Oleft__idem,axiom,
! [X92,X84,X94] :
( class_Lattices_Osemilattice__inf(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X84),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X84),X92)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X84),X92) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oleft__idem) ).
fof(fact_inf__sup__aci_I4_J,axiom,
! [X105,X93,X94] :
( class_Lattices_Olattice(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),X105)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),X105) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I4_J) ).
fof(fact_sup_Oleft__idem,axiom,
! [X92,X84,X94] :
( class_Lattices_Osemilattice__sup(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X84),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X84),X92)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X84),X92) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oleft__idem) ).
fof(fact_sup__left__idem,axiom,
! [X105,X93,X94] :
( class_Lattices_Osemilattice__sup(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),X105)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),X105) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__left__idem) ).
fof(fact_inf__sup__aci_I8_J,axiom,
! [X105,X93,X94] :
( class_Lattices_Olattice(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),X105)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),X105) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I8_J) ).
fof(fact_min__max_Osup__left__idem,axiom,
! [X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X93),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X93),X105)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X93),X105) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__left__idem) ).
fof(fact_min__max_Osup_Oleft__idem,axiom,
! [X92,X84,X94] :
( class_Orderings_Olinorder(X94)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X84),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X84),X92)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X84),X92) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup_Oleft__idem) ).
fof(fact_min__max_Oinf_Oleft__idem,axiom,
! [X92,X84,X94] :
( class_Orderings_Olinorder(X94)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X84),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X84),X92)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X84),X92) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf_Oleft__idem) ).
fof(fact_min__max_Oinf__left__idem,axiom,
! [X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X93),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X93),X105)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X93),X105) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__left__idem) ).
fof(fact_mult__left__idem,axiom,
! [X92,X84,X94] :
( class_Lattices_Oab__semigroup__idem__mult(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__idem) ).
fof(fact_drop__tl,axiom,
! [X297,X42,X94] : hAPP(hAPP(c_List_Odrop(X94),X42),hAPP(c_List_Otl(X94),X297)) = hAPP(c_List_Otl(X94),hAPP(hAPP(c_List_Odrop(X94),X42),X297)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__tl) ).
fof(fact_tl__drop,axiom,
! [X297,X42,X94] : hAPP(c_List_Otl(X94),hAPP(hAPP(c_List_Odrop(X94),X42),X297)) = hAPP(hAPP(c_List_Odrop(X94),X42),hAPP(c_List_Otl(X94),X297)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl__drop) ).
fof(fact_List_Oset_Osimps_I2_J,axiom,
! [X290,X16,X10] : hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290)) = hAPP(hAPP(c_Set_Oinsert(X10),X16),hAPP(c_List_Oset(X10),X290)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Oset_Osimps_I2_J) ).
fof(fact_card__atLeastAtMost,axiom,
! [X165,X162] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X162,X165)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X165)),X162),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__atLeastAtMost) ).
fof(fact_surj__id,axiom,
! [X10] : hAPP(c_Set_Oimage(X10,X10,c_Fun_Oid(X10)),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__id) ).
fof(fact_some__eq__ex,axiom,
! [X10,X19] :
( hBOOL(hAPP(X19,c_Hilbert__Choice_OEps(X10,X19)))
<=> ? [X147] : hBOOL(hAPP(X19,X147)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_some__eq__ex) ).
fof(fact_partition__filter1,axiom,
! [X290,X19,X10] : hAPP(c_Product__Type_Ofst(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Opartition(X10,X19,X290)) = hAPP(c_List_Ofilter(X10,X19),X290),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition__filter1) ).
fof(fact_dvd__1__left,axiom,
! [X103] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X103)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__1__left) ).
fof(fact_iso__tuple__UNIV__I,axiom,
! [X16,X10] : hBOOL(hAPP(hAPP(c_member(X10),X16),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iso__tuple__UNIV__I) ).
fof(fact_UNIV__I,axiom,
! [X16,X10] : hBOOL(hAPP(hAPP(c_member(X10),X16),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__I) ).
fof(fact_Compl__eq__Compl__iff,axiom,
! [X160,X154,X10] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X154) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X160)
<=> X154 = X160 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__eq__Compl__iff) ).
fof(fact_fun__Compl__def,axiom,
! [X16,X154,X13,X10] :
( class_Groups_Ouminus(X10)
=> hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X13,X10)),X154),X16) = hAPP(c_Groups_Ouminus__class_Ouminus(X10),hAPP(X154,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__Compl__def) ).
fof(fact_uminus__apply,axiom,
! [X16,X154,X13,X10] :
( class_Groups_Ouminus(X10)
=> hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X13,X10)),X154),X16) = hAPP(c_Groups_Ouminus__class_Ouminus(X10),hAPP(X154,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_uminus__apply) ).
fof(fact_nat__0__le,axiom,
! [X104] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X104))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X104)) = X104 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__0__le) ).
fof(fact_tsub__eq,axiom,
! [X93,X105] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X105),X93))
=> c_Nat__Transfer_Otsub(X93,X105) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X93),X105) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tsub__eq) ).
fof(fact_subtract__code__numeral__code,axiom,
! [X97,X42] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,X42)),hAPP(c_Code__Numeral_Oof__nat,X97)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X42),X97)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subtract__code__numeral__code) ).
fof(fact_full__small__int__def,axiom,
! [X141,X2] : c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,X2,X141) = c_Smallcheck_Ofull__small_H(X2,hAPP(c_Code__Numeral_Oint__of,X141),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X141))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_full__small__int__def) ).
fof(fact_int__eq__iff,axiom,
! [X73,X102] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X102) = X73
<=> ( X102 = hAPP(c_Int_Onat,X73)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__eq__iff) ).
fof(fact_semilattice__big_OF__eq,axiom,
! [X154,X225,X2,X10] :
( c_Big__Operators_Osemilattice__big(X10,X2,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(X225,X154) = hAPP(c_Finite__Set_Ofold1(X10,X2),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semilattice__big_OF__eq) ).
fof(fact_folding__one_Oeq__fold,axiom,
! [X154,X225,X2,X10] :
( c_Finite__Set_Ofolding__one(X10,X2,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(X225,X154) = hAPP(c_Finite__Set_Ofold1(X10,X2),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oeq__fold) ).
fof(fact_Union__UNIV,axiom,
! [X10] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__UNIV) ).
fof(fact_Union__empty,axiom,
! [X10] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__empty) ).
fof(fact_Inter__UNIV,axiom,
! [X10] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__UNIV) ).
fof(fact_Inter__empty,axiom,
! [X10] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__empty) ).
fof(fact_insert__absorb2,axiom,
! [X154,X16,X10] : hAPP(hAPP(c_Set_Oinsert(X10),X16),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Set_Oinsert(X10),X16),X154),
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,
! [X230,X10,X154,X13] :
( class_Complete__Lattice_Ocomplete__lattice(X13)
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,X13),X154),hAPP(c_COMBK(X13,X10),X230)) = X230 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__const) ).
fof(fact_SUP__const,axiom,
! [X230,X10,X154,X13] :
( class_Complete__Lattice_Ocomplete__lattice(X13)
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,X13),X154),hAPP(c_COMBK(X13,X10),X230)) = X230 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__const) ).
fof(fact_compl__unique,axiom,
! [X105,X93,X94] :
( class_Lattices_Oboolean__algebra(X94)
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),X105) = c_Orderings_Obot__class_Obot(X94)
=> ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),X105) = c_Orderings_Otop__class_Otop(X94)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X94),X93) = X105 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__unique) ).
fof(fact_mult__Suc__right,axiom,
! [X42,X97] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X97),hAPP(c_Nat_OSuc,X42)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X97),X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Suc__right) ).
fof(fact_finite__atLeastZeroLessThan__int,axiom,
! [X165] : 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)),X165))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastZeroLessThan__int) ).
fof(fact_transpose_Osimps_I2_J,axiom,
! [X331,X94] : c_List_Otranspose(X94,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X94)),c_List_Olist_ONil(X94)),X331)) = c_List_Otranspose(X94,X331),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose_Osimps_I2_J) ).
fof(fact_Field__empty,axiom,
! [X10] : hAPP(c_Relation_OField(X10),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__empty) ).
fof(fact_mod__less,axiom,
! [X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X97,X42) = X97 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__less) ).
fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
! [X165,X162] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X162),c_Groups_Oone__class_Oone(tc_Int_Oint)),X165) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X162,X165),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastPlusOneAtMost__greaterThanAtMost__int) ).
fof(fact_Sup__insert,axiom,
! [X154,X39,X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> c_Complete__Lattice_OSup__class_OSup(X10,hAPP(hAPP(c_Set_Oinsert(X10),X39),X154)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X39),c_Complete__Lattice_OSup__class_OSup(X10,X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__insert) ).
fof(fact_Inf__insert,axiom,
! [X154,X39,X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> c_Complete__Lattice_OInf__class_OInf(X10,hAPP(hAPP(c_Set_Oinsert(X10),X39),X154)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X39),c_Complete__Lattice_OInf__class_OInf(X10,X154)) ),
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,
! [X141,X2] : hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),X2),X141) = c_Smallcheck_Osmall_H(X2,hAPP(c_Code__Numeral_Oint__of,X141),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X141))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_small__int__def) ).
fof(fact_butlast__append,axiom,
! [X297,X94,X298] :
( ( X298 = c_List_Olist_ONil(X94)
=> c_List_Obutlast(X94,hAPP(hAPP(c_List_Oappend(X94),X297),X298)) = c_List_Obutlast(X94,X297) )
& ( X298 != c_List_Olist_ONil(X94)
=> c_List_Obutlast(X94,hAPP(hAPP(c_List_Oappend(X94),X297),X298)) = hAPP(hAPP(c_List_Oappend(X94),X297),c_List_Obutlast(X94,X298)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast__append) ).
fof(fact_butlast_Osimps_I2_J,axiom,
! [X93,X94,X297] :
( ( X297 = c_List_Olist_ONil(X94)
=> c_List_Obutlast(X94,hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)) = c_List_Olist_ONil(X94) )
& ( X297 != c_List_Olist_ONil(X94)
=> c_List_Obutlast(X94,hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)) = hAPP(hAPP(c_List_Olist_OCons(X94),X93),c_List_Obutlast(X94,X297)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast_Osimps_I2_J) ).
fof(fact_vimage__UNIV,axiom,
! [X2,X13,X10] : hAPP(c_Set_Ovimage(X10,X13,X2),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__UNIV) ).
fof(fact_vimage__empty,axiom,
! [X2,X13,X10] : hAPP(c_Set_Ovimage(X10,X13,X2),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__empty) ).
fof(fact_Image__empty,axiom,
! [X196,X10,X13] : hAPP(c_Relation_OImage(X13,X10,X196),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__empty) ).
fof(fact_image__empty,axiom,
! [X2,X10,X13] : hAPP(c_Set_Oimage(X13,X10,X2),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__empty) ).
fof(fact_listrel__refl__on,axiom,
! [X177,X154,X10] :
( c_Relation_Orefl__on(X10,X154,X177)
=> c_Relation_Orefl__on(tc_List_Olist(X10),c_List_Olists(X10,X154),c_List_Olistrel(X10,X177)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__refl__on) ).
fof(fact_equiv__listrel,axiom,
! [X177,X154,X10] :
( c_Equiv__Relations_Oequiv(X10,X154,X177)
=> c_Equiv__Relations_Oequiv(tc_List_Olist(X10),c_List_Olists(X10,X154),c_List_Olistrel(X10,X177)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__listrel) ).
fof(fact_mem__def,axiom,
! [X154,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
<=> hBOOL(hAPP(X154,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
fof(fact_com_Osize_I3_J,axiom,
! [X8,X29,X79] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X79,X29,X8)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X8)),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,
! [X103,X92,X84,X94] :
( class_Rings_Odvd(X94)
=> ( X84 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X103)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X92),X84)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvdI) ).
fof(fact_diff__is__0__eq,axiom,
! [X20,X102] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X102),X20) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).
fof(fact_diff__is__0__eq_H,axiom,
! [X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),X42))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42) = 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,
! [X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X97),X42) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__less) ).
fof(fact_Int__UNIV__right,axiom,
! [X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = X154,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__UNIV__right) ).
fof(fact_Un__empty__right,axiom,
! [X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) = X154,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty__right) ).
fof(fact_Diff__empty,axiom,
! [X154,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) = X154,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__empty) ).
fof(fact_double__complement,axiom,
! [X154,X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X154)) = X154,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__complement) ).
fof(fact_rel__pow__1,axiom,
! [X196,X10] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X196) = X196,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__1) ).
fof(fact_dom__empty,axiom,
! [X13,X10] : c_Map_Odom(X10,X13,hAPP(c_COMBK(tc_Option_Ooption(X13),X10),c_Option_Ooption_ONone(X13))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__empty) ).
fof(fact_ran__empty,axiom,
! [X10,X13] : c_Map_Oran(X13,X10,hAPP(c_COMBK(tc_Option_Ooption(X10),X13),c_Option_Ooption_ONone(X10))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ran__empty) ).
fof(fact_list__update__id,axiom,
! [X120,X297,X94] : hAPP(hAPP(c_List_Olist__update(X94,X297),X120),hAPP(hAPP(c_List_Onth(X94),X297),X120)) = X297,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__id) ).
fof(fact_square__eq__iff,axiom,
! [X38,X39,X10] :
( class_Rings_Oidom(X10)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X39) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X38),X38)
<=> ( X39 = X38
| X39 = hAPP(c_Groups_Ouminus__class_Ouminus(X10),X38) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_square__eq__iff) ).
fof(fact_add__Suc,axiom,
! [X42,X97] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X97)),X42) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc) ).
fof(fact_drop__butlast,axiom,
! [X297,X42,X94] : hAPP(hAPP(c_List_Odrop(X94),X42),c_List_Obutlast(X94,X297)) = c_List_Obutlast(X94,hAPP(hAPP(c_List_Odrop(X94),X42),X297)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__butlast) ).
fof(fact_butlast__drop,axiom,
! [X297,X42,X94] : c_List_Obutlast(X94,hAPP(hAPP(c_List_Odrop(X94),X42),X297)) = hAPP(hAPP(c_List_Odrop(X94),X42),c_List_Obutlast(X94,X297)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast__drop) ).
fof(fact_code__numeral__not__eq__zero,axiom,
! [X113] :
( X113 != 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)),X113)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral__not__eq__zero) ).
fof(fact_Domain__empty__iff,axiom,
! [X177,X13,X10] :
( hAPP(c_Relation_ODomain(X10,X13),X177) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
<=> X177 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X13),tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__empty__iff) ).
fof(fact_Range__empty__iff,axiom,
! [X177,X10,X13] :
( hAPP(c_Relation_ORange(X13,X10),X177) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
<=> X177 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X13,X10),tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__empty__iff) ).
fof(fact_abs__zmult__eq__1,axiom,
! [X42,X97] :
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X97),X42)) = c_Groups_Oone__class_Oone(tc_Int_Oint)
=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X97) = 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,
! [X105,X93] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X93),X105))
| X93 = X105
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X105),X93)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__linear) ).
fof(fact_nat__neq__iff,axiom,
! [X20,X102] :
( X102 != X20
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X20))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X102)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
fof(fact_card__atLeastLessThan__int,axiom,
! [X165,X162] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X162),X165)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X165),X162)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__atLeastLessThan__int) ).
fof(fact_abs__ge__self,axiom,
! [X84,X94] :
( class_Groups_Oordered__ab__group__add__abs(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),hAPP(c_Groups_Oabs__class_Oabs(X94),X84))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__ge__self) ).
fof(fact_card__greaterThanLessThan,axiom,
! [X165,X162] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X162,X165)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X165),hAPP(c_Nat_OSuc,X162)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__greaterThanLessThan) ).
fof(fact_zle__linear,axiom,
! [X133,X104] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X104),X133))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X133),X104)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__linear) ).
fof(fact_nat__le__linear,axiom,
! [X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),X42))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).
fof(fact_zdiv__zminus__zminus,axiom,
! [X92,X84] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X84)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X92)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),X92),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zminus__zminus) ).
fof(fact_zdiv__zminus2,axiom,
! [X92,X84] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X92)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X84)),X92),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zminus2) ).
fof(fact_drop__Suc,axiom,
! [X297,X42,X94] : hAPP(hAPP(c_List_Odrop(X94),hAPP(c_Nat_OSuc,X42)),X297) = hAPP(hAPP(c_List_Odrop(X94),X42),hAPP(c_List_Otl(X94),X297)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__Suc) ).
fof(fact_dom__eq__empty__conv,axiom,
! [X2,X13,X10] :
( c_Map_Odom(X10,X13,X2) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
<=> X2 = hAPP(c_COMBK(tc_Option_Ooption(X13),X10),c_Option_Ooption_ONone(X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dom__eq__empty__conv) ).
fof(fact_gr0__implies__Suc,axiom,
! [X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X42))
=> ? [X122] : X42 = hAPP(c_Nat_OSuc,X122) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0__implies__Suc) ).
fof(fact_gr0__conv__Suc,axiom,
! [X20] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20))
<=> ? [X122] : X20 = hAPP(c_Nat_OSuc,X122) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
fof(fact_min__max_OInf__fin_OF__eq,axiom,
! [X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X154) = hAPP(c_Finite__Set_Ofold1(X10,c_Orderings_Oord__class_Omin(X10)),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_OF__eq) ).
fof(fact_min__max_OSup__fin_OF__eq,axiom,
! [X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X154) = hAPP(c_Finite__Set_Ofold1(X10,c_Orderings_Oord__class_Omax(X10)),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_OF__eq) ).
fof(fact_fun__left__comm__insort,axiom,
! [X10] :
( class_Orderings_Olinorder(X10)
=> c_Finite__Set_Ofun__left__comm(X10,tc_List_Olist(X10),c_List_Olinorder__class_Oinsort__key(X10,X10,c_COMBI(X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__insort) ).
fof(fact_distinct__tl,axiom,
! [X297,X94] :
( hBOOL(hAPP(c_List_Odistinct(X94),X297))
=> hBOOL(hAPP(c_List_Odistinct(X94),hAPP(c_List_Otl(X94),X297))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__tl) ).
fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
! [X165,X162] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X162),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X165),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X162,X165),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThanPlusOne__atLeastAtMost__int) ).
fof(fact_neg__def,axiom,
! [X171] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X171))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X171),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__def) ).
fof(fact_card__distinct,axiom,
! [X290,X10] :
( hAPP(c_Finite__Set_Ocard(X10),hAPP(c_List_Oset(X10),X290)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290)
=> hBOOL(hAPP(c_List_Odistinct(X10),X290)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__distinct) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
! [X105,X93] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X93),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X105)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X93),X105)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J) ).
fof(fact_singleton__rev__conv,axiom,
! [X290,X16,X10] :
( hAPP(hAPP(c_List_Olist_OCons(X10),X16),c_List_Olist_ONil(X10)) = hAPP(c_List_Orev(X10),X290)
<=> X290 = hAPP(hAPP(c_List_Olist_OCons(X10),X16),c_List_Olist_ONil(X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__rev__conv) ).
fof(fact_rev__singleton__conv,axiom,
! [X16,X290,X10] :
( hAPP(c_List_Orev(X10),X290) = hAPP(hAPP(c_List_Olist_OCons(X10),X16),c_List_Olist_ONil(X10))
<=> X290 = hAPP(hAPP(c_List_Olist_OCons(X10),X16),c_List_Olist_ONil(X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__singleton__conv) ).
fof(fact_com_Osize_I14_J,axiom,
! [X8,X29] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(X29,X8)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X8)),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,
! [X177,X10] : c_List_Olistrel1(X10,hAPP(c_Relation_Oconverse(X10,X10),X177)) = hAPP(c_Relation_Oconverse(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olistrel1(X10,X177)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1__converse) ).
fof(fact_minus__diff__eq,axiom,
! [X92,X84,X94] :
( class_Groups_Oab__group__add(X94)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X94),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X84),X92)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X92),X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__diff__eq) ).
fof(fact_acc__wfD,axiom,
! [X16,X177,X10] :
( c_Wellfounded_Owf(X10,X177)
=> hBOOL(hAPP(hAPP(c_member(X10),X16),c_Wellfounded_Oacc(X10,X177))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__wfD) ).
fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
! [X93,X94] :
( class_Rings_Ocomm__ring__1(X94)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X94),X93) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),c_Groups_Oone__class_Oone(X94))),X93) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).
fof(fact_finite__atLeastLessThan__int,axiom,
! [X165,X162] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X162),X165))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastLessThan__int) ).
fof(fact_finite__atLeastLessThan,axiom,
! [X165,X162] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X162),X165))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastLessThan) ).
fof(fact_nat_Osize_I4_J,axiom,
! [X111] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,X111)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X111)),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,
! [X105,X93,X94] :
( class_Orderings_Oorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X105))
=> X105 != X93 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
fof(fact_order__less__imp__not__eq,axiom,
! [X105,X93,X94] :
( class_Orderings_Oorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X105))
=> X93 != X105 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
fof(fact_less__imp__neq,axiom,
! [X105,X93,X94] :
( class_Orderings_Oorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X105))
=> X93 != X105 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__neq) ).
fof(fact_zdvd1__eq,axiom,
! [X16] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X16),c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X16) = 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,
! [X103,X121,X94] :
( class_Rings_Olinordered__idom(X94)
=> ( hAPP(c_Groups_Oabs__class_Oabs(X94),X121) = hAPP(c_Groups_Oabs__class_Oabs(X94),X103)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X121),X103)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__if__abs__eq) ).
fof(fact_diff__eq__diff__eq,axiom,
! [X141,X18,X38,X39,X10] :
( class_Groups_Oab__group__add(X10)
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X39),X38) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X18),X141)
=> ( X39 = X38
<=> X18 = X141 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__eq) ).
fof(fact_option__map__Some,axiom,
! [X16,X2,X10,X13] : hAPP(hAPP(c_Option_Omap(X13,X10),X2),hAPP(c_Option_Ooption_OSome(X13),X16)) = hAPP(c_Option_Ooption_OSome(X10),hAPP(X2,X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option__map__Some) ).
fof(fact_rev__filter,axiom,
! [X290,X19,X10] : hAPP(c_List_Orev(X10),hAPP(c_List_Ofilter(X10,X19),X290)) = hAPP(c_List_Ofilter(X10,X19),hAPP(c_List_Orev(X10),X290)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__filter) ).
fof(fact_zmod__zminus1__not__zero,axiom,
! [X121,X103] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X103),X121) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X103,X121) != 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,
! [X121,X103] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X103,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X121)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X103,X121) != 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,
! [X20] :
( X20 != 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)),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neq0__conv) ).
fof(fact_add__right__imp__eq,axiom,
! [X81,X84,X92,X94] :
( class_Groups_Ocancel__semigroup__add(X94)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X92),X84) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X81),X84)
=> X92 = X81 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
fof(fact_add__right__cancel,axiom,
! [X18,X39,X38,X10] :
( class_Groups_Ocancel__semigroup__add(X10)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X38),X39) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X18),X39)
<=> X38 = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__cancel) ).
fof(fact_add__imp__eq,axiom,
! [X81,X92,X84,X94] :
( class_Groups_Ocancel__ab__semigroup__add(X94)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X81)
=> X92 = X81 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__imp__eq) ).
fof(fact_add__left__imp__eq,axiom,
! [X81,X92,X84,X94] :
( class_Groups_Ocancel__semigroup__add(X94)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X81)
=> X92 = X81 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
fof(fact_add__left__cancel,axiom,
! [X18,X38,X39,X10] :
( class_Groups_Ocancel__semigroup__add(X10)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X39),X38) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X39),X18)
<=> X38 = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__cancel) ).
fof(fact_com_Osimps_I2_J,axiom,
! [X5,X40,X82,X8,X29,X79] :
( c_Com_Ocom_OLocal(X79,X29,X8) = c_Com_Ocom_OLocal(X82,X40,X5)
<=> ( X79 = X82
& X29 = X40
& X8 = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I2_J) ).
fof(fact_com_Osimps_I4_J,axiom,
! [X63,X64,X40,X55,X56,X29] :
( c_Com_Ocom_OCond(X29,X56,X55) = c_Com_Ocom_OCond(X40,X64,X63)
<=> ( X29 = X40
& X56 = X64
& X55 = X63 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I4_J) ).
fof(fact_com_Osimps_I7_J,axiom,
! [X40,X14,X41,X29,X15,X30] :
( c_Com_Ocom_OCall(X30,X15,X29) = c_Com_Ocom_OCall(X41,X14,X40)
<=> ( X30 = X41
& X15 = X14
& X29 = X40 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I7_J) ).
fof(fact_nat__le__0,axiom,
! [X104] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X104),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Int_Onat,X104) = 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,
! [X113] :
( hAPP(c_Int_Onat,X113) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X113),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,
! [X16] :
( c_Nat__Transfer_Ois__nat(X16)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_is__nat__def) ).
fof(fact_add__Suc__right,axiom,
! [X42,X97] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),hAPP(c_Nat_OSuc,X42)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_com_Osimps_I36_J,axiom,
! [X63,X64,X40,X8,X29,X79] : c_Com_Ocom_OLocal(X79,X29,X8) != c_Com_Ocom_OCond(X40,X64,X63),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I36_J) ).
fof(fact_com_Osimps_I42_J,axiom,
! [X40,X14,X41,X8,X29,X79] : c_Com_Ocom_OLocal(X79,X29,X8) != c_Com_Ocom_OCall(X41,X14,X40),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I42_J) ).
fof(fact_com_Osimps_I37_J,axiom,
! [X8,X29,X79,X63,X64,X40] : c_Com_Ocom_OCond(X40,X64,X63) != c_Com_Ocom_OLocal(X79,X29,X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I37_J) ).
fof(fact_com_Osimps_I43_J,axiom,
! [X8,X29,X79,X40,X14,X41] : c_Com_Ocom_OCall(X41,X14,X40) != c_Com_Ocom_OLocal(X79,X29,X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I43_J) ).
fof(fact_com_Osimps_I56_J,axiom,
! [X40,X14,X41,X55,X56,X29] : c_Com_Ocom_OCond(X29,X56,X55) != c_Com_Ocom_OCall(X41,X14,X40),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I56_J) ).
fof(fact_com_Osimps_I57_J,axiom,
! [X55,X56,X29,X40,X14,X41] : c_Com_Ocom_OCall(X41,X14,X40) != c_Com_Ocom_OCond(X29,X56,X55),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I57_J) ).
fof(fact_lexn_Osimps_I1_J,axiom,
! [X177,X10] : hAPP(c_List_Olexn(X10,X177),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),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,
! [X104] : 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),X104))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).
fof(fact_zero__zle__int,axiom,
! [X42] : 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),X42))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__zle__int) ).
fof(fact_Diff__cancel,axiom,
! [X154,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X154) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__cancel) ).
fof(fact_wf__empty,axiom,
! [X10] : c_Wellfounded_Owf(X10,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__empty) ).
fof(fact_atLeastAtMost__singleton_H,axiom,
! [X38,X39,X10] :
( class_Orderings_Oorder(X10)
=> ( X39 = X38
=> c_SetInterval_Oord__class_OatLeastAtMost(X10,X39,X38) = hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMost__singleton_H) ).
fof(fact_sorted__list__of__set,axiom,
! [X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hAPP(c_List_Oset(X10),c_List_Olinorder__class_Osorted__list__of__set(X10,X154)) = X154
& c_List_Olinorder__class_Osorted(X10,c_List_Olinorder__class_Osorted__list__of__set(X10,X154))
& hBOOL(hAPP(c_List_Odistinct(X10),c_List_Olinorder__class_Osorted__list__of__set(X10,X154))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__list__of__set) ).
fof(fact_mod__mult__self1__is__0,axiom,
! [X84,X92,X94] :
( class_Divides_Osemiring__div(X94)
=> c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X84),X92) = c_Groups_Ozero__class_Ozero(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self1__is__0) ).
fof(fact_mod__mult__self2__is__0,axiom,
! [X92,X84,X94] :
( class_Divides_Osemiring__div(X94)
=> c_Divides_Odiv__class_Omod(X94,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92),X92) = c_Groups_Ozero__class_Ozero(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self2__is__0) ).
fof(fact_distinct__butlast,axiom,
! [X94,X297] :
( X297 != c_List_Olist_ONil(X94)
=> ( hBOOL(hAPP(c_List_Odistinct(X94),X297))
=> hBOOL(hAPP(c_List_Odistinct(X94),c_List_Obutlast(X94,X297))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__butlast) ).
fof(fact_card__greaterThanAtMost,axiom,
! [X165,X162] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X162,X165)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X165),X162),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__greaterThanAtMost) ).
fof(fact_list_Oinject,axiom,
! [X300,X96,X291,X39,X10] :
( hAPP(hAPP(c_List_Olist_OCons(X10),X39),X291) = hAPP(hAPP(c_List_Olist_OCons(X10),X96),X300)
<=> ( X39 = X96
& X291 = X300 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Oinject) ).
fof(fact_append__same__eq,axiom,
! [X299,X290,X289,X10] :
( hAPP(hAPP(c_List_Oappend(X10),X289),X290) = hAPP(hAPP(c_List_Oappend(X10),X299),X290)
<=> X289 = X299 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__same__eq) ).
fof(fact_same__append__eq,axiom,
! [X299,X289,X290,X10] :
( hAPP(hAPP(c_List_Oappend(X10),X290),X289) = hAPP(hAPP(c_List_Oappend(X10),X290),X299)
<=> X289 = X299 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_same__append__eq) ).
fof(fact_atLeastAtMost__singleton,axiom,
! [X39,X10] :
( class_Orderings_Oorder(X10)
=> c_SetInterval_Oord__class_OatLeastAtMost(X10,X39,X39) = hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMost__singleton) ).
fof(fact_WT_Oequations_I4_J,axiom,
! [X52,X51] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X51,X52)))
<=> ( hBOOL(hAPP(c_Com_OWT,X51))
& hBOOL(hAPP(c_Com_OWT,X52)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I4_J) ).
fof(fact_WT_OSemi,axiom,
! [X58,X61] :
( hBOOL(hAPP(c_Com_OWT,X61))
=> ( hBOOL(hAPP(c_Com_OWT,X58))
=> hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X61,X58))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_OSemi) ).
fof(fact_upto__empty,axiom,
! [X120,X119] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X119),X120))
=> c_List_Oupto(X120,X119) = c_List_Olist_ONil(tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upto__empty) ).
fof(fact_atMost__Suc,axiom,
! [X101] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X101)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X101)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X101)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atMost__Suc) ).
fof(fact_eq__number__of__0,axiom,
! [X168] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X168),c_Int_OPls)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__number__of__0) ).
fof(fact_neg__imp__number__of__eq__0,axiom,
! [X144] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144) = 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,
! [X168] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X168),c_Int_OPls)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__0__number__of) ).
fof(fact_inf__sup__absorb,axiom,
! [X105,X93,X94] :
( class_Lattices_Olattice(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),X105)) = X93 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__absorb) ).
fof(fact_sup__inf__absorb,axiom,
! [X105,X93,X94] :
( class_Lattices_Olattice(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),X105)) = X93 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__inf__absorb) ).
fof(fact_min__max_Osup__inf__absorb,axiom,
! [X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X93),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X93),X105)) = X93 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__inf__absorb) ).
fof(fact_min__max_Oinf__sup__absorb,axiom,
! [X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X93),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X93),X105)) = X93 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__sup__absorb) ).
fof(fact_nat__dvd__1__iff__1,axiom,
! [X102] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X102),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
<=> X102 = 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,
! [X20] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> X20 = 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,
! [X297,X93,X94] : hAPP(hAPP(c_List_Odrop(X94),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)) = X297,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__1__Cons) ).
fof(fact_diff__Suc__Suc,axiom,
! [X42,X97] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X97)),hAPP(c_Nat_OSuc,X42)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__Suc) ).
fof(fact_add__Suc__shift,axiom,
! [X42,X97] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X97)),X42) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),hAPP(c_Nat_OSuc,X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
fof(fact_fold1__def,axiom,
! [X154,X2,X10] : hAPP(c_Finite__Set_Ofold1(X10,X2),X154) = c_HOL_OThe(X10,c_Finite__Set_Ofold1Set(X10,X2,X154)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__def) ).
fof(fact_zmod__eq__0__iff,axiom,
! [X141,X102] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X102,X141) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
<=> ? [X153] : X102 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X141),X153) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__eq__0__iff) ).
fof(fact_mod__eq__0__iff,axiom,
! [X141,X102] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X102,X141) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ? [X153] : X102 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X141),X153) ),
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,
! [X16,X154] :
( c_Nat__Transfer_Onat__set(X154)
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X16),X154))
=> c_Nat__Transfer_Ois__nat(X16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J) ).
fof(fact_acyclic__converse,axiom,
! [X177,X10] :
( c_Wellfounded_Oacyclic(X10,hAPP(c_Relation_Oconverse(X10,X10),X177))
<=> c_Wellfounded_Oacyclic(X10,X177) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__converse) ).
fof(fact_distinct__card,axiom,
! [X290,X10] :
( hBOOL(hAPP(c_List_Odistinct(X10),X290))
=> hAPP(c_Finite__Set_Ocard(X10),hAPP(c_List_Oset(X10),X290)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__card) ).
fof(fact_Domain__converse,axiom,
! [X177,X13,X10] : hAPP(c_Relation_ODomain(X10,X13),hAPP(c_Relation_Oconverse(X13,X10),X177)) = hAPP(c_Relation_ORange(X13,X10),X177),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__converse) ).
fof(fact_Range__converse,axiom,
! [X177,X10,X13] : hAPP(c_Relation_ORange(X13,X10),hAPP(c_Relation_Oconverse(X10,X13),X177)) = hAPP(c_Relation_ODomain(X10,X13),X177),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__converse) ).
fof(fact_rtrancl__converse,axiom,
! [X177,X10] : c_Transitive__Closure_Ortrancl(X10,hAPP(c_Relation_Oconverse(X10,X10),X177)) = hAPP(c_Relation_Oconverse(X10,X10),c_Transitive__Closure_Ortrancl(X10,X177)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__converse) ).
fof(fact_Range__def,axiom,
! [X177,X10,X13] : hAPP(c_Relation_ORange(X13,X10),X177) = hAPP(c_Relation_ODomain(X10,X13),hAPP(c_Relation_Oconverse(X13,X10),X177)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__def) ).
fof(fact_list__update__nonempty,axiom,
! [X16,X101,X290,X10] :
( hAPP(hAPP(c_List_Olist__update(X10,X290),X101),X16) = c_List_Olist_ONil(X10)
<=> X290 = c_List_Olist_ONil(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__nonempty) ).
fof(fact_map__is__Nil__conv,axiom,
! [X290,X2,X10,X13] :
( hAPP(hAPP(c_List_Omap(X13,X10),X2),X290) = c_List_Olist_ONil(X10)
<=> X290 = c_List_Olist_ONil(X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__is__Nil__conv) ).
fof(fact_option__map__is__None,axiom,
! [X292,X2,X10,X13] :
( hAPP(hAPP(c_Option_Omap(X13,X10),X2),X292) = c_Option_Ooption_ONone(X10)
<=> X292 = c_Option_Ooption_ONone(X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option__map__is__None) ).
fof(fact_Nil__is__map__conv,axiom,
! [X290,X2,X13,X10] :
( c_List_Olist_ONil(X10) = hAPP(hAPP(c_List_Omap(X13,X10),X2),X290)
<=> X290 = c_List_Olist_ONil(X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nil__is__map__conv) ).
fof(fact_Option_Oset_Osimps_I2_J,axiom,
! [X16,X10] : c_Option_Oset(X10,hAPP(c_Option_Ooption_OSome(X10),X16)) = hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Option_Oset_Osimps_I2_J) ).
fof(fact_diffs0__imp__equal,axiom,
! [X42,X97] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X42),X97) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> X97 = X42 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).
fof(fact_setsum__empty,axiom,
! [X2,X13,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X10),X2),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__empty) ).
fof(fact_setsum_Oempty,axiom,
! [X1,X13,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13,X10),X1),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oempty) ).
fof(fact_setprod_Oempty,axiom,
! [X1,X13,X10] :
( class_Groups_Ocomm__monoid__mult(X10)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X13,X10),X1),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Oempty) ).
fof(fact_setprod__empty,axiom,
! [X2,X13,X10] :
( class_Groups_Ocomm__monoid__mult(X10)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X13,X10),X2),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__empty) ).
fof(fact_gr__implies__not0,axiom,
! [X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42))
=> X42 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
fof(fact_finite__UNIV,axiom,
! [X10] :
( class_Finite__Set_Ofinite(X10)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV) ).
fof(fact_divide__eq__eq,axiom,
! [X39,X18,X38,X10] :
( class_Fields_Ofield__inverse__zero(X10)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),X18) = X39
<=> ( ( X18 != c_Groups_Ozero__class_Ozero(X10)
=> X38 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X18) )
& ( X18 = c_Groups_Ozero__class_Ozero(X10)
=> X39 = c_Groups_Ozero__class_Ozero(X10) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__eq__eq) ).
fof(fact_eq__divide__eq,axiom,
! [X18,X38,X39,X10] :
( class_Fields_Ofield__inverse__zero(X10)
=> ( X39 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),X18)
<=> ( ( X18 != c_Groups_Ozero__class_Ozero(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X18) = X38 )
& ( X18 = c_Groups_Ozero__class_Ozero(X10)
=> X39 = c_Groups_Ozero__class_Ozero(X10) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__divide__eq) ).
fof(fact_of__nat__Suc,axiom,
! [X97,X94] :
( class_Rings_Osemiring__1(X94)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),hAPP(c_Nat_OSuc,X97)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),c_Groups_Oone__class_Oone(X94)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__Suc) ).
fof(fact_zero__less__Suc,axiom,
! [X42] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X42))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
fof(fact_sum_Osize_I3_J,axiom,
! [X84,X10,X94] : hAPP(c_Nat_Osize__class_Osize(tc_sum(X94,X10)),hAPP(c_Sum__Type_OInl(X94,X10),X84)) = 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,
! [X92,X10,X94] : hAPP(c_Nat_Osize__class_Osize(tc_sum(X94,X10)),hAPP(c_Sum__Type_OInr(X10,X94),X92)) = 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,
! [X44,X45] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X44))
=> X45 != X44 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl3) ).
fof(fact_less__not__refl2,axiom,
! [X97,X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),X97))
=> X97 != X42 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl2) ).
fof(fact_WT_Oequations_I6_J,axiom,
! [X51,X52] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X52,X51)))
<=> hBOOL(hAPP(c_Com_OWT,X51)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I6_J) ).
fof(fact_WTs__elim__cases_I6_J,axiom,
! [X18,X38] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X38,X18)))
=> hBOOL(hAPP(c_Com_OWT,X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WTs__elim__cases_I6_J) ).
fof(fact_atLeastLessThan__singleton,axiom,
! [X102] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X102),hAPP(c_Nat_OSuc,X102)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X102),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,
! [X84,X297,X94] :
( class_Orderings_Olinorder(X94)
=> ( c_List_Olinorder__class_Osorted(X94,X297)
=> c_List_Olinorder__class_Osorted(X94,c_List_Oremove1(X94,X84,X297)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__remove1) ).
fof(fact_mult__cancel2,axiom,
! [X20,X101,X102] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X102),X101) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X101)
<=> ( X102 = X20
| X101 = 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,
! [X20,X102,X101] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X101),X102) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X101),X20)
<=> ( X101 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X102 = X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
fof(fact_mult__cancel1,axiom,
! [X20,X102,X101] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X101),X102) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X101),X20)
<=> ( X102 = X20
| X101 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel1) ).
fof(fact_hd__append,axiom,
! [X298,X94,X297] :
( ( X297 = c_List_Olist_ONil(X94)
=> hAPP(c_List_Ohd(X94),hAPP(hAPP(c_List_Oappend(X94),X297),X298)) = hAPP(c_List_Ohd(X94),X298) )
& ( X297 != c_List_Olist_ONil(X94)
=> hAPP(c_List_Ohd(X94),hAPP(hAPP(c_List_Oappend(X94),X297),X298)) = hAPP(c_List_Ohd(X94),X297) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__append) ).
fof(fact_WTs__elim__cases_I7_J,axiom,
! [X87] :
( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X87)))
=> ~ ! [X90] : hAPP(c_Com_Obody,X87) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X90) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WTs__elim__cases_I7_J) ).
fof(fact_WT_Oequations_I7_J,axiom,
! [X39] :
( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X39)))
<=> ? [X90] : hAPP(c_Com_Obody,X39) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X90) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I7_J) ).
fof(fact_evalc__elim__cases_I1_J,axiom,
! [X44,X45] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X45),X44))
=> X44 = X45 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I1_J) ).
fof(fact_mult__sgn__abs,axiom,
! [X93,X94] :
( class_Rings_Olinordered__idom(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),c_Groups_Osgn__class_Osgn(X94,X93)),hAPP(c_Groups_Oabs__class_Oabs(X94),X93)) = X93 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__sgn__abs) ).
fof(fact_Ints__1,axiom,
! [X10] :
( class_Rings_Oring__1(X10)
=> hBOOL(hAPP(hAPP(c_member(X10),c_Groups_Oone__class_Oone(X10)),c_Int_Oring__1__class_OInts(X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__1) ).
fof(fact_Nats__1,axiom,
! [X10] :
( class_Rings_Osemiring__1(X10)
=> hBOOL(hAPP(hAPP(c_member(X10),c_Groups_Oone__class_Oone(X10)),c_Nat_Osemiring__1__class_ONats(X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nats__1) ).
fof(fact_Ints__0,axiom,
! [X10] :
( class_Rings_Oring__1(X10)
=> hBOOL(hAPP(hAPP(c_member(X10),c_Groups_Ozero__class_Ozero(X10)),c_Int_Oring__1__class_OInts(X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__0) ).
fof(fact_Nats__0,axiom,
! [X10] :
( class_Rings_Osemiring__1(X10)
=> hBOOL(hAPP(hAPP(c_member(X10),c_Groups_Ozero__class_Ozero(X10)),c_Nat_Osemiring__1__class_ONats(X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nats__0) ).
fof(fact_zero__le__one,axiom,
! [X94] :
( class_Rings_Olinordered__semidom(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Ozero__class_Ozero(X94)),c_Groups_Oone__class_Oone(X94))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__one) ).
fof(fact_zero__less__one,axiom,
! [X94] :
( class_Rings_Olinordered__semidom(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),c_Groups_Oone__class_Oone(X94))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__one) ).
fof(fact_divide__eq__imp,axiom,
! [X84,X92,X81,X94] :
( class_Rings_Odivision__ring(X94)
=> ( X81 != c_Groups_Ozero__class_Ozero(X94)
=> ( X92 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X81)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X92),X81) = X84 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__eq__imp) ).
fof(fact_nonzero__divide__eq__eq,axiom,
! [X39,X38,X18,X10] :
( class_Rings_Odivision__ring(X10)
=> ( X18 != c_Groups_Ozero__class_Ozero(X10)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),X18) = X39
<=> X38 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X18) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__divide__eq__eq) ).
fof(fact_nonzero__eq__divide__eq,axiom,
! [X38,X39,X18,X10] :
( class_Rings_Odivision__ring(X10)
=> ( X18 != c_Groups_Ozero__class_Ozero(X10)
=> ( X39 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),X18)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X18) = X38 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__eq__divide__eq) ).
fof(fact_eq__divide__imp,axiom,
! [X92,X84,X81,X94] :
( class_Rings_Odivision__ring(X94)
=> ( X81 != c_Groups_Ozero__class_Ozero(X94)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X81) = X92
=> X84 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X92),X81) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__divide__imp) ).
fof(fact_diff__minus__eq__add,axiom,
! [X92,X84,X94] :
( class_Groups_Ogroup__add(X94)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X84),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X92)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__minus__eq__add) ).
fof(fact_diff__eq,axiom,
! [X105,X93,X94] :
( class_Lattices_Oboolean__algebra(X94)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X93),X105) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X105)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq) ).
fof(fact_ab__diff__minus,axiom,
! [X92,X84,X94] :
( class_Groups_Oab__group__add(X94)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X84),X92) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__diff__minus) ).
fof(fact_diff__def,axiom,
! [X92,X84,X94] :
( class_Groups_Ogroup__add(X94)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X84),X92) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__def) ).
fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
! [X105,X93,X94] :
( class_Rings_Ocomm__ring__1(X94)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X93),X105) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X93),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X105)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).
fof(fact_mult__minus1,axiom,
! [X104,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OMin)),X104) = hAPP(c_Groups_Ouminus__class_Ouminus(X94),X104) ),
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,
! [X298,X94,X297] :
( X297 != c_List_Olist_ONil(X94)
=> hAPP(c_List_Ohd(X94),hAPP(hAPP(c_List_Oappend(X94),X297),X298)) = hAPP(c_List_Ohd(X94),X297) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__append2) ).
fof(fact_nat__add__right__cancel,axiom,
! [X20,X101,X102] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X101) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X101)
<=> X102 = X20 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
fof(fact_nat__add__left__cancel,axiom,
! [X20,X102,X101] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X101),X102) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X101),X20)
<=> X102 = X20 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
fof(fact_singleton__conv2,axiom,
! [X39,X10] : hAPP(c_Set_OCollect(X10),hAPP(c_fequal,X39)) = hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__conv2) ).
fof(fact_sorted__drop,axiom,
! [X42,X297,X94] :
( class_Orderings_Olinorder(X94)
=> ( c_List_Olinorder__class_Osorted(X94,X297)
=> c_List_Olinorder__class_Osorted(X94,hAPP(hAPP(c_List_Odrop(X94),X42),X297)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__drop) ).
fof(fact_sorted__take,axiom,
! [X42,X297,X94] :
( class_Orderings_Olinorder(X94)
=> ( c_List_Olinorder__class_Osorted(X94,X297)
=> c_List_Olinorder__class_Osorted(X94,hAPP(hAPP(c_List_Otake(X94),X42),X297)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__take) ).
fof(fact_finite_Oequations_I1_J,axiom,
! [X10] : hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_Oequations_I1_J) ).
fof(fact_finite_OemptyI,axiom,
! [X10] : hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_OemptyI) ).
fof(fact_Pow__not__empty,axiom,
! [X154,X10] : hAPP(c_Set_OPow(X10),X154) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__not__empty) ).
fof(fact_Compl__UNIV__eq,axiom,
! [X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__UNIV__eq) ).
fof(fact_Compl__empty__eq,axiom,
! [X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__empty__eq) ).
fof(fact_Pow__UNIV,axiom,
! [X10] : hAPP(c_Set_OPow(X10),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__UNIV) ).
fof(fact_Id__on__empty,axiom,
! [X10] : c_Relation_OId__on(X10,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__empty) ).
fof(fact_Int__absorb,axiom,
! [X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X154) = X154,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb) ).
fof(fact_Un__absorb,axiom,
! [X154,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X154) = X154,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb) ).
fof(fact_wf__in__rel,axiom,
! [X196,X10] :
( c_Wellfounded_Owf(X10,X196)
=> c_Wellfounded_OwfP(X10,c_FunDef_Oin__rel(X10,X10,X196)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__in__rel) ).
fof(fact_wf__mlex,axiom,
! [X2,X196,X10] :
( c_Wellfounded_Owf(X10,X196)
=> c_Wellfounded_Owf(X10,c_Wellfounded_Omlex__prod(X10,X2,X196)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__mlex) ).
fof(fact_Min_OF__eq,axiom,
! [X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> c_Big__Operators_Olinorder__class_OMin(X10,X154) = hAPP(c_Finite__Set_Ofold1(X10,c_Orderings_Oord__class_Omin(X10)),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_OF__eq) ).
fof(fact_Max_OF__eq,axiom,
! [X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> c_Big__Operators_Olinorder__class_OMax(X10,X154) = hAPP(c_Finite__Set_Ofold1(X10,c_Orderings_Oord__class_Omax(X10)),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_OF__eq) ).
fof(fact_Inf__fin_OF__eq,axiom,
! [X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> c_Big__Operators_Olattice__class_OInf__fin(X10,X154) = hAPP(c_Finite__Set_Ofold1(X10,c_Lattices_Osemilattice__inf__class_Oinf(X10)),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_OF__eq) ).
fof(fact_Sup__fin_OF__eq,axiom,
! [X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> c_Big__Operators_Olattice__class_OSup__fin(X10,X154) = hAPP(c_Finite__Set_Ofold1(X10,c_Lattices_Osemilattice__sup__class_Osup(X10)),X154) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_OF__eq) ).
fof(fact_lessI,axiom,
! [X42] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_OSuc,X42))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessI) ).
fof(fact_compl__inf__bot,axiom,
! [X93,X94] :
( class_Lattices_Oboolean__algebra(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X93)),X93) = c_Orderings_Obot__class_Obot(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__inf__bot) ).
fof(fact_compl__sup__top,axiom,
! [X93,X94] :
( class_Lattices_Oboolean__algebra(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X93)),X93) = c_Orderings_Otop__class_Otop(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__sup__top) ).
fof(fact_ab__left__minus,axiom,
! [X84,X94] :
( class_Groups_Oab__group__add(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X84)),X84) = c_Groups_Ozero__class_Ozero(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__left__minus) ).
fof(fact_left__minus,axiom,
! [X84,X94] :
( class_Groups_Ogroup__add(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X84)),X84) = c_Groups_Ozero__class_Ozero(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__minus) ).
fof(fact_last__append,axiom,
! [X297,X94,X298] :
( ( X298 = c_List_Olist_ONil(X94)
=> c_List_Olast(X94,hAPP(hAPP(c_List_Oappend(X94),X297),X298)) = c_List_Olast(X94,X297) )
& ( X298 != c_List_Olist_ONil(X94)
=> c_List_Olast(X94,hAPP(hAPP(c_List_Oappend(X94),X297),X298)) = c_List_Olast(X94,X298) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__append) ).
fof(fact_last__appendL,axiom,
! [X297,X94,X298] :
( X298 = c_List_Olist_ONil(X94)
=> c_List_Olast(X94,hAPP(hAPP(c_List_Oappend(X94),X297),X298)) = c_List_Olast(X94,X297) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__appendL) ).
fof(fact_diff__add__0,axiom,
! [X97,X42] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X42),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),X97)) = 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,
! [X20,X162,X10] : c_List_Osublist(X10,X162,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X20)) = hAPP(hAPP(c_List_Otake(X10),X20),X162),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__upt__eq__take) ).
fof(fact_one__dvd,axiom,
! [X84,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),c_Groups_Oone__class_Oone(X94)),X84)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__dvd) ).
fof(fact_bot__least,axiom,
! [X93,X94] :
( class_Orderings_Obot(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Orderings_Obot__class_Obot(X94)),X93)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__least) ).
fof(fact_divmod__int__correct,axiom,
! [X84,X92] :
( X92 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(X84,X92),c_Divides_Odivmod__int(X84,X92))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__correct) ).
fof(fact_pdivmod__posDivAlg,axiom,
! [X103,X121] :
( ( X121 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Opdivmod(X103,X121) = 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),X103)) )
& ( X121 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Opdivmod(X103,X121) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X103),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X121)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__posDivAlg) ).
fof(fact_sorted__single,axiom,
! [X93,X94] :
( class_Orderings_Olinorder(X94)
=> c_List_Olinorder__class_Osorted(X94,hAPP(hAPP(c_List_Olist_OCons(X94),X93),c_List_Olist_ONil(X94))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__single) ).
fof(fact_last__appendR,axiom,
! [X297,X94,X298] :
( X298 != c_List_Olist_ONil(X94)
=> c_List_Olast(X94,hAPP(hAPP(c_List_Oappend(X94),X297),X298)) = c_List_Olast(X94,X298) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__appendR) ).
fof(fact_last_Osimps,axiom,
! [X93,X94,X297] :
( ( X297 = c_List_Olist_ONil(X94)
=> c_List_Olast(X94,hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)) = X93 )
& ( X297 != c_List_Olist_ONil(X94)
=> c_List_Olast(X94,hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)) = c_List_Olast(X94,X297) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last_Osimps) ).
fof(fact_last__ConsR,axiom,
! [X93,X94,X297] :
( X297 != c_List_Olist_ONil(X94)
=> c_List_Olast(X94,hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)) = c_List_Olast(X94,X297) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__ConsR) ).
fof(fact_nat__gcd_Osimps,axiom,
! [X93,X105] :
( ( X105 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Nitpick_Onat__gcd(X93,X105) = X93 )
& ( X105 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Nitpick_Onat__gcd(X93,X105) = c_Nitpick_Onat__gcd(X105,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X93,X105)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__gcd_Osimps) ).
fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
! [X165,X162] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X162)),X165) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X162,X165),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastSucLessThan__greaterThanLessThan) ).
fof(fact_card__atLeastLessThan,axiom,
! [X165,X162] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X162),X165)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X165),X162),
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,
! [X298,X10,X94] : hAPP(hAPP(c_List_Ozip(X94,X10),c_List_Olist_ONil(X94)),X298) = c_List_Olist_ONil(tc_prod(X94,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__Nil) ).
fof(fact_top1I,axiom,
! [X16,X10] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top1I) ).
fof(fact_vimage__id,axiom,
! [X154,X10] : hAPP(c_Set_Ovimage(X10,X10,c_Fun_Oid(X10)),X154) = X154,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__id) ).
fof(fact_vimage__ident,axiom,
! [X78,X10] : hAPP(c_Set_Ovimage(X10,X10,c_COMBI(X10)),X78) = X78,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__ident) ).
fof(fact_image__id,axiom,
! [X78,X10] : hAPP(c_Set_Oimage(X10,X10,c_Fun_Oid(X10)),X78) = X78,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__id) ).
fof(fact_image__ident,axiom,
! [X78,X10] : hAPP(c_Set_Oimage(X10,X10,c_COMBI(X10)),X78) = X78,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__ident) ).
fof(fact_Projr_Osimps,axiom,
! [X93,X10,X94] : c_Sum__Type_OProjr(X94,X10,hAPP(c_Sum__Type_OInr(X10,X94),X93)) = X93,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Projr_Osimps) ).
fof(fact_Projl_Osimps,axiom,
! [X93,X10,X94] : c_Sum__Type_OProjl(X94,X10,hAPP(c_Sum__Type_OInl(X94,X10),X93)) = X93,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Projl_Osimps) ).
fof(fact_refl__rtrancl,axiom,
! [X177,X10] : c_Relation_Orefl__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X10,X177)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__rtrancl) ).
fof(fact_Compl__greaterThan,axiom,
! [X101,X10] :
( class_Orderings_Olinorder(X10)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),X101)) = hAPP(c_SetInterval_Oord__class_OatMost(X10),X101) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__greaterThan) ).
fof(fact_Compl__atLeast,axiom,
! [X101,X10] :
( class_Orderings_Olinorder(X10)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X10),X101)) = hAPP(c_SetInterval_Oord__class_OlessThan(X10),X101) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__atLeast) ).
fof(fact_Compl__lessThan,axiom,
! [X101,X10] :
( class_Orderings_Olinorder(X10)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X10),X101)) = hAPP(c_SetInterval_Oord__class_OatLeast(X10),X101) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__lessThan) ).
fof(fact_Compl__atMost,axiom,
! [X101,X10] :
( class_Orderings_Olinorder(X10)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X10),X101)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),X101) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__atMost) ).
fof(fact_hoare__derivs_Oequations_I1_J,axiom,
! [X39,X10] : c_Hoare__Mirabelle_Ohoare__derivs(X10,X39,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X10),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_Oequations_I1_J) ).
fof(fact_empty,axiom,
! [X210,X10] : c_Hoare__Mirabelle_Ohoare__derivs(X10,X210,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X10),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty) ).
fof(fact_Sup__fin__Sup,axiom,
! [X154,X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(X10,X154) = c_Complete__Lattice_OSup__class_OSup(X10,X154) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin__Sup) ).
fof(fact_Inf__fin__Inf,axiom,
! [X154,X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(X10,X154) = c_Complete__Lattice_OInf__class_OInf(X10,X154) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin__Inf) ).
fof(fact_add__numeral__0,axiom,
! [X84,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OPls)),X84) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__numeral__0) ).
fof(fact_add__is__1,axiom,
! [X20,X102] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X20) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( ( X102 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X102 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X20 = 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,
! [X20,X102] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X20)
<=> ( ( X102 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X102 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X20 = 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,
! [X10,X19] :
( ? [X147] : hBOOL(hAPP(X19,X147))
=> hBOOL(hAPP(X19,c_Hilbert__Choice_OEps(X10,X19))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_someI__ex) ).
fof(fact_someI,axiom,
! [X10,X16,X19] :
( hBOOL(hAPP(X19,X16))
=> hBOOL(hAPP(X19,c_Hilbert__Choice_OEps(X10,X19))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_someI) ).
fof(fact_tfl__some,axiom,
! [X10,X264] :
( ? [X3] : hBOOL(hAPP(X264,X3))
=> hBOOL(hAPP(X264,c_Hilbert__Choice_OEps(X10,X264))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tfl__some) ).
fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
! [X165,X162] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X162),X165) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X162,X165),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastSucAtMost__greaterThanAtMost) ).
fof(fact_square__eq__1__iff,axiom,
! [X16,X10] :
( class_Rings_Oring__1__no__zero__divisors(X10)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X16),X16) = c_Groups_Oone__class_Oone(X10)
<=> ( X16 = c_Groups_Oone__class_Oone(X10)
| X16 = hAPP(c_Groups_Ouminus__class_Ouminus(X10),c_Groups_Oone__class_Oone(X10)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_square__eq__1__iff) ).
fof(fact_Inl__inject,axiom,
! [X105,X93,X10,X94] :
( hAPP(c_Sum__Type_OInl(X94,X10),X93) = hAPP(c_Sum__Type_OInl(X94,X10),X105)
=> X93 = X105 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inl__inject) ).
fof(fact_sum_Osimps_I1_J,axiom,
! [X96,X39,X13,X10] :
( hAPP(c_Sum__Type_OInl(X10,X13),X39) = hAPP(c_Sum__Type_OInl(X10,X13),X96)
<=> X39 = X96 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I1_J) ).
fof(fact_Inr__inject,axiom,
! [X105,X93,X94,X10] :
( hAPP(c_Sum__Type_OInr(X10,X94),X93) = hAPP(c_Sum__Type_OInr(X10,X94),X105)
=> X93 = X105 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inr__inject) ).
fof(fact_sum_Osimps_I2_J,axiom,
! [X118,X38,X10,X13] :
( hAPP(c_Sum__Type_OInr(X13,X10),X38) = hAPP(c_Sum__Type_OInr(X13,X10),X118)
<=> X38 = X118 ),
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,
! [X297,X10,X94] : hAPP(hAPP(c_List_Ozip(X94,X10),X297),c_List_Olist_ONil(X10)) = c_List_Olist_ONil(tc_prod(X94,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip_Osimps_I1_J) ).
fof(fact_comm__monoid_Ocomm__neutral,axiom,
! [X39,X73,X2,X10] :
( c_Groups_Ocomm__monoid(X10,X2,X73)
=> hAPP(hAPP(X2,X39),X73) = X39 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__monoid_Ocomm__neutral) ).
fof(fact_folding__one__idem_Oidem,axiom,
! [X16,X225,X2,X10] :
( c_Finite__Set_Ofolding__one__idem(X10,X2,X225)
=> hAPP(hAPP(X2,X16),X16) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oidem) ).
fof(fact_com_Osize_I16_J,axiom,
! [X29,X15,X30] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(X30,X15,X29)) = 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,
! [X84,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X84),c_Groups_Ozero__class_Ozero(X94))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__0__right) ).
fof(fact_top__greatest,axiom,
! [X93,X94] :
( class_Orderings_Otop(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),c_Orderings_Otop__class_Otop(X94))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top__greatest) ).
fof(fact_Inl__not__Inr,axiom,
! [X92,X84,X10,X94] : hAPP(c_Sum__Type_OInl(X94,X10),X84) != hAPP(c_Sum__Type_OInr(X10,X94),X92),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inl__not__Inr) ).
fof(fact_sum_Osimps_I3_J,axiom,
! [X130,X84,X10,X94] : hAPP(c_Sum__Type_OInl(X94,X10),X84) != hAPP(c_Sum__Type_OInr(X10,X94),X130),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I3_J) ).
fof(fact_Inr__not__Inl,axiom,
! [X84,X92,X94,X10] : hAPP(c_Sum__Type_OInr(X10,X94),X92) != hAPP(c_Sum__Type_OInl(X94,X10),X84),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inr__not__Inl) ).
fof(fact_sum_Osimps_I4_J,axiom,
! [X126,X127,X128,X129] : hAPP(c_Sum__Type_OInr(X129,X128),X127) != hAPP(c_Sum__Type_OInl(X128,X129),X126),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I4_J) ).
fof(fact_last__ConsL,axiom,
! [X93,X94,X297] :
( X297 = c_List_Olist_ONil(X94)
=> c_List_Olast(X94,hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)) = X93 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__ConsL) ).
fof(fact_nat__rec__0,axiom,
! [X37,X12,X10] : hAPP(c_Nat_Onat_Onat__rec(X10,X12,X37),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__rec__0) ).
fof(fact_insert__not__empty,axiom,
! [X154,X39,X10] : hAPP(hAPP(c_Set_Oinsert(X10),X39),X154) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__not__empty) ).
fof(fact_empty__not__insert,axiom,
! [X154,X39,X10] : c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(X10),X39),X154),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__not__insert) ).
fof(fact_int__Suc,axiom,
! [X97] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X97)) = 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),X97)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__Suc) ).
fof(fact_diff__int__def__symmetric,axiom,
! [X133,X104] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X104),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X133)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X104),X133),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__int__def__symmetric) ).
fof(fact_diff__int__def,axiom,
! [X133,X104] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X104),X133) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X104),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X133)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__int__def) ).
fof(fact_tl_Osimps_I2_J,axiom,
! [X297,X93,X94] : hAPP(c_List_Otl(X94),hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)) = X297,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl_Osimps_I2_J) ).
fof(fact_hd_Osimps,axiom,
! [X297,X93,X94] : hAPP(c_List_Ohd(X94),hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297)) = X93,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd_Osimps) ).
fof(fact_power__eq__0__iff,axiom,
! [X20,X39,X10] :
( ( class_Power_Opower(X10)
& class_Rings_Omult__zero(X10)
& class_Rings_Ono__zero__divisors(X10)
& class_Rings_Ozero__neq__one(X10) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X10),X39),X20) = c_Groups_Ozero__class_Ozero(X10)
<=> ( X39 = c_Groups_Ozero__class_Ozero(X10)
& X20 != 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,
! [X105,X93] :
( c_Nat__Transfer_Ois__nat(X93)
=> ( c_Nat__Transfer_Ois__nat(X105)
=> c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X93,X105)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__function__closures_I2_J) ).
fof(fact_While,axiom,
! [X38,X18] :
( hBOOL(hAPP(c_Com_OWT,X18))
=> hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X38,X18))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_While) ).
fof(fact_divide__minus1,axiom,
! [X93,X94] :
( ( class_Fields_Ofield__inverse__zero(X94)
& class_Int_Onumber__ring(X94) )
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X93),hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(X94),X93) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__minus1) ).
fof(fact_wf__lexn,axiom,
! [X20,X177,X10] :
( c_Wellfounded_Owf(X10,X177)
=> c_Wellfounded_Owf(tc_List_Olist(X10),hAPP(c_List_Olexn(X10,X177),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__lexn) ).
fof(fact_list__update_Osimps_I1_J,axiom,
! [X144,X120,X94] : hAPP(hAPP(c_List_Olist__update(X94,c_List_Olist_ONil(X94)),X120),X144) = c_List_Olist_ONil(X94),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update_Osimps_I1_J) ).
fof(fact_list__update__code_I1_J,axiom,
! [X105,X120,X94] : hAPP(hAPP(c_List_Olist__update(X94,c_List_Olist_ONil(X94)),X120),X105) = c_List_Olist_ONil(X94),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__code_I1_J) ).
fof(fact_power__Suc__0,axiom,
! [X42] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X42) = 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,
! [X290,X10] : hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_List_Oset(X10),X290))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__set) ).
fof(fact_converse__converse,axiom,
! [X177,X10,X13] : hAPP(c_Relation_Oconverse(X13,X10),hAPP(c_Relation_Oconverse(X10,X13),X177)) = X177,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__converse) ).
fof(fact_lessThan__Suc,axiom,
! [X101] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X101)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X101),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X101)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__Suc) ).
fof(fact_Field__converse,axiom,
! [X177,X10] : hAPP(c_Relation_OField(X10),hAPP(c_Relation_Oconverse(X10,X10),X177)) = hAPP(c_Relation_OField(X10),X177),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__converse) ).
fof(fact_number__of__minus,axiom,
! [X133,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(c_Int_Onumber__class_Onumber__of(X94),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X133)) = hAPP(c_Groups_Ouminus__class_Ouminus(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),X133)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__minus) ).
fof(fact_of__int__minus,axiom,
! [X104,X94] :
( class_Rings_Oring__1(X94)
=> hAPP(c_Int_Oring__1__class_Oof__int(X94),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X104)) = hAPP(c_Groups_Ouminus__class_Ouminus(X94),hAPP(c_Int_Oring__1__class_Oof__int(X94),X104)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__minus) ).
fof(fact_arith__simps_I30_J,axiom,
! [X133,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),X133)) = hAPP(c_Int_Onumber__class_Onumber__of(X94),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X133)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arith__simps_I30_J) ).
fof(fact_nat__power__eq__Suc__0__iff,axiom,
! [X102,X16] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X16),X102) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( X102 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X16 = 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,
! [X105,X93,X94] :
( class_Orderings_Opreorder(X94)
=> ( X93 = X105
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X105)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__refl) ).
fof(fact_com_Osize_I6_J,axiom,
! [X8,X29] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(X29,X8)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X8)),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,
! [X92,X84,X94] :
( class_Groups_Ogroup__add(X94)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X92) = c_Groups_Ozero__class_Ozero(X94)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X94),X84) = X92 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__unique) ).
fof(fact_eq__neg__iff__add__eq__0,axiom,
! [X38,X39,X10] :
( class_Groups_Ogroup__add(X10)
=> ( X39 = hAPP(c_Groups_Ouminus__class_Ouminus(X10),X38)
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X39),X38) = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).
fof(fact_UNIV__def,axiom,
! [X10] : c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X10),hAPP(c_COMBK(tc_HOL_Obool,X10),c_fTrue)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__def) ).
fof(fact_empty__def,axiom,
! [X10] : c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X10),hAPP(c_COMBK(tc_HOL_Obool,X10),c_fFalse)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__def) ).
fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
! [X25,X16] :
( c_Nat__Transfer_Ois__nat(X16)
=> c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X16,X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__int__nat__set__function__closures) ).
fof(fact_mult__minus1__right,axiom,
! [X104,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X104),hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(X94),X104) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__minus1__right) ).
fof(fact_mult__eq__1__iff,axiom,
! [X20,X102] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X102),X20) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( X102 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X20 = 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,
! [X111] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X111)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X111)),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,
! [X84,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X94),X84),X84)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__refl) ).
fof(fact_order__refl,axiom,
! [X93,X94] :
( class_Orderings_Opreorder(X94)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X93)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__refl) ).
fof(fact_card__atLeastZeroLessThan__int,axiom,
! [X165] : 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)),X165)) = hAPP(c_Int_Onat,X165),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__atLeastZeroLessThan__int) ).
fof(fact_com_Osize_I8_J,axiom,
! [X29,X15,X30] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(X30,X15,X29)) = 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,
! [X104] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X104)),X104) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).
fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
! [X165,X162] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X162),hAPP(c_Nat_OSuc,X165)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X162,X165),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThanSuc__atLeastAtMost) ).
fof(fact_mod__int__def,axiom,
! [X92,X84] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X92) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X84,X92)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__int__def) ).
fof(fact_inf__commute,axiom,
! [X105,X93,X94] :
( class_Lattices_Osemilattice__inf(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),X105) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X105),X93) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__commute) ).
fof(fact_inf_Ocommute,axiom,
! [X92,X84,X94] :
( class_Lattices_Osemilattice__inf(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X84),X92) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X92),X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Ocommute) ).
fof(fact_inf__sup__aci_I1_J,axiom,
! [X105,X93,X94] :
( class_Lattices_Olattice(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),X105) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X105),X93) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I1_J) ).
fof(fact_sup_Ocommute,axiom,
! [X92,X84,X94] :
( class_Lattices_Osemilattice__sup(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X84),X92) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X92),X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Ocommute) ).
fof(fact_sup__commute,axiom,
! [X105,X93,X94] :
( class_Lattices_Osemilattice__sup(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),X105) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X105),X93) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__commute) ).
fof(fact_inf__sup__aci_I5_J,axiom,
! [X105,X93,X94] :
( class_Lattices_Olattice(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),X105) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X105),X93) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I5_J) ).
fof(fact_min__max_Osup__commute,axiom,
! [X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X93),X105) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X105),X93) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__commute) ).
fof(fact_min__max_Osup_Ocommute,axiom,
! [X92,X84,X94] :
( class_Orderings_Olinorder(X94)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X84),X92) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X92),X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup_Ocommute) ).
fof(fact_min__max_Oinf_Ocommute,axiom,
! [X92,X84,X94] :
( class_Orderings_Olinorder(X94)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X84),X92) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X92),X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf_Ocommute) ).
fof(fact_min__max_Oinf__commute,axiom,
! [X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X93),X105) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X105),X93) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__commute) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [X92,X84,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X92),X84) ),
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,
! [X81,X84,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),X81) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X81),X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_nat__zminus__int,axiom,
! [X42] : hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X42))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__zminus__int) ).
fof(fact_gr0I,axiom,
! [X42] :
( X42 != 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)),X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0I) ).
fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
! [X105,X93] :
( c_Nat__Transfer_Ois__nat(X93)
=> ( c_Nat__Transfer_Ois__nat(X105)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X93),X105)) ) ),
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,
! [X105,X93] :
( c_Nat__Transfer_Ois__nat(X93)
=> ( c_Nat__Transfer_Ois__nat(X105)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X93),X105)) ) ),
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,
! [X105,X93] :
( c_Nat__Transfer_Ois__nat(X93)
=> ( c_Nat__Transfer_Ois__nat(X105)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X93),X105)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J) ).
fof(fact_negative__eq__positive,axiom,
! [X102,X20] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X102)
<=> ( X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X102 = 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,
! [X5,X40,X8,X29,X79] : c_Com_Ocom_OLocal(X79,X29,X8) != c_Com_Ocom_OWhile(X40,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I38_J) ).
fof(fact_com_Osimps_I34_J,axiom,
! [X63,X64,X8,X29,X79] : c_Com_Ocom_OLocal(X79,X29,X8) != c_Com_Ocom_OSemi(X64,X63),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I34_J) ).
fof(fact_com_Osimps_I23_J,axiom,
! [X29,X30,X5,X40,X82] : c_Com_Ocom_OLocal(X82,X40,X5) != c_Com_Ocom_OAss(X30,X29),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I23_J) ).
fof(fact_com_Osimps_I52_J,axiom,
! [X5,X40,X55,X56,X29] : c_Com_Ocom_OCond(X29,X56,X55) != c_Com_Ocom_OWhile(X40,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I52_J) ).
fof(fact_com_Osimps_I45_J,axiom,
! [X55,X56,X63,X64,X40] : c_Com_Ocom_OCond(X40,X64,X63) != c_Com_Ocom_OSemi(X56,X55),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I45_J) ).
fof(fact_com_Osimps_I27_J,axiom,
! [X29,X30,X63,X64,X40] : c_Com_Ocom_OCond(X40,X64,X63) != c_Com_Ocom_OAss(X30,X29),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I27_J) ).
fof(fact_com_Osimps_I61_J,axiom,
! [X8,X29,X40,X14,X41] : c_Com_Ocom_OCall(X41,X14,X40) != c_Com_Ocom_OWhile(X29,X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I61_J) ).
fof(fact_com_Osimps_I51_J,axiom,
! [X55,X56,X40,X14,X41] : c_Com_Ocom_OCall(X41,X14,X40) != c_Com_Ocom_OSemi(X56,X55),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I51_J) ).
fof(fact_com_Osimps_I33_J,axiom,
! [X29,X30,X40,X14,X41] : c_Com_Ocom_OCall(X41,X14,X40) != c_Com_Ocom_OAss(X30,X29),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I33_J) ).
fof(fact_com_Osimps_I39_J,axiom,
! [X8,X29,X79,X5,X40] : c_Com_Ocom_OWhile(X40,X5) != c_Com_Ocom_OLocal(X79,X29,X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I39_J) ).
fof(fact_com_Osimps_I53_J,axiom,
! [X55,X56,X29,X5,X40] : c_Com_Ocom_OWhile(X40,X5) != c_Com_Ocom_OCond(X29,X56,X55),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I53_J) ).
fof(fact_com_Osimps_I60_J,axiom,
! [X40,X14,X41,X8,X29] : c_Com_Ocom_OWhile(X29,X8) != c_Com_Ocom_OCall(X41,X14,X40),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I60_J) ).
fof(fact_com_Osimps_I35_J,axiom,
! [X8,X29,X79,X63,X64] : c_Com_Ocom_OSemi(X64,X63) != c_Com_Ocom_OLocal(X79,X29,X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I35_J) ).
fof(fact_com_Osimps_I44_J,axiom,
! [X63,X64,X40,X55,X56] : c_Com_Ocom_OSemi(X56,X55) != c_Com_Ocom_OCond(X40,X64,X63),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I44_J) ).
fof(fact_com_Osimps_I50_J,axiom,
! [X40,X14,X41,X55,X56] : c_Com_Ocom_OSemi(X56,X55) != c_Com_Ocom_OCall(X41,X14,X40),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I50_J) ).
fof(fact_com_Osimps_I22_J,axiom,
! [X5,X40,X82,X29,X30] : c_Com_Ocom_OAss(X30,X29) != c_Com_Ocom_OLocal(X82,X40,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I22_J) ).
fof(fact_com_Osimps_I26_J,axiom,
! [X63,X64,X40,X29,X30] : c_Com_Ocom_OAss(X30,X29) != c_Com_Ocom_OCond(X40,X64,X63),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I26_J) ).
fof(fact_com_Osimps_I32_J,axiom,
! [X40,X14,X41,X29,X30] : c_Com_Ocom_OAss(X30,X29) != c_Com_Ocom_OCall(X41,X14,X40),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I32_J) ).
fof(fact_less__eq__nat_Osimps_I1_J,axiom,
! [X42] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
fof(fact_le0,axiom,
! [X42] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le0) ).
fof(fact_total__on__empty,axiom,
! [X177,X10] : c_Relation_Ototal__on(X10,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),X177),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__empty) ).
fof(fact_divisors__zero,axiom,
! [X92,X84,X94] :
( class_Rings_Ono__zero__divisors(X94)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92) = c_Groups_Ozero__class_Ozero(X94)
=> ( X84 = c_Groups_Ozero__class_Ozero(X94)
| X92 = c_Groups_Ozero__class_Ozero(X94) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divisors__zero) ).
fof(fact_no__zero__divisors,axiom,
! [X92,X84,X94] :
( class_Rings_Ono__zero__divisors(X94)
=> ( X84 != c_Groups_Ozero__class_Ozero(X94)
=> ( X92 != c_Groups_Ozero__class_Ozero(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X92) != c_Groups_Ozero__class_Ozero(X94) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_no__zero__divisors) ).
fof(fact_mult__eq__0__iff,axiom,
! [X38,X39,X10] :
( class_Rings_Oring__no__zero__divisors(X10)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X38) = c_Groups_Ozero__class_Ozero(X10)
<=> ( X39 = c_Groups_Ozero__class_Ozero(X10)
| X38 = c_Groups_Ozero__class_Ozero(X10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).
fof(fact_posDivAlg__0,axiom,
! [X92] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X92) = 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,
! [X92,X84] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),X92) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X84,X92)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__int__def) ).
fof(fact_power__0__Suc,axiom,
! [X42,X94] :
( ( class_Power_Opower(X94)
& class_Rings_Osemiring__0(X94) )
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),c_Groups_Ozero__class_Ozero(X94)),hAPP(c_Nat_OSuc,X42)) = c_Groups_Ozero__class_Ozero(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0__Suc) ).
fof(fact_divide__Numeral0,axiom,
! [X93,X94] :
( ( class_Fields_Ofield__inverse__zero(X94)
& class_Int_Onumber__ring(X94) )
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X93),hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__Numeral0) ).
fof(fact_abs__sgn,axiom,
! [X103,X94] :
( class_Rings_Olinordered__idom(X94)
=> hAPP(c_Groups_Oabs__class_Oabs(X94),X103) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X103),c_Groups_Osgn__class_Osgn(X94,X103)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__sgn) ).
fof(fact_com_Osimps_I40_J,axiom,
! [X14,X8,X29,X79] : c_Com_Ocom_OLocal(X79,X29,X8) != hAPP(c_Com_Ocom_OBODY,X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I40_J) ).
fof(fact_com_Osimps_I54_J,axiom,
! [X14,X55,X56,X29] : c_Com_Ocom_OCond(X29,X56,X55) != hAPP(c_Com_Ocom_OBODY,X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I54_J) ).
fof(fact_com_Osimps_I63_J,axiom,
! [X15,X40,X14,X41] : c_Com_Ocom_OCall(X41,X14,X40) != hAPP(c_Com_Ocom_OBODY,X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I63_J) ).
fof(fact_com_Osimps_I41_J,axiom,
! [X8,X29,X79,X14] : hAPP(c_Com_Ocom_OBODY,X14) != c_Com_Ocom_OLocal(X79,X29,X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I41_J) ).
fof(fact_com_Osimps_I55_J,axiom,
! [X55,X56,X29,X14] : hAPP(c_Com_Ocom_OBODY,X14) != c_Com_Ocom_OCond(X29,X56,X55),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I55_J) ).
fof(fact_com_Osimps_I62_J,axiom,
! [X40,X14,X41,X15] : hAPP(c_Com_Ocom_OBODY,X15) != c_Com_Ocom_OCall(X41,X14,X40),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I62_J) ).
fof(fact_lists__UNIV,axiom,
! [X10] : c_List_Olists(X10,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__UNIV) ).
fof(fact_map__ident,axiom,
! [X290,X10] : hAPP(hAPP(c_List_Omap(X10,X10),c_COMBI(X10)),X290) = X290,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__ident) ).
fof(fact_accp__wfPD,axiom,
! [X16,X177,X10] :
( c_Wellfounded_OwfP(X10,X177)
=> hBOOL(hAPP(c_Wellfounded_Oaccp(X10,X177),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__wfPD) ).
fof(fact_reflpE,axiom,
! [X16,X177,X10] :
( c_Predicate_Oreflp(X10,X177)
=> hBOOL(hAPP(hAPP(X177,X16),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reflpE) ).
fof(fact_equivp__reflp,axiom,
! [X16,X196,X10] :
( c_Equiv__Relations_Oequivp(X10,X196)
=> hBOOL(hAPP(hAPP(X196,X16),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivp__reflp) ).
fof(fact_sublist__empty,axiom,
! [X290,X10] : c_List_Osublist(X10,X290,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__empty) ).
fof(fact_right__inverse__eq,axiom,
! [X39,X38,X10] :
( class_Rings_Odivision__ring(X10)
=> ( X38 != c_Groups_Ozero__class_Ozero(X10)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X39),X38) = c_Groups_Oone__class_Oone(X10)
<=> X39 = X38 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__inverse__eq) ).
fof(fact_length__rev,axiom,
! [X297,X94] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),hAPP(c_List_Orev(X94),X297)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__rev) ).
fof(fact_length__rotate1,axiom,
! [X297,X94] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),hAPP(c_List_Orotate1(X94),X297)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__rotate1) ).
fof(fact_exE__some,axiom,
! [X10,X18,X19] :
( ? [X147] : hBOOL(hAPP(X19,X147))
=> ( X18 = c_Hilbert__Choice_OEps(X10,X19)
=> hBOOL(hAPP(X19,X18)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_exE__some) ).
fof(fact_funpow_Osimps_I1_J,axiom,
! [X2,X10] : hAPP(hAPP(c_Nat_Ocompow(X10,X10),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) = c_Fun_Oid(X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow_Osimps_I1_J) ).
fof(fact_option__map__None,axiom,
! [X2,X10,X13] : hAPP(hAPP(c_Option_Omap(X13,X10),X2),c_Option_Ooption_ONone(X13)) = c_Option_Ooption_ONone(X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option__map__None) ).
fof(fact_map_Osimps_I1_J,axiom,
! [X2,X10,X13] : hAPP(hAPP(c_List_Omap(X13,X10),X2),c_List_Olist_ONil(X13)) = c_List_Olist_ONil(X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map_Osimps_I1_J) ).
fof(fact_inf__compl__bot,axiom,
! [X93,X94] :
( class_Lattices_Oboolean__algebra(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X93)) = c_Orderings_Obot__class_Obot(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__compl__bot) ).
fof(fact_sup__compl__top,axiom,
! [X93,X94] :
( class_Lattices_Oboolean__algebra(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X93)) = c_Orderings_Otop__class_Otop(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__compl__top) ).
fof(fact_right__minus,axiom,
! [X84,X94] :
( class_Groups_Ogroup__add(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X84)) = c_Groups_Ozero__class_Ozero(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__minus) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
! [X42,X93] :
( c_Nat__Transfer_Ois__nat(X93)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X93),X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J) ).
fof(fact_zmult__eq__1__iff,axiom,
! [X20,X102] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X102),X20) = c_Groups_Oone__class_Oone(tc_Int_Oint)
<=> ( ( X102 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& X20 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
| ( X102 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
& X20 = 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_inf__eq__top__iff,axiom,
! [X25,X16,X10] :
( class_Lattices_Obounded__lattice__top(X10)
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X16),X25) = c_Orderings_Otop__class_Otop(X10)
<=> ( X16 = c_Orderings_Otop__class_Otop(X10)
& X25 = c_Orderings_Otop__class_Otop(X10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__eq__top__iff) ).
fof(fact_sup__eq__bot__iff,axiom,
! [X25,X16,X10] :
( class_Lattices_Obounded__lattice__bot(X10)
=> ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X16),X25) = c_Orderings_Obot__class_Obot(X10)
<=> ( X16 = c_Orderings_Obot__class_Obot(X10)
& X25 = c_Orderings_Obot__class_Obot(X10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__eq__bot__iff) ).
fof(fact_field__power__not__zero,axiom,
! [X42,X84,X94] :
( class_Rings_Oring__1__no__zero__divisors(X94)
=> ( X84 != c_Groups_Ozero__class_Ozero(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),X42) != c_Groups_Ozero__class_Ozero(X94) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__power__not__zero) ).
fof(fact_double__eq__0__iff,axiom,
! [X39,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X39),X39) = c_Groups_Ozero__class_Ozero(X10)
<=> X39 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
fof(fact_double__zero__sym,axiom,
! [X39,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( c_Groups_Ozero__class_Ozero(X10) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X39),X39)
<=> X39 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__zero__sym) ).
fof(fact_finite__lessThan,axiom,
! [X101] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X101))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__lessThan) ).
fof(fact_finite__atMost,axiom,
! [X101] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X101))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atMost) ).
fof(fact_minus__numeral__code_I5_J,axiom,
! [X133] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X133)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__numeral__code_I5_J) ).
fof(fact_eq__iff__diff__eq__0,axiom,
! [X38,X39,X10] :
( class_Groups_Oab__group__add(X10)
=> ( X39 = X38
<=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X39),X38) = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).
fof(fact_right__minus__eq,axiom,
! [X38,X39,X10] :
( class_Groups_Ogroup__add(X10)
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X39),X38) = c_Groups_Ozero__class_Ozero(X10)
<=> X39 = X38 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__minus__eq) ).
fof(fact_dvd_Oeq__refl,axiom,
! [X105,X93] :
( X93 = X105
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X93),X105)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oeq__refl) ).
fof(fact_eq__imp__le,axiom,
! [X42,X97] :
( X97 = X42
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__imp__le) ).
fof(fact_take__eq__Nil,axiom,
! [X290,X20,X10] :
( hAPP(hAPP(c_List_Otake(X10),X20),X290) = c_List_Olist_ONil(X10)
<=> ( X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X290 = c_List_Olist_ONil(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__eq__Nil) ).
fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
! [X42,X97] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X97),X42) = c_Groups_Oone__class_Oone(tc_Int_Oint)
=> ( X97 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| X97 = 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,
! [X39,X38,X10] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X10)
=> ( X38 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X38),X39)
<=> X39 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(fact_diff__Suc__1,axiom,
! [X42] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X42)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X42,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__1) ).
fof(fact_set__upto,axiom,
! [X163,X113] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X113,X163)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X113,X163),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__upto) ).
fof(fact_atLeastAtMost__upto,axiom,
! [X163,X113] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X113,X163) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X113,X163)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMost__upto) ).
fof(fact_add__numeral__0__right,axiom,
! [X84,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OPls)) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__numeral__0__right) ).
fof(fact_dvd_Oorder__refl,axiom,
! [X93] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X93),X93)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oorder__refl) ).
fof(fact_zle__refl,axiom,
! [X133] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X133),X133)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__refl) ).
fof(fact_le__refl,axiom,
! [X42] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__refl) ).
fof(fact_evalc_Oequations_I1_J,axiom,
! [X84] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X84),X84)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I1_J) ).
fof(fact_evalc_OSkip,axiom,
! [X45] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X45),X45)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OSkip) ).
fof(fact_append__is__Nil__conv,axiom,
! [X289,X290,X10] :
( hAPP(hAPP(c_List_Oappend(X10),X290),X289) = c_List_Olist_ONil(X10)
<=> ( X290 = c_List_Olist_ONil(X10)
& X289 = c_List_Olist_ONil(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__is__Nil__conv) ).
fof(fact_Nil__is__append__conv,axiom,
! [X289,X290,X10] :
( c_List_Olist_ONil(X10) = hAPP(hAPP(c_List_Oappend(X10),X290),X289)
<=> ( X290 = c_List_Olist_ONil(X10)
& X289 = c_List_Olist_ONil(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nil__is__append__conv) ).
fof(fact_Domain__rtrancl,axiom,
! [X196,X10] : hAPP(c_Relation_ODomain(X10,X10),c_Transitive__Closure_Ortrancl(X10,X196)) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__rtrancl) ).
fof(fact_Range__rtrancl,axiom,
! [X196,X10] : hAPP(c_Relation_ORange(X10,X10),c_Transitive__Closure_Ortrancl(X10,X196)) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__rtrancl) ).
fof(help_c__COMBK__1,axiom,
! [X335,X87,X10,X94] : hAPP(hAPP(c_COMBK(X94,X10),X87),X335) = X87,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_zdiv__minus1__right,axiom,
! [X84] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X84),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__minus1__right) ).
fof(fact_zmult__commute,axiom,
! [X133,X104] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X104),X133) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X133),X104),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__commute) ).
fof(fact_nat__mult__commute,axiom,
! [X42,X97] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X97),X42) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),X97),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
fof(fact_zadd__commute,axiom,
! [X133,X104] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X104),X133) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X133),X104),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__commute) ).
fof(fact_nat__add__commute,axiom,
! [X42,X97] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X42) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),X97),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(fact_Nitpick_Ofrac__def,axiom,
! [X92,X84,X94] : hAPP(hAPP(c_Nitpick_Ofrac(X94),X84),X92) = c_Nitpick_OAbs__Frac(X94,c_Nitpick_Onorm__frac(X84,X92)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Ofrac__def) ).
fof(fact_diff__0,axiom,
! [X84,X94] :
( class_Groups_Ogroup__add(X94)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),c_Groups_Ozero__class_Ozero(X94)),X84) = hAPP(c_Groups_Ouminus__class_Ouminus(X94),X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0) ).
fof(fact_append__self__conv2,axiom,
! [X289,X290,X10] :
( hAPP(hAPP(c_List_Oappend(X10),X290),X289) = X289
<=> X290 = c_List_Olist_ONil(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__self__conv2) ).
fof(fact_append__self__conv,axiom,
! [X289,X290,X10] :
( hAPP(hAPP(c_List_Oappend(X10),X290),X289) = X290
<=> X289 = c_List_Olist_ONil(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__self__conv) ).
fof(fact_self__append__conv,axiom,
! [X289,X10,X290] :
( X290 = hAPP(hAPP(c_List_Oappend(X10),X290),X289)
<=> X289 = c_List_Olist_ONil(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__append__conv) ).
fof(fact_self__append__conv2,axiom,
! [X290,X10,X289] :
( X289 = hAPP(hAPP(c_List_Oappend(X10),X290),X289)
<=> X290 = c_List_Olist_ONil(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__append__conv2) ).
fof(fact_power__0__left,axiom,
! [X42,X94] :
( ( class_Power_Opower(X94)
& class_Rings_Osemiring__0(X94) )
=> ( ( X42 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),c_Groups_Ozero__class_Ozero(X94)),X42) = c_Groups_Oone__class_Oone(X94) )
& ( X42 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),c_Groups_Ozero__class_Ozero(X94)),X42) = c_Groups_Ozero__class_Ozero(X94) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0__left) ).
fof(fact_list_Osimps_I3_J,axiom,
! [X308,X95,X94] : hAPP(hAPP(c_List_Olist_OCons(X94),X95),X308) != c_List_Olist_ONil(X94),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I3_J) ).
fof(fact_list_Osimps_I2_J,axiom,
! [X308,X95,X94] : c_List_Olist_ONil(X94) != hAPP(hAPP(c_List_Olist_OCons(X94),X95),X308),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I2_J) ).
fof(fact_WT_OBody,axiom,
! [X86] :
( hAPP(c_Com_Obody,X86) != c_Option_Ooption_ONone(tc_Com_Ocom)
=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X86))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_OBody) ).
fof(fact_distinct__upto,axiom,
! [X119,X120] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X120,X119))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__upto) ).
fof(fact_com_Osimps_I11_J,axiom,
! [X5,X40,X82] : c_Com_Ocom_OLocal(X82,X40,X5) != c_Com_Ocom_OSKIP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I11_J) ).
fof(fact_com_Osimps_I15_J,axiom,
! [X63,X64,X40] : c_Com_Ocom_OCond(X40,X64,X63) != c_Com_Ocom_OSKIP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I15_J) ).
fof(fact_com_Osimps_I21_J,axiom,
! [X40,X14,X41] : c_Com_Ocom_OCall(X41,X14,X40) != c_Com_Ocom_OSKIP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I21_J) ).
fof(fact_com_Osimps_I10_J,axiom,
! [X5,X40,X82] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X82,X40,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I10_J) ).
fof(fact_com_Osimps_I14_J,axiom,
! [X63,X64,X40] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X40,X64,X63),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I14_J) ).
fof(fact_com_Osimps_I20_J,axiom,
! [X40,X14,X41] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(X41,X14,X40),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I20_J) ).
fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
! [X177,X10] : c_List_Olistrel(X10,c_Transitive__Closure_Ortrancl(X10,X177)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(X10),c_List_Olistrel1(X10,X177)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__rtrancl__eq__rtrancl__listrel1) ).
fof(fact_max__ext__wf,axiom,
! [X177,X10] :
( c_Wellfounded_Owf(X10,X177)
=> c_Wellfounded_Owf(tc_fun(X10,tc_HOL_Obool),c_Wellfounded_Omax__ext(X10,X177)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext__wf) ).
fof(fact_min__ext__wf,axiom,
! [X177,X10] :
( c_Wellfounded_Owf(X10,X177)
=> c_Wellfounded_Owf(tc_fun(X10,tc_HOL_Obool),c_Wellfounded_Omin__ext(X10,X177)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__ext__wf) ).
fof(fact_listsum__rev,axiom,
! [X297,X94] :
( class_Groups_Ocomm__monoid__add(X94)
=> hAPP(c_List_Omonoid__add__class_Olistsum(X94),hAPP(c_List_Orev(X94),X297)) = hAPP(c_List_Omonoid__add__class_Olistsum(X94),X297) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__rev) ).
fof(fact_abs__idempotent,axiom,
! [X84,X94] :
( class_Groups_Oordered__ab__group__add__abs(X94)
=> hAPP(c_Groups_Oabs__class_Oabs(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),X84)) = hAPP(c_Groups_Oabs__class_Oabs(X94),X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__idempotent) ).
fof(fact_abs__minus__cancel,axiom,
! [X84,X94] :
( class_Groups_Oordered__ab__group__add__abs(X94)
=> hAPP(c_Groups_Oabs__class_Oabs(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X84)) = hAPP(c_Groups_Oabs__class_Oabs(X94),X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__minus__cancel) ).
fof(fact_abs__of__nat,axiom,
! [X42,X94] :
( class_Rings_Olinordered__idom(X94)
=> hAPP(c_Groups_Oabs__class_Oabs(X94),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),X42)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),X42) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__nat) ).
fof(fact_UNIV__not__empty,axiom,
! [X10] : c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__not__empty) ).
fof(fact_zmod__minus1__right,axiom,
! [X84] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,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,
! [X97] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X97,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,
! [X20,X102] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X102),X20) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X102 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X20 = 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,
! [X297,X93,X94] : hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297) != X297,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Cons__self2) ).
fof(fact_not__Cons__self,axiom,
! [X93,X94,X297] : X297 != hAPP(hAPP(c_List_Olist_OCons(X94),X93),X297),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Cons__self) ).
fof(fact_fun__left__comm__idem__insert,axiom,
! [X10] : c_Finite__Set_Ofun__left__comm__idem(X10,tc_fun(X10,tc_HOL_Obool),c_Set_Oinsert(X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem__insert) ).
fof(fact_top__apply,axiom,
! [X16,X13,X10] :
( class_Orderings_Otop(X10)
=> hAPP(c_Orderings_Otop__class_Otop(tc_fun(X13,X10)),X16) = c_Orderings_Otop__class_Otop(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top__apply) ).
fof(fact_bot__fun__def,axiom,
! [X16,X13,X10] :
( class_Orderings_Obot(X10)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(X13,X10)),X16) = c_Orderings_Obot__class_Obot(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__fun__def) ).
fof(fact_bot__apply,axiom,
! [X16,X13,X10] :
( class_Orderings_Obot(X10)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(X13,X10)),X16) = c_Orderings_Obot__class_Obot(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__apply) ).
fof(fact_minus__code__numeral__code,axiom,
! [X97,X42] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X42),X97) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,X42),X97),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__code__numeral__code) ).
fof(fact_sorted__tl,axiom,
! [X297,X94] :
( class_Orderings_Olinorder(X94)
=> ( c_List_Olinorder__class_Osorted(X94,X297)
=> c_List_Olinorder__class_Osorted(X94,hAPP(c_List_Otl(X94),X297)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__tl) ).
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_mult__eq__self__implies__10,axiom,
! [X42,X97] :
( X97 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X97),X42)
=> ( X42 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X97 = 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,
! [X94,X297] :
( X297 != c_List_Olist_ONil(X94)
=> hAPP(c_List_Ohd(X94),X297) = hAPP(hAPP(c_List_Onth(X94),X297),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,
! [X17,X19] :
( hBOOL(X19)
| hBOOL(hAPP(hAPP(c_fimplies,X19),X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fimplies__1) ).
fof(fact_single__valued__Id__on,axiom,
! [X154,X10] : c_Relation_Osingle__valued(X10,X10,c_Relation_OId__on(X10,X154)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__Id__on) ).
fof(fact_refl__on__Id__on,axiom,
! [X154,X10] : c_Relation_Orefl__on(X10,X154,c_Relation_OId__on(X10,X154)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__Id__on) ).
fof(fact_nat__mult__eq__1__iff,axiom,
! [X20,X102] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X102),X20) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ( X102 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X20 = 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,
! [X20,X102] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X20) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X102 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X20 = 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,
! [X20,X102] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X102),X20)
<=> ( X102 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X20 = 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,
! [X25,X16,X10] :
( ( class_Int_Onumber__ring(X10)
& class_Int_Oring__char__0(X10) )
=> ( hAPP(c_Int_Onumber__class_Onumber__of(X10),X16) = hAPP(c_Int_Onumber__class_Onumber__of(X10),X25)
<=> X16 = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__number__of) ).
fof(fact_converse__Id__on,axiom,
! [X154,X10] : hAPP(c_Relation_Oconverse(X10,X10),c_Relation_OId__on(X10,X154)) = c_Relation_OId__on(X10,X154),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__Id__on) ).
fof(help_c__fequal__2,axiom,
! [X25,X16] :
( X16 != X25
| hBOOL(hAPP(hAPP(c_fequal,X16),X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__2) ).
fof(fact_of__int__number__of__eq,axiom,
! [X144,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(c_Int_Oring__1__class_Oof__int(X94),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)) = hAPP(c_Int_Onumber__class_Onumber__of(X94),X144) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__number__of__eq) ).
fof(fact_of__int__of__nat__eq,axiom,
! [X42,X94] :
( class_Rings_Oring__1(X94)
=> hAPP(c_Int_Oring__1__class_Oof__int(X94),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X42)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),X42) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__of__nat__eq) ).
fof(fact_set__empty2,axiom,
! [X290,X10] :
( c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) = hAPP(c_List_Oset(X10),X290)
<=> X290 = c_List_Olist_ONil(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__empty2) ).
fof(fact_set__empty,axiom,
! [X290,X10] :
( hAPP(c_List_Oset(X10),X290) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
<=> X290 = c_List_Olist_ONil(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__empty) ).
fof(fact_WT_OAssign,axiom,
! [X39,X48] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(X48,X39))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_OAssign) ).
fof(fact_WT_Oequations_I2_J,axiom,
! [X52,X51] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(X51,X52))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I2_J) ).
fof(fact_set__rev,axiom,
! [X290,X10] : hAPP(c_List_Oset(X10),hAPP(c_List_Orev(X10),X290)) = hAPP(c_List_Oset(X10),X290),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rev) ).
fof(fact_set__rotate1,axiom,
! [X290,X10] : hAPP(c_List_Oset(X10),hAPP(c_List_Orotate1(X10),X290)) = hAPP(c_List_Oset(X10),X290),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rotate1) ).
fof(fact_power__power__power,axiom,
! [X10] :
( class_Power_Opower(X10)
=> c_Power_Opower__class_Opower(X10) = c_Power_Opower_Opower(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Otimes__class_Otimes(X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__power__power) ).
fof(fact_add__eq__self__zero,axiom,
! [X42,X97] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X42) = X97
=> X42 = 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,
! [X94,X297] :
( X297 != c_List_Olist_ONil(X94)
=> hAPP(c_List_Ohd(X94),hAPP(c_List_Orev(X94),X297)) = c_List_Olast(X94,X297) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__rev) ).
fof(fact_last__rev,axiom,
! [X94,X297] :
( X297 != c_List_Olist_ONil(X94)
=> c_List_Olast(X94,hAPP(c_List_Orev(X94),X297)) = hAPP(c_List_Ohd(X94),X297) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__rev) ).
fof(fact_sorted__list__of__set__empty,axiom,
! [X10] :
( class_Orderings_Olinorder(X10)
=> c_List_Olinorder__class_Osorted__list__of__set(X10,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) = c_List_Olist_ONil(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__list__of__set__empty) ).
fof(fact_Sup__UNIV,axiom,
! [X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> c_Complete__Lattice_OSup__class_OSup(X10,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__UNIV) ).
fof(fact_Sup__empty,axiom,
! [X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> c_Complete__Lattice_OSup__class_OSup(X10,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__empty) ).
fof(fact_Inf__UNIV,axiom,
! [X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> c_Complete__Lattice_OInf__class_OInf(X10,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__UNIV) ).
fof(fact_Inf__empty,axiom,
! [X10] :
( class_Complete__Lattice_Ocomplete__lattice(X10)
=> c_Complete__Lattice_OInf__class_OInf(X10,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__empty) ).
fof(fact_div__1,axiom,
! [X97] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X97),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X97,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__1) ).
fof(fact_Union__Pow__eq,axiom,
! [X154,X10] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),hAPP(c_Set_OPow(X10),X154)) = X154,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__Pow__eq) ).
fof(fact_inf__bot__left,axiom,
! [X93,X94] :
( class_Lattices_Obounded__lattice__bot(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),c_Orderings_Obot__class_Obot(X94)),X93) = c_Orderings_Obot__class_Obot(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__bot__left) ).
fof(fact_sup__top__left,axiom,
! [X93,X94] :
( class_Lattices_Obounded__lattice__top(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),c_Orderings_Otop__class_Otop(X94)),X93) = c_Orderings_Otop__class_Otop(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__top__left) ).
fof(fact_divide__zero__left,axiom,
! [X84,X94] :
( class_Rings_Odivision__ring(X94)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),c_Groups_Ozero__class_Ozero(X94)),X84) = c_Groups_Ozero__class_Ozero(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__zero__left) ).
fof(fact_power__one,axiom,
! [X42,X94] :
( class_Groups_Omonoid__mult(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),c_Groups_Oone__class_Oone(X94)),X42) = c_Groups_Oone__class_Oone(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one) ).
fof(fact_div__0,axiom,
! [X84,X94] :
( class_Divides_Osemiring__div(X94)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),c_Groups_Ozero__class_Ozero(X94)),X84) = c_Groups_Ozero__class_Ozero(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__0) ).
fof(fact_mult__zero__left,axiom,
! [X84,X94] :
( class_Rings_Omult__zero(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),c_Groups_Ozero__class_Ozero(X94)),X84) = c_Groups_Ozero__class_Ozero(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__zero__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
! [X84,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),c_Groups_Ozero__class_Ozero(X94)),X84) = c_Groups_Ozero__class_Ozero(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(fact_sorted__butlast,axiom,
! [X297,X94] :
( class_Orderings_Olinorder(X94)
=> ( X297 != c_List_Olist_ONil(X94)
=> ( c_List_Olinorder__class_Osorted(X94,X297)
=> c_List_Olinorder__class_Osorted(X94,c_List_Obutlast(X94,X297)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__butlast) ).
fof(fact_WT__bodiesD,axiom,
! [X92,X86] :
( c_Com_OWT__bodies
=> ( hAPP(c_Com_Obody,X86) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X92)
=> hBOOL(hAPP(c_Com_OWT,X92)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT__bodiesD) ).
fof(fact_of__int__m1,axiom,
! [X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(c_Int_Oring__1__class_Oof__int(X94),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OMin) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__m1) ).
fof(fact_card_Oempty,axiom,
! [X10] : hAPP(c_Finite__Set_Ocard(X10),c_Orderings_Obot__class_Obot(tc_fun(X10,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,
! [X94] :
( ( class_Int_Onumber__ring(X94)
& class_Rings_Olinordered__idom(X94) )
=> hAPP(c_Groups_Oabs__class_Oabs(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OMin)) = c_Groups_Oone__class_Oone(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__minus__one) ).
fof(fact_option_Osize_I4_J,axiom,
! [X84,X94] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X94)),hAPP(c_Option_Ooption_OSome(X94),X84)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Osize_I4_J) ).
fof(fact_atLeast0AtMost,axiom,
! [X20] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast0AtMost) ).
fof(fact_greaterThan__eq__iff,axiom,
! [X25,X16,X10] :
( class_Orderings_Olinorder(X10)
=> ( hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),X16) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),X25)
<=> X16 = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__eq__iff) ).
fof(fact_atLeast__eq__iff,axiom,
! [X25,X16,X10] :
( class_Orderings_Olinorder(X10)
=> ( hAPP(c_SetInterval_Oord__class_OatLeast(X10),X16) = hAPP(c_SetInterval_Oord__class_OatLeast(X10),X25)
<=> X16 = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__eq__iff) ).
fof(fact_lessThan__eq__iff,axiom,
! [X25,X16,X10] :
( class_Orderings_Olinorder(X10)
=> ( hAPP(c_SetInterval_Oord__class_OlessThan(X10),X16) = hAPP(c_SetInterval_Oord__class_OlessThan(X10),X25)
<=> X16 = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__eq__iff) ).
fof(fact_atMost__eq__iff,axiom,
! [X25,X16,X10] :
( class_Orderings_Olinorder(X10)
=> ( hAPP(c_SetInterval_Oord__class_OatMost(X10),X16) = hAPP(c_SetInterval_Oord__class_OatMost(X10),X25)
<=> X16 = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atMost__eq__iff) ).
fof(fact_compl__eq__compl__iff,axiom,
! [X25,X16,X10] :
( class_Lattices_Oboolean__algebra(X10)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(X10),X16) = hAPP(c_Groups_Ouminus__class_Ouminus(X10),X25)
<=> X16 = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__eq__compl__iff) ).
fof(fact_neg__equal__iff__equal,axiom,
! [X38,X39,X10] :
( class_Groups_Ogroup__add(X10)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(X10),X39) = hAPP(c_Groups_Ouminus__class_Ouminus(X10),X38)
<=> X39 = X38 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).
fof(fact_of__int__eq__iff,axiom,
! [X73,X131,X10] :
( class_Int_Oring__char__0(X10)
=> ( hAPP(c_Int_Oring__1__class_Oof__int(X10),X131) = hAPP(c_Int_Oring__1__class_Oof__int(X10),X73)
<=> X131 = X73 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__eq__iff) ).
fof(fact_of__nat__eq__iff,axiom,
! [X20,X102,X10] :
( class_Nat_Osemiring__char__0(X10)
=> ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),X102) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),X20)
<=> X102 = X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__eq__iff) ).
fof(fact_inf__top__left,axiom,
! [X93,X94] :
( class_Lattices_Obounded__lattice__top(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),c_Orderings_Otop__class_Otop(X94)),X93) = X93 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__top__left) ).
fof(fact_sup__bot__left,axiom,
! [X93,X94] :
( class_Lattices_Obounded__lattice__bot(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),c_Orderings_Obot__class_Obot(X94)),X93) = X93 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__bot__left) ).
fof(fact_mult__1,axiom,
! [X84,X94] :
( class_Groups_Ocomm__monoid__mult(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),c_Groups_Oone__class_Oone(X94)),X84) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1) ).
fof(fact_mult__1__left,axiom,
! [X84,X94] :
( class_Groups_Omonoid__mult(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),c_Groups_Oone__class_Oone(X94)),X84) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
! [X84,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),c_Groups_Oone__class_Oone(X94)),X84) = X84 ),
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,
! [X84,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),c_Groups_Ozero__class_Ozero(X94)),X84) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_add__0,axiom,
! [X84,X94] :
( class_Groups_Ocomm__monoid__add(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),c_Groups_Ozero__class_Ozero(X94)),X84) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0) ).
fof(fact_add__0__left,axiom,
! [X84,X94] :
( class_Groups_Omonoid__add(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),c_Groups_Ozero__class_Ozero(X94)),X84) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__left) ).
fof(fact_divide__self__if,axiom,
! [X84,X94] :
( class_Rings_Odivision__ring__inverse__zero(X94)
=> ( ( X84 = c_Groups_Ozero__class_Ozero(X94)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X84),X84) = c_Groups_Ozero__class_Ozero(X94) )
& ( X84 != c_Groups_Ozero__class_Ozero(X94)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X84),X84) = c_Groups_Oone__class_Oone(X94) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__self__if) ).
fof(fact_mod__0,axiom,
! [X84,X94] :
( class_Divides_Osemiring__div(X94)
=> c_Divides_Odiv__class_Omod(X94,c_Groups_Ozero__class_Ozero(X94),X84) = c_Groups_Ozero__class_Ozero(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__0) ).
fof(fact_mod__by__1,axiom,
! [X84,X94] :
( class_Divides_Osemiring__div(X94)
=> c_Divides_Odiv__class_Omod(X94,X84,c_Groups_Oone__class_Oone(X94)) = c_Groups_Ozero__class_Ozero(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__by__1) ).
fof(fact_set__empty__eq,axiom,
! [X215,X10] :
( c_Option_Oset(X10,X215) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
<=> X215 = c_Option_Ooption_ONone(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__empty__eq) ).
fof(fact_inf__bot__right,axiom,
! [X93,X94] :
( class_Lattices_Obounded__lattice__bot(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),c_Orderings_Obot__class_Obot(X94)) = c_Orderings_Obot__class_Obot(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__bot__right) ).
fof(fact_sup__top__right,axiom,
! [X93,X94] :
( class_Lattices_Obounded__lattice__top(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),c_Orderings_Otop__class_Otop(X94)) = c_Orderings_Otop__class_Otop(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__top__right) ).
fof(fact_divide__zero,axiom,
! [X84,X94] :
( class_Rings_Odivision__ring__inverse__zero(X94)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X84),c_Groups_Ozero__class_Ozero(X94)) = c_Groups_Ozero__class_Ozero(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__zero) ).
fof(fact_div__by__0,axiom,
! [X84,X94] :
( class_Divides_Osemiring__div(X94)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),X84),c_Groups_Ozero__class_Ozero(X94)) = c_Groups_Ozero__class_Ozero(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__by__0) ).
fof(fact_mult__zero__right,axiom,
! [X84,X94] :
( class_Rings_Omult__zero(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),c_Groups_Ozero__class_Ozero(X94)) = c_Groups_Ozero__class_Ozero(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__zero__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [X84,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),c_Groups_Ozero__class_Ozero(X94)) = c_Groups_Ozero__class_Ozero(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(fact_wf__lex,axiom,
! [X177,X10] :
( c_Wellfounded_Owf(X10,X177)
=> c_Wellfounded_Owf(tc_List_Olist(X10),c_List_Olex(X10,X177)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__lex) ).
fof(fact_wf__lenlex,axiom,
! [X177,X10] :
( c_Wellfounded_Owf(X10,X177)
=> c_Wellfounded_Owf(tc_List_Olist(X10),c_List_Olenlex(X10,X177)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__lenlex) ).
fof(fact_eq__Nil__appendI,axiom,
! [X94,X298,X297] :
( X297 = X298
=> X297 = hAPP(hAPP(c_List_Oappend(X94),c_List_Olist_ONil(X94)),X298) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__Nil__appendI) ).
fof(fact_divide__self,axiom,
! [X84,X94] :
( class_Rings_Odivision__ring(X94)
=> ( X84 != c_Groups_Ozero__class_Ozero(X94)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X84),X84) = c_Groups_Oone__class_Oone(X94) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__self) ).
fof(fact_div__self,axiom,
! [X84,X94] :
( class_Divides_Osemiring__div(X94)
=> ( X84 != c_Groups_Ozero__class_Ozero(X94)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),X84),X84) = c_Groups_Oone__class_Oone(X94) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__self) ).
fof(fact_mod__by__0,axiom,
! [X84,X94] :
( class_Divides_Osemiring__div(X94)
=> c_Divides_Odiv__class_Omod(X94,X84,c_Groups_Ozero__class_Ozero(X94)) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__by__0) ).
fof(fact_fun__left__comm,axiom,
! [X10] :
( class_Groups_Oab__semigroup__mult(X10)
=> c_Finite__Set_Ofun__left__comm(X10,X10,c_Groups_Otimes__class_Otimes(X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm) ).
fof(fact_fun__left__comm__idem__inf,axiom,
! [X10] :
( class_Lattices_Osemilattice__inf(X10)
=> c_Finite__Set_Ofun__left__comm__idem(X10,X10,c_Lattices_Osemilattice__inf__class_Oinf(X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem__inf) ).
fof(fact_fun__left__comm__idem__sup,axiom,
! [X10] :
( class_Lattices_Osemilattice__sup(X10)
=> c_Finite__Set_Ofun__left__comm__idem(X10,X10,c_Lattices_Osemilattice__sup__class_Osup(X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem__sup) ).
fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
! [X10] :
( class_Orderings_Olinorder(X10)
=> c_Finite__Set_Ofun__left__comm__idem(X10,X10,c_Orderings_Oord__class_Omax(X10)) ),
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,
! [X10] :
( class_Orderings_Olinorder(X10)
=> c_Finite__Set_Ofun__left__comm__idem(X10,X10,c_Orderings_Oord__class_Omin(X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ofun__left__comm__idem__inf) ).
fof(fact_fun__left__comm__idem,axiom,
! [X10] :
( class_Lattices_Oab__semigroup__idem__mult(X10)
=> c_Finite__Set_Ofun__left__comm__idem(X10,X10,c_Groups_Otimes__class_Otimes(X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem) ).
fof(fact_Domain__Id__on,axiom,
! [X154,X10] : hAPP(c_Relation_ODomain(X10,X10),c_Relation_OId__on(X10,X154)) = X154,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Id__on) ).
fof(fact_Range__Id__on,axiom,
! [X154,X10] : hAPP(c_Relation_ORange(X10,X10),c_Relation_OId__on(X10,X154)) = X154,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Id__on) ).
fof(fact_power__0,axiom,
! [X84,X94] :
( class_Power_Opower(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
! [X93,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(fact_inf__top__right,axiom,
! [X93,X94] :
( class_Lattices_Obounded__lattice__top(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),c_Orderings_Otop__class_Otop(X94)) = X93 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__top__right) ).
fof(fact_sup__bot__right,axiom,
! [X93,X94] :
( class_Lattices_Obounded__lattice__bot(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),c_Orderings_Obot__class_Obot(X94)) = X93 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__bot__right) ).
fof(fact_divide__1,axiom,
! [X84,X94] :
( class_Rings_Odivision__ring(X94)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X94),X84),c_Groups_Oone__class_Oone(X94)) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__1) ).
fof(fact_diff__0__right,axiom,
! [X84,X94] :
( class_Groups_Ogroup__add(X94)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X84),c_Groups_Ozero__class_Ozero(X94)) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__right) ).
fof(fact_div__by__1,axiom,
! [X84,X94] :
( class_Divides_Osemiring__div(X94)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X94),X84),c_Groups_Oone__class_Oone(X94)) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__by__1) ).
fof(fact_mult_Ocomm__neutral,axiom,
! [X84,X94] :
( class_Groups_Ocomm__monoid__mult(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),c_Groups_Oone__class_Oone(X94)) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).
fof(fact_mult__1__right,axiom,
! [X84,X94] :
( class_Groups_Omonoid__mult(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),c_Groups_Oone__class_Oone(X94)) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
! [X84,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),c_Groups_Oone__class_Oone(X94)) = X84 ),
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,
! [X84,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),c_Groups_Ozero__class_Ozero(X94)) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_add_Ocomm__neutral,axiom,
! [X84,X94] :
( class_Groups_Ocomm__monoid__add(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),c_Groups_Ozero__class_Ozero(X94)) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(fact_add__0__right,axiom,
! [X84,X94] :
( class_Groups_Omonoid__add(X94)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),X84),c_Groups_Ozero__class_Ozero(X94)) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__right) ).
fof(fact_double__compl,axiom,
! [X93,X94] :
( class_Lattices_Oboolean__algebra(X94)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X93)) = X93 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__compl) ).
fof(fact_minus__minus,axiom,
! [X84,X94] :
( class_Groups_Ogroup__add(X94)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X94),hAPP(c_Groups_Ouminus__class_Ouminus(X94),X84)) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__minus) ).
fof(fact_abs__int__eq,axiom,
! [X97] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X97)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X97),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__int__eq) ).
fof(fact_of__int__int__eq,axiom,
! [X42] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X42)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__int__eq) ).
fof(fact_mod__self,axiom,
! [X84,X94] :
( class_Divides_Osemiring__div(X94)
=> c_Divides_Odiv__class_Omod(X94,X84,X84) = c_Groups_Ozero__class_Ozero(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__self) ).
fof(fact_rev__is__rev__conv,axiom,
! [X289,X290,X10] :
( hAPP(c_List_Orev(X10),X290) = hAPP(c_List_Orev(X10),X289)
<=> X290 = X289 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__is__rev__conv) ).
fof(fact_option_Oinject,axiom,
! [X96,X39,X10] :
( hAPP(c_Option_Ooption_OSome(X10),X39) = hAPP(c_Option_Ooption_OSome(X10),X96)
<=> X39 = X96 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Oinject) ).
fof(fact_inc__shift__def,axiom,
! [X103,X144] :
( ( X144 = X103
=> c_Random_Oinc__shift(X144,X103) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
& ( X144 != X103
=> c_Random_Oinc__shift(X144,X103) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X103),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,
! [X298,X94] : hAPP(hAPP(c_List_Oappend(X94),c_List_Olist_ONil(X94)),X298) = X298,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__Nil) ).
fof(fact_Suc__eq__plus1__left,axiom,
! [X42] : hAPP(c_Nat_OSuc,X42) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(fact_sublist__nil,axiom,
! [X154,X10] : c_List_Osublist(X10,c_List_Olist_ONil(X10),X154) = c_List_Olist_ONil(X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__nil) ).
fof(fact_remove1_Osimps_I1_J,axiom,
! [X93,X94] : c_List_Oremove1(X94,X93,c_List_Olist_ONil(X94)) = c_List_Olist_ONil(X94),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1_Osimps_I1_J) ).
fof(fact_atLeastLessThan0,axiom,
! [X102] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X102),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,
! [X84,X94] :
( class_Groups_Omonoid__mult(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
! [X93,X94] :
( class_Rings_Ocomm__semiring__1(X94)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X93 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(fact_diff__self,axiom,
! [X84,X94] :
( class_Groups_Ogroup__add(X94)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X94),X84),X84) = c_Groups_Ozero__class_Ozero(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self) ).
fof(fact_list_Osize_I1_J,axiom,
! [X11,X10] : c_List_Olist_Olist__size(X10,X11,c_List_Olist_ONil(X10)) = 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,
! [X11,X10] : c_Option_Ooption_Ooption__size(X10,X11,c_Option_Ooption_ONone(X10)) = 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,
! [X297,X94] : hAPP(hAPP(c_List_Otake(X94),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X297) = c_List_Olist_ONil(X94),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__0) ).
fof(fact_drop__Nil,axiom,
! [X42,X94] : hAPP(hAPP(c_List_Odrop(X94),X42),c_List_Olist_ONil(X94)) = c_List_Olist_ONil(X94),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__Nil) ).
fof(fact_take__Nil,axiom,
! [X42,X94] : hAPP(hAPP(c_List_Otake(X94),X42),c_List_Olist_ONil(X94)) = c_List_Olist_ONil(X94),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Nil) ).
fof(fact_minus__equation__iff,axiom,
! [X38,X39,X10] :
( class_Groups_Ogroup__add(X10)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(X10),X39) = X38
<=> hAPP(c_Groups_Ouminus__class_Ouminus(X10),X38) = X39 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__equation__iff) ).
fof(fact_equation__minus__iff,axiom,
! [X38,X39,X10] :
( class_Groups_Ogroup__add(X10)
=> ( X39 = hAPP(c_Groups_Ouminus__class_Ouminus(X10),X38)
<=> X38 = hAPP(c_Groups_Ouminus__class_Ouminus(X10),X39) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equation__minus__iff) ).
fof(fact_nat__list__def,axiom,
! [X162] :
( c_List_Onat__list(X162)
<=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X162)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__list__def) ).
fof(fact_card__atMost,axiom,
! [X165] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X165)) = hAPP(c_Nat_OSuc,X165),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__atMost) ).
fof(fact_nat__of__number,axiom,
! [X103] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X103)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X103),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of__number) ).
fof(fact_nat__number__of,axiom,
! [X133] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X133),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of) ).
fof(fact_nat__number__of__def,axiom,
! [X144] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__def) ).
fof(fact_Suc__eq__plus1,axiom,
! [X42] : hAPP(c_Nat_OSuc,X42) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(fact_sgn__sgn,axiom,
! [X84,X94] :
( class_Rings_Olinordered__idom(X94)
=> c_Groups_Osgn__class_Osgn(X94,c_Groups_Osgn__class_Osgn(X94,X84)) = c_Groups_Osgn__class_Osgn(X94,X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__sgn) ).
fof(fact_inf__idem,axiom,
! [X93,X94] :
( class_Lattices_Osemilattice__inf(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),X93) = X93 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__idem) ).
fof(fact_inf_Oidem,axiom,
! [X84,X94] :
( class_Lattices_Osemilattice__inf(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X84),X84) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oidem) ).
fof(fact_Inf__fin_Oidem,axiom,
! [X93,X94] :
( class_Lattices_Olattice(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X93),X93) = X93 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oidem) ).
fof(fact_sup_Oidem,axiom,
! [X84,X94] :
( class_Lattices_Osemilattice__sup(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X84),X84) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oidem) ).
fof(fact_sup__idem,axiom,
! [X93,X94] :
( class_Lattices_Osemilattice__sup(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),X93) = X93 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__idem) ).
fof(fact_Sup__fin_Oidem,axiom,
! [X93,X94] :
( class_Lattices_Olattice(X94)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X93),X93) = X93 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oidem) ).
fof(fact_Max_Oidem,axiom,
! [X93,X94] :
( class_Orderings_Olinorder(X94)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X93),X93) = X93 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oidem) ).
fof(fact_min__max_Osup_Oidem,axiom,
! [X84,X94] :
( class_Orderings_Olinorder(X94)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X84),X84) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup_Oidem) ).
fof(fact_Min_Oidem,axiom,
! [X93,X94] :
( class_Orderings_Olinorder(X94)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X93),X93) = X93 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oidem) ).
fof(fact_min__max_Oinf_Oidem,axiom,
! [X84,X94] :
( class_Orderings_Olinorder(X94)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X84),X84) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf_Oidem) ).
fof(fact_mult__idem,axiom,
! [X93,X94] :
( class_Lattices_Oab__semigroup__idem__mult(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X93),X93) = X93 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__idem) ).
fof(fact_times_Oidem,axiom,
! [X84,X94] :
( class_Lattices_Oab__semigroup__idem__mult(X94)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X84) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times_Oidem) ).
fof(fact_length__0__conv,axiom,
! [X290,X10] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> X290 = c_List_Olist_ONil(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__0__conv) ).
fof(fact_mult__Min,axiom,
! [X103] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X103) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X103),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Min) ).
fof(fact_atLeast0LessThan,axiom,
! [X20] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast0LessThan) ).
fof(fact_drop__0,axiom,
! [X297,X94] : hAPP(hAPP(c_List_Odrop(X94),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X297) = X297,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__0) ).
fof(fact_append__Nil2,axiom,
! [X297,X94] : hAPP(hAPP(c_List_Oappend(X94),X297),c_List_Olist_ONil(X94)) = X297,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__Nil2) ).
fof(fact_rev__rev__ident,axiom,
! [X297,X94] : hAPP(c_List_Orev(X94),hAPP(c_List_Orev(X94),X297)) = X297,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__rev__ident) ).
fof(fact_the_Osimps,axiom,
! [X93,X94] : hAPP(c_Option_Othe(X94),hAPP(c_Option_Ooption_OSome(X94),X93)) = X93,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the_Osimps) ).
fof(fact_zmod__zero,axiom,
! [X92] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X92) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zero) ).
fof(fact_neg__nat,axiom,
! [X104] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X104))
=> hAPP(c_Int_Onat,X104) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__nat) ).
fof(fact_atLeast__Suc__greaterThan,axiom,
! [X101] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X101)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X101),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__Suc__greaterThan) ).
fof(fact_lessThan__Suc__atMost,axiom,
! [X101] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X101)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X101),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__Suc__atMost) ).
fof(fact_less__eq__Suc__le__raw,axiom,
! [X20] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le__raw) ).
fof(fact_DIVISION__BY__ZERO,axiom,
! [X84] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
& c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DIVISION__BY__ZERO) ).
fof(fact_iszero__Numeral0,axiom,
! [X94] :
( class_Int_Onumber__ring(X94)
=> c_Int_Oiszero(X94,hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OPls)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iszero__Numeral0) ).
fof(fact_Option_Omap_Oid,axiom,
! [X10] : hAPP(c_Option_Omap(X10,X10),c_Fun_Oid(X10)) = c_Fun_Oid(tc_Option_Ooption(X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Option_Omap_Oid) ).
fof(fact_Option_Omap_Oidentity,axiom,
! [X10] : hAPP(c_Option_Omap(X10,X10),c_COMBI(X10)) = c_Fun_Oid(tc_Option_Ooption(X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Option_Omap_Oidentity) ).
fof(fact_List_Omap_Oid,axiom,
! [X10] : hAPP(c_List_Omap(X10,X10),c_Fun_Oid(X10)) = c_Fun_Oid(tc_List_Olist(X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Omap_Oid) ).
fof(fact_List_Omap_Oidentity,axiom,
! [X10] : hAPP(c_List_Omap(X10,X10),c_COMBI(X10)) = c_Fun_Oid(tc_List_Olist(X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Omap_Oidentity) ).
fof(fact_transfer__int__nat__relations_I1_J,axiom,
! [X25,X16] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X16) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25)
<=> X16 = X25 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__relations_I1_J) ).
fof(fact_int__int__eq,axiom,
! [X20,X102] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X102) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20)
<=> X102 = X20 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__int__eq) ).
fof(fact_zmod__self,axiom,
! [X84] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X84) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__self) ).
fof(fact_rev__swap,axiom,
! [X289,X290,X10] :
( hAPP(c_List_Orev(X10),X290) = X289
<=> X290 = hAPP(c_List_Orev(X10),X289) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__swap) ).
fof(fact_min__0L,axiom,
! [X42] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X42) = 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,
! [X42] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X42) = 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,
! [X92] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X92) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zero) ).
fof(fact_mult__0,axiom,
! [X42] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X42) = 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,
! [X94] : hBOOL(hAPP(c_List_Odistinct(X94),c_List_Olist_ONil(X94))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct_Osimps_I1_J) ).
fof(fact_New__DSequence_Opos__single__def,axiom,
! [X208,X93,X94] : hAPP(c_New__DSequence_Opos__single(X94,X93),X208) = c_Lazy__Sequence_Osingle(X94,X93),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__single__def) ).
fof(fact_New__DSequence_Oneg__single__def,axiom,
! [X208,X93,X94] : hAPP(c_New__DSequence_Oneg__single(X94,X93),X208) = c_Lazy__Sequence_Ohb__single(X94,X93),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__single__def) ).
fof(fact_rtrancl__idemp,axiom,
! [X177,X10] : c_Transitive__Closure_Ortrancl(X10,c_Transitive__Closure_Ortrancl(X10,X177)) = c_Transitive__Closure_Ortrancl(X10,X177),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__idemp) ).
fof(fact_List_Oset_Osimps_I1_J,axiom,
! [X10] : hAPP(c_List_Oset(X10),c_List_Olist_ONil(X10)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Oset_Osimps_I1_J) ).
fof(fact_max__0L,axiom,
! [X42] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X42) = X42,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__0L) ).
fof(fact_zmult__1,axiom,
! [X104] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X104) = X104,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1) ).
fof(fact_nat__mult__1,axiom,
! [X42] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X42) = X42,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1) ).
fof(fact_zadd__0,axiom,
! [X104] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X104) = X104,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__0) ).
fof(fact_plus__nat_Oadd__0,axiom,
! [X42] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X42) = X42,
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,
! [X84] :
( X84 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X84),X84) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__self) ).
fof(fact_option_Oexhaust,axiom,
! [X94,X105] :
( X105 != c_Option_Ooption_ONone(X94)
=> ~ ! [X116] : X105 != hAPP(c_Option_Ooption_OSome(X94),X116) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Oexhaust) ).
fof(fact_not__Some__eq,axiom,
! [X10,X16] :
( ! [X90] : X16 != hAPP(c_Option_Ooption_OSome(X10),X90)
<=> X16 = c_Option_Ooption_ONone(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Some__eq) ).
fof(fact_not__None__eq,axiom,
! [X10,X16] :
( X16 != c_Option_Ooption_ONone(X10)
<=> ? [X90] : X16 = hAPP(c_Option_Ooption_OSome(X10),X90) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__None__eq) ).
fof(fact_arith__simps_I31_J,axiom,
! [X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X94),c_Groups_Oone__class_Oone(X94)) = hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OMin) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arith__simps_I31_J) ).
fof(fact_number__of__Min,axiom,
! [X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(X94),c_Groups_Oone__class_Oone(X94)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__Min) ).
fof(fact_min__0R,axiom,
! [X42] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X42),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,
! [X97] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X97),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,
! [X39,X10] :
( class_Groups_Ogroup__add(X10)
=> ( c_Groups_Ozero__class_Ozero(X10) = hAPP(c_Groups_Ouminus__class_Ouminus(X10),X39)
<=> c_Groups_Ozero__class_Ozero(X10) = X39 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__equal__iff__equal) ).
fof(fact_abs__eq__0,axiom,
! [X39,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> ( hAPP(c_Groups_Oabs__class_Oabs(X10),X39) = c_Groups_Ozero__class_Ozero(X10)
<=> X39 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__eq__0) ).
fof(fact_neg__equal__0__iff__equal,axiom,
! [X39,X10] :
( class_Groups_Ogroup__add(X10)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(X10),X39) = c_Groups_Ozero__class_Ozero(X10)
<=> X39 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__0__iff__equal) ).
fof(fact_max__0R,axiom,
! [X42] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X42),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X42,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__0R) ).
fof(fact_minus__nat_Odiff__0,axiom,
! [X97] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X97,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).
fof(fact_zmult__1__right,axiom,
! [X104] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X104),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X104,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1__right) ).
fof(fact_nat__mult__1__right,axiom,
! [X42] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X42,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
fof(fact_zadd__0__right,axiom,
! [X104] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X104),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X104,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__0__right) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X97] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X97,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_card__lessThan,axiom,
! [X165] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X165)) = X165,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__lessThan) ).
fof(fact_zminus__zminus,axiom,
! [X104] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X104)) = X104,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zminus) ).
fof(fact_filter_Osimps_I1_J,axiom,
! [X19,X10] : hAPP(c_List_Ofilter(X10,X19),c_List_Olist_ONil(X10)) = c_List_Olist_ONil(X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter_Osimps_I1_J) ).
fof(fact_finite,axiom,
! [X154,X10] :
( class_Finite__Set_Ofinite(X10)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite) ).
fof(fact_finite__code,axiom,
! [X154,X10] :
( class_Finite__Set_Ofinite(X10)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__code) ).
fof(fact_of__int__eq__0__iff,axiom,
! [X73,X10] :
( class_Int_Oring__char__0(X10)
=> ( hAPP(c_Int_Oring__1__class_Oof__int(X10),X73) = c_Groups_Ozero__class_Ozero(X10)
<=> X73 = 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,
! [X73,X10] :
( class_Int_Oring__char__0(X10)
=> ( c_Groups_Ozero__class_Ozero(X10) = hAPP(c_Int_Oring__1__class_Oof__int(X10),X73)
<=> X73 = 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,
! [X97] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X97) = 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,
! [X103,X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(c_Int_Onumber__class_Onumber__of(X94),X103) = hAPP(c_Int_Oring__1__class_Oof__int(X94),X103) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__eq) ).
fof(fact_Option_Oset_Osimps_I1_J,axiom,
! [X10] : c_Option_Oset(X10,c_Option_Ooption_ONone(X10)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Option_Oset_Osimps_I1_J) ).
fof(fact_com_Osimps_I5_J,axiom,
! [X5,X40,X8,X29] :
( c_Com_Ocom_OWhile(X29,X8) = c_Com_Ocom_OWhile(X40,X5)
<=> ( X29 = X40
& X8 = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I5_J) ).
fof(fact_com_Osimps_I3_J,axiom,
! [X63,X64,X55,X56] :
( c_Com_Ocom_OSemi(X56,X55) = c_Com_Ocom_OSemi(X64,X63)
<=> ( X56 = X64
& X55 = X63 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I3_J) ).
fof(fact_com_Osimps_I1_J,axiom,
! [X40,X41,X29,X30] :
( c_Com_Ocom_OAss(X30,X29) = c_Com_Ocom_OAss(X41,X40)
<=> ( X30 = X41
& X29 = X40 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I1_J) ).
fof(fact_neg__equal__zero,axiom,
! [X39,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(X10),X39) = X39
<=> X39 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__zero) ).
fof(fact_equal__neg__zero,axiom,
! [X39,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( X39 = hAPP(c_Groups_Ouminus__class_Ouminus(X10),X39)
<=> X39 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equal__neg__zero) ).
fof(fact_com_Osize_I10_J,axiom,
! [X29,X30] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(X30,X29)) = 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,
! [X103] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X103),c_Int_OPls) = X103,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I1_J) ).
fof(fact_add__Pls__right,axiom,
! [X103] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X103),c_Int_OPls) = X103,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls__right) ).
fof(fact_nat__int,axiom,
! [X42] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X42)) = X42,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__int) ).
fof(arity_prod__Smallcheck_Osmall,axiom,
! [X334,X333] :
( ( class_Smallcheck_Osmall(X333)
& class_Smallcheck_Osmall(X334) )
=> class_Smallcheck_Osmall(tc_prod(X333,X334)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod__Smallcheck_Osmall) ).
fof(arity_prod__Finite__Set_Ofinite,axiom,
! [X334,X333] :
( ( class_Finite__Set_Ofinite(X333)
& class_Finite__Set_Ofinite(X334) )
=> class_Finite__Set_Ofinite(tc_prod(X333,X334)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod__Finite__Set_Ofinite) ).
fof(arity_fun__Finite__Set_Ofinite,axiom,
! [X334,X333] :
( ( class_Finite__Set_Ofinite(X333)
& class_Finite__Set_Ofinite(X334) )
=> class_Finite__Set_Ofinite(tc_fun(X333,X334)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Finite__Set_Ofinite) ).
fof(arity_sum__Finite__Set_Ofinite,axiom,
! [X334,X333] :
( ( class_Finite__Set_Ofinite(X333)
& class_Finite__Set_Ofinite(X334) )
=> class_Finite__Set_Ofinite(tc_sum(X333,X334)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_sum__Finite__Set_Ofinite) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
! [X105,X93] :
( c_Nat__Transfer_Ois__nat(X93)
=> ( c_Nat__Transfer_Ois__nat(X105)
=> c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X93,X105)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J) ).
fof(fact_com_Osimps_I47_J,axiom,
! [X55,X56,X5,X40] : c_Com_Ocom_OWhile(X40,X5) != c_Com_Ocom_OSemi(X56,X55),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I47_J) ).
fof(fact_com_Osimps_I29_J,axiom,
! [X29,X30,X5,X40] : c_Com_Ocom_OWhile(X40,X5) != c_Com_Ocom_OAss(X30,X29),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I29_J) ).
fof(fact_com_Osimps_I46_J,axiom,
! [X5,X40,X55,X56] : c_Com_Ocom_OSemi(X56,X55) != c_Com_Ocom_OWhile(X40,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I46_J) ).
fof(fact_com_Osimps_I28_J,axiom,
! [X5,X40,X29,X30] : c_Com_Ocom_OAss(X30,X29) != c_Com_Ocom_OWhile(X40,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I28_J) ).
fof(fact_com_Osimps_I25_J,axiom,
! [X29,X30,X63,X64] : c_Com_Ocom_OSemi(X64,X63) != c_Com_Ocom_OAss(X30,X29),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I25_J) ).
fof(fact_com_Osimps_I24_J,axiom,
! [X63,X64,X29,X30] : c_Com_Ocom_OAss(X30,X29) != c_Com_Ocom_OSemi(X64,X63),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I24_J) ).
fof(fact_add__Pls,axiom,
! [X103] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X103) = X103,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls) ).
fof(fact_rev__is__Nil__conv,axiom,
! [X290,X10] :
( hAPP(c_List_Orev(X10),X290) = c_List_Olist_ONil(X10)
<=> X290 = c_List_Olist_ONil(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__is__Nil__conv) ).
fof(fact_rotate1__is__Nil__conv,axiom,
! [X290,X10] :
( hAPP(c_List_Orotate1(X10),X290) = c_List_Olist_ONil(X10)
<=> X290 = c_List_Olist_ONil(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate1__is__Nil__conv) ).
fof(fact_Nil__is__rev__conv,axiom,
! [X290,X10] :
( c_List_Olist_ONil(X10) = hAPP(c_List_Orev(X10),X290)
<=> X290 = c_List_Olist_ONil(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nil__is__rev__conv) ).
fof(fact_mult__Pls,axiom,
! [X133] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X133) = c_Int_OPls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Pls) ).
fof(fact_wf__finite__psubset,axiom,
! [X10] : c_Wellfounded_Owf(tc_fun(X10,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__finite__psubset) ).
fof(fact_com_Osize_I15_J,axiom,
! [X24] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,X24)) = 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,
! [X94] : c_List_Otranspose(X94,c_List_Olist_ONil(tc_List_Olist(X94))) = c_List_Olist_ONil(tc_List_Olist(X94)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose_Osimps_I1_J) ).
fof(fact_com_Osimps_I59_J,axiom,
! [X8,X29,X14] : hAPP(c_Com_Ocom_OBODY,X14) != c_Com_Ocom_OWhile(X29,X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I59_J) ).
fof(fact_com_Osimps_I49_J,axiom,
! [X68,X69,X43] : hAPP(c_Com_Ocom_OBODY,X43) != c_Com_Ocom_OSemi(X69,X68),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I49_J) ).
fof(fact_com_Osimps_I31_J,axiom,
! [X29,X30,X14] : hAPP(c_Com_Ocom_OBODY,X14) != c_Com_Ocom_OAss(X30,X29),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I31_J) ).
fof(fact_com_Osimps_I58_J,axiom,
! [X14,X8,X29] : c_Com_Ocom_OWhile(X29,X8) != hAPP(c_Com_Ocom_OBODY,X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I58_J) ).
fof(fact_com_Osimps_I48_J,axiom,
! [X43,X68,X69] : c_Com_Ocom_OSemi(X69,X68) != hAPP(c_Com_Ocom_OBODY,X43),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I48_J) ).
fof(fact_com_Osimps_I30_J,axiom,
! [X14,X29,X30] : c_Com_Ocom_OAss(X30,X29) != hAPP(c_Com_Ocom_OBODY,X14),
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,
! [X25,X16] :
( hAPP(c_Int_ORep__Integ,X16) = hAPP(c_Int_ORep__Integ,X25)
<=> X16 = X25 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ__inject) ).
fof(fact_Code__Numeral_Onat__of__inject,axiom,
! [X162,X101] :
( hAPP(c_Code__Numeral_Onat__of,X101) = hAPP(c_Code__Numeral_Onat__of,X162)
<=> X101 = X162 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Code__Numeral_Onat__of__inject) ).
fof(fact_code__numeral_Onat__of__inject,axiom,
! [X25,X16] :
( hAPP(c_Code__Numeral_Onat__of,X16) = hAPP(c_Code__Numeral_Onat__of,X25)
<=> X16 = X25 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Onat__of__inject) ).
fof(fact_Code__Numeral_Oof__nat__inject,axiom,
! [X102,X20] :
( hAPP(c_Code__Numeral_Oof__nat,X20) = hAPP(c_Code__Numeral_Oof__nat,X102)
<=> X20 = X102 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Code__Numeral_Oof__nat__inject) ).
fof(fact_nat_Oinject,axiom,
! [X109,X110] :
( hAPP(c_Nat_OSuc,X110) = hAPP(c_Nat_OSuc,X109)
<=> X110 = X109 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Oinject) ).
fof(fact_Suc__inject,axiom,
! [X105,X93] :
( hAPP(c_Nat_OSuc,X93) = hAPP(c_Nat_OSuc,X105)
=> X93 = X105 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__inject) ).
fof(fact_com_Osimps_I6_J,axiom,
! [X14,X15] :
( hAPP(c_Com_Ocom_OBODY,X15) = hAPP(c_Com_Ocom_OBODY,X14)
<=> X15 = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I6_J) ).
fof(fact_sgn__0__0,axiom,
! [X39,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Groups_Osgn__class_Osgn(X10,X39) = c_Groups_Ozero__class_Ozero(X10)
<=> X39 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__0__0) ).
fof(fact_list_Osize_I3_J,axiom,
! [X94] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),c_List_Olist_ONil(X94)) = 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,
! [X94] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X94)),c_Option_Ooption_ONone(X94)) = 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,
! [X119,X120] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X120,X119)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__upto) ).
fof(fact_option_Osimps_I3_J,axiom,
! [X95,X94] : hAPP(c_Option_Ooption_OSome(X94),X95) != c_Option_Ooption_ONone(X94),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Osimps_I3_J) ).
fof(fact_option_Osimps_I2_J,axiom,
! [X95,X94] : c_Option_Ooption_ONone(X94) != hAPP(c_Option_Ooption_OSome(X94),X95),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Osimps_I2_J) ).
fof(fact_some__sym__eq__trivial,axiom,
! [X16,X10] : c_Hilbert__Choice_OEps(X10,hAPP(c_fequal,X16)) = X16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_some__sym__eq__trivial) ).
fof(fact_the__sym__eq__trivial,axiom,
! [X16,X10] : c_HOL_OThe(X10,hAPP(c_fequal,X16)) = X16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__sym__eq__trivial) ).
fof(fact_listsum__simps_I1_J,axiom,
! [X94] :
( class_Groups_Omonoid__add(X94)
=> hAPP(c_List_Omonoid__add__class_Olistsum(X94),c_List_Olist_ONil(X94)) = c_Groups_Ozero__class_Ozero(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__simps_I1_J) ).
fof(fact_abs__one,axiom,
! [X94] :
( class_Rings_Olinordered__idom(X94)
=> hAPP(c_Groups_Oabs__class_Oabs(X94),c_Groups_Oone__class_Oone(X94)) = c_Groups_Oone__class_Oone(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__one) ).
fof(fact_abs__zero,axiom,
! [X94] :
( class_Groups_Oordered__ab__group__add__abs(X94)
=> hAPP(c_Groups_Oabs__class_Oabs(X94),c_Groups_Ozero__class_Ozero(X94)) = c_Groups_Ozero__class_Ozero(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__zero) ).
fof(fact_compl__top__eq,axiom,
! [X94] :
( class_Lattices_Oboolean__algebra(X94)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X94),c_Orderings_Otop__class_Otop(X94)) = c_Orderings_Obot__class_Obot(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__top__eq) ).
fof(fact_compl__bot__eq,axiom,
! [X94] :
( class_Lattices_Oboolean__algebra(X94)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X94),c_Orderings_Obot__class_Obot(X94)) = c_Orderings_Otop__class_Otop(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__bot__eq) ).
fof(fact_minus__zero,axiom,
! [X94] :
( class_Groups_Ogroup__add(X94)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X94),c_Groups_Ozero__class_Ozero(X94)) = c_Groups_Ozero__class_Ozero(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__zero) ).
fof(arity_fun__Lattices_Obounded__lattice,axiom,
! [X333,X334] :
( class_Lattices_Obounded__lattice(X334)
=> class_Lattices_Obounded__lattice(tc_fun(X333,X334)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice) ).
fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
! [X333,X334] :
( class_Lattices_Obounded__lattice(X334)
=> class_Lattices_Obounded__lattice__top(tc_fun(X333,X334)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice__top) ).
fof(arity_fun__Orderings_Otop,axiom,
! [X333,X334] :
( class_Orderings_Otop(X334)
=> class_Orderings_Otop(tc_fun(X333,X334)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Otop) ).
fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
! [X333,X334] :
( class_Complete__Lattice_Ocomplete__lattice(X334)
=> class_Complete__Lattice_Ocomplete__lattice(tc_fun(X333,X334)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Complete__Lattice_Ocomplete__lattice) ).
fof(arity_fun__Lattices_Odistrib__lattice,axiom,
! [X333,X334] :
( class_Lattices_Odistrib__lattice(X334)
=> class_Lattices_Odistrib__lattice(tc_fun(X333,X334)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Odistrib__lattice) ).
fof(arity_fun__Lattices_Osemilattice__inf,axiom,
! [X333,X334] :
( class_Lattices_Olattice(X334)
=> class_Lattices_Osemilattice__inf(tc_fun(X333,X334)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__inf) ).
fof(arity_fun__Lattices_Osemilattice__sup,axiom,
! [X333,X334] :
( class_Lattices_Olattice(X334)
=> class_Lattices_Osemilattice__sup(tc_fun(X333,X334)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__sup) ).
fof(arity_fun__Lattices_Olattice,axiom,
! [X333,X334] :
( class_Lattices_Olattice(X334)
=> class_Lattices_Olattice(tc_fun(X333,X334)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Olattice) ).
fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
! [X333,X334] :
( class_Lattices_Obounded__lattice(X334)
=> class_Lattices_Obounded__lattice__bot(tc_fun(X333,X334)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice__bot) ).
fof(arity_fun__Orderings_Obot,axiom,
! [X333,X334] :
( class_Orderings_Obot(X334)
=> class_Orderings_Obot(tc_fun(X333,X334)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Obot) ).
fof(arity_fun__Groups_Ominus,axiom,
! [X333,X334] :
( class_Groups_Ominus(X334)
=> class_Groups_Ominus(tc_fun(X333,X334)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).
fof(arity_fun__Groups_Ouminus,axiom,
! [X333,X334] :
( class_Groups_Ouminus(X334)
=> class_Groups_Ouminus(tc_fun(X333,X334)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).
fof(arity_fun__Lattices_Oboolean__algebra,axiom,
! [X333,X334] :
( class_Lattices_Oboolean__algebra(X334)
=> class_Lattices_Oboolean__algebra(tc_fun(X333,X334)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).
fof(arity_fun__Orderings_Oord,axiom,
! [X333,X334] :
( class_Orderings_Oord(X334)
=> class_Orderings_Oord(tc_fun(X333,X334)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(arity_fun__Orderings_Opreorder,axiom,
! [X333,X334] :
( class_Orderings_Opreorder(X334)
=> class_Orderings_Opreorder(tc_fun(X333,X334)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(arity_fun__Orderings_Oorder,axiom,
! [X333,X334] :
( class_Orderings_Oorder(X334)
=> class_Orderings_Oorder(tc_fun(X333,X334)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(fact_wf__acyclic,axiom,
! [X177,X10] :
( c_Wellfounded_Owf(X10,X177)
=> c_Wellfounded_Oacyclic(X10,X177) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__acyclic) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
! [X104] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X104)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J) ).
fof(fact_Rep__Integ__inverse,axiom,
! [X16] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X16)) = X16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ__inverse) ).
fof(fact_nat__of__of__nat,axiom,
! [X42] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X42)) = X42,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of__of__nat) ).
fof(fact_of__nat__nat__of,axiom,
! [X103] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X103)) = X103,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__nat__of) ).
fof(fact_nat__of__inverse,axiom,
! [X93] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X93)) = X93,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of__inverse) ).
fof(fact_iszero__def,axiom,
! [X73,X10] :
( class_Rings_Osemiring__1(X10)
=> ( c_Int_Oiszero(X10,X73)
<=> X73 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iszero__def) ).
fof(fact_int__eq__0__conv,axiom,
! [X20] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
<=> X20 = 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,
! [X94] :
( class_Rings_Oring__1(X94)
=> hAPP(c_Int_Oring__1__class_Oof__int(X94),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__1) ).
fof(fact_of__int__0,axiom,
! [X94] :
( class_Rings_Oring__1(X94)
=> hAPP(c_Int_Oring__1__class_Oof__int(X94),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__0) ).
fof(fact_of__nat__1,axiom,
! [X94] :
( class_Rings_Osemiring__1(X94)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__1) ).
fof(fact_of__nat__0,axiom,
! [X94] :
( class_Rings_Osemiring__1(X94)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__0) ).
fof(fact_int__number__of__def,axiom,
! [X133] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X133),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__number__of__def) ).
fof(fact_com_Osize_I2_J,axiom,
! [X29,X30] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(X30,X29)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I2_J) ).
fof(fact_sgn0,axiom,
! [X94] :
( class_Groups_Osgn__if(X94)
=> c_Groups_Osgn__class_Osgn(X94,c_Groups_Ozero__class_Ozero(X94)) = c_Groups_Ozero__class_Ozero(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn0) ).
fof(fact_max__ord__max,axiom,
! [X10] :
( class_Orderings_Oord(X10)
=> c_Orderings_Oord__class_Omax(X10) = c_Orderings_Oord_Omax(X10,c_Orderings_Oord__class_Oless__eq(X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ord__max) ).
fof(fact_min__ord__min,axiom,
! [X10] :
( class_Orderings_Oord(X10)
=> c_Orderings_Oord__class_Omin(X10) = c_Orderings_Oord_Omin(X10,c_Orderings_Oord__class_Oless__eq(X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__ord__min) ).
fof(fact_rev_Osimps_I1_J,axiom,
! [X94] : hAPP(c_List_Orev(X94),c_List_Olist_ONil(X94)) = c_List_Olist_ONil(X94),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev_Osimps_I1_J) ).
fof(fact_tl_Osimps_I1_J,axiom,
! [X94] : hAPP(c_List_Otl(X94),c_List_Olist_ONil(X94)) = c_List_Olist_ONil(X94),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl_Osimps_I1_J) ).
fof(fact_number__of__Pls,axiom,
! [X94] :
( class_Int_Onumber__ring(X94)
=> hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OPls) = c_Groups_Ozero__class_Ozero(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__Pls) ).
fof(fact_semiring__norm_I112_J,axiom,
! [X94] :
( class_Int_Onumber__ring(X94)
=> c_Groups_Ozero__class_Ozero(X94) = hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OPls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I112_J) ).
fof(fact_com_Osize_I7_J,axiom,
! [X24] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,X24)) = 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,
! [X16,X10] :
( c_Option_Ois__none(X10,X16)
<=> X16 = c_Option_Ooption_ONone(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_is__none__def) ).
fof(fact_sorted_Oequations_I1_J,axiom,
! [X94] :
( class_Orderings_Olinorder(X94)
=> c_List_Olinorder__class_Osorted(X94,c_List_Olist_ONil(X94)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted_Oequations_I1_J) ).
fof(fact_sorted_ONil,axiom,
! [X94] :
( class_Orderings_Olinorder(X94)
=> c_List_Olinorder__class_Osorted(X94,c_List_Olist_ONil(X94)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted_ONil) ).
fof(fact_iszero__0,axiom,
! [X94] :
( class_Rings_Osemiring__1(X94)
=> c_Int_Oiszero(X94,c_Groups_Ozero__class_Ozero(X94)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iszero__0) ).
fof(fact_vname_Osize_I3_J,axiom,
! [X100] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OGlb(X100)) = 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,
! [X89] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OLoc(X89)) = 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,
! [X208,X94] : hAPP(c_New__DSequence_Opos__empty(X94),X208) = c_Lazy__Sequence_Oempty(X94),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__empty__def) ).
fof(fact_butlast_Osimps_I1_J,axiom,
! [X94] : c_List_Obutlast(X94,c_List_Olist_ONil(X94)) = c_List_Olist_ONil(X94),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast_Osimps_I1_J) ).
fof(fact_Suc__not__Zero,axiom,
! [X97] : hAPP(c_Nat_OSuc,X97) != 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,
! [X98] : hAPP(c_Nat_OSuc,X98) != 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,
! [X97] : hAPP(c_Nat_OSuc,X97) != 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,
! [X97] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X97),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(fact_nat_Osimps_I2_J,axiom,
! [X99] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X99),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
fof(fact_Zero__neq__Suc,axiom,
! [X97] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X97),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_nat_Oexhaust,axiom,
! [X105] :
( X105 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ~ ! [X117] : X105 != hAPP(c_Nat_OSuc,X117) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Oexhaust) ).
fof(fact_com_Osimps_I17_J,axiom,
! [X5,X40] : c_Com_Ocom_OWhile(X40,X5) != c_Com_Ocom_OSKIP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I17_J) ).
fof(fact_com_Osimps_I13_J,axiom,
! [X70,X71] : c_Com_Ocom_OSemi(X71,X70) != c_Com_Ocom_OSKIP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I13_J) ).
fof(fact_com_Osimps_I9_J,axiom,
! [X40,X41] : c_Com_Ocom_OAss(X41,X40) != c_Com_Ocom_OSKIP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I9_J) ).
fof(fact_com_Osimps_I16_J,axiom,
! [X5,X40] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X40,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I16_J) ).
fof(fact_com_Osimps_I12_J,axiom,
! [X70,X71] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X71,X70),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I12_J) ).
fof(fact_com_Osimps_I8_J,axiom,
! [X40,X41] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(X41,X40),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I8_J) ).
fof(fact_inf__min,axiom,
! [X10] :
( ( class_Lattices_Osemilattice__inf(X10)
& class_Orderings_Olinorder(X10) )
=> c_Lattices_Osemilattice__inf__class_Oinf(X10) = c_Orderings_Oord__class_Omin(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__min) ).
fof(fact_sup__max,axiom,
! [X10] :
( ( class_Lattices_Osemilattice__sup(X10)
& class_Orderings_Olinorder(X10) )
=> c_Lattices_Osemilattice__sup__class_Osup(X10) = c_Orderings_Oord__class_Omax(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__max) ).
fof(fact_Suc__n__not__n,axiom,
! [X42] : hAPP(c_Nat_OSuc,X42) != X42,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
fof(fact_n__not__Suc__n,axiom,
! [X42] : X42 != hAPP(c_Nat_OSuc,X42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(fact_id__def,axiom,
! [X261,X94] : hAPP(c_Fun_Oid(X94),X261) = X261,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__def) ).
fof(fact_id__apply,axiom,
! [X93,X94] : hAPP(c_Fun_Oid(X94),X93) = X93,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__apply) ).
fof(fact_Collect__def,axiom,
! [X19,X10] : hAPP(c_Set_OCollect(X10),X19) = X19,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(help_c__COMBI__1,axiom,
! [X87,X94] : hAPP(c_COMBI(X94),X87) = X87,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBI__1) ).
fof(fact_is__none__code_I1_J,axiom,
! [X94] : c_Option_Ois__none(X94,c_Option_Ooption_ONone(X94)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_is__none__code_I1_J) ).
fof(fact_zero__neq__one,axiom,
! [X94] :
( class_Rings_Ozero__neq__one(X94)
=> c_Groups_Ozero__class_Ozero(X94) != c_Groups_Oone__class_Oone(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__neq__one) ).
fof(fact_one__neq__zero,axiom,
! [X94] :
( class_Rings_Ozero__neq__one(X94)
=> c_Groups_Oone__class_Oone(X94) != c_Groups_Ozero__class_Ozero(X94) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__neq__zero) ).
fof(fact_com_Osimps_I19_J,axiom,
! [X43] : hAPP(c_Com_Ocom_OBODY,X43) != c_Com_Ocom_OSKIP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I19_J) ).
fof(fact_com_Osimps_I18_J,axiom,
! [X43] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,X43),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I18_J) ).
fof(fact_beyond__zero,axiom,
! [X103] : c_Quickcheck_Obeyond(X103,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__than,axiom,
! [X141] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X141)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__int__ge__less__than) ).
fof(fact_wf__int__ge__less__than2,axiom,
! [X141] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X141)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__int__ge__less__than2) ).
fof(fact_number__of__is__id,axiom,
! [X103] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X103) = X103,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__is__id) ).
fof(fact_nat__size,axiom,
! [X42] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X42) = X42,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__size) ).
fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
! [X334] :
( class_Finite__Set_Ofinite(X334)
=> class_Finite__Set_Ofinite(tc_Option_Ooption(X334)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Option__Ooption__Finite__Set_Ofinite) ).
fof(fact_vname_Osimps_I1_J,axiom,
! [X106,X107] :
( c_Com_Ovname_OGlb(X107) = c_Com_Ovname_OGlb(X106)
<=> X107 = X106 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vname_Osimps_I1_J) ).
fof(fact_vname_Osimps_I2_J,axiom,
! [X82,X79] :
( c_Com_Ovname_OLoc(X79) = c_Com_Ovname_OLoc(X82)
<=> X79 = X82 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vname_Osimps_I2_J) ).
fof(fact_vname_Osimps_I3_J,axiom,
! [X108,X100] : c_Com_Ovname_OGlb(X100) != c_Com_Ovname_OLoc(X108),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vname_Osimps_I3_J) ).
fof(fact_vname_Osimps_I4_J,axiom,
! [X100,X108] : c_Com_Ovname_OLoc(X108) != c_Com_Ovname_OGlb(X100),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vname_Osimps_I4_J) ).
fof(fact_vname_Osize_I1_J,axiom,
! [X100] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(X100)) = 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,
! [X89] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(X89)) = 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,
! [X10] : c_Equiv__Relations_Oequivp(X10,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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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,
class_Rings_Oordered__ring(tc_Int_Oint),
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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,
! [X101,X10] :
( class_Rings_Oring__1(X10)
=> ( ( X101 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hAPP(c_Int_Oring__1__class_Oof__int(X10),X101) = c_Groups_Ozero__class_Ozero(X10) )
& ( X101 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Int_Oring__1__class_Oof__int(X10),X101) = hAPP(c_Groups_Ouminus__class_Ouminus(X10),hAPP(c_Int_Oring__1__class_Oof__int(X10),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X101))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Int_Oring__1__class_Oof__int(X10),X101) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X10),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X10,X10)),tc_fun(tc_Int_Oint,X10)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,X10),X10),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X10,X10)),tc_fun(tc_Int_Oint,X10)),tc_Int_Oint),c_COMBB(tc_fun(X10,X10),X10,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X10,tc_fun(tc_fun(X10,X10),X10),tc_Int_Oint),c_HOL_OLet(X10,X10)),c_Int_Oring__1__class_Oof__int(X10)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X10,X10),tc_fun(X10,X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,X10)),tc_fun(tc_fun(X10,X10),tc_fun(X10,X10)),tc_Int_Oint),c_COMBS(X10,X10,X10)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X10,X10),tc_fun(X10,tc_fun(X10,X10))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,X10)),tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_fun(X10,X10))),tc_Int_Oint),c_COMBB(X10,tc_fun(X10,X10),X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_fun(X10,X10)),tc_Int_Oint),c_If(X10)),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(X10,X10,X10),c_Groups_Oplus__class_Oplus(X10)),c_COMBI(X10))))),hAPP(hAPP(c_COMBC(X10,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X10),c_Groups_Oplus__class_Oplus(X10)),hAPP(hAPP(c_COMBS(X10,X10,X10),c_Groups_Oplus__class_Oplus(X10)),c_COMBI(X10)))),c_Groups_Oone__class_Oone(X10))))),c_Divides_Odivmod__int(X101,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,
! [X105,X93,X94] :
( class_Rings_Olinordered__idom(X94)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X93),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(X94),X105),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X94))) ),
inference(fof_simplification,[status(thm)],[fact_not__sum__power2__lt__zero]) ).
fof(i_0_5165,plain,
! [X84,X94] :
( class_Rings_Olinordered__idom(X94)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Power_Opower__class_Opower(X94),X84),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X94))) ),
inference(fof_simplification,[status(thm)],[fact_power2__less__0]) ).
fof(i_0_5166,plain,
! [X144,X133] :
( ( 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),X133)))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X133))) = 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),X144),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)))),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),X133)))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X133))) = 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),X144)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
inference(fof_simplification,[status(thm)],[fact_zmod__number__of__Bit1]) ).
fof(i_0_5167,plain,
! [X133,X144] :
( 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),X144)))
=> ( ( 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),X133)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144))))
=> c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)) = 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),X133)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144))) )
& ( ~ 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),X133)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144))))
=> c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133),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),X144)))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_negDivAlg__eqn__number__of]) ).
fof(i_0_5168,plain,
! [X133] :
( 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),X133)))
=> ( ( 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),X133))))
=> c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)) = 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),X133))) )
& ( ~ 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),X133))))
=> c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)),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),X133)))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_negDivAlg__eqn__1__number__of]) ).
fof(i_0_5169,plain,
! [X133,X144] :
( 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),X144)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)) = 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),X133)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133),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),X144)))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_posDivAlg__eqn__number__of]) ).
fof(i_0_5170,plain,
! [X133] :
( 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),X133)))
=> ( ( 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),X133)))
=> c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)) = 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),X133)))
=> c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)),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),X133)))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_posDivAlg__eqn__1__number__of]) ).
fof(i_0_5171,plain,
! [X84,X92] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X92))
=> ( ( 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),X84),X92)))
=> c_Divides_OnegDivAlg(X84,X92) = 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),X84),X92)) )
& ( ~ 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),X84),X92)))
=> c_Divides_OnegDivAlg(X84,X92) = hAPP(c_Divides_Oadjust(X92),c_Divides_OnegDivAlg(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)))),X92))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_negDivAlg__eqn]) ).
fof(i_0_5172,plain,
! [X84,X92] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X92))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),X92))
=> c_Divides_OposDivAlg(X84,X92) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X84),X92))
=> c_Divides_OposDivAlg(X84,X92) = hAPP(c_Divides_Oadjust(X92),c_Divides_OposDivAlg(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)))),X92))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_posDivAlg__eqn]) ).
fof(i_0_5173,plain,
! [X168,X131,X10] :
( class_Int_Onumber__ring(X10)
=> ( ( 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),X131)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X168)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X131))) = hAPP(hAPP(c_HOL_OLet(X10,X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X168)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X131))),hAPP(hAPP(c_COMBS(X10,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X10),c_Groups_Otimes__class_Otimes(X10)),hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X168)))),c_COMBI(X10))) )
& ( ~ 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),X131)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X168)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X131))) = c_Groups_Oone__class_Oone(X10) ) ) ),
inference(fof_simplification,[status(thm)],[fact_power__number__of__odd__number__of]) ).
fof(i_0_5174,plain,
! [X73,X131,X10] :
( class_Int_Onumber__ring(X10)
=> ( ( 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),X131)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),X73),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X131))) = hAPP(hAPP(c_HOL_OLet(X10,X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X73),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X131))),hAPP(hAPP(c_COMBS(X10,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X10),c_Groups_Otimes__class_Otimes(X10)),hAPP(c_Groups_Otimes__class_Otimes(X10),X73))),c_COMBI(X10))) )
& ( ~ 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),X131)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),X73),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X131))) = c_Groups_Oone__class_Oone(X10) ) ) ),
inference(fof_simplification,[status(thm)],[fact_power__number__of__odd]) ).
fof(i_0_5175,plain,
! [X73,X131] :
( ( 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),X131)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X73),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X131))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X73),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X131))),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),X73))),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),X131)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X73),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X131))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
inference(fof_simplification,[status(thm)],[fact_zpower__number__of__odd]) ).
fof(i_0_5176,plain,
! [X16,X177,X10] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X10,X10),X177)),c_Transitive__Closure_Ortrancl(X10,X177)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X16)),c_Transitive__Closure_Otrancl(X10,X177))) ),
inference(fof_simplification,[status(thm)],[fact_irrefl__tranclI]) ).
fof(i_0_5177,plain,
! [X141,X18,X38,X39] :
( 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),X39,X38)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X18,X141)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X39),X38))
| ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X18),X39))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X38),X141))
& ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X18),X39))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X39),X18)) )
| ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X38),X141))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X141),X38)) ) ) ) )
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X18),X141)) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_OatLeastatMost__psubset__iff]) ).
fof(i_0_5178,plain,
! [X177,X10] :
( c_Wellfounded_Oacyclic(X10,X177)
<=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X3)),c_Transitive__Closure_Otrancl(X10,X177))) ),
inference(fof_simplification,[status(thm)],[fact_acyclic__def]) ).
fof(i_0_5179,plain,
! [X144,X133] :
( ( 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),X133)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X144))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X133))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)) )
& ( ~ 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),X133)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X144))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X133))) = 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),X144)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X133)) ) ),
inference(fof_simplification,[status(thm)],[fact_zdiv__number__of__Bit1]) ).
fof(i_0_5180,plain,
! [X177,X10] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X3)),c_Transitive__Closure_Otrancl(X10,X177)))
=> c_Wellfounded_Oacyclic(X10,X177) ),
inference(fof_simplification,[status(thm)],[fact_acyclicI]) ).
fof(i_0_5181,plain,
! [X131] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X131)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X131)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X131)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X131)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X131)),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,
! [X42,X97] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X97)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X42)))
=> c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X97),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X42)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X97)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X97)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X42))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X97)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X42)))
=> c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X97),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X42)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
inference(fof_simplification,[status(thm)],[fact_upt__rec__number__of]) ).
fof(i_0_5183,plain,
! [X133,X94] :
( ( class_Int_Onumber__ring(X94)
& class_Int_Oring__char__0(X94) )
=> ~ c_Int_Oiszero(X94,hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OBit1(X133))) ),
inference(fof_simplification,[status(thm)],[fact_iszero__number__of__Bit1]) ).
fof(i_0_5184,plain,
! [X94] :
( class_Int_Onumber__ring(X94)
=> ~ c_Int_Oiszero(X94,hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OBit1(c_Int_OPls))) ),
inference(fof_simplification,[status(thm)],[fact_not__iszero__Numeral1]) ).
fof(i_0_5185,plain,
! [X42,X144] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),X42)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X42) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),X42)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X144))),X42) ) ),
inference(fof_simplification,[status(thm)],[fact_Suc__nat__number__of__add]) ).
fof(i_0_5186,plain,
! [X119,X120] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X120),X119))
=> c_List_Oupt(X120,hAPP(c_Nat_OSuc,X119)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X120,X119)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X119),c_List_Olist_ONil(tc_Nat_Onat))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X120),X119))
=> c_List_Oupt(X120,hAPP(c_Nat_OSuc,X119)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
inference(fof_simplification,[status(thm)],[fact_upt__Suc]) ).
fof(i_0_5187,plain,
! [X119,X120] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),X119))
=> c_List_Oupt(X120,X119) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X120),c_List_Oupt(hAPP(c_Nat_OSuc,X120),X119)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X120),X119))
=> c_List_Oupt(X120,X119) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
inference(fof_simplification,[status(thm)],[fact_upt__rec]) ).
fof(i_0_5188,plain,
! [X101,X20,X19] :
( epred1_3(X19,X20,X101)
<=> ( ( X101 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(X19,X20)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X101))
=> ! [X152,X123] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X123))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X123),X101))
& X20 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X101),X152)),X123) )
=> hBOOL(hAPP(X19,X123)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ! [X152,X123] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),X123))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X123),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& X20 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X101),X152)),X123) )
=> hBOOL(hAPP(X19,X123)) ) ) ) ),
introduced(definition) ).
fof(i_0_5189,plain,
! [X101,X20,X19] :
( epred2_3(X19,X20,X101)
<=> ( ( X101 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(X19,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)),X101))
=> ! [X152] :
( ? [X123] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X123))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X123),X101))
& X20 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X101),X152)),X123) )
=> hBOOL(hAPP(X19,X152)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ! [X152] :
( ? [X123] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),X123))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X123),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& X20 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X101),X152)),X123) )
=> hBOOL(hAPP(X19,X152)) ) ) ) ),
introduced(definition) ).
fof(i_0_5190,plain,
! [X144] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X144),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),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),X144),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X144)) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__number__of__diff__1]) ).
fof(i_0_5191,plain,
! [X144] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X144),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),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),X144),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X144)) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__number__of__add__1]) ).
fof(i_0_5192,plain,
! [X144] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X144),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),X144)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X144),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),X144)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X144)) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__1__add__number__of]) ).
fof(i_0_5193,plain,
! [X144] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X144)) ) ),
inference(fof_simplification,[status(thm)],[fact_Suc__nat__number__of]) ).
fof(i_0_5194,plain,
! [X21957] : c_Divides_Oadjust(X21957) = 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)),X21957))))),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)),X21957))))),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,
! [X21326] : c_Int_Osucc(c_Int_OBit0(X21326)) = c_Int_OBit1(X21326),
inference(variable_rename,[status(thm)],[fact_succ__Bit0]) ).
fof(i_0_5196,plain,
! [X21286] : c_Int_OBit0(X21286) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21286),X21286),
inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).
fof(i_0_5197,plain,
! [X21103] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X21103),c_Int_OMin) = c_Int_Osucc(X21103),
inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I2_J]) ).
fof(i_0_5198,plain,
! [X196,X1,X2,X195,X125,X18,X13,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),X18),hAPP(c_Set_Oimage(tc_prod(X125,X195),tc_prod(X10,X13),c_Product__Type_Omap__pair(X125,X10,X195,X13,X2,X1)),X196)))
=> ~ ! [X3,X90] :
( X18 = hAPP(hAPP(c_Product__Type_OPair(X10,X13),hAPP(X2,X3)),hAPP(X1,X90))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X125,X195)),hAPP(hAPP(c_Product__Type_OPair(X125,X195),X3),X90)),X196)) ) ),
inference(fof_simplification,[status(thm)],[fact_prod__fun__imageE]) ).
fof(i_0_5199,plain,
! [X22039,X22040] :
( ( X22040 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odivmod__int(X22040,X22039) = 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)) )
& ( X22039 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odivmod__int(X22040,X22039) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22040)
| X22040 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( X22039 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odivmod__int(X22040,X22039) = 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,X22039))),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)),X22039)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22040))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22039),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22040),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(X22040,X22039)),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),X22039))))),c_Divides_Opdivmod(X22040,X22039))))
| X22040 = 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,
! [X29435,X29436,X29437,X29438] : c_Product__Type_Oapsnd(X29438,X29437,X29436,X29435) = c_Product__Type_Omap__pair(X29436,X29436,X29438,X29437,c_Fun_Oid(X29436),X29435),
inference(variable_rename,[status(thm)],[fact_apsnd__def]) ).
fof(i_0_5201,plain,
! [X22041,X22042] :
( ( X22042 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odivmod__int(X22042,X22041) = 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)) )
& ( X22041 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odivmod__int(X22042,X22041) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22042)
| X22042 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( X22041 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odivmod__int(X22042,X22041) = 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,X22041))),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,X22042)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X22041))),c_Divides_Opdivmod(X22042,X22041)),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),X22041))))),c_Divides_Opdivmod(X22042,X22041))))
| X22042 = 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,
! [X22903,X22904,X22905] : c_Nitpick_Oplus__frac(X22905,X22904,X22903) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X22905),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(X22905),X22904),hAPP(c_Nitpick_Odenom(X22905),X22903))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,X22905),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,X22905),tc_Int_Oint),c_Nitpick_Ofrac(X22905)),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(X22905),X22904))),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(X22905),X22904))))),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(X22905),X22903))),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(X22905),X22903)))))),c_COMBI(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[fact_Nitpick_Oplus__frac__def]) ).
fof(i_0_5203,plain,
! [X28008] : c_Nitpick_Odenom(X28008) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X28008,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X28008)),
inference(variable_rename,[status(thm)],[fact_Nitpick_Odenom__def]) ).
fof(i_0_5204,plain,
! [X28002] : c_Nitpick_Onum(X28002) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X28002,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X28002)),
inference(variable_rename,[status(thm)],[fact_Nitpick_Onum__def]) ).
fof(i_0_5205,plain,
! [X30158,X30159,X30160,X30161] :
( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X30161,tc_fun(X30161,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X30161,tc_fun(tc_prod(X30161,X30161),tc_HOL_Obool),tc_fun(X30161,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30161,tc_fun(tc_fun(tc_prod(X30161,X30161),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X30161,X30161),tc_HOL_Obool),tc_fun(X30161,tc_HOL_Obool)),X30161),c_COMBC(X30161,tc_fun(tc_prod(X30161,X30161),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30161,tc_prod(X30161,X30161)),tc_fun(X30161,tc_fun(tc_fun(tc_prod(X30161,X30161),tc_HOL_Obool),tc_HOL_Obool)),X30161),hAPP(c_COMBB(tc_prod(X30161,X30161),tc_fun(tc_fun(tc_prod(X30161,X30161),tc_HOL_Obool),tc_HOL_Obool),X30161),c_member(tc_prod(X30161,X30161)))),c_Product__Type_OPair(X30161,X30161)))),X30160)),c_fequal),X30159),X30158))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30161,X30161)),hAPP(hAPP(c_Product__Type_OPair(X30161,X30161),X30159),X30158)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30161,X30161),tc_HOL_Obool)),X30160),c_Relation_OId(X30161)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30161,X30161)),hAPP(hAPP(c_Product__Type_OPair(X30161,X30161),X30159),X30158)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30161,X30161),tc_HOL_Obool)),X30160),c_Relation_OId(X30161))))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X30161,tc_fun(X30161,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X30161,tc_fun(tc_prod(X30161,X30161),tc_HOL_Obool),tc_fun(X30161,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30161,tc_fun(tc_fun(tc_prod(X30161,X30161),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X30161,X30161),tc_HOL_Obool),tc_fun(X30161,tc_HOL_Obool)),X30161),c_COMBC(X30161,tc_fun(tc_prod(X30161,X30161),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30161,tc_prod(X30161,X30161)),tc_fun(X30161,tc_fun(tc_fun(tc_prod(X30161,X30161),tc_HOL_Obool),tc_HOL_Obool)),X30161),hAPP(c_COMBB(tc_prod(X30161,X30161),tc_fun(tc_fun(tc_prod(X30161,X30161),tc_HOL_Obool),tc_HOL_Obool),X30161),c_member(tc_prod(X30161,X30161)))),c_Product__Type_OPair(X30161,X30161)))),X30160)),c_fequal),X30159),X30158)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reflcl__set__eq])]) ).
fof(i_0_5206,plain,
! [X30242] : c_Transitive__Closure_Ortrancl(X30242,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X30242,X30242),tc_HOL_Obool))) = c_Relation_OId(X30242),
inference(variable_rename,[status(thm)],[fact_rtrancl__empty]) ).
fof(i_0_5207,plain,
! [X21906,X21907,X21908] : hAPP(c_Divides_Oadjust(X21908),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X21907),X21906)) = 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),X21906),X21908)),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)))),X21907)),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)))),X21907)),X21906))),
inference(variable_rename,[status(thm)],[fact_adjust__eq]) ).
fof(i_0_5208,plain,
! [X30154,X30155,X30156,X30157] : c_Transitive__Closure_Otrancl(X30157,hAPP(hAPP(c_Set_Oinsert(tc_prod(X30157,X30157)),hAPP(hAPP(c_Product__Type_OPair(X30157,X30157),X30156),X30155)),X30154)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30157,X30157),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X30157,X30154)),hAPP(c_Set_OCollect(tc_prod(X30157,X30157)),hAPP(c_Product__Type_Oprod_Oprod__case(X30157,X30157,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X30157,tc_fun(X30157,tc_HOL_Obool),tc_fun(X30157,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X30157,tc_HOL_Obool),tc_fun(X30157,tc_HOL_Obool)),X30157),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X30157)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X30157),c_fconj),hAPP(hAPP(c_COMBC(X30157,tc_fun(tc_prod(X30157,X30157),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X30157,X30157),tc_fun(tc_fun(tc_prod(X30157,X30157),tc_HOL_Obool),tc_HOL_Obool),X30157),c_member(tc_prod(X30157,X30157))),hAPP(hAPP(c_COMBC(X30157,X30157,tc_prod(X30157,X30157)),c_Product__Type_OPair(X30157,X30157)),X30156))),c_Transitive__Closure_Ortrancl(X30157,X30154))))),hAPP(hAPP(c_COMBC(X30157,tc_fun(tc_prod(X30157,X30157),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X30157,X30157),tc_fun(tc_fun(tc_prod(X30157,X30157),tc_HOL_Obool),tc_HOL_Obool),X30157),c_member(tc_prod(X30157,X30157))),hAPP(c_Product__Type_OPair(X30157,X30157),X30155))),c_Transitive__Closure_Ortrancl(X30157,X30154)))))),
inference(variable_rename,[status(thm)],[fact_trancl__insert]) ).
fof(i_0_5209,plain,
! [X30174,X30175] : c_Transitive__Closure_Otrancl(X30175,X30174) = hAPP(hAPP(c_Relation_Orel__comp(X30175,X30175,X30175),X30174),c_Transitive__Closure_Ortrancl(X30175,X30174)),
inference(variable_rename,[status(thm)],[fact_trancl__unfold__left]) ).
fof(i_0_5210,plain,
! [X21980,X21981] :
( ( X21980 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(c_Int_Oring__1__class_Oof__int(X21981),X21980) = c_Groups_Ozero__class_Ozero(X21981)
| ~ class_Rings_Oring__1(X21981) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21980),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Oring__1__class_Oof__int(X21981),X21980) = hAPP(c_Groups_Ouminus__class_Ouminus(X21981),hAPP(c_Int_Oring__1__class_Oof__int(X21981),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21980)))
| X21980 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ class_Rings_Oring__1(X21981) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21980),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Oring__1__class_Oof__int(X21981),X21980) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X21981),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X21981,X21981)),tc_fun(tc_Int_Oint,X21981)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X21981,X21981),X21981),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X21981,X21981)),tc_fun(tc_Int_Oint,X21981)),tc_Int_Oint),c_COMBB(tc_fun(X21981,X21981),X21981,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X21981,tc_fun(tc_fun(X21981,X21981),X21981),tc_Int_Oint),c_HOL_OLet(X21981,X21981)),c_Int_Oring__1__class_Oof__int(X21981)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X21981,X21981),tc_fun(X21981,X21981)),hAPP(hAPP(c_COMBB(tc_fun(X21981,tc_fun(X21981,X21981)),tc_fun(tc_fun(X21981,X21981),tc_fun(X21981,X21981)),tc_Int_Oint),c_COMBS(X21981,X21981,X21981)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X21981,X21981),tc_fun(X21981,tc_fun(X21981,X21981))),hAPP(hAPP(c_COMBB(tc_fun(X21981,tc_fun(X21981,X21981)),tc_fun(tc_fun(X21981,X21981),tc_fun(X21981,tc_fun(X21981,X21981))),tc_Int_Oint),c_COMBB(X21981,tc_fun(X21981,X21981),X21981)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X21981,tc_fun(X21981,X21981)),tc_Int_Oint),c_If(X21981)),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(X21981,X21981,X21981),c_Groups_Oplus__class_Oplus(X21981)),c_COMBI(X21981))))),hAPP(hAPP(c_COMBC(X21981,X21981,X21981),hAPP(hAPP(c_COMBB(X21981,tc_fun(X21981,X21981),X21981),c_Groups_Oplus__class_Oplus(X21981)),hAPP(hAPP(c_COMBS(X21981,X21981,X21981),c_Groups_Oplus__class_Oplus(X21981)),c_COMBI(X21981)))),c_Groups_Oone__class_Oone(X21981))))),c_Divides_Odivmod__int(X21980,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| X21980 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ class_Rings_Oring__1(X21981) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5163])])]) ).
fof(i_0_5211,plain,
! [X31667,X31668,X31669,X31670] : c_Map_Omap__add(X31670,X31669,X31668,c_Map_Omap__of(X31670,X31669,X31667)) = c_List_Ofoldr(tc_prod(X31670,X31669),tc_fun(X31670,tc_Option_Ooption(X31669)),hAPP(c_Product__Type_Oprod_Oprod__case(X31670,X31669,tc_fun(tc_fun(X31670,tc_Option_Ooption(X31669)),tc_fun(X31670,tc_Option_Ooption(X31669)))),hAPP(hAPP(c_COMBC(X31670,tc_fun(X31669,tc_Option_Ooption(X31669)),tc_fun(X31669,tc_fun(tc_fun(X31670,tc_Option_Ooption(X31669)),tc_fun(X31670,tc_Option_Ooption(X31669))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X31669),tc_fun(tc_fun(X31670,tc_Option_Ooption(X31669)),tc_fun(X31670,tc_Option_Ooption(X31669)))),tc_fun(tc_fun(X31669,tc_Option_Ooption(X31669)),tc_fun(X31669,tc_fun(tc_fun(X31670,tc_Option_Ooption(X31669)),tc_fun(X31670,tc_Option_Ooption(X31669))))),X31670),c_COMBB(tc_Option_Ooption(X31669),tc_fun(tc_fun(X31670,tc_Option_Ooption(X31669)),tc_fun(X31670,tc_Option_Ooption(X31669))),X31669)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X31670,tc_Option_Ooption(X31669)),tc_fun(tc_Option_Ooption(X31669),tc_fun(X31670,tc_Option_Ooption(X31669)))),tc_fun(tc_Option_Ooption(X31669),tc_fun(tc_fun(X31670,tc_Option_Ooption(X31669)),tc_fun(X31670,tc_Option_Ooption(X31669)))),X31670),c_COMBC(tc_fun(X31670,tc_Option_Ooption(X31669)),tc_Option_Ooption(X31669),tc_fun(X31670,tc_Option_Ooption(X31669)))),hAPP(c_COMBC(tc_fun(X31670,tc_Option_Ooption(X31669)),X31670,tc_fun(tc_Option_Ooption(X31669),tc_fun(X31670,tc_Option_Ooption(X31669)))),c_Fun_Ofun__upd(X31670,tc_Option_Ooption(X31669)))))),c_Option_Ooption_OSome(X31669))),X31667,X31668),
inference(variable_rename,[status(thm)],[fact_map__add__map__of__foldr]) ).
fof(i_0_5212,plain,
! [X34293,X34294,X34295,X34296,X34297] : c_List_Ofoldr(X34297,X34296,X34295,X34294,X34293) = hAPP(c_List_Ofoldl(X34296,X34297,hAPP(c_COMBC(X34297,X34296,X34296),X34295),X34293),hAPP(c_List_Orev(X34297),X34294)),
inference(variable_rename,[status(thm)],[fact_foldr__foldl]) ).
fof(i_0_5213,plain,
! [X21413,X21414,X21415] :
( ( X21414 = c_Groups_Ozero__class_Ozero(X21415)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21415),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21415),hAPP(hAPP(c_Power_Opower__class_Opower(X21415),X21414),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(X21415),X21413),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X21415)))
| ~ class_Rings_Olinordered__idom(X21415) )
& ( X21413 = c_Groups_Ozero__class_Ozero(X21415)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21415),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21415),hAPP(hAPP(c_Power_Opower__class_Opower(X21415),X21414),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(X21415),X21413),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X21415)))
| ~ class_Rings_Olinordered__idom(X21415) )
& ( X21414 != c_Groups_Ozero__class_Ozero(X21415)
| X21413 != c_Groups_Ozero__class_Ozero(X21415)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21415),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21415),hAPP(hAPP(c_Power_Opower__class_Opower(X21415),X21414),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(X21415),X21413),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X21415)))
| ~ class_Rings_Olinordered__idom(X21415) ) ),
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,
! [X21419,X21420,X21421] :
( ~ class_Rings_Olinordered__idom(X21421)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21421),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21421),hAPP(hAPP(c_Power_Opower__class_Opower(X21421),X21420),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(X21421),X21419),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X21421))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5164])]) ).
fof(i_0_5215,plain,
! [X34352,X34353,X34354,X34355] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X34355)),c_List_Otranspose__rel(X34355)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X34355)),hAPP(hAPP(c_List_Olist_OCons(X34355),X34354),X34353)),X34352)))
| c_List_Otranspose(X34355,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X34355)),hAPP(hAPP(c_List_Olist_OCons(X34355),X34354),X34353)),X34352)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X34355)),hAPP(hAPP(c_List_Olist_OCons(X34355),X34354),c_List_Oconcat(X34355,hAPP(hAPP(c_List_Omap(tc_List_Olist(X34355),tc_List_Olist(X34355)),c_List_Olist_Olist__case(tc_List_Olist(X34355),X34355,c_List_Olist_ONil(X34355),hAPP(hAPP(c_COMBB(tc_List_Olist(X34355),tc_fun(tc_List_Olist(X34355),tc_List_Olist(X34355)),X34355),c_COMBK(tc_List_Olist(X34355),tc_List_Olist(X34355))),hAPP(hAPP(c_COMBC(X34355,tc_List_Olist(X34355),tc_List_Olist(X34355)),c_List_Olist_OCons(X34355)),c_List_Olist_ONil(X34355))))),X34352)))),c_List_Otranspose(X34355,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X34355)),X34353),c_List_Oconcat(tc_List_Olist(X34355),hAPP(hAPP(c_List_Omap(tc_List_Olist(X34355),tc_List_Olist(tc_List_Olist(X34355))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X34355)),X34355,c_List_Olist_ONil(tc_List_Olist(X34355)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X34355),tc_List_Olist(tc_List_Olist(X34355))),X34355),hAPP(hAPP(c_COMBC(tc_List_Olist(X34355),tc_List_Olist(tc_List_Olist(X34355)),tc_List_Olist(tc_List_Olist(X34355))),c_List_Olist_OCons(tc_List_Olist(X34355))),c_List_Olist_ONil(tc_List_Olist(X34355)))))),X34352))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose_Opsimps_I3_J])]) ).
fof(i_0_5216,plain,
! [X34261,X34262] : c_List_Oconcat(X34262,X34261) = hAPP(c_List_Ofoldl(tc_List_Olist(X34262),tc_List_Olist(X34262),c_List_Oappend(X34262),c_List_Olist_ONil(X34262)),X34261),
inference(variable_rename,[status(thm)],[fact_concat__conv__foldl]) ).
fof(i_0_5217,plain,
! [X34322,X34323,X34324,X34325] : c_List_Otranspose(X34325,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X34325)),hAPP(hAPP(c_List_Olist_OCons(X34325),X34324),X34323)),X34322)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X34325)),hAPP(hAPP(c_List_Olist_OCons(X34325),X34324),c_List_Oconcat(X34325,hAPP(hAPP(c_List_Omap(tc_List_Olist(X34325),tc_List_Olist(X34325)),c_List_Olist_Olist__case(tc_List_Olist(X34325),X34325,c_List_Olist_ONil(X34325),hAPP(hAPP(c_COMBB(tc_List_Olist(X34325),tc_fun(tc_List_Olist(X34325),tc_List_Olist(X34325)),X34325),c_COMBK(tc_List_Olist(X34325),tc_List_Olist(X34325))),hAPP(hAPP(c_COMBC(X34325,tc_List_Olist(X34325),tc_List_Olist(X34325)),c_List_Olist_OCons(X34325)),c_List_Olist_ONil(X34325))))),X34322)))),c_List_Otranspose(X34325,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X34325)),X34323),c_List_Oconcat(tc_List_Olist(X34325),hAPP(hAPP(c_List_Omap(tc_List_Olist(X34325),tc_List_Olist(tc_List_Olist(X34325))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X34325)),X34325,c_List_Olist_ONil(tc_List_Olist(X34325)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X34325),tc_List_Olist(tc_List_Olist(X34325))),X34325),hAPP(hAPP(c_COMBC(tc_List_Olist(X34325),tc_List_Olist(tc_List_Olist(X34325)),tc_List_Olist(tc_List_Olist(X34325))),c_List_Olist_OCons(tc_List_Olist(X34325))),c_List_Olist_ONil(tc_List_Olist(X34325)))))),X34322))))),
inference(variable_rename,[status(thm)],[fact_transpose_Osimps_I3_J]) ).
fof(i_0_5218,plain,
! [X21446,X21447,X21448] :
( ~ class_Rings_Olinordered__idom(X21448)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21448),X21447),c_Groups_Ozero__class_Ozero(X21448)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21448),hAPP(hAPP(c_Power_Opower__class_Opower(X21448),X21447),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)))),X21446)))),c_Groups_Ozero__class_Ozero(X21448))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_odd__power__less__zero])]) ).
fof(i_0_5219,plain,
! [X54,X177,X125,X284,X13,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),X284),hAPP(hAPP(c_Relation_Orel__comp(X10,X125,X13),X177),X54)))
=> ~ ! [X3,X90,X159] :
( X284 = hAPP(hAPP(c_Product__Type_OPair(X10,X13),X3),X159)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X125)),hAPP(hAPP(c_Product__Type_OPair(X10,X125),X3),X90)),X177))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X125,X13)),hAPP(hAPP(c_Product__Type_OPair(X125,X13),X90),X159)),X54)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_rel__compE]) ).
fof(i_0_5220,plain,
! [X21443,X21444,X21445] :
( ~ class_Rings_Olinordered__idom(X21445)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21445),c_Groups_Ozero__class_Ozero(X21445)),hAPP(hAPP(c_Power_Opower__class_Opower(X21445),X21444),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)))),X21443)))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21445),c_Groups_Ozero__class_Ozero(X21445)),X21444)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_odd__0__le__power__imp__0__le])]) ).
fof(i_0_5221,plain,
! [X77,X20,X54,X39,X19,X48] :
( c_Natural_Oevaln(c_Com_Ocom_OCall(X48,X19,X39),X54,X20,X77)
=> ~ ! [X67] :
( X77 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X67),hAPP(c_Natural_Ogetlocs,X54))),X48),hAPP(hAPP(c_Natural_Ogetlocs,X67),c_Com_ORes))
=> ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X19),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X54),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X39,X54)),X20,X67) ) ),
inference(fof_simplification,[status(thm)],[fact_evaln__elim__cases_I7_J]) ).
fof(i_0_5222,plain,
! [X21440,X21441,X21442] :
( ~ class_Int_Onumber__ring(X21442)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21442),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21442),X21441),X21440)),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(X21442),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21442),hAPP(hAPP(c_Power_Opower__class_Opower(X21442),X21441),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(X21442),X21440),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(X21442),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21442),hAPP(c_Int_Onumber__class_Onumber__of(X21442),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21441)),X21440)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__diff])]) ).
fof(i_0_5223,plain,
! [X21422,X21423,X21424] :
( ~ class_Int_Onumber__ring(X21424)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21424),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21424),X21423),X21422)),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(X21424),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21424),hAPP(hAPP(c_Power_Opower__class_Opower(X21424),X21423),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(X21424),X21422),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(X21424),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21424),hAPP(c_Int_Onumber__class_Onumber__of(X21424),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21423)),X21422)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__sum])]) ).
fof(i_0_5224,plain,
! [X101,X113] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X113),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)))),X101)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X101),X113))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X113),X101)) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_OgreaterThan__iff]) ).
fof(i_0_5225,plain,
! [X101,X113] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X113),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)))),X101)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X113),X101))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X101),X113)) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_OlessThan__iff]) ).
fof(i_0_5226,plain,
! [X2,X154,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> c_Nitpick_Osetsum_H(X10,X13,X2,X154) = hAPP(c_List_Omonoid__add__class_Olistsum(X13),hAPP(hAPP(c_List_Omap(X10,X13),X2),c_Hilbert__Choice_OEps(tc_List_Olist(X10),hAPP(hAPP(c_COMBS(tc_List_Olist(X10),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X10)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X10)),c_fequal),c_List_Oset(X10))),X154))),c_List_Odistinct(X10))))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> c_Nitpick_Osetsum_H(X10,X13,X2,X154) = c_Groups_Ozero__class_Ozero(X13) ) ) ),
inference(fof_simplification,[status(thm)],[fact_Nitpick_Osetsum_H__def]) ).
fof(i_0_5227,plain,
! [X21416,X21417,X21418] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21418),c_Groups_Ozero__class_Ozero(X21418)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21418),hAPP(hAPP(c_Power_Opower__class_Opower(X21418),X21417),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(X21418),X21416),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| X21417 != c_Groups_Ozero__class_Ozero(X21418)
| X21416 != c_Groups_Ozero__class_Ozero(X21418)
| ~ class_Rings_Olinordered__idom(X21418) )
& ( X21417 = c_Groups_Ozero__class_Ozero(X21418)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21418),c_Groups_Ozero__class_Ozero(X21418)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21418),hAPP(hAPP(c_Power_Opower__class_Opower(X21418),X21417),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(X21418),X21416),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ~ class_Rings_Olinordered__idom(X21418) )
& ( X21416 = c_Groups_Ozero__class_Ozero(X21418)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21418),c_Groups_Ozero__class_Ozero(X21418)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21418),hAPP(hAPP(c_Power_Opower__class_Opower(X21418),X21417),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(X21418),X21416),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ~ class_Rings_Olinordered__idom(X21418) ) ),
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,
! [X33841,X33842,X33843,X33844] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33844)),X33843))),c_List_Ofoldr(tc_List_Olist(X33842),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X33842)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X33842))),X33841,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(X33844)),X33843)),c_List_Ofoldr(tc_List_Olist(X33842),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X33842)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(X33842),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X33842)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X33842)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(X33842),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X33842)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X33842),tc_List_Olist(X33842),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X33842)))),X33841),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(variable_rename,[status(thm)],[fact_transpose__aux__max]) ).
fof(i_0_5229,plain,
! [X34192,X34193,X34194,X34195] : hAPP(hAPP(c_List_Omap(tc_prod(X34195,tc_Nat_Onat),X34195),c_Product__Type_Ofst(X34195,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X34195,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X34195,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(X34195,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X34195,tc_Nat_Onat))),X34194)),hAPP(hAPP(c_List_Ozip(X34195,tc_Nat_Onat),X34193),c_List_Oupt(X34192,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34192),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34195)),X34193)))))) = hAPP(hAPP(c_List_Omap(tc_prod(X34195,tc_Nat_Onat),X34195),c_Product__Type_Ofst(X34195,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X34195,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X34195,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(X34195,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X34195,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(X34195,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(X34195,tc_Nat_Onat))),X34192))),X34194)),hAPP(hAPP(c_List_Ozip(X34195,tc_Nat_Onat),X34193),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34195)),X34193))))),
inference(variable_rename,[status(thm)],[fact_sublist__shift__lemma]) ).
fof(i_0_5230,plain,
! [X34103,X34104] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34104),X34103)) = c_List_Oupt(X34104,X34103),
inference(variable_rename,[status(thm)],[fact_sorted__list__of__set__range]) ).
fof(i_0_5231,plain,
! [X202,X1,X10,X203] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X203),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
=> c_Random__Sequence_ORandom(X10,X1,X203,X202) = 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(X10)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X10)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X203),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
=> c_Random__Sequence_ORandom(X10,X1,X203,X202) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X10,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(X10)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(X1,X202)),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(X10)))),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(X10)))),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(X10)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(X10,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(X10)))),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(X10)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(X10,X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X203),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X202))),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(X10)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X10))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X10)))),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(X10)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(X10,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(X10)))),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(X10)))),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(X10))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X10)))),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(X10)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X10)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X10))))),tc_prod(X10,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(X10)),hAPP(hAPP(c_COMBB(X10,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X10)))),tc_prod(X10,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(X10)),c_Product__Type_Ofst(X10,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))) ) ),
inference(fof_simplification,[status(thm)],[fact_Random_Osimps]) ).
fof(i_0_5232,plain,
! [X21254,X21255] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21255)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21254)) = 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)))),X21255)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21254)),
inference(variable_rename,[status(thm)],[fact_Suc__div__eq__add3__div__number__of]) ).
fof(i_0_5233,plain,
! [X21191,X21192] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21192)))),X21191) = 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)))),X21192)),X21191),
inference(variable_rename,[status(thm)],[fact_Suc__div__eq__add3__div]) ).
fof(i_0_5234,plain,
! [X22570,X22571] : hAPP(c_New__DSequence_Opos__not__seq(X22571),X22570) = c_Lazy__Sequence_Ohb__not__seq(hAPP(X22571,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)))),X22570))),
inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__not__seq__def]) ).
fof(i_0_5235,plain,
! [X166,X18,X125,X13,X73,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X73),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X13,X125,tc_fun(X10,tc_HOL_Obool)),X18),X166)))
=> ~ ! [X3,X90] :
( X166 = hAPP(hAPP(c_Product__Type_OPair(X13,X125),X3),X90)
=> ~ hBOOL(hAPP(hAPP(c_member(X10),X73),hAPP(hAPP(X18,X3),X90))) ) ),
inference(fof_simplification,[status(thm)],[fact_mem__splitE]) ).
fof(i_0_5236,plain,
! [X168,X154,X16,X73,X2,X13,X10] :
( c_Finite__Set_Ofun__left__comm(X10,X13,X2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X13,X2,X73,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)),X168))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ~ ! [X90] :
( X168 = hAPP(hAPP(X2,X16),X90)
=> ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X13,X2,X73,X154),X90)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__graph__insertE]) ).
fof(i_0_5237,plain,
! [X21456] :
( ( X21456 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| hAPP(c_Code__Numeral_Oint__of,X21456) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X21456,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,X21456) = 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),X21456),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| X21456 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X21456,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,X21456) = 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),X21456),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))
| X21456 = 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,
! [X21410,X21411,X21412] :
( ~ class_Rings_Olinordered__idom(X21412)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21412),c_Groups_Ozero__class_Ozero(X21412)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21412),hAPP(hAPP(c_Power_Opower__class_Opower(X21412),X21411),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(X21412),X21410),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,X13,X154,X10] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),hAPP(c_Set_Oimage(X10,X13,X2),X154)))
=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
& ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X154))),hAPP(hAPP(c_COMBC(X10,X13,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X13,tc_fun(X13,tc_HOL_Obool),X10),c_fequal),X2)),hAPP(X2,X3)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_pigeonhole__infinite]) ).
fof(i_0_5240,plain,
! [X34333,X34334,X34335] :
( ( c_List_Oconcat(X34335,X34334) != c_List_Oconcat(X34335,X34333)
| X34334 = X34333
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34335))),X34334) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34335))),X34333)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X34335),tc_List_Olist(X34335))),esk495_3(X34333,X34334,X34335)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X34335),tc_List_Olist(X34335))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X34335),tc_List_Olist(X34335)),X34334),X34333)))) )
& ( X34334 != X34333
| c_List_Oconcat(X34335,X34334) = c_List_Oconcat(X34335,X34333)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34335))),X34334) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34335))),X34333)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X34335),tc_List_Olist(X34335))),esk495_3(X34333,X34334,X34335)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X34335),tc_List_Olist(X34335))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X34335),tc_List_Olist(X34335)),X34334),X34333)))) )
& ( c_List_Oconcat(X34335,X34334) != c_List_Oconcat(X34335,X34333)
| X34334 = X34333
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34335))),X34334) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34335))),X34333)
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X34335),tc_List_Olist(X34335),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X34335),tc_fun(tc_List_Olist(X34335),tc_Nat_Onat),tc_fun(tc_List_Olist(X34335),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X34335),tc_Nat_Onat),tc_fun(tc_List_Olist(X34335),tc_HOL_Obool)),tc_List_Olist(X34335)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X34335))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X34335)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X34335))))),c_Nat_Osize__class_Osize(tc_List_Olist(X34335)))),esk495_3(X34333,X34334,X34335))) )
& ( X34334 != X34333
| c_List_Oconcat(X34335,X34334) = c_List_Oconcat(X34335,X34333)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34335))),X34334) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34335))),X34333)
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X34335),tc_List_Olist(X34335),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X34335),tc_fun(tc_List_Olist(X34335),tc_Nat_Onat),tc_fun(tc_List_Olist(X34335),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X34335),tc_Nat_Onat),tc_fun(tc_List_Olist(X34335),tc_HOL_Obool)),tc_List_Olist(X34335)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X34335))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X34335)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X34335))))),c_Nat_Osize__class_Osize(tc_List_Olist(X34335)))),esk495_3(X34333,X34334,X34335))) ) ),
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_5241,plain,
! [X34329,X34330,X34331] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X34331),tc_List_Olist(X34331))),esk494_3(X34329,X34330,X34331)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X34331),tc_List_Olist(X34331))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X34331),tc_List_Olist(X34331)),X34330),X34329))))
| X34330 = X34329
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34331))),X34330) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34331))),X34329)
| c_List_Oconcat(X34331,X34330) != c_List_Oconcat(X34331,X34329) )
& ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X34331),tc_List_Olist(X34331),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X34331),tc_fun(tc_List_Olist(X34331),tc_Nat_Onat),tc_fun(tc_List_Olist(X34331),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X34331),tc_Nat_Onat),tc_fun(tc_List_Olist(X34331),tc_HOL_Obool)),tc_List_Olist(X34331)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X34331))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X34331)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X34331))))),c_Nat_Osize__class_Osize(tc_List_Olist(X34331)))),esk494_3(X34329,X34330,X34331)))
| X34330 = X34329
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34331))),X34330) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34331))),X34329)
| c_List_Oconcat(X34331,X34330) != c_List_Oconcat(X34331,X34329) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_concat__injective])])])]) ).
fof(i_0_5242,plain,
! [X21982,X21983,X21984,X21985,X21986] : hAPP(c_Nat_Onat_Onat__rec(X21986,X21985,X21984),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21983)),X21982)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X21986),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X21983))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X21986,X21986),hAPP(hAPP(c_COMBC(tc_Int_Oint,X21986,tc_fun(X21986,X21986)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X21986,tc_fun(X21986,X21986)),tc_Int_Oint),c_If(X21986)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(X21986,X21985,X21984),X21982))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X21986,X21986),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X21986,X21986),tc_Int_Oint),X21984),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)),X21982))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X21986,tc_Int_Oint),c_Nat_Onat_Onat__rec(X21986,X21985,X21984)),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)),X21982))))),
inference(variable_rename,[status(thm)],[fact_nat__rec__add__eq__if]) ).
fof(i_0_5243,plain,
! [X21160] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21160),c_Int_OMin) = c_Int_Opred(X21160),
inference(variable_rename,[status(thm)],[fact_add__Min__right]) ).
fof(i_0_5244,plain,
! [X21256,X21257] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21257),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)))),X21256)),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)))),X21257)) = 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),X21256),c_Groups_Oone__class_Oone(tc_Int_Oint)),X21257))),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,
! [X21260,X21261] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21261),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)))),X21260))),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)))),X21261)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21260),c_Groups_Oone__class_Oone(tc_Int_Oint))),X21261) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__zdiv__mult__2])]) ).
fof(i_0_5246,plain,
! [X21262,X21263] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21263))
| 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)))),X21262))),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)))),X21263)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21262),X21263) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zdiv__mult__2])]) ).
fof(i_0_5247,plain,
! [X21911,X21912] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21912) != hAPP(c_Nat_OSuc,X21911)
| 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(X21912))),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)),X21911))))) )
& ( ~ 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(X21912))),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)),X21911)))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21912) = hAPP(c_Nat_OSuc,X21911) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of__Suc])]) ).
fof(i_0_5248,plain,
! [X21913,X21914] :
( ( hAPP(c_Nat_OSuc,X21914) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21913)
| 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(X21913))),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)),X21914))))) )
& ( ~ 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(X21913))),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)),X21914)))))
| hAPP(c_Nat_OSuc,X21914) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21913) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__eq__number__of])]) ).
fof(i_0_5249,plain,
! [X154,X10] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> c_Nitpick_Ocard_H(X10,X154) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_Hilbert__Choice_OEps(tc_List_Olist(X10),hAPP(hAPP(c_COMBS(tc_List_Olist(X10),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X10)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X10)),c_fequal),c_List_Oset(X10))),X154))),c_List_Odistinct(X10)))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> c_Nitpick_Ocard_H(X10,X154) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_simplification,[status(thm)],[fact_Nitpick_Ocard_H__def]) ).
fof(i_0_5250,plain,
! [X113,X230] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X230))
=> 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)),X230))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X113)))) = 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)),X230))),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,X113))))) ),
inference(fof_simplification,[status(thm)],[fact_card__less__Suc2]) ).
fof(i_0_5251,plain,
! [X21383,X21384,X21385] :
( ~ class_Rings_Olinordered__semidom(X21385)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21385),hAPP(hAPP(c_Power_Opower__class_Opower(X21385),X21384),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(X21385),X21383),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(X21385),c_Groups_Ozero__class_Ozero(X21385)),X21383))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21385),X21384),X21383)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__le__imp__le])]) ).
fof(i_0_5252,plain,
! [X21407,X21408,X21409] :
( ~ class_Rings_Olinordered__semidom(X21409)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21409),hAPP(hAPP(c_Power_Opower__class_Opower(X21409),X21408),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(X21409),X21407),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(X21409),c_Groups_Ozero__class_Ozero(X21409)),X21407))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21409),X21408),X21407)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__less__imp__less])]) ).
fof(i_0_5253,plain,
! [X160,X13,X141,X154,X18,X10] :
( ( hBOOL(hAPP(hAPP(c_member(X10),X18),X154))
=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X141),X154))
=> hAPP(c_Set_Ovimage(X13,X10,hAPP(hAPP(c_COMBC(X13,X10,X10),hAPP(hAPP(c_COMBC(X13,X10,tc_fun(X10,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_fun(X10,X10)),X13),c_If(X10)),hAPP(hAPP(c_COMBC(X13,tc_fun(X13,tc_HOL_Obool),tc_HOL_Obool),c_member(X13)),X160))),X18)),X141)),X154) = c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X141),X154))
=> hAPP(c_Set_Ovimage(X13,X10,hAPP(hAPP(c_COMBC(X13,X10,X10),hAPP(hAPP(c_COMBC(X13,X10,tc_fun(X10,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_fun(X10,X10)),X13),c_If(X10)),hAPP(hAPP(c_COMBC(X13,tc_fun(X13,tc_HOL_Obool),tc_HOL_Obool),c_member(X13)),X160))),X18)),X141)),X154) = X160 ) ) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X18),X154))
=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X141),X154))
=> hAPP(c_Set_Ovimage(X13,X10,hAPP(hAPP(c_COMBC(X13,X10,X10),hAPP(hAPP(c_COMBC(X13,X10,tc_fun(X10,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_fun(X10,X10)),X13),c_If(X10)),hAPP(hAPP(c_COMBC(X13,tc_fun(X13,tc_HOL_Obool),tc_HOL_Obool),c_member(X13)),X160))),X18)),X141)),X154) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X13,tc_HOL_Obool)),X160) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X141),X154))
=> hAPP(c_Set_Ovimage(X13,X10,hAPP(hAPP(c_COMBC(X13,X10,X10),hAPP(hAPP(c_COMBC(X13,X10,tc_fun(X10,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_fun(X10,X10)),X13),c_If(X10)),hAPP(hAPP(c_COMBC(X13,tc_fun(X13,tc_HOL_Obool),tc_HOL_Obool),c_member(X13)),X160))),X18)),X141)),X154) = c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_vimage__if]) ).
fof(i_0_5254,plain,
! [X21264,X21265] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21265))
| 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)))),X21264)),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)))),X21265)) = 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,X21264,X21265))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zmod__mult__2])]) ).
fof(i_0_5255,plain,
! [X21248,X21249] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21249))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21248)) = 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)))),X21249),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21248)),
inference(variable_rename,[status(thm)],[fact_Suc__mod__eq__add3__mod__number__of]) ).
fof(i_0_5256,plain,
! [X21425,X21426,X21427] :
( ~ class_Rings_Olinordered__idom(X21427)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21427),c_Groups_Ozero__class_Ozero(X21427)),hAPP(hAPP(c_Power_Opower__class_Opower(X21427),X21426),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)))),X21425)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__even__power_H])]) ).
fof(i_0_5257,plain,
! [X21250,X21251] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21251))),X21250) = 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)))),X21251),X21250),
inference(variable_rename,[status(thm)],[fact_Suc__mod__eq__add3__mod]) ).
fof(i_0_5258,plain,
! [X21252,X21253] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21253,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21252)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21253,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)))),X21252)),
inference(variable_rename,[status(thm)],[fact_mod__Suc__eq__mod__add3]) ).
fof(i_0_5259,plain,
! [X21189,X21190] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X21190),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21189)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X21190),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)))),X21189)),
inference(variable_rename,[status(thm)],[fact_div__Suc__eq__div__add3]) ).
fof(i_0_5260,plain,
! [X30151,X30152,X30153] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30153,X30153),tc_HOL_Obool)),X30152),X30151))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30153,X30153),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X30153,X30153,X30153),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X30153,X30153),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X30153,X30152)),X30151)),X30152)),X30151))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30153,X30153),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X30153,X30152)),X30151)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__Int__subset])]) ).
fof(i_0_5261,plain,
! [X18,X38,X39,X216,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X216))
=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X39),X216))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),hAPP(hAPP(c_COMBC(X10,X13,X13),hAPP(hAPP(c_COMBS(X10,X13,tc_fun(X13,X13)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X13,tc_fun(X13,X13)),X10),c_If(X13)),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X39))),X38)),X18)),X216) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),hAPP(X38,X39)),hAPP(hAPP(c_Power_Opower__class_Opower(X13),X18),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X216)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X216))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),hAPP(hAPP(c_COMBC(X10,X13,X13),hAPP(hAPP(c_COMBS(X10,X13,tc_fun(X13,X13)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X13,tc_fun(X13,X13)),X10),c_If(X13)),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X39))),X38)),X18)),X216) = hAPP(hAPP(c_Power_Opower__class_Opower(X13),X18),hAPP(c_Finite__Set_Ocard(X10),X216)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setprod__gen__delta]) ).
fof(i_0_5262,plain,
! [X38,X39,X216,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X216))
=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X39),X216))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),hAPP(hAPP(c_COMBC(X10,X13,X13),hAPP(hAPP(c_COMBS(X10,X13,tc_fun(X13,X13)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X13,tc_fun(X13,X13)),X10),c_If(X13)),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X39))),X38)),c_Groups_Ozero__class_Ozero(X13))),X216) = hAPP(X38,X39) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X216))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),hAPP(hAPP(c_COMBC(X10,X13,X13),hAPP(hAPP(c_COMBS(X10,X13,tc_fun(X13,X13)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X13,tc_fun(X13,X13)),X10),c_If(X13)),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X39))),X38)),c_Groups_Ozero__class_Ozero(X13))),X216) = c_Groups_Ozero__class_Ozero(X13) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum__delta]) ).
fof(i_0_5263,plain,
! [X38,X39,X216,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X216))
=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X39),X216))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),hAPP(hAPP(c_COMBC(X10,X13,X13),hAPP(hAPP(c_COMBS(X10,X13,tc_fun(X13,X13)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X13,tc_fun(X13,X13)),X10),c_If(X13)),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X39))),X38)),c_Groups_Oone__class_Oone(X13))),X216) = hAPP(X38,X39) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X216))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),hAPP(hAPP(c_COMBC(X10,X13,X13),hAPP(hAPP(c_COMBS(X10,X13,tc_fun(X13,X13)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X13,tc_fun(X13,X13)),X10),c_If(X13)),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X39))),X38)),c_Groups_Oone__class_Oone(X13))),X216) = c_Groups_Oone__class_Oone(X13) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setprod__delta]) ).
fof(i_0_5264,plain,
! [X21926,X21927] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21927)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21926)))
| 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(X21926))),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),X21927)),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(X21926))),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),X21927)),c_Int_Onat)))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21927)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21926))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__number__of])]) ).
fof(i_0_5265,plain,
! [X21922,X21923] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21923)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21922)))
| 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(X21922))),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),X21923)),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(X21922))),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),X21923)),c_Int_Onat)))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21923)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21922))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__number__of])]) ).
fof(i_0_5266,plain,
! [X22773,X22774,X22775,X22776,X22777,X22778,X22779] : hAPP(c_Product__Type_Oapsnd(X22779,X22778,X22777,X22776),hAPP(c_Product__Type_Oapfst(X22775,X22777,X22779,X22774),X22773)) = hAPP(c_Product__Type_Oapfst(X22775,X22777,X22778,X22774),hAPP(c_Product__Type_Oapsnd(X22779,X22778,X22775,X22776),X22773)),
inference(variable_rename,[status(thm)],[fact_apsnd__apfst__commute]) ).
fof(i_0_5267,plain,
! [X29431,X29432,X29433,X29434] : c_Product__Type_Oapfst(X29434,X29433,X29432,X29431) = c_Product__Type_Omap__pair(X29434,X29433,X29432,X29432,X29431,c_Fun_Oid(X29432)),
inference(variable_rename,[status(thm)],[fact_apfst__def]) ).
fof(i_0_5268,plain,
! [X177,X168,X165,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Oappend(X10),X16),X165)),hAPP(hAPP(c_List_Oappend(X10),X16),X168))),c_List_Olexord(X10,X177)))
=> ( ! [X116] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X116),X116)),X177))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X165),X168)),c_List_Olexord(X10,X177))) ) ),
inference(fof_simplification,[status(thm)],[fact_lexord__append__leftD]) ).
fof(i_0_5269,plain,
! [X21391,X21392] :
( ~ class_Rings_Olinordered__idom(X21392)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21392),hAPP(hAPP(c_Power_Opower__class_Opower(X21392),X21391),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X21392))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5165])]) ).
fof(i_0_5270,plain,
! [X196,X20,X73,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X73)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X20),X196)))
=> ( ( X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> X16 != X73 )
=> ~ ! [X90,X122] :
( X20 = hAPP(c_Nat_OSuc,X122)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X90)),X196))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X90),X73)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X122),X196))) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_rel__pow__E2]) ).
fof(i_0_5271,plain,
! [X31718,X31719,X31720,X31721,X31722,X31723,X31724,X31726,X31727,X31728,X31729,X31730,X31731,X31732,X31733] :
( ( hAPP(X31720,X31719) = hAPP(c_Option_Ooption_OSome(X31724),esk435_7(X31718,X31719,X31720,X31721,X31722,X31723,X31724))
| c_Map_Omap__comp(X31724,X31723,X31722,X31721,X31720,X31719) != hAPP(c_Option_Ooption_OSome(X31723),X31718) )
& ( hAPP(X31721,esk435_7(X31718,X31719,X31720,X31721,X31722,X31723,X31724)) = hAPP(c_Option_Ooption_OSome(X31723),X31718)
| c_Map_Omap__comp(X31724,X31723,X31722,X31721,X31720,X31719) != hAPP(c_Option_Ooption_OSome(X31723),X31718) )
& ( hAPP(X31728,X31727) != hAPP(c_Option_Ooption_OSome(X31732),X31733)
| hAPP(X31729,X31733) != hAPP(c_Option_Ooption_OSome(X31731),X31726)
| c_Map_Omap__comp(X31732,X31731,X31730,X31729,X31728,X31727) = hAPP(c_Option_Ooption_OSome(X31731),X31726) ) ),
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,
! [X31702,X31703,X31704,X31705,X31706,X31707] : c_Map_Omap__comp(X31707,X31706,X31705,X31704,X31703,X31702) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X31706),X31707,c_Option_Ooption_ONone(X31706),X31704),hAPP(X31703,X31702)),
inference(variable_rename,[status(thm)],[fact_map__comp__def]) ).
fof(i_0_5273,plain,
! [X38,X39] :
( 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)))),X39,X38) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
<=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X39),X38))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X38),X39)) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_OatLeastLessThan__empty__iff]) ).
fof(i_0_5274,plain,
! [X162,X101] :
( 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)))),X101,X162) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
<=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X101),X162))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X162),X101)) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_OgreaterThanAtMost__empty__iff]) ).
fof(i_0_5275,plain,
! [X38,X39] :
( 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)))),X39,X38)
<=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X39),X38))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X38),X39)) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_OatLeastLessThan__empty__iff2]) ).
fof(i_0_5276,plain,
! [X162,X101] :
( 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)))),X101,X162)
<=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X101),X162))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X162),X101)) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_OgreaterThanAtMost__empty__iff2]) ).
fof(i_0_5277,plain,
! [X25,X16,X2,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X10,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),X16),X25))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25),X16)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(X2,X16)),hAPP(X2,X25))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Ostrict__monoD]) ).
fof(i_0_5278,plain,
! [X21431,X21432,X21433] :
( ~ class_Groups_Omonoid__mult(X21433)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21433),X21432),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)))),X21431))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21433),X21432),hAPP(hAPP(c_Power_Opower__class_Opower(X21433),hAPP(hAPP(c_Power_Opower__class_Opower(X21433),X21432),X21431)),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,
! [X77,X54,X39,X19,X48] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(X48,X19,X39)),X54),X77))
=> ~ ! [X67] :
( X77 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X67),hAPP(c_Natural_Ogetlocs,X54))),X48),hAPP(hAPP(c_Natural_Ogetlocs,X67),c_Com_ORes))
=> ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X19)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X54),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X39,X54))),X67)) ) ),
inference(fof_simplification,[status(thm)],[fact_evalc__elim__cases_I7_J]) ).
fof(i_0_5280,plain,
! [X27750,X27751,X27752,X27753,X27754,X27755,X27756] : hAPP(c_Product__Type_Oapsnd(X27756,X27755,X27754,X27753),hAPP(c_Product__Type_Oapsnd(X27752,X27756,X27754,X27751),X27750)) = hAPP(c_Product__Type_Oapsnd(X27752,X27755,X27754,hAPP(c_Fun_Ocomp(X27756,X27755,X27752,X27753),X27751)),X27750),
inference(variable_rename,[status(thm)],[fact_apsnd__compose]) ).
fof(i_0_5281,plain,
! [X27743,X27744,X27745,X27746,X27747,X27748,X27749] : hAPP(c_Product__Type_Oapfst(X27749,X27748,X27747,X27746),hAPP(c_Product__Type_Oapfst(X27745,X27749,X27747,X27744),X27743)) = hAPP(c_Product__Type_Oapfst(X27745,X27748,X27747,hAPP(c_Fun_Ocomp(X27749,X27748,X27745,X27746),X27744)),X27743),
inference(variable_rename,[status(thm)],[fact_apfst__compose]) ).
fof(i_0_5282,plain,
! [X21393,X21394,X21395] :
( ( X21394 = c_Groups_Ozero__class_Ozero(X21395)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21395),hAPP(hAPP(c_Power_Opower__class_Opower(X21395),X21394),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(X21395),X21393),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X21395)
| ~ class_Rings_Olinordered__idom(X21395) )
& ( X21393 = c_Groups_Ozero__class_Ozero(X21395)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21395),hAPP(hAPP(c_Power_Opower__class_Opower(X21395),X21394),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(X21395),X21393),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X21395)
| ~ class_Rings_Olinordered__idom(X21395) )
& ( X21394 != c_Groups_Ozero__class_Ozero(X21395)
| X21393 != c_Groups_Ozero__class_Ozero(X21395)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21395),hAPP(hAPP(c_Power_Opower__class_Opower(X21395),X21394),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(X21395),X21393),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(X21395)
| ~ class_Rings_Olinordered__idom(X21395) ) ),
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,
! [X53,X20,X54,X18,X39,X78] :
( c_Natural_Oevaln(c_Com_Ocom_OLocal(X78,X39,X18),X54,X20,X53)
=> ~ ! [X67] :
( X53 = hAPP(hAPP(hAPP(c_Natural_Oupdate,X67),c_Com_Ovname_OLoc(X78)),hAPP(hAPP(c_Natural_Ogetlocs,X54),X78))
=> ~ c_Natural_Oevaln(X18,hAPP(hAPP(hAPP(c_Natural_Oupdate,X54),c_Com_Ovname_OLoc(X78)),hAPP(X39,X54)),X20,X67) ) ),
inference(fof_simplification,[status(thm)],[fact_evaln__elim__cases_I3_J]) ).
fof(i_0_5284,plain,
! [X34196,X34197,X34198] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk491_3(X34196,X34197,X34198)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34197))),X34198)))
| c_List_Otranspose(X34197,X34198) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X34197)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X34197)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X34197),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X34197)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X34197)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X34197),hAPP(hAPP(c_COMBB(tc_List_Olist(X34197),tc_fun(tc_Nat_Onat,X34197),tc_Nat_Onat),c_List_Onth(X34197)),hAPP(c_List_Onth(tc_List_Olist(X34197)),X34198))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34197))),X34198)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X34196))
| X34198 = c_List_Olist_ONil(tc_List_Olist(X34197)) )
& ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34197)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X34197)),X34198),esk491_3(X34196,X34197,X34198))) != X34196
| c_List_Otranspose(X34197,X34198) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X34197)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X34197)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X34197),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X34197)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X34197)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X34197),hAPP(hAPP(c_COMBB(tc_List_Olist(X34197),tc_fun(tc_Nat_Onat,X34197),tc_Nat_Onat),c_List_Onth(X34197)),hAPP(c_List_Onth(tc_List_Olist(X34197)),X34198))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34197))),X34198)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X34196))
| X34198 = c_List_Olist_ONil(tc_List_Olist(X34197)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk491_3(X34196,X34197,X34198)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34197))),X34198)))
| c_List_Otranspose(X34197,X34198) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X34197)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X34197)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X34197),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X34197)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X34197)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X34197),hAPP(hAPP(c_COMBB(tc_List_Olist(X34197),tc_fun(tc_Nat_Onat,X34197),tc_Nat_Onat),c_List_Onth(X34197)),hAPP(c_List_Onth(tc_List_Olist(X34197)),X34198))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34197))),X34198)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X34196))
| X34196 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34197)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X34197)),X34198),esk491_3(X34196,X34197,X34198))) != X34196
| c_List_Otranspose(X34197,X34198) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X34197)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X34197)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X34197),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X34197)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X34197)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X34197),hAPP(hAPP(c_COMBB(tc_List_Olist(X34197),tc_fun(tc_Nat_Onat,X34197),tc_Nat_Onat),c_List_Onth(X34197)),hAPP(c_List_Onth(tc_List_Olist(X34197)),X34198))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34197))),X34198)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X34196))
| X34196 != 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,
! [X21258,X21259] :
( ( ~ 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),X21259)))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X21258)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21259))) = 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),X21258),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21259)))),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),X21259)))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X21258)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21259))) = 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),X21258)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21259)))),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,
! [X22088,X22089,X22090] :
( ( 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),esk87_3(X22088,X22089,X22090)),esk88_3(X22088,X22089,X22090))))
| hBOOL(hAPP(hAPP(X22088,X22090),X22089))
| ~ 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),X22090),X22089))) )
& ( 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),esk87_3(X22088,X22089,X22090)),esk88_3(X22088,X22089,X22090))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk88_3(X22088,X22089,X22090)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(X22088,esk87_3(X22088,X22089,X22090)),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)))),esk88_3(X22088,X22089,X22090))))
| hBOOL(hAPP(hAPP(X22088,X22090),X22089))
| ~ 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),X22090),X22089))) )
& ( ~ hBOOL(hAPP(hAPP(X22088,esk87_3(X22088,X22089,X22090)),esk88_3(X22088,X22089,X22090)))
| hBOOL(hAPP(hAPP(X22088,X22090),X22089))
| ~ 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),X22090),X22089))) ) ),
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,
! [X38,X39,X216,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X216))
=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X39),X216))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),hAPP(hAPP(c_COMBC(X10,X13,X13),hAPP(hAPP(c_COMBS(X10,X13,tc_fun(X13,X13)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X13,tc_fun(X13,X13)),X10),c_If(X13)),hAPP(c_fequal,X39))),X38)),c_Groups_Ozero__class_Ozero(X13))),X216) = hAPP(X38,X39) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X216))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),hAPP(hAPP(c_COMBC(X10,X13,X13),hAPP(hAPP(c_COMBS(X10,X13,tc_fun(X13,X13)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X13,tc_fun(X13,X13)),X10),c_If(X13)),hAPP(c_fequal,X39))),X38)),c_Groups_Ozero__class_Ozero(X13))),X216) = c_Groups_Ozero__class_Ozero(X13) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum__delta_H]) ).
fof(i_0_5288,plain,
! [X38,X39,X216,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X216))
=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X39),X216))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),hAPP(hAPP(c_COMBC(X10,X13,X13),hAPP(hAPP(c_COMBS(X10,X13,tc_fun(X13,X13)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X13,tc_fun(X13,X13)),X10),c_If(X13)),hAPP(c_fequal,X39))),X38)),c_Groups_Oone__class_Oone(X13))),X216) = hAPP(X38,X39) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X216))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),hAPP(hAPP(c_COMBC(X10,X13,X13),hAPP(hAPP(c_COMBS(X10,X13,tc_fun(X13,X13)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X13,tc_fun(X13,X13)),X10),c_If(X13)),hAPP(c_fequal,X39))),X38)),c_Groups_Oone__class_Oone(X13))),X216) = c_Groups_Oone__class_Oone(X13) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setprod__delta_H]) ).
fof(i_0_5289,plain,
! [X22160,X22161,X22162] :
( ( 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),esk92_3(X22160,X22161,X22162)),esk93_3(X22160,X22161,X22162))))
| hBOOL(hAPP(hAPP(X22160,X22162),X22161))
| ~ 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),X22162),X22161))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk92_3(X22160,X22161,X22162)),esk93_3(X22160,X22161,X22162)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk93_3(X22160,X22161,X22162)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(X22160,esk92_3(X22160,X22161,X22162)),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)))),esk93_3(X22160,X22161,X22162))))
| hBOOL(hAPP(hAPP(X22160,X22162),X22161))
| ~ 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),X22162),X22161))) )
& ( ~ hBOOL(hAPP(hAPP(X22160,esk92_3(X22160,X22161,X22162)),esk93_3(X22160,X22161,X22162)))
| hBOOL(hAPP(hAPP(X22160,X22162),X22161))
| ~ 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),X22162),X22161))) ) ),
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,
! [X177,X289,X25,X290,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X290),hAPP(hAPP(c_List_Olist_OCons(X10),X25),X289))),c_List_Olistrel(X10,X177)))
=> ~ ! [X3,X303] :
( X290 = hAPP(hAPP(c_List_Olist_OCons(X10),X3),X303)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X25)),X177))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X303),X289)),c_List_Olistrel(X10,X177))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_listrel__Cons2]) ).
fof(i_0_5291,plain,
! [X196,X20,X73,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X73)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),hAPP(c_Nat_OSuc,X20)),X196)))
=> ~ ! [X90] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X90)),X196))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X90),X73)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X20),X196))) ) ),
inference(fof_simplification,[status(thm)],[fact_rel__pow__Suc__E2]) ).
fof(i_0_5292,plain,
! [X22936,X22937,X22938] : c_Nitpick_Otimes__frac(X22938,X22937,X22936) = hAPP(hAPP(c_Nitpick_Ofrac(X22938),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X22938),X22937)),hAPP(c_Nitpick_Onum(X22938),X22936))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(X22938),X22937)),hAPP(c_Nitpick_Odenom(X22938),X22936))),
inference(variable_rename,[status(thm)],[fact_Nitpick_Otimes__frac__def]) ).
fof(i_0_5293,plain,
! [X196,X20,X73,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X73)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X20),X196)))
=> ( ( X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> X16 != X73 )
=> ~ ! [X90,X122] :
( X20 = hAPP(c_Nat_OSuc,X122)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X90)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X122),X196)))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X90),X73)),X196)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_rel__pow__E]) ).
fof(i_0_5294,plain,
! [X196,X20,X73,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X73)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),hAPP(c_Nat_OSuc,X20)),X196)))
=> ~ ! [X90] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X90)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X20),X196)))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X90),X73)),X196)) ) ),
inference(fof_simplification,[status(thm)],[fact_rel__pow__Suc__E]) ).
fof(i_0_5295,plain,
! [X21943,X21944] :
( ( ~ 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),X21943)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21944))))
| c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21943),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21944)) = 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),X21943)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21944)))
| ~ 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),X21944))) )
& ( 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),X21943)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21944))))
| c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21943),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21944)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21944)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21943),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),X21944))))
| ~ 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),X21944))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5167])])]) ).
fof(i_0_5296,plain,
! [X22043,X22044] :
( ( ~ 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),X22044),X22043)))
| c_Divides_OnegDivAlg(X22044,X22043) = 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),X22044),X22043))
| ~ 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),X22044),X22043))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22043),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_OnegDivAlg(X22044,X22043) = 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),X22044),X22043))
| ~ 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),X22044),X22043))) )
& ( 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),X22044),X22043)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22043),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_OnegDivAlg(X22044,X22043) = hAPP(c_Divides_Oadjust(X22043),c_Divides_OnegDivAlg(X22044,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)))),X22043)))
| ~ 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),X22044),X22043))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negDivAlg_Opsimps])])]) ).
fof(i_0_5297,plain,
! [X21861] :
( ( ~ 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),X21861))))
| c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21861)) = 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),X21861)))
| ~ 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),X21861))) )
& ( 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),X21861))))
| c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21861)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21861)),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),X21861))))
| ~ 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),X21861))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5168])])]) ).
fof(i_0_5298,plain,
! [X22074,X22075] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22075),X22074))
| c_Divides_OposDivAlg(X22075,X22074) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22075)
| ~ 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),X22075),X22074))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22074),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_OposDivAlg(X22075,X22074) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22075)
| ~ 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),X22075),X22074))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22075),X22074))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22074),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_OposDivAlg(X22075,X22074) = hAPP(c_Divides_Oadjust(X22074),c_Divides_OposDivAlg(X22075,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)))),X22074)))
| ~ 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),X22075),X22074))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg_Opsimps])])]) ).
fof(i_0_5299,plain,
! [X21978,X21979] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21978)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21979)))
| c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21978),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21979)) = 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),X21978))
| ~ 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),X21979))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21978)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21979)))
| c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21978),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21979)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21979)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21978),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),X21979))))
| ~ 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),X21979))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5169])])]) ).
fof(i_0_5300,plain,
! [X21428,X21429,X21430] :
( ~ class_Rings_Ocomm__semiring__1(X21430)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21430),X21429),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)))),X21428))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21430),X21429),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21430),hAPP(hAPP(c_Power_Opower__class_Opower(X21430),X21429),X21428)),hAPP(hAPP(c_Power_Opower__class_Opower(X21430),X21429),X21428))) ),
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,
! [X27130,X27131,X27132] : 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),X27132)),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))),X27131))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X27130))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X27130)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X27132),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X27132),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),X27130),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X27131)))),
inference(variable_rename,[status(thm)],[fact_arith__series__int]) ).
fof(i_0_5302,plain,
! [X21924,X21925] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21925)),hAPP(c_Nat_OSuc,X21924)))
| 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(X21925))),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)),X21924)))) )
& ( ~ 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(X21925))),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)),X21924))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21925)),hAPP(c_Nat_OSuc,X21924))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__number__of__Suc])]) ).
fof(i_0_5303,plain,
! [X21920,X21921] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21921)),hAPP(c_Nat_OSuc,X21920)))
| 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(X21921))),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)),X21920)))) )
& ( ~ 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(X21921))),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)),X21920))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21921)),hAPP(c_Nat_OSuc,X21920))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of__Suc])]) ).
fof(i_0_5304,plain,
! [X21954] :
( ( ~ 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),X21954)))
| c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21954)) = 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),X21954))) )
& ( 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),X21954)))
| c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21954)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21954)),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),X21954))))
| ~ 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),X21954))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5170])])]) ).
fof(i_0_5305,plain,
! [X21266,X21267] :
( ~ class_Rings_Osemiring__1(X21267)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21266))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X21267),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)))),X21266))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21267),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X21267),hAPP(c_Int_Onat,X21266))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X21267),hAPP(c_Int_Onat,X21266))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__double])]) ).
fof(i_0_5306,plain,
! [X21945,X21946] :
( ( ~ 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),X21945),X21946)))
| c_Divides_OnegDivAlg(X21945,X21946) = 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),X21945),X21946))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21946)) )
& ( 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),X21945),X21946)))
| c_Divides_OnegDivAlg(X21945,X21946) = hAPP(c_Divides_Oadjust(X21946),c_Divides_OnegDivAlg(X21945,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)))),X21946)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21946)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5171])])]) ).
fof(i_0_5307,plain,
! [X21935,X21936] :
( ( ~ 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),X21936),X21935)))
| c_Divides_OnegDivAlg(X21936,X21935) = 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),X21936),X21935)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21935),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_OnegDivAlg(X21936,X21935) = 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),X21936),X21935)) )
& ( 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),X21936),X21935)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21935),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_OnegDivAlg(X21936,X21935) = hAPP(c_Divides_Oadjust(X21935),c_Divides_OnegDivAlg(X21936,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)))),X21935))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negDivAlg_Osimps])])]) ).
fof(i_0_5308,plain,
! [X21976,X21977] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21976),X21977))
| c_Divides_OposDivAlg(X21976,X21977) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21976)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21977)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21976),X21977))
| c_Divides_OposDivAlg(X21976,X21977) = hAPP(c_Divides_Oadjust(X21977),c_Divides_OposDivAlg(X21976,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)))),X21977)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21977)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5172])])]) ).
fof(i_0_5309,plain,
! [X21955,X21956] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21956),X21955))
| c_Divides_OposDivAlg(X21956,X21955) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21956) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21955),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_OposDivAlg(X21956,X21955) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21956) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21956),X21955))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21955),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_OposDivAlg(X21956,X21955) = hAPP(c_Divides_Oadjust(X21955),c_Divides_OposDivAlg(X21956,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)))),X21955))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg_Osimps])])]) ).
fof(i_0_5310,plain,
! [X21449,X21450] :
( ~ class_Rings_Oring__1(X21450)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21450),hAPP(c_Groups_Ouminus__class_Ouminus(X21450),c_Groups_Oone__class_Oone(X21450))),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)))),X21449))) = hAPP(c_Groups_Ouminus__class_Ouminus(X21450),c_Groups_Oone__class_Oone(X21450)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus1__odd])]) ).
fof(i_0_5311,plain,
! [X21404,X21405,X21406] :
( ~ class_Rings_Oring__1(X21406)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21406),hAPP(c_Groups_Ouminus__class_Ouminus(X21406),X21405)),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)))),X21404)) = hAPP(hAPP(c_Power_Opower__class_Opower(X21406),X21405),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)))),X21404)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus__even])]) ).
fof(i_0_5312,plain,
! [X21453,X21454] :
( ~ class_Int_Onumber__ring(X21454)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21454),hAPP(c_Int_Onumber__class_Onumber__of(X21454),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)))),X21453))) = hAPP(c_Int_Onumber__class_Onumber__of(X21454),c_Int_OMin) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__m1__odd])]) ).
fof(i_0_5313,plain,
! [X21233] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21233))) = 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)))),X21233),
inference(variable_rename,[status(thm)],[fact_Suc3__eq__add__3]) ).
fof(i_0_5314,plain,
! [X154,X177,X13,X38,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X38),hAPP(c_Relation_OImage(X13,X10,X177),X154)))
=> ~ ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X13,X10)),hAPP(hAPP(c_Product__Type_OPair(X13,X10),X3),X38)),X177))
=> ~ hBOOL(hAPP(hAPP(c_member(X13),X3),X154)) ) ),
inference(fof_simplification,[status(thm)],[fact_ImageE]) ).
fof(i_0_5315,plain,
! [X21949,X21950,X21951,X21952,X21953] : c_Nat_Onat_Onat__case(X21953,X21952,X21951,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21950)),X21949)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X21953),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X21950))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X21953,X21953),hAPP(hAPP(c_COMBC(tc_Int_Oint,X21953,tc_fun(X21953,X21953)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X21953,tc_fun(X21953,X21953)),tc_Int_Oint),c_If(X21953)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(X21953,X21952,X21951,X21949))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X21953,tc_Int_Oint),X21951),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)),X21949)))),
inference(variable_rename,[status(thm)],[fact_nat__case__add__eq__if]) ).
fof(i_0_5316,plain,
! [X21438] :
( ( ~ 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,X21438,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,X21438,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,X21438,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,X21438,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,
! [X22189,X22190,X22191,X22192,X22193,X22194] :
( ( hAPP(c_Product__Type_Oapsnd(X22194,X22193,X22192,X22191),X22190) != hAPP(c_Product__Type_Oapsnd(X22194,X22193,X22192,X22189),X22190)
| hAPP(X22191,hAPP(c_Product__Type_Osnd(X22192,X22194),X22190)) = hAPP(X22189,hAPP(c_Product__Type_Osnd(X22192,X22194),X22190)) )
& ( hAPP(X22191,hAPP(c_Product__Type_Osnd(X22192,X22194),X22190)) != hAPP(X22189,hAPP(c_Product__Type_Osnd(X22192,X22194),X22190))
| hAPP(c_Product__Type_Oapsnd(X22194,X22193,X22192,X22191),X22190) = hAPP(c_Product__Type_Oapsnd(X22194,X22193,X22192,X22189),X22190) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_apsnd__eq__conv])]) ).
fof(i_0_5318,plain,
! [X22757,X22758,X22759,X22760,X22761,X22762] :
( ( hAPP(c_Product__Type_Oapfst(X22762,X22761,X22760,X22759),X22758) != hAPP(c_Product__Type_Oapfst(X22762,X22761,X22760,X22757),X22758)
| hAPP(X22759,hAPP(c_Product__Type_Ofst(X22762,X22760),X22758)) = hAPP(X22757,hAPP(c_Product__Type_Ofst(X22762,X22760),X22758)) )
& ( hAPP(X22759,hAPP(c_Product__Type_Ofst(X22762,X22760),X22758)) != hAPP(X22757,hAPP(c_Product__Type_Ofst(X22762,X22760),X22758))
| hAPP(c_Product__Type_Oapfst(X22762,X22761,X22760,X22759),X22758) = hAPP(c_Product__Type_Oapfst(X22762,X22761,X22760,X22757),X22758) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_apfst__eq__conv])]) ).
fof(i_0_5319,plain,
! [X30311] : c_Relation_OId(X30311) = hAPP(c_Set_OCollect(tc_prod(X30311,X30311)),hAPP(hAPP(c_COMBB(tc_fun(X30311,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X30311,X30311)),c_HOL_OEx(X30311)),hAPP(hAPP(c_COMBC(tc_prod(X30311,X30311),tc_fun(X30311,tc_prod(X30311,X30311)),tc_fun(X30311,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X30311,X30311),tc_HOL_Obool),tc_fun(tc_fun(X30311,tc_prod(X30311,X30311)),tc_fun(X30311,tc_HOL_Obool)),tc_prod(X30311,X30311)),c_COMBB(tc_prod(X30311,X30311),tc_HOL_Obool,X30311)),c_fequal)),hAPP(hAPP(c_COMBS(X30311,X30311,tc_prod(X30311,X30311)),c_Product__Type_OPair(X30311,X30311)),c_COMBI(X30311))))),
inference(variable_rename,[status(thm)],[fact_Id__def]) ).
fof(i_0_5320,plain,
! [X22736,X22737,X22738,X22739,X22740,X22741,X22742] : hAPP(c_Product__Type_Oapsnd(X22742,X22741,X22740,X22739),hAPP(c_Product__Type_Oapfst(X22738,X22740,X22742,X22737),X22736)) = hAPP(hAPP(c_Product__Type_OPair(X22740,X22741),hAPP(X22737,hAPP(c_Product__Type_Ofst(X22738,X22742),X22736))),hAPP(X22739,hAPP(c_Product__Type_Osnd(X22738,X22742),X22736))),
inference(variable_rename,[status(thm)],[fact_apsnd__apfst]) ).
fof(i_0_5321,plain,
! [X22729,X22730,X22731,X22732,X22733,X22734,X22735] : hAPP(c_Product__Type_Oapfst(X22735,X22734,X22733,X22732),hAPP(c_Product__Type_Oapsnd(X22731,X22733,X22735,X22730),X22729)) = hAPP(hAPP(c_Product__Type_OPair(X22734,X22733),hAPP(X22732,hAPP(c_Product__Type_Ofst(X22735,X22731),X22729))),hAPP(X22730,hAPP(c_Product__Type_Osnd(X22735,X22731),X22729))),
inference(variable_rename,[status(thm)],[fact_apfst__apsnd]) ).
fof(i_0_5322,plain,
! [X2,X10] :
( class_Orderings_Oorder(X10)
=> ( ! [X3,X90] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X90))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X90),X3)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(X2,X3)),hAPP(X2,X90))) )
=> c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X10,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,
! [X21459,X21460] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21460),c_Groups_Ozero__class_Ozero(X21460)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21460),X21459),hAPP(c_Int_Onumber__class_Onumber__of(X21460),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21460),c_Groups_Ozero__class_Ozero(X21460)),X21459))
| ~ class_Fields_Olinordered__field__inverse__zero(X21460)
| ~ class_Int_Onumber__ring(X21460) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21460),c_Groups_Ozero__class_Ozero(X21460)),X21459))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21460),c_Groups_Ozero__class_Ozero(X21460)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21460),X21459),hAPP(c_Int_Onumber__class_Onumber__of(X21460),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21460)
| ~ class_Int_Onumber__ring(X21460) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_half__gt__zero__iff])])]) ).
fof(i_0_5324,plain,
! [X22572,X22573] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X22573)),hAPP(c_Nat_OSuc,X22572)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X22573))),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,X22572))),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)),X22572)))),
inference(variable_rename,[status(thm)],[fact_max__Suc__number__of]) ).
fof(i_0_5325,plain,
! [X21389,X21390] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21390),c_Groups_Ozero__class_Ozero(X21390)),hAPP(hAPP(c_Power_Opower__class_Opower(X21390),X21389),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| X21389 != c_Groups_Ozero__class_Ozero(X21390)
| ~ class_Rings_Olinordered__idom(X21390) )
& ( X21389 = c_Groups_Ozero__class_Ozero(X21390)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21390),c_Groups_Ozero__class_Ozero(X21390)),hAPP(hAPP(c_Power_Opower__class_Opower(X21390),X21389),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(X21390) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power2])])]) ).
fof(i_0_5326,plain,
! [X22424,X22425] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X22425)),hAPP(c_Nat_OSuc,X22424)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X22425))),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)),X22424)))),
inference(variable_rename,[status(thm)],[fact_min__Suc__number__of]) ).
fof(i_0_5327,plain,
! [X22033,X22034,X22035,X22036] : hAPP(c_Nat_Onat_Onat__rec(X22036,X22035,X22034),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X22033)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X22036),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X22033))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X22036,X22036),hAPP(hAPP(c_COMBC(tc_Int_Oint,X22036,tc_fun(X22036,X22036)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X22036,tc_fun(X22036,X22036)),tc_Int_Oint),c_If(X22036)),c_Nat__Numeral_Oneg)),X22035)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X22036,X22036),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X22036,X22036),tc_Int_Oint),X22034),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X22036,tc_Int_Oint),c_Nat_Onat_Onat__rec(X22036,X22035,X22034)),c_Int_Onat)))),
inference(variable_rename,[status(thm)],[fact_nat__rec__number__of]) ).
fof(i_0_5328,plain,
! [X34206,X34207] : c_List_Oconcat(X34207,hAPP(hAPP(c_List_Omap(tc_List_Olist(X34207),tc_List_Olist(X34207)),c_List_Olist_Olist__case(tc_List_Olist(X34207),X34207,c_List_Olist_ONil(X34207),hAPP(hAPP(c_COMBB(tc_List_Olist(X34207),tc_fun(tc_List_Olist(X34207),tc_List_Olist(X34207)),X34207),c_COMBK(tc_List_Olist(X34207),tc_List_Olist(X34207))),hAPP(hAPP(c_COMBC(X34207,tc_List_Olist(X34207),tc_List_Olist(X34207)),c_List_Olist_OCons(X34207)),c_List_Olist_ONil(X34207))))),X34206)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X34207),X34207),c_List_Ohd(X34207)),hAPP(c_List_Ofilter(tc_List_Olist(X34207),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X34207)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X34207),tc_List_Olist(X34207),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X34207)))),X34206)),
inference(variable_rename,[status(thm)],[fact_transpose__aux__filter__head]) ).
fof(i_0_5329,plain,
! [X34361,X34362] : c_List_Oconcat(tc_List_Olist(X34362),hAPP(hAPP(c_List_Omap(tc_List_Olist(X34362),tc_List_Olist(tc_List_Olist(X34362))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X34362)),X34362,c_List_Olist_ONil(tc_List_Olist(X34362)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X34362),tc_List_Olist(tc_List_Olist(X34362))),X34362),hAPP(hAPP(c_COMBC(tc_List_Olist(X34362),tc_List_Olist(tc_List_Olist(X34362)),tc_List_Olist(tc_List_Olist(X34362))),c_List_Olist_OCons(tc_List_Olist(X34362))),c_List_Olist_ONil(tc_List_Olist(X34362)))))),X34361)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X34362),tc_List_Olist(X34362)),c_List_Otl(X34362)),hAPP(c_List_Ofilter(tc_List_Olist(X34362),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X34362)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X34362),tc_List_Olist(X34362),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X34362)))),X34361)),
inference(variable_rename,[status(thm)],[fact_transpose__aux__filter__tail]) ).
fof(i_0_5330,plain,
! [X30239,X30240,X30241] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30241,X30241),tc_HOL_Obool)),c_Relation_OId(X30241)),X30240))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30241,X30241),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X30241,X30241,X30241),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X30241,X30241),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X30241,X30239)),X30240)),X30239)),X30240))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30241,X30241),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X30241,X30239)),X30240)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__Int__subset])]) ).
fof(i_0_5331,plain,
! [X177,X290,X289,X25,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X25),X289)),X290)),c_List_Olistrel(X10,X177)))
=> ~ ! [X90,X304] :
( X290 = hAPP(hAPP(c_List_Olist_OCons(X10),X90),X304)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X25),X90)),X177))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X289),X304)),c_List_Olistrel(X10,X177))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_listrel__Cons1]) ).
fof(i_0_5332,plain,
! [X21369,X21370,X21371] :
( ~ class_Groups_Omonoid__mult(X21371)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21371),X21370),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)))),X21369)) = hAPP(hAPP(c_Power_Opower__class_Opower(X21371),hAPP(hAPP(c_Power_Opower__class_Opower(X21371),X21370),X21369)),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,
! [X34010,X34011,X34012] : c_List_Osublist(X34012,X34011,X34010) = hAPP(hAPP(c_List_Omap(tc_prod(X34012,tc_Nat_Onat),X34012),c_Product__Type_Ofst(X34012,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X34012,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X34012,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(X34012,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X34012,tc_Nat_Onat))),X34010)),hAPP(hAPP(c_List_Ozip(X34012,tc_Nat_Onat),X34011),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34012)),X34011))))),
inference(variable_rename,[status(thm)],[fact_sublist__def]) ).
fof(i_0_5334,plain,
! [X50,X52,X51,X2,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X10,X2,hAPP(hAPP(c_Set_Oinsert(X10),X51),X52)),X50))
<=> ? [X116,X246] :
( hAPP(hAPP(c_Set_Oinsert(X10),X51),X52) = hAPP(hAPP(c_Set_Oinsert(X10),X116),X246)
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X10,X2,X116,X246),X50))
& ~ hBOOL(hAPP(hAPP(c_member(X10),X116),X246)) ) ),
inference(fof_simplification,[status(thm)],[fact_fold1Set_Oequations]) ).
fof(i_0_5335,plain,
! [X22944,X22945] : c_Nitpick_Ouminus__frac(X22945,X22944) = c_Nitpick_OAbs__Frac(X22945,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(X22945),X22944))),hAPP(c_Nitpick_Odenom(X22945),X22944))),
inference(variable_rename,[status(thm)],[fact_Nitpick_Ouminus__frac__def]) ).
fof(i_0_5336,plain,
! [X22195,X22196,X22197,X22198,X22199] : hAPP(c_Product__Type_Osnd(X22199,X22198),hAPP(c_Product__Type_Oapsnd(X22197,X22198,X22199,X22196),X22195)) = hAPP(X22196,hAPP(c_Product__Type_Osnd(X22199,X22197),X22195)),
inference(variable_rename,[status(thm)],[fact_snd__apsnd]) ).
fof(i_0_5337,plain,
! [X22763,X22764,X22765,X22766,X22767] : hAPP(c_Product__Type_Ofst(X22767,X22766),hAPP(c_Product__Type_Oapfst(X22765,X22767,X22766,X22764),X22763)) = hAPP(X22764,hAPP(c_Product__Type_Ofst(X22765,X22766),X22763)),
inference(variable_rename,[status(thm)],[fact_fst__apfst]) ).
fof(i_0_5338,plain,
! [X22309,X22310,X22311,X22312,X22313] : hAPP(c_Product__Type_Ofst(X22313,X22312),hAPP(c_Product__Type_Oapsnd(X22311,X22312,X22313,X22310),X22309)) = hAPP(c_Product__Type_Ofst(X22313,X22311),X22309),
inference(variable_rename,[status(thm)],[fact_fst__apsnd]) ).
fof(i_0_5339,plain,
! [X22768,X22769,X22770,X22771,X22772] : hAPP(c_Product__Type_Osnd(X22772,X22771),hAPP(c_Product__Type_Oapfst(X22770,X22772,X22771,X22769),X22768)) = hAPP(c_Product__Type_Osnd(X22770,X22771),X22768),
inference(variable_rename,[status(thm)],[fact_snd__apfst]) ).
fof(i_0_5340,plain,
! [X19,X52,X51,X192] :
( 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)),X192),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X51),X52))))
=> ( ! [X247,X164,X152] :
( 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)),X247),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X164),X152))))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X164),X152))
=> ( hAPP(X247,X152) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
=> hBOOL(hAPP(hAPP(hAPP(X19,X247),X164),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X152),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) )
=> hBOOL(hAPP(hAPP(hAPP(X19,X247),X164),X152)) ) )
=> hBOOL(hAPP(hAPP(hAPP(X19,X192),X51),X52)) ) ),
inference(fof_simplification,[status(thm)],[fact_small_H_Opinduct]) ).
fof(i_0_5341,plain,
! [X21972,X21973,X21974,X21975] : c_Nat_Onat_Onat__case(X21975,X21974,X21973,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21972)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X21975),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X21972))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X21975,X21975),hAPP(hAPP(c_COMBC(tc_Int_Oint,X21975,tc_fun(X21975,X21975)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X21975,tc_fun(X21975,X21975)),tc_Int_Oint),c_If(X21975)),c_Nat__Numeral_Oneg)),X21974)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X21975,tc_Int_Oint),X21973),c_Int_Onat))),
inference(variable_rename,[status(thm)],[fact_nat__case__number__of]) ).
fof(i_0_5342,plain,
! [X22725,X22726] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X22726)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X22725)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X22725))),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,X22726))),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),X22726)),c_Int_Onat)))),
inference(variable_rename,[status(thm)],[fact_max__number__of__Suc]) ).
fof(i_0_5343,plain,
! [X22426,X22427] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X22427)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X22426)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X22426))),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),X22427)),c_Int_Onat)))),
inference(variable_rename,[status(thm)],[fact_min__number__of__Suc]) ).
fof(i_0_5344,plain,
! [X21455] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21455))
| 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),X21455),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,
! [X21457,X21458] :
( ~ class_Fields_Olinordered__field__inverse__zero(X21458)
| ~ class_Int_Onumber__ring(X21458)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21458),c_Groups_Ozero__class_Ozero(X21458)),X21457))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21458),c_Groups_Ozero__class_Ozero(X21458)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21458),X21457),hAPP(c_Int_Onumber__class_Onumber__of(X21458),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,
! [X21401,X21402,X21403] :
( ~ class_Rings_Ocomm__semiring__1(X21403)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21403),X21402),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)))),X21401)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21403),hAPP(hAPP(c_Power_Opower__class_Opower(X21403),X21402),X21401)),hAPP(hAPP(c_Power_Opower__class_Opower(X21403),X21402),X21401)) ),
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,
! [X21439] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X21439))
| 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),X21439),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,
! [X21231,X21232] :
( ~ class_Groups_Omonoid__mult(X21232)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21232),X21231),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(X21232),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21232),X21231),X21231)),X21231) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power3__eq__cube])]) ).
fof(i_0_5349,plain,
! [X21381,X21382] :
( ~ class_Rings_Olinordered__idom(X21382)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21382),c_Groups_Ozero__class_Ozero(X21382)),hAPP(hAPP(c_Power_Opower__class_Opower(X21382),X21381),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,
! [X21434,X21435] :
( ~ class_Rings_Oring__1(X21435)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21435),hAPP(c_Groups_Ouminus__class_Ouminus(X21435),c_Groups_Oone__class_Oone(X21435))),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)))),X21434)) = c_Groups_Oone__class_Oone(X21435) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus1__even])]) ).
fof(i_0_5351,plain,
! [X21451,X21452] :
( ~ class_Int_Onumber__ring(X21452)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21452),hAPP(c_Int_Onumber__class_Onumber__of(X21452),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)))),X21451)) = c_Groups_Oone__class_Oone(X21452) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__m1__even])]) ).
fof(i_0_5352,plain,
! [X168,X174] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X174),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X174)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X174),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X174)) = 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),X168),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X174)))),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,
! [X73,X146] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X146))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X73)),hAPP(c_Int_Onat,X146)) = hAPP(c_Int_Onat,X73) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X146))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X73)),hAPP(c_Int_Onat,X146)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X73),X146)),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,
! [X39,X16,X154,X38,X10] :
( class_Groups_Oab__semigroup__mult(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X10,c_Groups_Otimes__class_Otimes(X10),X38,X154),X16))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X38),X154))
=> hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X10,c_Groups_Otimes__class_Otimes(X10),X39,hAPP(hAPP(c_Set_Oinsert(X10),X38),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))),X16)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_fold__graph__permute__diff]) ).
fof(i_0_5355,plain,
! [X34341,X34342,X34343,X34344] : c_List_Oconcat(X34344,hAPP(hAPP(c_List_Omap(X34343,tc_List_Olist(X34344)),hAPP(hAPP(c_COMBC(X34343,tc_List_Olist(X34344),tc_List_Olist(X34344)),hAPP(hAPP(c_COMBB(X34344,tc_fun(tc_List_Olist(X34344),tc_List_Olist(X34344)),X34343),c_List_Olist_OCons(X34344)),X34342)),c_List_Olist_ONil(X34344))),X34341)) = hAPP(hAPP(c_List_Omap(X34343,X34344),X34342),X34341),
inference(variable_rename,[status(thm)],[fact_concat__map__singleton]) ).
fof(i_0_5356,plain,
! [X22956,X22957,X22958] :
( ( ~ c_Nitpick_Oless__eq__frac(X22958,X22957,X22956)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X22958),c_Nitpick_Oplus__frac(X22958,X22957,c_Nitpick_Ouminus__frac(X22958,X22956)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X22958),c_Nitpick_Oplus__frac(X22958,X22957,c_Nitpick_Ouminus__frac(X22958,X22956)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Nitpick_Oless__eq__frac(X22958,X22957,X22956) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Oless__eq__frac__def])]) ).
fof(i_0_5357,plain,
! [X22953,X22954,X22955] :
( ( ~ c_Nitpick_Oless__frac(X22955,X22954,X22953)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X22955),c_Nitpick_Oplus__frac(X22955,X22954,c_Nitpick_Ouminus__frac(X22955,X22953)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X22955),c_Nitpick_Oplus__frac(X22955,X22954,c_Nitpick_Ouminus__frac(X22955,X22953)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Nitpick_Oless__frac(X22955,X22954,X22953) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Oless__frac__def])]) ).
fof(i_0_5358,plain,
! [X21386,X21387,X21388] :
( ~ class_Rings_Olinordered__semidom(X21388)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21388),X21387),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(X21388),X21386),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(X21388),c_Groups_Ozero__class_Ozero(X21388)),X21387))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21388),c_Groups_Ozero__class_Ozero(X21388)),X21386))
| X21387 = X21386 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__imp__eq])]) ).
fof(i_0_5359,plain,
! [X21398] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21398),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| X21398 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X21398 = 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,
! [X21377] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21377))),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),X21377),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,
! [X21372,X21373] :
( ~ class_Rings_Olinordered__idom(X21373)
| hAPP(c_Groups_Oabs__class_Oabs(X21373),hAPP(hAPP(c_Power_Opower__class_Opower(X21373),X21372),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(X21373),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_abs__power2])]) ).
fof(i_0_5362,plain,
! [X22939,X22940,X22941] :
( ~ class_Rings_Oinverse(X22941)
| ~ class_Rings_Oring__1(X22941)
| c_Nitpick_Oof__frac(X22940,X22941,X22939) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22941),hAPP(c_Int_Oring__1__class_Oof__int(X22941),hAPP(c_Nitpick_Onum(X22940),X22939))),hAPP(c_Int_Oring__1__class_Oof__int(X22941),hAPP(c_Nitpick_Odenom(X22940),X22939))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Oof__frac__def])]) ).
fof(i_0_5363,plain,
! [X177,X276,X13,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),X276),hAPP(c_Relation_Oconverse(X13,X10),X177)))
=> ~ ! [X3,X90] :
( X276 = hAPP(hAPP(c_Product__Type_OPair(X10,X13),X90),X3)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X13,X10)),hAPP(hAPP(c_Product__Type_OPair(X13,X10),X3),X90)),X177)) ) ),
inference(fof_simplification,[status(thm)],[fact_converseE]) ).
fof(i_0_5364,plain,
! [X2,X20,X102,X10] :
( class_Groups_Oab__group__add(X10)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X10)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,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,X102,X20)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),hAPP(X2,X102)),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X10)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,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,X102,X20)) = c_Groups_Ozero__class_Ozero(X10) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum__natinterval__difff]) ).
fof(i_0_5365,plain,
! [X25,X2,X290,X289,X13,X16,X10] :
( ( hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Otake(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13)),X289)),X290))))
=> c_Map_Omap__upds(X10,X13,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),X2),X16),hAPP(c_Option_Ooption_OSome(X13),X25)),X290,X289) = c_Map_Omap__upds(X10,X13,X2,X290,X289) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Otake(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13)),X289)),X290))))
=> c_Map_Omap__upds(X10,X13,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),X2),X16),hAPP(c_Option_Ooption_OSome(X13),X25)),X290,X289) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),c_Map_Omap__upds(X10,X13,X2,X290,X289)),X16),hAPP(c_Option_Ooption_OSome(X13),X25)) ) ),
inference(fof_simplification,[status(thm)],[fact_map__upd__upds__conv__if]) ).
fof(i_0_5366,plain,
! [X73,X25,X154,X38,X10] :
( class_Groups_Oab__semigroup__mult(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X10,c_Groups_Otimes__class_Otimes(X10),X38,X154),X25))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X38),X154))
=> hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X10,c_Groups_Otimes__class_Otimes(X10),X73,hAPP(hAPP(c_Set_Oinsert(X10),X38),X154)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X73),X25))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_fold__graph__insert__swap]) ).
fof(i_0_5367,plain,
! [X25,X73,X2,X13,X154,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X13,X2,X73,X154),X25))
=> hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X13,X2,X73,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)),hAPP(hAPP(X2,X16),X25))) ) ),
inference(fof_simplification,[status(thm)],[fact_fold__graph_OinsertI]) ).
fof(i_0_5368,plain,
! [X31799,X31800,X31801,X31802,X31803,X31804,X31806,X31807,X31808,X31809,X31810,X31811,X31812] :
( ( hAPP(X31800,X31799) = hAPP(c_Option_Ooption_OSome(X31804),esk436_6(X31799,X31800,X31801,X31802,X31803,X31804))
| hAPP(X31800,X31799) = c_Option_Ooption_ONone(X31804)
| c_Map_Omap__comp(X31804,X31803,X31802,X31801,X31800,X31799) != c_Option_Ooption_ONone(X31803) )
& ( hAPP(X31801,esk436_6(X31799,X31800,X31801,X31802,X31803,X31804)) = c_Option_Ooption_ONone(X31803)
| hAPP(X31800,X31799) = c_Option_Ooption_ONone(X31804)
| c_Map_Omap__comp(X31804,X31803,X31802,X31801,X31800,X31799) != c_Option_Ooption_ONone(X31803) )
& ( hAPP(X31807,X31806) != c_Option_Ooption_ONone(X31811)
| c_Map_Omap__comp(X31811,X31810,X31809,X31808,X31807,X31806) = c_Option_Ooption_ONone(X31810) )
& ( hAPP(X31807,X31806) != hAPP(c_Option_Ooption_OSome(X31811),X31812)
| hAPP(X31808,X31812) != c_Option_Ooption_ONone(X31810)
| c_Map_Omap__comp(X31811,X31810,X31809,X31808,X31807,X31806) = c_Option_Ooption_ONone(X31810) ) ),
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,
! [X30626,X30627,X30628,X30629] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30629,X30629)),hAPP(hAPP(c_Product__Type_OPair(X30629,X30629),X30628),esk387_4(X30626,X30627,X30628,X30629))),X30626))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30629,X30629)),hAPP(hAPP(c_Product__Type_OPair(X30629,X30629),X30628),X30627)),c_Transitive__Closure_Otrancl(X30629,X30626))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30629,X30629)),hAPP(hAPP(c_Product__Type_OPair(X30629,X30629),esk387_4(X30626,X30627,X30628,X30629)),X30627)),c_Transitive__Closure_Ortrancl(X30629,X30626)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30629,X30629)),hAPP(hAPP(c_Product__Type_OPair(X30629,X30629),X30628),X30627)),c_Transitive__Closure_Otrancl(X30629,X30626))) ) ),
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,
! [X30631,X30632,X30633,X30634] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30634,X30634)),hAPP(hAPP(c_Product__Type_OPair(X30634,X30634),X30633),esk388_4(X30631,X30632,X30633,X30634))),c_Transitive__Closure_Ortrancl(X30634,X30631)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30634,X30634)),hAPP(hAPP(c_Product__Type_OPair(X30634,X30634),X30633),X30632)),c_Transitive__Closure_Otrancl(X30634,X30631))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30634,X30634)),hAPP(hAPP(c_Product__Type_OPair(X30634,X30634),esk388_4(X30631,X30632,X30633,X30634)),X30632)),X30631))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30634,X30634)),hAPP(hAPP(c_Product__Type_OPair(X30634,X30634),X30633),X30632)),c_Transitive__Closure_Otrancl(X30634,X30631))) ) ),
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,
! [X22751,X22752,X22753,X22754,X22755,X22756] : hAPP(c_Product__Type_Oapfst(X22756,X22755,X22754,X22753),hAPP(hAPP(c_Product__Type_OPair(X22756,X22754),X22752),X22751)) = hAPP(hAPP(c_Product__Type_OPair(X22755,X22754),hAPP(X22753,X22752)),X22751),
inference(variable_rename,[status(thm)],[fact_apfst__conv]) ).
fof(i_0_5372,plain,
! [X22140,X22141,X22142,X22143,X22144,X22145] : hAPP(c_Product__Type_Oapsnd(X22145,X22144,X22143,X22142),hAPP(hAPP(c_Product__Type_OPair(X22143,X22145),X22141),X22140)) = hAPP(hAPP(c_Product__Type_OPair(X22143,X22144),X22141),hAPP(X22142,X22140)),
inference(variable_rename,[status(thm)],[fact_apsnd__conv]) ).
fof(i_0_5373,plain,
! [X53,X160,X197,X141] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X141),X197))
=> ! [X3] :
( ! [X227] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X227),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X197)))
=> ! [X249] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X249),X160))
=> X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X249),X227) ) )
=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X141),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X53)))
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X141),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X197)),X53))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_bset_I10_J]) ).
fof(i_0_5374,plain,
! [X53,X154,X197,X141] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X141),X197))
=> ! [X3] :
( ! [X227] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X227),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X197)))
=> ! [X249] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X249),X154))
=> X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X249),X227) ) )
=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X141),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X53)))
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X141),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X197)),X53))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_aset_I10_J]) ).
fof(i_0_5375,plain,
! [X313,X38,X102,X13,X312,X39,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),hAPP(c_List_Oset(X10),X312)))
=> c_Map_Omap__upds(X10,X13,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),X102),X39),hAPP(c_Option_Ooption_OSome(X13),X38)),X312,X313) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),c_Map_Omap__upds(X10,X13,X102,X312,X313)),X39),hAPP(c_Option_Ooption_OSome(X13),X38)) ),
inference(fof_simplification,[status(thm)],[fact_map__upds__twist]) ).
fof(i_0_5376,plain,
! [X53,X54,X18,X39,X78] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(X78,X39,X18)),X54),X53))
=> ~ ! [X67] :
( X53 = hAPP(hAPP(hAPP(c_Natural_Oupdate,X67),c_Com_Ovname_OLoc(X78)),hAPP(hAPP(c_Natural_Ogetlocs,X54),X78))
=> ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X18),hAPP(hAPP(hAPP(c_Natural_Oupdate,X54),c_Com_Ovname_OLoc(X78)),hAPP(X39,X54))),X67)) ) ),
inference(fof_simplification,[status(thm)],[fact_evalc__elim__cases_I3_J]) ).
fof(i_0_5377,plain,
! [X33958,X33959] : c_List_Ofoldr(tc_List_Olist(X33959),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X33959)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X33959))),c_List_Otranspose(X33959,X33958),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X33959))),hAPP(c_List_Ofilter(tc_List_Olist(X33959),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X33959)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X33959),tc_List_Olist(X33959),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X33959)))),X33958)),
inference(variable_rename,[status(thm)],[fact_transpose__max__length]) ).
fof(i_0_5378,plain,
! [X21378,X21379] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21379)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21378))) = 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),X21379),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21378))),
inference(variable_rename,[status(thm)],[fact_zmod__number__of__Bit0]) ).
fof(i_0_5379,plain,
! [X21374,X21375] :
( ~ class_Rings_Olinordered__idom(X21375)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21375),hAPP(c_Groups_Oabs__class_Oabs(X21375),X21374)),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(X21375),X21374),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,
! [X21365,X21366] :
( ~ class_Rings_Oring__1(X21366)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21366),hAPP(c_Groups_Ouminus__class_Ouminus(X21366),X21365)),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(X21366),X21365),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,
! [X21376] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21376)),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,X21376,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,
! [X19,X154,X225,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X225))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X225),X154))
=> ( hBOOL(hAPP(X19,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))
=> ( ! [X116,X251] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X251))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X116),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X116),X251))
=> ( hBOOL(hAPP(X19,X251))
=> hBOOL(hAPP(X19,hAPP(hAPP(c_Set_Oinsert(X10),X116),X251))) ) ) ) )
=> hBOOL(hAPP(X19,X225)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_finite__subset__induct]) ).
fof(i_0_5383,plain,
! [X21350,X21351] :
( ~ class_Int_Onumber__ring(X21351)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21351),hAPP(c_Int_Onumber__class_Onumber__of(X21351),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21350) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21351),X21350),X21350) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2])]) ).
fof(i_0_5384,plain,
! [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)))),X21367) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21367),X21367),
inference(variable_rename,[status(thm)],[fact_nat__mult__2]) ).
fof(i_0_5385,plain,
! [X21363] : 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)))),X21363) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21363)),
inference(variable_rename,[status(thm)],[fact_add__2__eq__Suc]) ).
fof(i_0_5386,plain,
! [X16,X154,X225,X1,X73,X2,X13,X10] :
( c_Finite__Set_Ofolding__image__simple(X10,X13,X2,X73,X1,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X13),X16),X154))
=> hAPP(X225,hAPP(hAPP(c_Set_Oinsert(X13),X16),X154)) = hAPP(hAPP(X2,hAPP(X1,X16)),hAPP(X225,X154)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_folding__image__simple_Oinsert]) ).
fof(i_0_5387,plain,
! [X177,X13,X38,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X38),hAPP(c_Relation_ORange(X13,X10),X177)))
=> ~ ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X13,X10)),hAPP(hAPP(c_Product__Type_OPair(X13,X10),X3),X38)),X177)) ),
inference(fof_simplification,[status(thm)],[fact_RangeE]) ).
fof(i_0_5388,plain,
! [X30137,X30138,X30139,X30140,X30141] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30141,X30141)),hAPP(hAPP(c_Product__Type_OPair(X30141,X30141),X30140),X30139)),c_Transitive__Closure_Otrancl(X30141,X30138)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30141,X30141)),hAPP(hAPP(c_Product__Type_OPair(X30141,X30141),X30139),X30137)),c_Transitive__Closure_Otrancl(X30141,X30138)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30141,X30141)),hAPP(hAPP(c_Product__Type_OPair(X30141,X30141),X30140),X30137)),c_Transitive__Closure_Otrancl(X30141,X30138))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__trans])]) ).
fof(i_0_5389,plain,
! [X30413,X30414,X30415,X30416] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30416,X30416)),hAPP(hAPP(c_Product__Type_OPair(X30416,X30416),X30415),X30414)),hAPP(c_Relation_Oconverse(X30416,X30416),c_Transitive__Closure_Otrancl(X30416,X30413))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30416,X30416)),hAPP(hAPP(c_Product__Type_OPair(X30416,X30416),X30415),X30414)),c_Transitive__Closure_Otrancl(X30416,hAPP(c_Relation_Oconverse(X30416,X30416),X30413)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__converseI])]) ).
fof(i_0_5390,plain,
! [X30409,X30410,X30411,X30412] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30412,X30412)),hAPP(hAPP(c_Product__Type_OPair(X30412,X30412),X30411),X30410)),c_Transitive__Closure_Otrancl(X30412,hAPP(c_Relation_Oconverse(X30412,X30412),X30409))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30412,X30412)),hAPP(hAPP(c_Product__Type_OPair(X30412,X30412),X30411),X30410)),hAPP(c_Relation_Oconverse(X30412,X30412),c_Transitive__Closure_Otrancl(X30412,X30409)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__converseD])]) ).
fof(i_0_5391,plain,
! [X25,X102,X13,X197,X16,X10] :
( ( hBOOL(hAPP(hAPP(c_member(X10),X16),X197))
=> c_Map_Orestrict__map(X10,X13,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),X102),X16),X25),X197) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),c_Map_Orestrict__map(X10,X13,X102,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X197),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))),X16),X25) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X197))
=> c_Map_Orestrict__map(X10,X13,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),X102),X16),X25),X197) = c_Map_Orestrict__map(X10,X13,X102,X197) ) ),
inference(fof_simplification,[status(thm)],[fact_restrict__fun__upd]) ).
fof(i_0_5392,plain,
! [X16,X154,X39,X2,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X10,X2,X39,X154),X16))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hBOOL(hAPP(c_Finite__Set_Ofold1Set(X10,X2,hAPP(hAPP(c_Set_Oinsert(X10),X39),X154)),X16)) ) ),
inference(fof_simplification,[status(thm)],[fact_fold1Set_Ointros]) ).
fof(i_0_5393,plain,
! [X21399,X21400] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X21400),X21399),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(X21400)
| X21399 = c_Groups_Oone__class_Oone(X21400)
| X21399 = hAPP(c_Groups_Ouminus__class_Ouminus(X21400),c_Groups_Oone__class_Oone(X21400))
| ~ class_Rings_Oring__1__no__zero__divisors(X21400) )
& ( X21399 != c_Groups_Oone__class_Oone(X21400)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21400),X21399),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X21400)
| ~ class_Rings_Oring__1__no__zero__divisors(X21400) )
& ( X21399 != hAPP(c_Groups_Ouminus__class_Ouminus(X21400),c_Groups_Oone__class_Oone(X21400))
| hAPP(hAPP(c_Power_Opower__class_Opower(X21400),X21399),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X21400)
| ~ class_Rings_Oring__1__no__zero__divisors(X21400) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__1__iff])])]) ).
fof(i_0_5394,plain,
! [X21356,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)))) != c_Groups_Ozero__class_Ozero(X21357)
| X21356 = c_Groups_Ozero__class_Ozero(X21357)
| ~ class_Rings_Oring__1__no__zero__divisors(X21357) )
& ( X21356 != c_Groups_Ozero__class_Ozero(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)))) = c_Groups_Ozero__class_Ozero(X21357)
| ~ class_Rings_Oring__1__no__zero__divisors(X21357) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__eq__power2])])]) ).
fof(i_0_5395,plain,
! [X73,X25,X16,X299,X290,X13,X289,X10] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X289) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13)),X290)
=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X299) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13)),X290)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X13),X16),hAPP(c_List_Oset(X13),X290)))
=> ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X13,tc_Option_Ooption(X10)),c_Map_Omap__of(X13,X10,hAPP(hAPP(c_List_Ozip(X13,X10),X290),X289))),X16),hAPP(c_Option_Ooption_OSome(X10),X25)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X13,tc_Option_Ooption(X10)),c_Map_Omap__of(X13,X10,hAPP(hAPP(c_List_Ozip(X13,X10),X290),X299))),X16),hAPP(c_Option_Ooption_OSome(X10),X73))
=> c_Map_Omap__of(X13,X10,hAPP(hAPP(c_List_Ozip(X13,X10),X290),X289)) = c_Map_Omap__of(X13,X10,hAPP(hAPP(c_List_Ozip(X13,X10),X290),X299)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_map__of__zip__upd]) ).
fof(i_0_5396,plain,
! [X34319,X34320,X34321] : hAPP(c_List_Orotate(X34321,X34320),hAPP(c_List_Orev(X34321),X34319)) = hAPP(c_List_Orev(X34321),hAPP(c_List_Orotate(X34321,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34321)),X34319)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X34320,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34321)),X34319)))),X34319)),
inference(variable_rename,[status(thm)],[fact_rotate__rev]) ).
fof(i_0_5397,plain,
! [X33516,X33517] : c_List_Orotate(X33517,X33516) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X33517),tc_List_Olist(X33517)),X33516),c_List_Orotate1(X33517)),
inference(variable_rename,[status(thm)],[fact_rotate__def]) ).
fof(i_0_5398,plain,
! [X30281,X30282,X30283,X30284,X30285] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30285,X30285)),hAPP(hAPP(c_Product__Type_OPair(X30285,X30285),X30284),X30283)),c_Transitive__Closure_Ortrancl(X30285,X30282)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30285,X30285)),hAPP(hAPP(c_Product__Type_OPair(X30285,X30285),X30283),X30281)),c_Transitive__Closure_Otrancl(X30285,X30282)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30285,X30285)),hAPP(hAPP(c_Product__Type_OPair(X30285,X30285),X30284),X30281)),c_Transitive__Closure_Otrancl(X30285,X30282))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__trancl__trancl])]) ).
fof(i_0_5399,plain,
! [X30276,X30277,X30278,X30279,X30280] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30280,X30280)),hAPP(hAPP(c_Product__Type_OPair(X30280,X30280),X30279),X30278)),c_Transitive__Closure_Otrancl(X30280,X30277)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30280,X30280)),hAPP(hAPP(c_Product__Type_OPair(X30280,X30280),X30278),X30276)),c_Transitive__Closure_Ortrancl(X30280,X30277)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30280,X30280)),hAPP(hAPP(c_Product__Type_OPair(X30280,X30280),X30279),X30276)),c_Transitive__Closure_Otrancl(X30280,X30277))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__rtrancl__trancl])]) ).
fof(i_0_5400,plain,
! [X30127,X30128,X30129,X30130,X30131] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30131,X30131)),hAPP(hAPP(c_Product__Type_OPair(X30131,X30131),X30130),X30129)),X30128))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30131,X30131)),hAPP(hAPP(c_Product__Type_OPair(X30131,X30131),X30129),X30127)),c_Transitive__Closure_Otrancl(X30131,X30128)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30131,X30131)),hAPP(hAPP(c_Product__Type_OPair(X30131,X30131),X30130),X30127)),c_Transitive__Closure_Otrancl(X30131,X30128))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__into__trancl2])]) ).
fof(i_0_5401,plain,
! [X30132,X30133,X30134,X30135,X30136] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30136,X30136)),hAPP(hAPP(c_Product__Type_OPair(X30136,X30136),X30135),X30134)),c_Transitive__Closure_Otrancl(X30136,X30133)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30136,X30136)),hAPP(hAPP(c_Product__Type_OPair(X30136,X30136),X30134),X30132)),X30133))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30136,X30136)),hAPP(hAPP(c_Product__Type_OPair(X30136,X30136),X30135),X30132)),c_Transitive__Closure_Otrancl(X30136,X30133))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Transitive__Closure_Otrancl__into__trancl])]) ).
fof(i_0_5402,plain,
! [X10,X39,X19] :
( ( hBOOL(hAPP(X19,X39))
=> hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X39))),X19)) = hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) )
& ( ~ hBOOL(hAPP(X19,X39))
=> hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X39))),X19)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
inference(fof_simplification,[status(thm)],[fact_Collect__conv__if]) ).
fof(i_0_5403,plain,
! [X31782,X31783,X31784,X31785,X31786,X31787,X31788] : c_List_Ofoldr(X31788,X31787,X31786,hAPP(hAPP(c_List_Omap(X31785,X31788),X31784),X31783),X31782) = c_List_Ofoldr(X31785,X31787,hAPP(c_Fun_Ocomp(X31788,tc_fun(X31787,X31787),X31785,X31786),X31784),X31783,X31782),
inference(variable_rename,[status(thm)],[fact_foldr__map]) ).
fof(i_0_5404,plain,
! [X30148,X30149,X30150] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30150,X30150),tc_HOL_Obool)),X30149),hAPP(hAPP(c_Product__Type_OSigma(X30150,X30150),X30148),hAPP(c_COMBK(tc_fun(X30150,tc_HOL_Obool),X30150),X30148))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30150,X30150),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X30150,X30149)),hAPP(hAPP(c_Product__Type_OSigma(X30150,X30150),X30148),hAPP(c_COMBK(tc_fun(X30150,tc_HOL_Obool),X30150),X30148)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__subset__Sigma])]) ).
fof(i_0_5405,plain,
! [X21937,X21938,X21939] :
( ( ~ 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),X21938)))
| hAPP(hAPP(c_Power_Opower__class_Opower(X21939),hAPP(c_Int_Onumber__class_Onumber__of(X21939),X21937)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X21938))) = hAPP(hAPP(c_HOL_OLet(X21939,X21939),hAPP(hAPP(c_Power_Opower__class_Opower(X21939),hAPP(c_Int_Onumber__class_Onumber__of(X21939),X21937)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21938))),hAPP(hAPP(c_COMBS(X21939,X21939,X21939),hAPP(hAPP(c_COMBB(X21939,tc_fun(X21939,X21939),X21939),c_Groups_Otimes__class_Otimes(X21939)),hAPP(c_Groups_Otimes__class_Otimes(X21939),hAPP(c_Int_Onumber__class_Onumber__of(X21939),X21937)))),c_COMBI(X21939)))
| ~ class_Int_Onumber__ring(X21939) )
& ( 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),X21938)))
| hAPP(hAPP(c_Power_Opower__class_Opower(X21939),hAPP(c_Int_Onumber__class_Onumber__of(X21939),X21937)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X21938))) = c_Groups_Oone__class_Oone(X21939)
| ~ class_Int_Onumber__ring(X21939) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5173])])]) ).
fof(i_0_5406,plain,
! [X38,X39] :
( 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),X39),X38)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X38),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> c_Nitpick_Onorm__frac(X39,X38) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X39),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X38),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( ( ( X39 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X38 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
=> c_Nitpick_Onorm__frac(X39,X38) = 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)) )
& ( ~ ( X39 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X38 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
=> c_Nitpick_Onorm__frac(X39,X38) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X39),X38)),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),X39))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X38))) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_norm__frac_Opsimps]) ).
fof(i_0_5407,plain,
! [X33077,X33078,X33079,X33080,X33081,X33082] : c_List_Ofoldr(X33082,X33081,X33080,hAPP(hAPP(c_List_Oappend(X33082),X33079),X33078),X33077) = c_List_Ofoldr(X33082,X33081,X33080,X33079,c_List_Ofoldr(X33082,X33081,X33080,X33078,X33077)),
inference(variable_rename,[status(thm)],[fact_foldr__append]) ).
fof(i_0_5408,plain,
! [X160,X16,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),X160)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X16),X160))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X154),X160)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X160))
=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),X160)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160)) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_psubset__insert__iff]) ).
fof(i_0_5409,plain,
! [X25,X177,X10] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X3)),X177))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X25),X25)),c_List_Olexord(X10,X177))) ),
inference(fof_simplification,[status(thm)],[fact_lexord__irreflexive]) ).
fof(i_0_5410,plain,
! [X21343,X21344] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X21344)),c_Int_OBit1(X21343)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(X21344)),X21343)),
inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I8_J]) ).
fof(i_0_5411,plain,
! [X154,X39,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,hAPP(hAPP(c_Set_Oinsert(X10),X39),X154))
<=> ( c_Fun_Oinj__on(X10,X13,X2,X154)
& ~ hBOOL(hAPP(hAPP(c_member(X13),hAPP(X2,X39)),hAPP(c_Set_Oimage(X10,X13,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))))) ) ),
inference(fof_simplification,[status(thm)],[fact_inj__on__insert]) ).
fof(i_0_5412,plain,
! [X29414,X29415] : c_Product__Type_Oapfst(X29415,X29415,X29414,c_Fun_Oid(X29415)) = c_Fun_Oid(tc_prod(X29415,X29414)),
inference(variable_rename,[status(thm)],[fact_apfst__id]) ).
fof(i_0_5413,plain,
! [X29416,X29417] : c_Product__Type_Oapsnd(X29417,X29417,X29416,c_Fun_Oid(X29417)) = c_Fun_Oid(tc_prod(X29416,X29417)),
inference(variable_rename,[status(thm)],[fact_apsnd__id]) ).
fof(i_0_5414,plain,
! [X30180,X30181] : c_Transitive__Closure_Otrancl(X30181,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30181,X30181),tc_HOL_Obool)),X30180),c_Relation_OId(X30181))) = c_Transitive__Closure_Ortrancl(X30181,X30180),
inference(variable_rename,[status(thm)],[fact_trancl__reflcl]) ).
fof(i_0_5415,plain,
! [X160,X16,X154,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),X160)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),X160)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_subset__insert__iff]) ).
fof(i_0_5416,plain,
! [X21183,X21184] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(X21184),X21183) != c_Groups_Oone__class_Oone(X21184)
| c_Int_Oiszero(X21184,hAPP(c_Int_Onumber__class_Onumber__of(X21184),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21183),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
| ~ class_Int_Onumber__ring(X21184) )
& ( ~ c_Int_Oiszero(X21184,hAPP(c_Int_Onumber__class_Onumber__of(X21184),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21183),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
| hAPP(c_Int_Onumber__class_Onumber__of(X21184),X21183) = c_Groups_Oone__class_Oone(X21184)
| ~ class_Int_Onumber__ring(X21184) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I4_J])])]) ).
fof(i_0_5417,plain,
! [X21181,X21182] :
( ( c_Groups_Oone__class_Oone(X21182) != hAPP(c_Int_Onumber__class_Onumber__of(X21182),X21181)
| c_Int_Oiszero(X21182,hAPP(c_Int_Onumber__class_Onumber__of(X21182),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),X21181))))
| ~ class_Int_Onumber__ring(X21182) )
& ( ~ c_Int_Oiszero(X21182,hAPP(c_Int_Onumber__class_Onumber__of(X21182),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),X21181))))
| c_Groups_Oone__class_Oone(X21182) = hAPP(c_Int_Onumber__class_Onumber__of(X21182),X21181)
| ~ class_Int_Onumber__ring(X21182) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I2_J])])]) ).
fof(i_0_5418,plain,
! [X113,X141,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),X141),X113))))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X141),X113))
=> c_Smallcheck_Osmall_H(X2,X141,X113) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X141),X113))
=> c_Smallcheck_Osmall_H(X2,X141,X113) = 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,X141,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X113),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(X2,X113)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_small_H_Opsimps]) ).
fof(i_0_5419,plain,
! [X39,X38] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X38),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> c_Nitpick_Onorm__frac(X39,X38) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X39),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X38),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( ( ( X39 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X38 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
=> c_Nitpick_Onorm__frac(X39,X38) = 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)) )
& ( ~ ( X39 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X38 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
=> c_Nitpick_Onorm__frac(X39,X38) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X39),X38)),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),X39))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X38))) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_norm__frac_Osimps]) ).
fof(i_0_5420,plain,
! [X30262,X30263,X30264,X30265,X30266] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30266,X30266)),hAPP(hAPP(c_Product__Type_OPair(X30266,X30266),X30265),X30264)),X30263))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30266,X30266)),hAPP(hAPP(c_Product__Type_OPair(X30266,X30266),X30264),X30262)),c_Transitive__Closure_Ortrancl(X30266,X30263)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30266,X30266)),hAPP(hAPP(c_Product__Type_OPair(X30266,X30266),X30265),X30262)),c_Transitive__Closure_Otrancl(X30266,X30263))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__into__trancl2])]) ).
fof(i_0_5421,plain,
! [X30271,X30272,X30273,X30274,X30275] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30275,X30275)),hAPP(hAPP(c_Product__Type_OPair(X30275,X30275),X30274),X30273)),c_Transitive__Closure_Ortrancl(X30275,X30272)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30275,X30275)),hAPP(hAPP(c_Product__Type_OPair(X30275,X30275),X30273),X30271)),X30272))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30275,X30275)),hAPP(hAPP(c_Product__Type_OPair(X30275,X30275),X30274),X30271)),c_Transitive__Closure_Otrancl(X30275,X30272))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__into__trancl1])]) ).
fof(i_0_5422,plain,
! [X21930,X21931,X21932] :
( ( ~ 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),X21931)))
| hAPP(hAPP(c_Power_Opower__class_Opower(X21932),X21930),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X21931))) = hAPP(hAPP(c_HOL_OLet(X21932,X21932),hAPP(hAPP(c_Power_Opower__class_Opower(X21932),X21930),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21931))),hAPP(hAPP(c_COMBS(X21932,X21932,X21932),hAPP(hAPP(c_COMBB(X21932,tc_fun(X21932,X21932),X21932),c_Groups_Otimes__class_Otimes(X21932)),hAPP(c_Groups_Otimes__class_Otimes(X21932),X21930))),c_COMBI(X21932)))
| ~ class_Int_Onumber__ring(X21932) )
& ( 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),X21931)))
| hAPP(hAPP(c_Power_Opower__class_Opower(X21932),X21930),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X21931))) = c_Groups_Oone__class_Oone(X21932)
| ~ class_Int_Onumber__ring(X21932) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5174])])]) ).
fof(i_0_5423,plain,
! [X21396,X21397] :
( ~ class_Groups_Omonoid__mult(X21397)
| ~ class_Int_Onumber(X21397)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21397),hAPP(c_Int_Onumber__class_Onumber__of(X21397),X21396)),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(X21397),hAPP(c_Int_Onumber__class_Onumber__of(X21397),X21396)),hAPP(c_Int_Onumber__class_Onumber__of(X21397),X21396)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__square__number__of])]) ).
fof(i_0_5424,plain,
! [X30122,X30123,X30124,X30125,X30126] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30126,X30126)),hAPP(hAPP(c_Product__Type_OPair(X30126,X30126),X30125),X30124)),X30123))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30126,X30126)),hAPP(hAPP(c_Product__Type_OPair(X30126,X30126),X30124),X30122)),X30123))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30126,X30126)),hAPP(hAPP(c_Product__Type_OPair(X30126,X30126),X30125),X30122)),c_Transitive__Closure_Otrancl(X30126,X30123))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__r__into__trancl])]) ).
fof(i_0_5425,plain,
! [X177,X13,X39,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X39),hAPP(c_Relation_ODomain(X10,X13),X177)))
=> ~ ! [X90] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X39),X90)),X177)) ),
inference(fof_simplification,[status(thm)],[fact_DomainE]) ).
fof(i_0_5426,plain,
! [X21380] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21380),X21380)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X21380,
inference(variable_rename,[status(thm)],[fact_add__self__div__2]) ).
fof(i_0_5427,plain,
! [X141,X18,X38,X39] :
( 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),X39,X38)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X18,X141)))
<=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X39),X38))
| ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X18),X39))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X38),X141)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_OatLeastatMost__subset__iff]) ).
fof(i_0_5428,plain,
! [X21352,X21353] :
( ~ class_Int_Onumber__ring(X21353)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21353),X21352),hAPP(c_Int_Onumber__class_Onumber__of(X21353),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21353),X21352),X21352) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2__right])]) ).
fof(i_0_5429,plain,
! [X21360,X21361] :
( ~ class_Groups_Omonoid__mult(X21361)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21361),X21360),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(X21361),X21360),X21360) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__square])]) ).
fof(i_0_5430,plain,
! [X21358,X21359] :
( ~ class_Rings_Ocomm__semiring__1(X21359)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21359),X21358),X21358) = hAPP(hAPP(c_Power_Opower__class_Opower(X21359),X21358),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,
! [X39,X18,X38,X160,X154,X125,X13,X10] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_fun(X125,tc_HOL_Obool))),X154),X160),X38),X18))
=> ( ~ hBOOL(hAPP(hAPP(hAPP(X160,X39),X38),X18))
=> ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X154)) ) ),
inference(fof_simplification,[status(thm)],[fact_INF2__E]) ).
fof(i_0_5432,plain,
! [X21368] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21368),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),X21368),X21368),
inference(variable_rename,[status(thm)],[fact_nat__mult__2__right]) ).
fof(i_0_5433,plain,
! [X21362] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21362),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,X21362)),
inference(variable_rename,[status(thm)],[fact_add__2__eq__Suc_H]) ).
fof(i_0_5434,plain,
! [X21364] :
( ~ class_Rings_Osemiring__1(X21364)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21364),c_Groups_Oone__class_Oone(X21364)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X21364) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__power2])]) ).
fof(i_0_5435,plain,
! [X21355] :
( ~ class_Rings_Osemiring__1(X21355)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21355),c_Groups_Ozero__class_Ozero(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(X21355) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__power2])]) ).
fof(i_0_5436,plain,
! [X21933,X21934] :
( ( ~ 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),X21934)))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X21933),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X21934))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X21933),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21934))),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),X21933))),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),X21934)))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X21933),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X21934))) = 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,
! [X30142,X30143,X30144,X30145] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30145,X30145)),X30144),c_Transitive__Closure_Otrancl(X30145,X30143)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30145,X30145),tc_HOL_Obool)),X30143),X30142))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30145,X30145)),X30144),c_Transitive__Closure_Otrancl(X30145,X30142))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__mono])]) ).
fof(i_0_5438,plain,
! [X105,X93,X94] :
( class_Rings_Olinordered__ring(X94)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X93),X93)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X105),X105))),c_Groups_Ozero__class_Ozero(X94))) ),
inference(fof_simplification,[status(thm)],[fact_not__sum__squares__lt__zero]) ).
fof(i_0_5439,plain,
! [X30110,X30111] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30111,X30111),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X30111,X30110)),hAPP(hAPP(c_Product__Type_OSigma(X30111,X30111),hAPP(c_Relation_OField(X30111),X30110)),hAPP(c_COMBK(tc_fun(X30111,tc_HOL_Obool),X30111),hAPP(c_Relation_OField(X30111),X30110))))),
inference(variable_rename,[status(thm)],[fact_trancl__subset__Field2]) ).
fof(i_0_5440,plain,
! [X25,X16,X160,X154,X13,X10] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_fun(X13,tc_HOL_Obool))),X154),X160),X16),X25))
=> ( ~ hBOOL(hAPP(hAPP(X154,X16),X25))
=> hBOOL(hAPP(hAPP(X160,X16),X25)) ) ),
inference(fof_simplification,[status(thm)],[fact_sup2E]) ).
fof(i_0_5441,plain,
! [X30258,X30259,X30260,X30261] :
( ( X30260 != X30259
| X30260 = X30259
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30261,X30261)),hAPP(hAPP(c_Product__Type_OPair(X30261,X30261),X30260),X30259)),c_Transitive__Closure_Ortrancl(X30261,X30258))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30261,X30261)),hAPP(hAPP(c_Product__Type_OPair(X30261,X30261),X30260),X30259)),c_Transitive__Closure_Otrancl(X30261,X30258)))
| X30260 = X30259
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30261,X30261)),hAPP(hAPP(c_Product__Type_OPair(X30261,X30261),X30260),X30259)),c_Transitive__Closure_Ortrancl(X30261,X30258))) )
& ( X30260 != X30259
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30261,X30261)),hAPP(hAPP(c_Product__Type_OPair(X30261,X30261),X30260),X30259)),c_Transitive__Closure_Ortrancl(X30261,X30258))) )
& ( X30260 = X30259
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30261,X30261)),hAPP(hAPP(c_Product__Type_OPair(X30261,X30261),X30260),X30259)),c_Transitive__Closure_Otrancl(X30261,X30258)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30261,X30261)),hAPP(hAPP(c_Product__Type_OPair(X30261,X30261),X30260),X30259)),c_Transitive__Closure_Ortrancl(X30261,X30258))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__eq__or__trancl])])]) ).
fof(i_0_5442,plain,
! [X30170,X30171,X30172,X30173] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30173,X30173)),hAPP(hAPP(c_Product__Type_OPair(X30173,X30173),X30172),X30171)),c_Transitive__Closure_Otrancl(X30173,X30170)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30173,X30173)),hAPP(hAPP(c_Product__Type_OPair(X30173,X30173),X30172),X30171)),c_Transitive__Closure_Ortrancl(X30173,X30170))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__into__rtrancl])]) ).
fof(i_0_5443,plain,
! [X25,X16,X160,X154,X13,X10] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_fun(X13,tc_HOL_Obool))),X154),X160),X16),X25))
=> ~ ( hBOOL(hAPP(hAPP(X154,X16),X25))
=> ~ hBOOL(hAPP(hAPP(X160,X16),X25)) ) ),
inference(fof_simplification,[status(thm)],[fact_inf2E]) ).
fof(i_0_5444,plain,
! [X21197,X21198] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X21198)),c_Int_OBit1(X21197)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21198),X21197)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21198),X21197))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X21198)),c_Int_OBit1(X21197))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I34_J])]) ).
fof(i_0_5445,plain,
! [X21195,X21196] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X21196)),c_Int_OBit1(X21195)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21196),X21195)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21196),X21195))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X21196)),c_Int_OBit1(X21195))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I16_J])]) ).
fof(i_0_5446,plain,
! [X21201,X21202] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21202)),c_Int_OBit1(X21201)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21202),X21201)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21202),X21201))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21202)),c_Int_OBit1(X21201))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I17_J])]) ).
fof(i_0_5447,plain,
! [X21199,X21200] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21200)),c_Int_OBit1(X21199)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21200),X21199)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21200),X21199))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21200)),c_Int_OBit1(X21199))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I16_J])]) ).
fof(i_0_5448,plain,
! [X30321,X30322,X30323] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X30323,X30323),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X30323,X30323),X30322)),c_Transitive__Closure_Ortrancl(X30323,X30322)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X30323,X30323),tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30323,X30323)),hAPP(hAPP(c_Product__Type_OPair(X30323,X30323),X30321),X30321)),c_Transitive__Closure_Otrancl(X30323,X30322))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5176])]) ).
fof(i_0_5449,plain,
! [X33998,X33999] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X33999))),c_List_Otranspose(X33999,X33998)) = c_List_Ofoldr(tc_List_Olist(X33999),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X33999)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X33999))),X33998,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_length__transpose]) ).
fof(i_0_5450,plain,
! [X30513,X30514,X30515,X30517,X30518,X30519,X30520] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk369_3(X30513,X30514,X30515)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30515,X30515)),X30514),c_Transitive__Closure_Otrancl(X30515,X30513))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30515,X30515)),X30514),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30515,X30515),tc_HOL_Obool),esk369_3(X30513,X30514,X30515)),X30513)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30515,X30515)),X30514),c_Transitive__Closure_Otrancl(X30515,X30513))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30520))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30519,X30519)),X30518),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30519,X30519),tc_HOL_Obool),X30520),X30517)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30519,X30519)),X30518),c_Transitive__Closure_Otrancl(X30519,X30517))) ) ),
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,
! [X34266,X34267,X34268] : c_List_Oconcat(X34268,hAPP(hAPP(c_List_Oappend(tc_List_Olist(X34268)),X34267),X34266)) = hAPP(hAPP(c_List_Oappend(X34268),c_List_Oconcat(X34268,X34267)),c_List_Oconcat(X34268,X34266)),
inference(variable_rename,[status(thm)],[fact_concat__append]) ).
fof(i_0_5452,plain,
! [X113,X39,X290,X10] :
( hBOOL(hAPP(c_List_Odistinct(X10),X290))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),X290)),hAPP(hAPP(c_Set_Oinsert(X10),hAPP(hAPP(c_List_Onth(X10),X290),X113)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))))
=> hBOOL(hAPP(c_List_Odistinct(X10),hAPP(hAPP(c_List_Olist__update(X10,X290),X113),X39))) ) ),
inference(fof_simplification,[status(thm)],[fact_distinct__list__update]) ).
fof(i_0_5453,plain,
! [X154,X2,X13,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),hAPP(c_Set_Oimage(X13,X10,X2),X154))),hAPP(c_Finite__Set_Ocard(X13),X154)))
=> ~ c_Fun_Oinj__on(X13,X10,X2,X154) ),
inference(fof_simplification,[status(thm)],[fact_pigeonhole]) ).
fof(i_0_5454,plain,
! [X30267,X30268,X30269,X30270] :
( ( X30269 != X30268
| X30269 = X30268
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30270,X30270)),hAPP(hAPP(c_Product__Type_OPair(X30270,X30270),X30269),X30268)),c_Transitive__Closure_Ortrancl(X30270,X30267))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30270,X30270)),hAPP(hAPP(c_Product__Type_OPair(X30270,X30270),X30269),X30268)),c_Transitive__Closure_Otrancl(X30270,X30267)))
| X30269 = X30268
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30270,X30270)),hAPP(hAPP(c_Product__Type_OPair(X30270,X30270),X30269),X30268)),c_Transitive__Closure_Ortrancl(X30270,X30267))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtranclD])])]) ).
fof(i_0_5455,plain,
! [X30106,X30107,X30108,X30109] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30109,X30109)),hAPP(hAPP(c_Product__Type_OPair(X30109,X30109),X30108),X30107)),X30106))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30109,X30109)),hAPP(hAPP(c_Product__Type_OPair(X30109,X30109),X30108),X30107)),c_Transitive__Closure_Otrancl(X30109,X30106))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl_Or__into__trancl])]) ).
fof(i_0_5456,plain,
! [X25228,X25229,X25230,X25231] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25229),X25231))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25231),X25230))
| ~ 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),X25231,X25230)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25229,X25228))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25230),X25228))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25231),X25230))
| ~ 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),X25231,X25230)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25229,X25228))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25230),X25228))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25229),X25231))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25231),X25230))
| ~ 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),X25231,X25230)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25229,X25228))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25228),X25230))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25229),X25231))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25231),X25230))
| ~ 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),X25231,X25230)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25229,X25228))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25230),X25228))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25231),X25229))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25231),X25230))
| ~ 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),X25231,X25230)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25229,X25228))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25228),X25230))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25231),X25229))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25231),X25230))
| ~ 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),X25231,X25230)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25229,X25228))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25229),X25228))
| ~ 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),X25231,X25230)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25229,X25228))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25231),X25230))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25229),X25228))
| 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),X25231,X25230)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25229,X25228))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25229),X25231))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25231),X25229))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25229),X25231))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25230),X25228))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25229),X25228))
| 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),X25231,X25230)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25229,X25228))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25230),X25228))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25228),X25230))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25229),X25231))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25230),X25228))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25229),X25228))
| 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),X25231,X25230)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25229,X25228))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5177])])]) ).
fof(i_0_5457,plain,
! [X131,X18,X38,X10] :
( ( class_Fields_Olinordered__field__inverse__zero(X10)
& class_Int_Onumber(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),X18)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),X18))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),X18)),X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131))) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_divide__le__eq__number__of]) ).
fof(i_0_5458,plain,
! [X131,X18,X38,X10] :
( ( class_Fields_Olinordered__field__inverse__zero(X10)
& class_Int_Onumber(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),X18)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),X18))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),X18)),X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131))) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_divide__less__eq__number__of]) ).
fof(i_0_5459,plain,
! [X18,X38,X131,X10] :
( ( class_Fields_Olinordered__field__inverse__zero(X10)
& class_Int_Onumber(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),X18)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),X18)),X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),X18))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),c_Groups_Ozero__class_Ozero(X10))) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_le__divide__eq__number__of]) ).
fof(i_0_5460,plain,
! [X18,X38,X131,X10] :
( ( class_Fields_Olinordered__field__inverse__zero(X10)
& class_Int_Onumber(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),X18)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),X18)),X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),X18))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),c_Groups_Ozero__class_Ozero(X10))) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__divide__eq__number__of]) ).
fof(i_0_5461,plain,
! [X10,X39,X19] :
( ( hBOOL(hAPP(X19,X39))
=> hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(c_fequal,X39))),X19)) = hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) )
& ( ~ hBOOL(hAPP(X19,X39))
=> hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(c_fequal,X39))),X19)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
inference(fof_simplification,[status(thm)],[fact_Collect__conv__if2]) ).
fof(i_0_5462,plain,
! [X33545,X33546,X33547] : hAPP(c_List_Orotate(X33547,X33546),X33545) = hAPP(hAPP(c_List_Oappend(X33547),hAPP(hAPP(c_List_Odrop(X33547),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X33546,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33547)),X33545))),X33545)),hAPP(hAPP(c_List_Otake(X33547),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X33546,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33547)),X33545))),X33545)),
inference(variable_rename,[status(thm)],[fact_rotate__drop__take]) ).
fof(i_0_5463,plain,
! [X30100,X30101,X30102,X30103,X30104] :
( ( ~ c_Wellfounded_Oacyclic(X30101,X30100)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30101,X30101)),hAPP(hAPP(c_Product__Type_OPair(X30101,X30101),X30102),X30102)),c_Transitive__Closure_Otrancl(X30101,X30100))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30104,X30104)),hAPP(hAPP(c_Product__Type_OPair(X30104,X30104),esk366_2(X30103,X30104)),esk366_2(X30103,X30104))),c_Transitive__Closure_Otrancl(X30104,X30103)))
| c_Wellfounded_Oacyclic(X30104,X30103) ) ),
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,
! [X289,X290,X25,X16,X13,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X16),X25)),hAPP(c_List_Oset(tc_prod(X10,X13)),hAPP(hAPP(c_List_Ozip(X10,X13),X290),X289))))
=> ~ ( hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
=> ~ hBOOL(hAPP(hAPP(c_member(X13),X25),hAPP(c_List_Oset(X13),X289))) ) ),
inference(fof_simplification,[status(thm)],[fact_in__set__zipE]) ).
fof(i_0_5465,plain,
! [X273,X274,X275,X13,X102,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X102),c_Map_Odom(X10,X13,X275)))
=> c_Map_Omap__add(X10,X13,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),X274),X102),hAPP(c_Option_Ooption_OSome(X13),X273)),X275) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),c_Map_Omap__add(X10,X13,X274,X275)),X102),hAPP(c_Option_Ooption_OSome(X13),X273)) ),
inference(fof_simplification,[status(thm)],[fact_map__add__upd__left]) ).
fof(i_0_5466,plain,
! [X177,X16,X25,X10] :
( c_Wellfounded_Oacyclic(X10,hAPP(hAPP(c_Set_Oinsert(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X25),X16)),X177))
<=> ( c_Wellfounded_Oacyclic(X10,X177)
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),c_Transitive__Closure_Ortrancl(X10,X177))) ) ),
inference(fof_simplification,[status(thm)],[fact_acyclic__insert]) ).
fof(i_0_5467,plain,
! [X177,X16,X25,X10] :
( c_Wellfounded_Owf(X10,hAPP(hAPP(c_Set_Oinsert(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X25),X16)),X177))
<=> ( c_Wellfounded_Owf(X10,X177)
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),c_Transitive__Closure_Ortrancl(X10,X177))) ) ),
inference(fof_simplification,[status(thm)],[fact_wf__insert]) ).
fof(i_0_5468,plain,
! [X30146,X30147] : c_Transitive__Closure_Otrancl(X30147,X30146) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30147,X30147),tc_HOL_Obool)),X30146),hAPP(hAPP(c_Relation_Orel__comp(X30147,X30147,X30147),c_Transitive__Closure_Otrancl(X30147,X30146)),X30146)),
inference(variable_rename,[status(thm)],[fact_trancl__unfold]) ).
fof(i_0_5469,plain,
! [X177,X10] :
( c_Wellfounded_Owf(X10,X177)
<=> ! [X271] :
( ? [X3] : hBOOL(hAPP(hAPP(c_member(X10),X3),X271))
=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X271))
& ! [X90] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X90),X3)),X177))
=> ~ hBOOL(hAPP(hAPP(c_member(X10),X90),X271)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_wf__eq__minimal]) ).
fof(i_0_5470,plain,
! [X21331,X21332] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X21332)),c_Int_OBit0(X21331)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21332),X21331)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21332),X21331))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X21332)),c_Int_OBit0(X21331))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I33_J])]) ).
fof(i_0_5471,plain,
! [X21329,X21330] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X21330)),c_Int_OBit0(X21329)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21330),X21329)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21330),X21329))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X21330)),c_Int_OBit0(X21329))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I15_J])]) ).
fof(i_0_5472,plain,
! [X21305,X21306] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21306)),c_Int_OBit0(X21305)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21306),X21305)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21306),X21305))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21306)),c_Int_OBit0(X21305))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I15_J])]) ).
fof(i_0_5473,plain,
! [X21303,X21304] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21304)),c_Int_OBit0(X21303)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21304),X21303)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21304),X21303))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21304)),c_Int_OBit0(X21303))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I16_J])]) ).
fof(i_0_5474,plain,
! [X102,X13,X197,X16,X10] :
( ( hBOOL(hAPP(hAPP(c_member(X10),X16),X197))
=> hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),c_Map_Orestrict__map(X10,X13,X102,X197)),X16),c_Option_Ooption_ONone(X13)) = c_Map_Orestrict__map(X10,X13,X102,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X197),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X197))
=> hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),c_Map_Orestrict__map(X10,X13,X102,X197)),X16),c_Option_Ooption_ONone(X13)) = c_Map_Orestrict__map(X10,X13,X102,X197) ) ),
inference(fof_simplification,[status(thm)],[fact_fun__upd__None__restrict]) ).
fof(i_0_5475,plain,
! [X21054,X21055] : c_Nitpick_Oint__lcm(X21055,X21054) = 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),X21055)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X21054)))),
inference(variable_rename,[status(thm)],[fact_Nitpick_Oint__lcm__def]) ).
fof(i_0_5476,plain,
! [X21044,X21045] : c_Nitpick_Onat__lcm(X21045,X21044) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21045),X21044)),c_Nitpick_Onat__gcd(X21045,X21044)),
inference(variable_rename,[status(thm)],[fact_Nitpick_Onat__lcm__def]) ).
fof(i_0_5477,plain,
! [X32289,X32290,X32291,X32292,X32293,X32294] : c_List_Ofoldr(X32294,X32293,X32292,hAPP(hAPP(c_List_Olist_OCons(X32294),X32291),X32290),X32289) = hAPP(hAPP(X32292,X32291),c_List_Ofoldr(X32294,X32293,X32292,X32290,X32289)),
inference(variable_rename,[status(thm)],[fact_foldr_Osimps_I2_J]) ).
fof(i_0_5478,plain,
! [X16,X39,X177,X10] :
( c_Wellfounded_Owf(X10,X177)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X16)),X177))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X39)),X177)) ) ),
inference(fof_simplification,[status(thm)],[fact_wf__not__sym]) ).
fof(i_0_5479,plain,
! [X16,X39,X177,X10] :
( c_Wellfounded_Owf(X10,X177)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X16)),X177))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X39)),X177)) ) ),
inference(fof_simplification,[status(thm)],[fact_wf__asym]) ).
fof(i_0_5480,plain,
! [X199,X20,X102] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X102,X20),X199))
<=> ( X102 = 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),X199)),X20)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X199))
& ( X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X199) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X20 != 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)),X20))
=> ( 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),X199)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X199)),X20)) ) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X199)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X199)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_divmod__nat__rel__def]) ).
fof(i_0_5481,plain,
! [X39,X131,X38,X10] :
( ( class_Fields_Olinordered__field__inverse__zero(X10)
& class_Int_Onumber(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131))),X39))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131))),X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X39)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_divide__le__eq__number__of1]) ).
fof(i_0_5482,plain,
! [X39,X131,X38,X10] :
( ( class_Fields_Olinordered__field__inverse__zero(X10)
& class_Int_Onumber(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131))),X39))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131))),X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X39)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_divide__less__eq__number__of1]) ).
fof(i_0_5483,plain,
! [X21216] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(X21216)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21216))),
inference(variable_rename,[status(thm)],[fact_minus__Bit1]) ).
fof(i_0_5484,plain,
! [X53,X20,X54,X18,X38] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X38,X18),X54,X20,X53)
=> ( ( X53 = X54
=> hBOOL(hAPP(X38,X54)) )
=> ~ ( hBOOL(hAPP(X38,X54))
=> ! [X67] :
( c_Natural_Oevaln(X18,X54,X20,X67)
=> ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X38,X18),X67,X20,X53) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_evaln__WHILE__case]) ).
fof(i_0_5485,plain,
! [X65,X72,X52,X50,X51] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X51,X50),X52,X72,X65)
<=> ( ( X65 = X52
& ~ hBOOL(hAPP(X51,X52)) )
| ( hBOOL(hAPP(X51,X52))
& ? [X67] :
( c_Natural_Oevaln(X50,X52,X72,X67)
& c_Natural_Oevaln(c_Com_Ocom_OWhile(X51,X50),X67,X72,X65) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_evaln_Oequations_I8_J]) ).
fof(i_0_5486,plain,
! [X44,X42,X45,X62,X58] :
( c_Natural_Oevaln(c_Com_Ocom_OSemi(X58,X62),X45,X42,X44)
=> ~ ! [X67] :
( c_Natural_Oevaln(X58,X45,X42,X67)
=> ~ c_Natural_Oevaln(X62,X67,X42,X44) ) ),
inference(fof_simplification,[status(thm)],[fact_evaln__elim__cases_I4_J]) ).
fof(i_0_5487,plain,
! [X30096,X30097] :
( ( ~ 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),X30097),X30096)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30097),X30096)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30097),X30096))
| 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),X30097),X30096)),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,
! [X177,X154,X48,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X48),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X154),X177)))
=> ~ ! [X3] :
( X48 = hAPP(c_Relation_OImage(X10,X10,X177),hAPP(hAPP(c_Set_Oinsert(X10),X3),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))
=> ~ hBOOL(hAPP(hAPP(c_member(X10),X3),X154)) ) ),
inference(fof_simplification,[status(thm)],[fact_quotientE]) ).
fof(i_0_5489,plain,
! [X22261,X22262] :
( ( X22262 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Divides_Odivmod__nat(X22261,X22262) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22261) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22261),X22262))
| c_Divides_Odivmod__nat(X22261,X22262) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22261) )
& ( X22262 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22261),X22262))
| c_Divides_Odivmod__nat(X22261,X22262) = 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),X22261),X22262),X22262)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__if])])]) ).
fof(i_0_5490,plain,
! [X23003,X23004] : c_Divides_Odivmod__nat(X23004,X23003) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X23004,X23003)),
inference(variable_rename,[status(thm)],[fact_divmod__nat__def]) ).
fof(i_0_5491,plain,
! [X21207] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21207)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21207),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21207),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21207)),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,
! [X323,X324,X325,X326,X10] :
( hAPP(hAPP(c_List_Oappend(X10),X326),X325) = hAPP(hAPP(c_List_Oappend(X10),X324),X323)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X326)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X324)))
=> ( X326 = hAPP(hAPP(c_List_Otake(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X326)),X324)
& X325 = hAPP(hAPP(c_List_Oappend(X10),hAPP(hAPP(c_List_Odrop(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X326)),X324)),X323) ) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X326)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X324)))
=> ( hAPP(hAPP(c_List_Otake(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X324)),X326) = X324
& hAPP(hAPP(c_List_Oappend(X10),hAPP(hAPP(c_List_Odrop(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X324)),X326)),X325) = X323 ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_append__eq__append__conv__if]) ).
fof(i_0_5493,plain,
! [X21211] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X21211)),c_Int_OMin))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21211),c_Int_OMin)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21211),c_Int_OMin))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X21211)),c_Int_OMin)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I30_J])]) ).
fof(i_0_5494,plain,
! [X21228] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X21228)),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21228),c_Int_OPls)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21228),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X21228)),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I29_J])]) ).
fof(i_0_5495,plain,
! [X21209] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21209)),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21209),c_Int_OPls)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21209),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21209)),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I12_J])]) ).
fof(i_0_5496,plain,
! [X21213] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21213)),c_Int_OMin))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21213),c_Int_OMin)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21213),c_Int_OMin))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21213)),c_Int_OMin)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I13_J])]) ).
fof(i_0_5497,plain,
! [X21215] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X21215))))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21215))) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21215)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X21215)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__number__of__Bit1])]) ).
fof(i_0_5498,plain,
! [X21234,X21235] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21235),c_Groups_Oone__class_Oone(X21235)),hAPP(c_Int_Onumber__class_Onumber__of(X21235),X21234)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X21234))
| ~ class_Int_Onumber__ring(X21235)
| ~ class_Rings_Olinordered__idom(X21235) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X21234))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21235),c_Groups_Oone__class_Oone(X21235)),hAPP(c_Int_Onumber__class_Onumber__of(X21235),X21234)))
| ~ class_Int_Onumber__ring(X21235)
| ~ class_Rings_Olinordered__idom(X21235) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I2_J])])]) ).
fof(i_0_5499,plain,
! [X21238,X21239] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21239),c_Groups_Oone__class_Oone(X21239)),hAPP(c_Int_Onumber__class_Onumber__of(X21239),X21238)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X21238))
| ~ class_Int_Onumber__ring(X21239)
| ~ class_Rings_Olinordered__idom(X21239) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X21238))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21239),c_Groups_Oone__class_Oone(X21239)),hAPP(c_Int_Onumber__class_Onumber__of(X21239),X21238)))
| ~ class_Int_Onumber__ring(X21239)
| ~ class_Rings_Olinordered__idom(X21239) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I2_J])])]) ).
fof(i_0_5500,plain,
! [X131,X38,X39,X10] :
( ( class_Fields_Olinordered__field__inverse__zero(X10)
& class_Int_Onumber(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131))))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131))),X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),c_Groups_Ozero__class_Ozero(X10))) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_le__divide__eq__number__of1]) ).
fof(i_0_5501,plain,
! [X131,X38,X39,X10] :
( ( class_Fields_Olinordered__field__inverse__zero(X10)
& class_Int_Onumber(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131))))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131))),X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),c_Groups_Ozero__class_Ozero(X10))) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__divide__eq__number__of1]) ).
fof(i_0_5502,plain,
! [X13,X10,X154,X25,X16,X160] :
( ( ~ hBOOL(hAPP(hAPP(X160,X16),X25))
=> hBOOL(hAPP(hAPP(X154,X16),X25)) )
=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_fun(X13,tc_HOL_Obool))),X154),X160),X16),X25)) ),
inference(fof_simplification,[status(thm)],[fact_sup2CI]) ).
fof(i_0_5503,plain,
! [X196,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),c_Wellfounded_Oacc(X10,X196)))
=> ~ ! [X159] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X159),X16)),X196))
=> hBOOL(hAPP(hAPP(c_member(X10),X159),c_Wellfounded_Oacc(X10,X196))) ) ),
inference(fof_simplification,[status(thm)],[fact_not__acc__down]) ).
fof(i_0_5504,plain,
! [X38,X154,X10] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X38),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))
=> c_Partial__Function_Oflat__lub(X10,X38,X154) = X38 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X38),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))
=> c_Partial__Function_Oflat__lub(X10,X38,X154) = c_HOL_OThe(X10,hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X38),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ),
inference(fof_simplification,[status(thm)],[fact_flat__lub__def]) ).
fof(i_0_5505,plain,
! [X53,X54,X18,X38] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X38,X18)),X54),X53))
=> ( ( X53 = X54
=> hBOOL(hAPP(X38,X54)) )
=> ~ ( hBOOL(hAPP(X38,X54))
=> ! [X67] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X18),X54),X67))
=> ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X38,X18)),X67),X53)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_evalc__WHILE__case]) ).
fof(i_0_5506,plain,
! [X66,X52,X50,X51] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X51,X50)),X52),X66))
<=> ( ( X66 = X52
& ~ hBOOL(hAPP(X51,X52)) )
| ( hBOOL(hAPP(X51,X52))
& ? [X67] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X50),X52),X67))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X51,X50)),X67),X66)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_evalc_Oequations_I8_J]) ).
fof(i_0_5507,plain,
! [X21436,X21437] :
( ( ~ 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),X21437)))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X21436))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21437))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21436)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21437)) )
& ( 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),X21437)))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X21436))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21437))) = 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),X21436)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21437)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5179])]) ).
fof(i_0_5508,plain,
! [X30548,X30549] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X30549,X30549)),hAPP(hAPP(c_Product__Type_OPair(X30549,X30549),esk376_2(X30548,X30549)),esk376_2(X30548,X30549))),c_Transitive__Closure_Otrancl(X30549,X30548)))
| c_Wellfounded_Oacyclic(X30549,X30548) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5180])])]) ).
fof(i_0_5509,plain,
! [X177,X290,X10] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_ONil(X10)),X290)),c_List_Olistrel1(X10,X177))),
inference(fof_simplification,[status(thm)],[fact_not__Nil__listrel1]) ).
fof(i_0_5510,plain,
! [X177,X289,X10] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_ONil(X10)),X289)),c_List_Olex(X10,X177))),
inference(fof_simplification,[status(thm)],[fact_Nil__notin__lex]) ).
fof(i_0_5511,plain,
! [X25,X2,X13,X154,X16,X10] :
( ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Set_Oimage(X10,X13,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,X13),X2),X16),X25)),X154) = hAPP(hAPP(c_Set_Oinsert(X13),X25),hAPP(c_Set_Oimage(X10,X13,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Set_Oimage(X10,X13,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,X13),X2),X16),X25)),X154) = hAPP(c_Set_Oimage(X10,X13,X2),X154) ) ),
inference(fof_simplification,[status(thm)],[fact_fun__upd__image]) ).
fof(i_0_5512,plain,
! [X177,X290,X10] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X290),c_List_Olist_ONil(X10))),c_List_Olistrel1(X10,X177))),
inference(fof_simplification,[status(thm)],[fact_not__listrel1__Nil]) ).
fof(i_0_5513,plain,
! [X177,X16,X10] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X16),c_List_Olist_ONil(X10))),c_List_Olexord(X10,X177))),
inference(fof_simplification,[status(thm)],[fact_lexord__Nil__right]) ).
fof(i_0_5514,plain,
! [X177,X290,X10] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X290),c_List_Olist_ONil(X10))),c_List_Olex(X10,X177))),
inference(fof_simplification,[status(thm)],[fact_Nil2__notin__lex]) ).
fof(i_0_5515,plain,
! [X33596,X33597,X33598] :
( ~ class_Groups_Omonoid__add(X33598)
| hAPP(c_List_Ofoldl(X33598,X33598,c_Groups_Oplus__class_Oplus(X33598),X33597),X33596) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X33598),X33597),c_List_Ofoldr(X33598,X33598,c_Groups_Oplus__class_Oplus(X33598),X33596,c_Groups_Ozero__class_Ozero(X33598))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__foldr1__lemma])]) ).
fof(i_0_5516,plain,
! [X30255,X30256,X30257] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30257,X30257)),hAPP(hAPP(c_Product__Type_OPair(X30257,X30257),X30256),X30255)),c_Relation_OId(X30257)))
| X30256 = X30255 )
& ( X30256 != X30255
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30257,X30257)),hAPP(hAPP(c_Product__Type_OPair(X30257,X30257),X30256),X30255)),c_Relation_OId(X30257))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__in__Id__conv])]) ).
fof(i_0_5517,plain,
! [X16,X285,X10,X13] :
( hAPP(c_Map_Omap__of(X13,X10,X285),X16) = c_Option_Ooption_ONone(X10)
<=> ~ hBOOL(hAPP(hAPP(c_member(X13),X16),hAPP(c_Set_Oimage(tc_prod(X13,X10),X13,c_Product__Type_Ofst(X13,X10)),hAPP(c_List_Oset(tc_prod(X13,X10)),X285)))) ),
inference(fof_simplification,[status(thm)],[fact_map__of__eq__None__iff]) ).
fof(i_0_5518,plain,
! [X21354] :
( ~ class_Int_Onumber__ring(X21354)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21354),c_Groups_Oone__class_Oone(X21354)),c_Groups_Oone__class_Oone(X21354)) = hAPP(c_Int_Onumber__class_Onumber__of(X21354),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,
! [X289,X2,X13,X290,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
=> hAPP(c_Map_Omap__upds(X10,X13,X2,X290,X289),X16) = hAPP(X2,X16) ),
inference(fof_simplification,[status(thm)],[fact_map__upds__apply__nontin]) ).
fof(i_0_5520,plain,
! [X1,X2,X13,X154,X39,X10] :
( ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(c_Fun_Ooverride__on(X10,X13,X2,X1,X154),X39) = hAPP(X1,X39) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(c_Fun_Ooverride__on(X10,X13,X2,X1,X154),X39) = hAPP(X2,X39) ) ),
inference(fof_simplification,[status(thm)],[fact_override__on__def]) ).
fof(i_0_5521,plain,
! [X21868,X21869] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21869))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21869),X21868))
| c_Divides_Odivmod__nat(X21868,X21869) = 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),X21868),X21869)),X21869))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21868),X21869),X21869)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__step])]) ).
fof(i_0_5522,plain,
! [X44,X45,X62,X58] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X58,X62)),X45),X44))
=> ~ ! [X67] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X58),X45),X67))
=> ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X62),X67),X44)) ) ),
inference(fof_simplification,[status(thm)],[fact_evalc__elim__cases_I4_J]) ).
fof(i_0_5523,plain,
! [X34288,X34289,X34290,X34291,X34292] : hAPP(c_List_Ofoldl(X34292,X34291,X34290,X34289),X34288) = c_List_Ofoldr(X34291,X34292,hAPP(c_COMBC(X34292,X34291,X34292),X34290),hAPP(c_List_Orev(X34291),X34288),X34289),
inference(variable_rename,[status(thm)],[fact_foldl__foldr]) ).
fof(i_0_5524,plain,
! [X1,X2,X13,X154,X39,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(c_Fun_Ooverride__on(X10,X13,X2,X1,X154),X39) = hAPP(X2,X39) ),
inference(fof_simplification,[status(thm)],[fact_override__on__apply__notin]) ).
fof(i_0_5525,plain,
! [X1,X154,X225,X73,X2,X13,X10] :
( c_Big__Operators_Ocomm__monoid__big(X10,X13,X2,X73,X225)
=> ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X154))
=> hAPP(hAPP(X225,X1),X154) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X10,X13,X2),X1),X73),X154) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X154))
=> hAPP(hAPP(X225,X1),X154) = X73 ) ) ),
inference(fof_simplification,[status(thm)],[fact_comm__monoid__big_OF__eq]) ).
fof(i_0_5526,plain,
! [X23793,X23794,X23795,X23796] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23796,X23796)),hAPP(hAPP(c_Product__Type_OPair(X23796,X23796),X23795),X23794)),hAPP(c_Wellfounded_Omeasure(X23796),X23793)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X23793,X23795)),hAPP(X23793,X23794))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X23793,X23795)),hAPP(X23793,X23794)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X23796,X23796)),hAPP(hAPP(c_Product__Type_OPair(X23796,X23796),X23795),X23794)),hAPP(c_Wellfounded_Omeasure(X23796),X23793))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measure])]) ).
fof(i_0_5527,plain,
! [X24386] : c_Wellfounded_Omeasure(X24386) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X24386),c_Wellfounded_Oless__than),
inference(variable_rename,[status(thm)],[fact_measure__def]) ).
fof(i_0_5528,plain,
! [X160,X154,X38,X39,X13,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X13)),hAPP(hAPP(c_Product__Type_OPair(X10,X13),X39),X38)),hAPP(hAPP(c_Product__Type_OSigma(X10,X13),X154),X160)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> ~ hBOOL(hAPP(hAPP(c_member(X13),X38),hAPP(X160,X39))) ) ),
inference(fof_simplification,[status(thm)],[fact_SigmaE2]) ).
fof(i_0_5529,plain,
! [X34249,X34250,X34251,X34252] : hAPP(hAPP(c_List_Omap(X34252,X34251),X34250),c_List_Oconcat(X34252,X34249)) = c_List_Oconcat(X34251,hAPP(hAPP(c_List_Omap(tc_List_Olist(X34252),tc_List_Olist(X34251)),hAPP(c_List_Omap(X34252,X34251),X34250)),X34249)),
inference(variable_rename,[status(thm)],[fact_map__concat]) ).
fof(i_0_5530,plain,
! [X21312,X21313] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X21313)),c_Int_OBit0(X21312)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X21313),X21312)),
inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I9_J]) ).
fof(i_0_5531,plain,
! [X21309,X21310] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X21310)),c_Int_OBit0(X21309)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21310),X21309)),
inference(variable_rename,[status(thm)],[fact_add__Bit1__Bit0]) ).
fof(i_0_5532,plain,
! [X290,X13,X16,X2,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),hAPP(X2,X16)),hAPP(c_Set_Oimage(X13,X10,X2),hAPP(c_List_Oset(X13),X290))))
=> c_List_Olinorder__class_Oinsort__insert__key(X13,X10,X2,X16,X290) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X13,X10,X2),X16),X290) ) ),
inference(fof_simplification,[status(thm)],[fact_insort__insert__insort__key]) ).
fof(i_0_5533,plain,
! [X30433,X30434,X30435] :
( ( ~ c_Relation_Ototal__on(X30435,X30434,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X30435,X30435),tc_HOL_Obool)),X30433),c_Relation_OId(X30435)))
| c_Relation_Ototal__on(X30435,X30434,X30433) )
& ( ~ c_Relation_Ototal__on(X30435,X30434,X30433)
| c_Relation_Ototal__on(X30435,X30434,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X30435,X30435),tc_HOL_Obool)),X30433),c_Relation_OId(X30435))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_total__on__diff__Id])]) ).
fof(i_0_5534,plain,
! [X21246,X21247] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),X21247))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21246)),X21247) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21246),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21247),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,
! [X21337,X21338] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(X21338)),X21337) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21338),X21337))),X21337),
inference(variable_rename,[status(thm)],[fact_mult__Bit1]) ).
fof(i_0_5536,plain,
! [X21349] :
( ( 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(X21349))))
| ~ 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),X21349))) )
& ( 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(X21349))))
| ~ 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),X21349))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of1])])]) ).
fof(i_0_5537,plain,
! [X21345,X21346] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X21346)),c_Int_OBit1(X21345)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21346),c_Int_Osucc(X21345))),
inference(variable_rename,[status(thm)],[fact_add__Bit1__Bit1]) ).
fof(i_0_5538,plain,
! [X21299,X21300] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21300)),c_Int_OBit1(X21299)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21300),X21299)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21300),X21299))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21300)),c_Int_OBit1(X21299))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I14_J])]) ).
fof(i_0_5539,plain,
! [X21297,X21298] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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__eq(tc_Int_Oint),c_Int_OBit0(X21298)),c_Int_OBit1(X21297))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I32_J])]) ).
fof(i_0_5540,plain,
! [X21335,X21336] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21336)),c_Int_OBit1(X21335)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21336),X21335)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21336),X21335))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21336)),c_Int_OBit1(X21335))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I15_J])]) ).
fof(i_0_5541,plain,
! [X21333,X21334] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21334)),c_Int_OBit1(X21333)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21334),X21333)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21334),X21333))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21334)),c_Int_OBit1(X21333))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I14_J])]) ).
fof(i_0_5542,plain,
! [X21919] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21919)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X21919)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21919)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X21919)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21919)),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,
! [X30120,X30121] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X30121,X30121)),c_Transitive__Closure_Otrancl(X30121,X30120)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X30121,X30121)),X30120)) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X30121,X30121)),X30120))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X30121,X30121)),c_Transitive__Closure_Otrancl(X30121,X30120))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__trancl])]) ).
fof(i_0_5544,plain,
! [X160,X39,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X160))
=> hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),X160))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_card__Diff__insert]) ).
fof(i_0_5545,plain,
! [X34257,X34258] : hAPP(c_List_Orev(X34258),c_List_Oconcat(X34258,X34257)) = c_List_Oconcat(X34258,hAPP(hAPP(c_List_Omap(tc_List_Olist(X34258),tc_List_Olist(X34258)),c_List_Orev(X34258)),hAPP(c_List_Orev(tc_List_Olist(X34258)),X34257))),
inference(variable_rename,[status(thm)],[fact_rev__concat]) ).
fof(i_0_5546,plain,
! [X73,X1,X39,X154,X10,X13] :
( class_Groups_Oab__semigroup__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13,X10,c_Groups_Otimes__class_Otimes(X13)),X1),X73),hAPP(hAPP(c_Set_Oinsert(X10),X39),X154)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),hAPP(X1,X39)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13,X10,c_Groups_Otimes__class_Otimes(X13)),X1),X73),X154)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_fold__image__insert]) ).
fof(i_0_5547,plain,
! [X34210,X34211,X34212] : hAPP(c_List_Ofilter(X34212,X34211),c_List_Oconcat(X34212,X34210)) = c_List_Oconcat(X34212,hAPP(hAPP(c_List_Omap(tc_List_Olist(X34212),tc_List_Olist(X34212)),c_List_Ofilter(X34212,X34211)),X34210)),
inference(variable_rename,[status(thm)],[fact_filter__concat]) ).
fof(i_0_5548,plain,
! [X39,X18,X38,X10] :
( class_Fields_Olinordered__field__inverse__zero(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),X18)),X39))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X18))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X18)),X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X39)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_divide__le__eq]) ).
fof(i_0_5549,plain,
! [X39,X18,X38,X10] :
( class_Fields_Olinordered__field__inverse__zero(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),X18)),X39))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X18))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X18)),X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X39)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_divide__less__eq]) ).
fof(i_0_5550,plain,
! [X33488,X33489,X33490] :
( ( ~ hBOOL(hAPP(c_List_Odistinct(X33490),hAPP(c_List_Orotate(X33490,X33489),X33488)))
| hBOOL(hAPP(c_List_Odistinct(X33490),X33488)) )
& ( ~ hBOOL(hAPP(c_List_Odistinct(X33490),X33488))
| hBOOL(hAPP(c_List_Odistinct(X33490),hAPP(c_List_Orotate(X33490,X33489),X33488))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__rotate])]) ).
fof(i_0_5551,plain,
! [X25,X196,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_Relation_ODomain(X10,X10),X196)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X25)),c_Transitive__Closure_Ortrancl(X10,X196)))
<=> X16 = X25 ) ),
inference(fof_simplification,[status(thm)],[fact_Not__Domain__rtrancl]) ).
fof(i_0_5552,plain,
! [X21307,X21308] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X21308)),c_Int_OBit1(X21307)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21308),X21307)),
inference(variable_rename,[status(thm)],[fact_add__Bit0__Bit1]) ).
fof(i_0_5553,plain,
! [X1,X154,X225,X73,X2,X13,X10] :
( c_Big__Operators_Ocomm__monoid__big(X10,X13,X2,X73,X225)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X13),X154))
=> hAPP(hAPP(X225,X1),X154) = X73 ) ),
inference(fof_simplification,[status(thm)],[fact_comm__monoid__big_Oinfinite]) ).
fof(i_0_5554,plain,
! [X21187,X21188] :
( ~ class_Int_Onumber__ring(X21188)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21188),hAPP(c_Int_Onumber__class_Onumber__of(X21188),X21187)),c_Groups_Oone__class_Oone(X21188)) = hAPP(c_Int_Onumber__class_Onumber__of(X21188),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21187),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,
! [X290,X16,X2,X10,X13] :
( class_Orderings_Olinorder(X13)
=> ( hBOOL(hAPP(c_List_Odistinct(X10),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X13,X2),X16),X290)))
<=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
& hBOOL(hAPP(c_List_Odistinct(X10),X290)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_distinct__insort]) ).
fof(i_0_5556,plain,
! [X21185,X21186] :
( ~ class_Int_Onumber__ring(X21186)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21186),c_Groups_Oone__class_Oone(X21186)),hAPP(c_Int_Onumber__class_Onumber__of(X21186),X21185)) = hAPP(c_Int_Onumber__class_Onumber__of(X21186),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),X21185))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__special_I1_J])]) ).
fof(i_0_5557,plain,
! [X30112,X30113,X30114] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30114,X30114)),X30113),X30112))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30114,X30114)),X30113),c_Transitive__Closure_Otrancl(X30114,X30112))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__into__trancl_H])]) ).
fof(i_0_5558,plain,
! [X34246,X34247,X34248] : c_List_Oconcat(X34248,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X34248)),X34247),X34246)) = hAPP(hAPP(c_List_Oappend(X34248),X34247),c_List_Oconcat(X34248,X34246)),
inference(variable_rename,[status(thm)],[fact_concat_Osimps_I2_J]) ).
fof(i_0_5559,plain,
! [X21244,X21245] :
( ~ class_Int_Onumber__ring(X21245)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21245),c_Groups_Oone__class_Oone(X21245)),hAPP(c_Int_Onumber__class_Onumber__of(X21245),X21244)) = hAPP(c_Int_Onumber__class_Onumber__of(X21245),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X21244)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__special_I2_J])]) ).
fof(i_0_5560,plain,
! [X141,X18,X38,X39,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X39,X38)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X18,X141)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),X38))
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X18),X39))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X38),X141))
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),X39))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X38),X141)) ) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X18),X141)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_atLeastatMost__psubset__iff]) ).
fof(i_0_5561,plain,
! [X34114,X34115] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X34115)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X34114)))
| c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X34115),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X34114)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X34115)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X34115)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X34114))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X34115)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X34114)))
| c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X34115),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X34114)) = 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,
! [X225,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X16),X225))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(tc_fun(X10,tc_HOL_Obool)),X16),X225)))
=> ! [X227] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X227),hAPP(hAPP(c_Set_Oinsert(tc_fun(X10,tc_HOL_Obool)),X16),X225)))
=> ( X3 != X227
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X3),X227) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ) )
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X16),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X225)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
inference(fof_simplification,[status(thm)],[fact_insert__partition]) ).
fof(i_0_5563,plain,
! [X30178,X30179] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30179,X30179),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X30179,X30178)),c_Relation_OId(X30179)) = c_Transitive__Closure_Ortrancl(X30179,X30178),
inference(variable_rename,[status(thm)],[fact_reflcl__trancl]) ).
fof(i_0_5564,plain,
! [X93,X298,X297,X94,X42] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)))
=> hAPP(hAPP(c_List_Olist__update(X94,hAPP(hAPP(c_List_Oappend(X94),X297),X298)),X42),X93) = hAPP(hAPP(c_List_Oappend(X94),hAPP(hAPP(c_List_Olist__update(X94,X297),X42),X93)),X298) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)))
=> hAPP(hAPP(c_List_Olist__update(X94,hAPP(hAPP(c_List_Oappend(X94),X297),X298)),X42),X93) = hAPP(hAPP(c_List_Oappend(X94),X297),hAPP(hAPP(c_List_Olist__update(X94,X298),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297))),X93)) ) ),
inference(fof_simplification,[status(thm)],[fact_list__update__append]) ).
fof(i_0_5565,plain,
! [X18,X38,X39,X10] :
( class_Fields_Olinordered__field__inverse__zero(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),X18)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X18)),X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X18))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),c_Groups_Ozero__class_Ozero(X10))) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_le__divide__eq]) ).
fof(i_0_5566,plain,
! [X18,X38,X39,X10] :
( class_Fields_Olinordered__field__inverse__zero(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X38),X18)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X18)),X38)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X18))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X39),X18))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X18),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),c_Groups_Ozero__class_Ozero(X10))) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__divide__eq]) ).
fof(i_0_5567,plain,
! [X21221,X21222] :
( ~ class_Int_Onumber__ring(X21222)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21222),hAPP(c_Int_Onumber__class_Onumber__of(X21222),c_Int_OBit1(c_Int_OPls))),X21221) = X21221 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__numeral__1])]) ).
fof(i_0_5568,plain,
! [X33528,X33529,X33530] : c_List_Orotate(X33530,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33529),X33528)) = hAPP(c_Fun_Ocomp(tc_List_Olist(X33530),tc_List_Olist(X33530),tc_List_Olist(X33530),c_List_Orotate(X33530,X33529)),c_List_Orotate(X33530,X33528)),
inference(variable_rename,[status(thm)],[fact_rotate__add]) ).
fof(i_0_5569,plain,
! [X141,X18,X38,X39,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X39,X38)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X18,X141)))
<=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),X38))
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X18),X39))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X38),X141)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_atLeastatMost__subset__iff]) ).
fof(i_0_5570,plain,
! [X21236,X21237] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21237),hAPP(c_Int_Onumber__class_Onumber__of(X21237),X21236)),c_Groups_Oone__class_Oone(X21237)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21236),c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(X21237)
| ~ class_Rings_Olinordered__idom(X21237) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21236),c_Int_OBit1(c_Int_OPls)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21237),hAPP(c_Int_Onumber__class_Onumber__of(X21237),X21236)),c_Groups_Oone__class_Oone(X21237)))
| ~ class_Int_Onumber__ring(X21237)
| ~ class_Rings_Olinordered__idom(X21237) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I4_J])])]) ).
fof(i_0_5571,plain,
! [X21240,X21241] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21241),hAPP(c_Int_Onumber__class_Onumber__of(X21241),X21240)),c_Groups_Oone__class_Oone(X21241)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21240),c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(X21241)
| ~ class_Rings_Olinordered__idom(X21241) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21240),c_Int_OBit1(c_Int_OPls)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21241),hAPP(c_Int_Onumber__class_Onumber__of(X21241),X21240)),c_Groups_Oone__class_Oone(X21241)))
| ~ class_Int_Onumber__ring(X21241)
| ~ class_Rings_Olinordered__idom(X21241) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I4_J])])]) ).
fof(i_0_5572,plain,
! [X30636,X30637] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30637,X30637)),X30636),c_Relation_OId(X30637)))
| X30636 = hAPP(hAPP(c_Product__Type_OPair(X30637,X30637),esk389_2(X30636,X30637)),esk389_2(X30636,X30637)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IdE])])]) ).
fof(i_0_5573,plain,
! [X72,X52,X50,X66,X51] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X51,X66,X50)),X52),X72))
<=> ( ( hBOOL(hAPP(X51,X52))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X66),X52),X72)) )
| ( ~ hBOOL(hAPP(X51,X52))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X50),X52),X72)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_evalc_Oequations_I6_J]) ).
fof(i_0_5574,plain,
! [X72,X52,X66,X50,X51] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X51,X50,X66)),X52),X72))
<=> ( ( hBOOL(hAPP(X51,X52))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X50),X52),X72)) )
| ( ~ hBOOL(hAPP(X51,X52))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X66),X52),X72)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_evalc_Oequations_I5_J]) ).
fof(i_0_5575,plain,
! [X53,X54,X74,X75,X38] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X38,X75,X74)),X54),X53))
=> ( ( hBOOL(hAPP(X38,X54))
=> ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X75),X54),X53)) )
=> ~ ( ~ hBOOL(hAPP(X38,X54))
=> ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X74),X54),X53)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_evalc__elim__cases_I5_J]) ).
fof(i_0_5576,plain,
! [X21229] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X21229)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X21229)),
inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I4_J]) ).
fof(i_0_5577,plain,
! [X30168,X30169] : hBOOL(hAPP(hAPP(c_member(tc_prod(X30169,X30169)),hAPP(hAPP(c_Product__Type_OPair(X30169,X30169),X30168),X30168)),c_Relation_OId(X30169))),
inference(variable_rename,[status(thm)],[fact_IdI]) ).
fof(i_0_5578,plain,
! [X34263,X34264,X34265] : hAPP(c_List_Ofoldl(tc_List_Olist(X34265),tc_List_Olist(X34265),c_List_Oappend(X34265),X34264),X34263) = hAPP(hAPP(c_List_Oappend(X34265),X34264),c_List_Oconcat(X34265,X34263)),
inference(variable_rename,[status(thm)],[fact_foldl__conv__concat]) ).
fof(i_0_5579,plain,
! [X21314,X21315] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X21315)),c_Int_OBit1(X21314)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X21315),X21314)),
inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I10_J]) ).
fof(i_0_5580,plain,
! [X290,X16,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
=> c_List_Olinorder__class_Oinsort__insert__key(X10,X10,c_COMBI(X10),X16,X290) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X10,c_COMBI(X10)),X16),X290) ) ),
inference(fof_simplification,[status(thm)],[fact_insort__insert__insort]) ).
fof(i_0_5581,plain,
! [X177,X10] :
( c_Relation_Oirrefl(X10,X177)
<=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X3)),X177)) ),
inference(fof_simplification,[status(thm)],[fact_irrefl__def]) ).
fof(i_0_5582,plain,
! [X39,X177,X10] :
( c_Wellfounded_Owf(X10,X177)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X39)),X177)) ),
inference(fof_simplification,[status(thm)],[fact_wf__not__refl]) ).
fof(i_0_5583,plain,
! [X39,X177,X10] :
( c_Wellfounded_Owf(X10,X177)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X39),X39)),X177)) ),
inference(fof_simplification,[status(thm)],[fact_wf__irrefl]) ).
fof(i_0_5584,plain,
! [X30237,X30238] : c_Transitive__Closure_Ortrancl(X30238,X30237) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30238,X30238),tc_HOL_Obool)),c_Relation_OId(X30238)),hAPP(hAPP(c_Relation_Orel__comp(X30238,X30238,X30238),c_Transitive__Closure_Ortrancl(X30238,X30237)),X30237)),
inference(variable_rename,[status(thm)],[fact_rtrancl__unfold]) ).
fof(i_0_5585,plain,
! [X39,X160,X154,X13,X38,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X38),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13,tc_fun(X10,tc_HOL_Obool)),X154),X160)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X38),hAPP(X160,X39)))
=> ~ hBOOL(hAPP(hAPP(c_member(X13),X39),X154)) ) ),
inference(fof_simplification,[status(thm)],[fact_INT__E]) ).
fof(i_0_5586,plain,
! [X21208] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X21208)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X21208)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X21208))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X21208))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I22_J])]) ).
fof(i_0_5587,plain,
! [X21227] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X21227)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X21227)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X21227))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X21227))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I5_J])]) ).
fof(i_0_5588,plain,
! [X21212] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X21212)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X21212)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X21212))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X21212))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I26_J])]) ).
fof(i_0_5589,plain,
! [X21214] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X21214)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X21214)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X21214))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X21214))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I9_J])]) ).
fof(i_0_5590,plain,
! [X21896,X21897,X21898] :
( ~ class_Int_Onumber__ring(X21898)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21898),hAPP(c_Int_Onumber__class_Onumber__of(X21898),X21897)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X21896))) = hAPP(hAPP(c_HOL_OLet(X21898,X21898),hAPP(hAPP(c_Power_Opower__class_Opower(X21898),hAPP(c_Int_Onumber__class_Onumber__of(X21898),X21897)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21896))),hAPP(hAPP(c_COMBS(X21898,X21898,X21898),c_Groups_Otimes__class_Otimes(X21898)),c_COMBI(X21898))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__number__of__even__number__of])]) ).
fof(i_0_5591,plain,
! [X16,X25,X154,X2,X13,X10] :
( c_Fun_Oinj__on(X10,X13,X2,X154)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X13),X25),hAPP(c_Set_Oimage(X10,X13,X2),X154)))
=> c_Fun_Oinj__on(X10,X13,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,X13),X2),X16),X25),X154) ) ),
inference(fof_simplification,[status(thm)],[fact_inj__on__fun__updI]) ).
fof(i_0_5592,plain,
! [X16,X25,X18] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18),X25))
=> 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)),X18)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X16),X25)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16),X18)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),X18)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18),X25))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16),X25))
=> 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)),X18)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X16),X25)) = 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),X16),X25))
=> 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)),X18)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X16),X25)) = 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,
! [X33599,X33600] :
( ~ class_Groups_Omonoid__add(X33600)
| hAPP(c_List_Ofoldl(X33600,X33600,c_Groups_Oplus__class_Oplus(X33600),c_Groups_Ozero__class_Ozero(X33600)),X33599) = c_List_Ofoldr(X33600,X33600,c_Groups_Oplus__class_Oplus(X33600),X33599,c_Groups_Ozero__class_Ozero(X33600)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__foldr1])]) ).
fof(i_0_5594,plain,
! [X34166,X34167,X34168,X34169,X34170] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34170),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X34169),X34168)))
| hAPP(hAPP(c_List_Onth(X34167),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X34167),X34166),c_List_Oupt(X34168,X34169))),X34170) = hAPP(X34166,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34168),X34170)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__map__upt])]) ).
fof(i_0_5595,plain,
! [X33491,X33492,X33493,X33494] : hAPP(c_List_Orotate(X33494,X33493),hAPP(c_List_Orotate(X33494,X33492),X33491)) = hAPP(c_List_Orotate(X33494,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33493),X33492)),X33491),
inference(variable_rename,[status(thm)],[fact_rotate__rotate]) ).
fof(i_0_5596,plain,
! [X33578,X33579,X33580] :
( ~ class_Groups_Oab__semigroup__add(X33580)
| c_List_Ofoldr(X33580,X33580,c_Groups_Oplus__class_Oplus(X33580),X33579,X33578) = hAPP(c_List_Ofoldl(X33580,X33580,c_Groups_Oplus__class_Oplus(X33580),X33578),X33579) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldr__conv__foldl])]) ).
fof(i_0_5597,plain,
! [X2,X13,X290,X16,X10] :
( ( hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
=> hAPP(c_Map_Omap__of(X10,X13,hAPP(hAPP(c_List_Ozip(X10,X13),X290),hAPP(hAPP(c_List_Omap(X10,X13),X2),X290))),X16) = hAPP(c_Option_Ooption_OSome(X13),hAPP(X2,X16)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
=> hAPP(c_Map_Omap__of(X10,X13,hAPP(hAPP(c_List_Ozip(X10,X13),X290),hAPP(hAPP(c_List_Omap(X10,X13),X2),X290))),X16) = c_Option_Ooption_ONone(X13) ) ),
inference(fof_simplification,[status(thm)],[fact_map__of__zip__map]) ).
fof(i_0_5598,plain,
! [X33507,X33508,X33509] : hAPP(c_List_Orotate(X33509,X33508),X33507) = hAPP(c_List_Orotate(X33509,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X33508,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33509)),X33507))),X33507),
inference(variable_rename,[status(thm)],[fact_rotate__conv__mod]) ).
fof(i_0_5599,plain,
! [X21217,X21218] :
( ~ class_Int_Onumber__ring(X21218)
| ~ class_Int_Oring__char__0(X21218)
| ~ c_Int_Oiszero(X21218,hAPP(c_Int_Onumber__class_Onumber__of(X21218),c_Int_OBit1(X21217))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5183])]) ).
fof(i_0_5600,plain,
! [X25,X102,X13,X154,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Set_Oimage(X10,tc_Option_Ooption(X13),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,tc_Option_Ooption(X13)),X102),X16),hAPP(c_Option_Ooption_OSome(X13),X25))),X154) = hAPP(c_Set_Oimage(X10,tc_Option_Ooption(X13),X102),X154) ),
inference(fof_simplification,[status(thm)],[fact_image__map__upd]) ).
fof(i_0_5601,plain,
! [X21321] : c_Int_Opred(c_Int_OBit0(X21321)) = c_Int_OBit1(c_Int_Opred(X21321)),
inference(variable_rename,[status(thm)],[fact_pred__Bit0]) ).
fof(i_0_5602,plain,
! [X39,X2,X154,X10,X13] :
( class_Fields_Ofield(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( hAPP(X2,X39) != c_Groups_Ozero__class_Ozero(X13)
=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),X154)),hAPP(X2,X39)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),X154) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setprod__diff1]) ).
fof(i_0_5603,plain,
! [X30309,X30310] : c_Relation_Orefl__on(X30310,c_Orderings_Otop__class_Otop(tc_fun(X30310,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30310,X30310),tc_HOL_Obool)),X30309),c_Relation_OId(X30310))),
inference(variable_rename,[status(thm)],[fact_refl__reflcl]) ).
fof(i_0_5604,plain,
! [X2,X39,X154,X10,X13] :
( class_Groups_Oab__group__add(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X13),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),X154)),hAPP(X2,X39)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),X154) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum__diff1]) ).
fof(i_0_5605,plain,
! [X34274,X34275] : hAPP(c_List_Oset(X34275),c_List_Oconcat(X34275,X34274)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X34275),tc_fun(X34275,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X34275)),X34274)),c_List_Oset(X34275)),
inference(variable_rename,[status(thm)],[fact_set__concat]) ).
fof(i_0_5606,plain,
! [X34213,X34214] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34214)),c_List_Oconcat(X34214,X34213)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X34214),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X34214))),X34213)),
inference(variable_rename,[status(thm)],[fact_length__concat]) ).
fof(i_0_5607,plain,
! [X39,X38,X160,X154,X13,X10] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X13,tc_HOL_Obool)),X154),X160),X38))
=> ( ~ hBOOL(hAPP(hAPP(X160,X39),X38))
=> ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X154)) ) ),
inference(fof_simplification,[status(thm)],[fact_INF1__E]) ).
fof(i_0_5608,plain,
! [X34349,X34350,X34351] :
( ( X34350 != c_List_Olist_ONil(X34351)
| c_List_Ofoldr(X34351,X34351,c_Orderings_Oord__class_Omax(X34351),X34350,X34349) = X34349
| ~ c_List_Olinorder__class_Osorted(X34351,hAPP(c_List_Orev(X34351),X34350))
| ~ class_Orderings_Olinorder(X34351) )
& ( X34350 = c_List_Olist_ONil(X34351)
| c_List_Ofoldr(X34351,X34351,c_Orderings_Oord__class_Omax(X34351),X34350,X34349) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X34351),hAPP(hAPP(c_List_Onth(X34351),X34350),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X34349)
| ~ c_List_Olinorder__class_Osorted(X34351,hAPP(c_List_Orev(X34351),X34350))
| ~ class_Orderings_Olinorder(X34351) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldr__max__sorted])])]) ).
fof(i_0_5609,plain,
! [X19,X290,X16,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
=> ( ~ hBOOL(hAPP(X19,X16))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),hAPP(c_List_Ofilter(X10,X19),X290))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290))) ) ),
inference(fof_simplification,[status(thm)],[fact_length__filter__less]) ).
fof(i_0_5610,plain,
! [X30223,X30224] : c_Transitive__Closure_Ortrancl(X30224,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30224,X30224),tc_HOL_Obool)),X30223),c_Relation_OId(X30224))) = c_Transitive__Closure_Ortrancl(X30224,X30223),
inference(variable_rename,[status(thm)],[fact_rtrancl__reflcl]) ).
fof(i_0_5611,plain,
! [X30205,X30206] : c_Transitive__Closure_Ortrancl(X30206,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X30206,X30206),tc_HOL_Obool)),X30205),c_Relation_OId(X30206))) = c_Transitive__Closure_Ortrancl(X30206,X30205),
inference(variable_rename,[status(thm)],[fact_rtrancl__r__diff__Id]) ).
fof(i_0_5612,plain,
! [X30312,X30313] : c_Relation_Oirrefl(X30313,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X30313,X30313),tc_HOL_Obool)),X30312),c_Relation_OId(X30313))),
inference(variable_rename,[status(thm)],[fact_irrefl__diff__Id]) ).
fof(i_0_5613,plain,
! [X21230] :
( ~ class_Int_Onumber__ring(X21230)
| ~ c_Int_Oiszero(X21230,hAPP(c_Int_Onumber__class_Onumber__of(X21230),c_Int_OBit1(c_Int_OPls))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5184])]) ).
fof(i_0_5614,plain,
! [X143,X149,X92,X84] :
( X84 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X92),X149)),X143)
=> ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X143))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X143),X92)) ) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X92))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X92),X143))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X143),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(X84,X92),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X149),X143))) ) ),
inference(fof_simplification,[status(thm)],[fact_divmod__int__relI]) ).
fof(i_0_5615,plain,
! [X21341] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X21341)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X21341)),
inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I5_J]) ).
fof(i_0_5616,plain,
! [X2,X154,X39,X10] :
( ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),X154)),hAPP(X2,X39)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),X154) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum__diff1__nat]) ).
fof(i_0_5617,plain,
! [X30397,X30398] :
( ~ c_Wellfounded_Owf(X30398,hAPP(c_Relation_Oconverse(X30398,X30398),X30397))
| c_Wellfounded_Owf(X30398,hAPP(c_Relation_Oconverse(X30398,X30398),c_Transitive__Closure_Otrancl(X30398,X30397))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__converse__trancl])]) ).
fof(i_0_5618,plain,
! [X2,X113,X141] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X141),X113))
=> c_Smallcheck_Osmall_H(X2,X141,X113) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X141),X113))
=> c_Smallcheck_Osmall_H(X2,X141,X113) = 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,X141,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X113),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(X2,X113)) ) ),
inference(fof_simplification,[status(thm)],[fact_small_H_Osimps]) ).
fof(i_0_5619,plain,
! [X34228,X34229,X34230,X34231,X34232] :
( ( c_List_Oconcat(X34229,X34228) != c_List_Olist_ONil(X34229)
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X34229)),X34230),hAPP(c_List_Oset(tc_List_Olist(X34229)),X34228)))
| X34230 = c_List_Olist_ONil(X34229) )
& ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X34232)),esk492_2(X34231,X34232)),hAPP(c_List_Oset(tc_List_Olist(X34232)),X34231)))
| c_List_Oconcat(X34232,X34231) = c_List_Olist_ONil(X34232) )
& ( esk492_2(X34231,X34232) != c_List_Olist_ONil(X34232)
| c_List_Oconcat(X34232,X34231) = c_List_Olist_ONil(X34232) ) ),
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,
! [X34234,X34235,X34236,X34237,X34238] :
( ( c_List_Olist_ONil(X34235) != c_List_Oconcat(X34235,X34234)
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X34235)),X34236),hAPP(c_List_Oset(tc_List_Olist(X34235)),X34234)))
| X34236 = c_List_Olist_ONil(X34235) )
& ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X34238)),esk493_2(X34237,X34238)),hAPP(c_List_Oset(tc_List_Olist(X34238)),X34237)))
| c_List_Olist_ONil(X34238) = c_List_Oconcat(X34238,X34237) )
& ( esk493_2(X34237,X34238) != c_List_Olist_ONil(X34238)
| c_List_Olist_ONil(X34238) = c_List_Oconcat(X34238,X34237) ) ),
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,
! [X34048,X34049,X34050] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34050),X34049))
| c_List_Oupt(X34050,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34049),X34048)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X34050,X34049)),c_List_Oupt(X34049,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34049),X34048))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__add__eq__append])]) ).
fof(i_0_5622,plain,
! [X2,X102,X20,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)),X102))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X102,hAPP(c_Nat_OSuc,X20))) = c_Groups_Ozero__class_Ozero(X10) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)),X102))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X102,hAPP(c_Nat_OSuc,X20))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X102,X20))),hAPP(X2,hAPP(c_Nat_OSuc,X20))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum__cl__ivl__Suc]) ).
fof(i_0_5623,plain,
! [X160,X154,X18,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X18),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X18),X154))
=> hBOOL(hAPP(hAPP(c_member(X10),X18),X160)) ) ),
inference(fof_simplification,[status(thm)],[fact_UnE]) ).
fof(i_0_5624,plain,
! [X16,X154,X225,X2,X13,X10] :
( c_Finite__Set_Ofolding(X10,X13,X2,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(X225,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(c_Fun_Ocomp(X13,X13,X13,hAPP(X225,X154)),hAPP(X2,X16)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_folding_Oinsert]) ).
fof(i_0_5625,plain,
! [X21325] : c_Int_Osucc(c_Int_OBit1(X21325)) = c_Int_OBit0(c_Int_Osucc(X21325)),
inference(variable_rename,[status(thm)],[fact_succ__Bit1]) ).
fof(i_0_5626,plain,
! [X59,X42,X45,X87] :
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X87),X45,X42,X59)
=> ~ ! [X83] :
( X42 = hAPP(c_Nat_OSuc,X83)
=> ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X87)),X45,X83,X59) ) ),
inference(fof_simplification,[status(thm)],[fact_evaln__elim__cases_I6_J]) ).
fof(i_0_5627,plain,
! [X21891,X21892,X21893] :
( ~ class_Int_Onumber__ring(X21893)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21893),X21892),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X21891))) = hAPP(hAPP(c_HOL_OLet(X21893,X21893),hAPP(hAPP(c_Power_Opower__class_Opower(X21893),X21892),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21891))),hAPP(hAPP(c_COMBS(X21893,X21893,X21893),c_Groups_Otimes__class_Otimes(X21893)),c_COMBI(X21893))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__number__of__even])]) ).
fof(i_0_5628,plain,
! [X160,X154,X18,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X18),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160)))
<=> ( hBOOL(hAPP(hAPP(c_member(X10),X18),X154))
& ~ hBOOL(hAPP(hAPP(c_member(X10),X18),X160)) ) ),
inference(fof_simplification,[status(thm)],[fact_Diff__iff]) ).
fof(i_0_5629,plain,
! [X160,X154,X18,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X18),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160)))
=> ~ hBOOL(hAPP(hAPP(c_member(X10),X18),X160)) ),
inference(fof_simplification,[status(thm)],[fact_DiffD2]) ).
fof(i_0_5630,plain,
! [X101,X154,X10] :
( hAPP(c_Finite__Set_Ocard(X10),X154) = hAPP(c_Nat_OSuc,X101)
<=> ? [X193,X231] :
( X154 = hAPP(hAPP(c_Set_Oinsert(X10),X193),X231)
& ~ hBOOL(hAPP(hAPP(c_member(X10),X193),X231))
& hAPP(c_Finite__Set_Ocard(X10),X231) = X101
& ( X101 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> X231 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_card__Suc__eq]) ).
fof(i_0_5631,plain,
! [X34059,X34060,X34061] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34061),X34060)),X34059))
| hAPP(hAPP(c_List_Otake(tc_Nat_Onat),X34060),c_List_Oupt(X34061,X34059)) = c_List_Oupt(X34061,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34061),X34060)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__upt])]) ).
fof(i_0_5632,plain,
! [X33499,X33500,X33501,X33502,X33503] : hAPP(c_List_Orotate(X33503,X33502),hAPP(hAPP(c_List_Omap(X33501,X33503),X33500),X33499)) = hAPP(hAPP(c_List_Omap(X33501,X33503),X33500),hAPP(c_List_Orotate(X33501,X33502),X33499)),
inference(variable_rename,[status(thm)],[fact_rotate__map]) ).
fof(i_0_5633,plain,
! [X30399,X30400] : c_Transitive__Closure_Otrancl(X30400,hAPP(c_Relation_Oconverse(X30400,X30400),X30399)) = hAPP(c_Relation_Oconverse(X30400,X30400),c_Transitive__Closure_Otrancl(X30400,X30399)),
inference(variable_rename,[status(thm)],[fact_trancl__converse]) ).
fof(i_0_5634,plain,
! [X289,X13,X25,X16,X2,X10] :
( class_Orderings_Olinorder(X10)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(X2,X16)),hAPP(X2,X25)))
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X13,X10,X2),X16),hAPP(hAPP(c_List_Olist_OCons(X13),X25),X289)) = hAPP(hAPP(c_List_Olist_OCons(X13),X16),hAPP(hAPP(c_List_Olist_OCons(X13),X25),X289)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(X2,X16)),hAPP(X2,X25)))
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X13,X10,X2),X16),hAPP(hAPP(c_List_Olist_OCons(X13),X25),X289)) = hAPP(hAPP(c_List_Olist_OCons(X13),X25),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X13,X10,X2),X16),X289)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_insort__key_Osimps_I2_J]) ).
fof(i_0_5635,plain,
! [X42,X97] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X97)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X42)))
=> c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X97),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X42)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X97)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X97)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X42))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X97)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X42)))
=> c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X97),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X42)) = c_List_Olist_ONil(tc_Int_Oint) ) ),
inference(fof_simplification,[status(thm)],[fact_upto__rec__number__of]) ).
fof(i_0_5636,plain,
! [X160,X154,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),X160)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160)) ) ),
inference(fof_simplification,[status(thm)],[fact_subset__insert]) ).
fof(i_0_5637,plain,
! [X160,X154,X18,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X18),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(X10),X18),X154))
=> ~ hBOOL(hAPP(hAPP(c_member(X10),X18),X160)) ) ),
inference(fof_simplification,[status(thm)],[fact_IntE]) ).
fof(i_0_5638,plain,
! [X163,X113] :
( 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),X113),X163)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X113),X163))
=> c_List_Oupto(X113,X163) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X113),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X113),c_Groups_Oone__class_Oone(tc_Int_Oint)),X163)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X113),X163))
=> c_List_Oupto(X113,X163) = c_List_Olist_ONil(tc_Int_Oint) ) ) ),
inference(fof_simplification,[status(thm)],[fact_upto_Opsimps]) ).
fof(i_0_5639,plain,
! [X73,X16,X154,X2,X13,X10] :
( c_Finite__Set_Ofun__left__comm(X10,X13,X2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(hAPP(c_Finite__Set_Ofold(X10,X13,X2),X73),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(X2,X16),hAPP(hAPP(c_Finite__Set_Ofold(X10,X13,X2),X73),X154)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__insert]) ).
fof(i_0_5640,plain,
! [X76,X77,X75,X54,X38] :
( ~ hBOOL(hAPP(X38,X54))
=> ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X75),X54),X77))
=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X38,X76,X75)),X54),X77)) ) ),
inference(fof_simplification,[status(thm)],[fact_evalc_OIfFalse]) ).
fof(i_0_5641,plain,
! [X16,X289,X13,X290,X10] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13)),X289)
=> ( hAPP(c_Map_Omap__of(X10,X13,hAPP(hAPP(c_List_Ozip(X10,X13),X290),X289)),X16) = c_Option_Ooption_ONone(X13)
<=> ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290))) ) ),
inference(fof_simplification,[status(thm)],[fact_map__of__zip__is__None]) ).
fof(i_0_5642,plain,
! [X168,X2,X13,X290,X25,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X25),hAPP(c_List_Oset(X10),X290)))
=> hAPP(hAPP(c_List_Omap(X10,X13),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10,X13),X2),X25),X168)),X290) = hAPP(hAPP(c_List_Omap(X10,X13),X2),X290) ),
inference(fof_simplification,[status(thm)],[fact_map__fun__upd]) ).
fof(i_0_5643,plain,
! [X241,X290,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
=> ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),c_List_Osublist(X10,X290,X241)))) ),
inference(fof_simplification,[status(thm)],[fact_notin__set__sublistI]) ).
fof(i_0_5644,plain,
! [X25,X290,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
=> ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),c_List_Oremove1(X10,X25,X290)))) ),
inference(fof_simplification,[status(thm)],[fact_notin__set__remove1]) ).
fof(i_0_5645,plain,
! [X34154,X34155,X34156] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34156),X34155)),X34154))
| hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(X34156,X34154)),X34155) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34156),X34155) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__upt])]) ).
fof(i_0_5646,plain,
! [X21894,X21895] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X21895),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X21894))) = 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),X21894))),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,X10,X13] :
( class_Orderings_Oord(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,X13)),X2),X1))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X13)),X2),X1))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X13)),X1),X2)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__fun__def]) ).
fof(i_0_5648,plain,
! [X297,X93,X94,X120] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X120),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X94),X93)))
=> hAPP(c_Random_Opick(X94,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X94)),X93),X297)),X120) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X94),X93) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X120),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X94),X93)))
=> hAPP(c_Random_Opick(X94,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X94)),X93),X297)),X120) = hAPP(c_Random_Opick(X94,X297),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X120),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X94),X93))) ) ),
inference(fof_simplification,[status(thm)],[fact_pick_Osimps]) ).
fof(i_0_5649,plain,
! [X198,X154,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X154),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X198)))
=> ~ ! [X270] :
( hBOOL(hAPP(hAPP(c_member(X10),X154),X270))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X270),X198)) ) ),
inference(fof_simplification,[status(thm)],[fact_UnionE]) ).
fof(i_0_5650,plain,
! [X21272,X21273] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21273)),c_Int_OBit0(X21272)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21273),X21272)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21273),X21272))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21273)),c_Int_OBit0(X21272))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I13_J])]) ).
fof(i_0_5651,plain,
! [X21270,X21271] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21271)),c_Int_OBit0(X21270)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21271),X21270)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21271),X21270))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21271)),c_Int_OBit0(X21270))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I31_J])]) ).
fof(i_0_5652,plain,
! [X21276,X21277] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21277)),c_Int_OBit0(X21276)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21277),X21276)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21277),X21276))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21277)),c_Int_OBit0(X21276))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I13_J])]) ).
fof(i_0_5653,plain,
! [X21274,X21275] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21275)),c_Int_OBit0(X21274)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21275),X21274)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21275),X21274))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21275)),c_Int_OBit0(X21274))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I14_J])]) ).
fof(i_0_5654,plain,
! [X16,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X154)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(X10),X154) ) ) ),
inference(fof_simplification,[status(thm)],[fact_card__Diff__singleton__if]) ).
fof(i_0_5655,plain,
! [X21242,X21243] :
( ~ class_Int_Onumber__ring(X21243)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21243),hAPP(c_Int_Onumber__class_Onumber__of(X21243),X21242)),c_Groups_Oone__class_Oone(X21243)) = hAPP(c_Int_Onumber__class_Onumber__of(X21243),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21242),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,
! [X131,X168,X10] :
( ( class_Int_Onumber(X10)
& class_Orderings_Olinorder(X10) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X168)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)))
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X131)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X168))) ) ),
inference(fof_simplification,[status(thm)],[fact_le__number__of__eq__not__less]) ).
fof(i_0_5657,plain,
! [X25,X16,X13,X10] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X10,tc_fun(X13,tc_HOL_Obool))),X16),X25)),
inference(fof_simplification,[status(thm)],[fact_bot2E]) ).
fof(i_0_5658,plain,
! [X66,X72,X52,X65,X50,X51] :
( c_Natural_Oevaln(c_Com_Ocom_OCond(X51,X50,X65),X52,X72,X66)
<=> ( ( hBOOL(hAPP(X51,X52))
& c_Natural_Oevaln(X50,X52,X72,X66) )
| ( ~ hBOOL(hAPP(X51,X52))
& c_Natural_Oevaln(X65,X52,X72,X66) ) ) ),
inference(fof_simplification,[status(thm)],[fact_evaln_Oequations_I5_J]) ).
fof(i_0_5659,plain,
! [X66,X72,X52,X50,X65,X51] :
( c_Natural_Oevaln(c_Com_Ocom_OCond(X51,X65,X50),X52,X72,X66)
<=> ( ( hBOOL(hAPP(X51,X52))
& c_Natural_Oevaln(X65,X52,X72,X66) )
| ( ~ hBOOL(hAPP(X51,X52))
& c_Natural_Oevaln(X50,X52,X72,X66) ) ) ),
inference(fof_simplification,[status(thm)],[fact_evaln_Oequations_I6_J]) ).
fof(i_0_5660,plain,
! [X53,X20,X54,X74,X75,X38] :
( c_Natural_Oevaln(c_Com_Ocom_OCond(X38,X75,X74),X54,X20,X53)
=> ( ( hBOOL(hAPP(X38,X54))
=> ~ c_Natural_Oevaln(X75,X54,X20,X53) )
=> ~ ( ~ hBOOL(hAPP(X38,X54))
=> ~ c_Natural_Oevaln(X74,X54,X20,X53) ) ) ),
inference(fof_simplification,[status(thm)],[fact_evaln__elim__cases_I5_J]) ).
fof(i_0_5661,plain,
! [X105,X155,X156,X126] :
( X126 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X156),X155)),X105)
=> ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X156))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X105))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X105),X156)) ) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X156))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X156),X105))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X105),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
=> ( X156 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X126,X156) = X105 ) ) ),
inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__mod__eq]) ).
fof(i_0_5662,plain,
! [X32772,X32773,X32774,X32775] : c_List_Ofoldr(X32775,X32774,X32773,c_List_Olist_ONil(X32775),X32772) = X32772,
inference(variable_rename,[status(thm)],[fact_foldr_Osimps_I1_J]) ).
fof(i_0_5663,plain,
! [X157,X105,X156,X126] :
( X126 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X156),X105)),X157)
=> ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X156))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X157))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X157),X156)) ) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X156))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X156),X157))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X157),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
=> ( X156 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X126),X156) = X105 ) ) ),
inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__div__eq]) ).
fof(i_0_5664,plain,
! [X33521,X33522,X33523] : hAPP(c_List_Orotate(X33523,hAPP(c_Nat_OSuc,X33522)),X33521) = hAPP(c_List_Orotate1(X33523),hAPP(c_List_Orotate(X33523,X33522),X33521)),
inference(variable_rename,[status(thm)],[fact_rotate__Suc]) ).
fof(i_0_5665,plain,
! [X73,X16,X154,X2,X13,X10] :
( c_Finite__Set_Ofun__left__comm(X10,X13,X2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(hAPP(c_Finite__Set_Ofold(X10,X13,X2),X73),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X13,X2),hAPP(hAPP(X2,X16),X73)),X154) ) ) ),
inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__insert2]) ).
fof(i_0_5666,plain,
! [X34033,X34034,X34035,X34036] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34036),X34035))
| c_List_Oupt(X34036,X34035) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X34034),X34033) )
& ( X34036 = X34034
| c_List_Oupt(X34036,X34035) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X34034),X34033) )
& ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34036),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X34035) = X34033
| c_List_Oupt(X34036,X34035) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X34034),X34033) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34036),X34035))
| X34036 != X34034
| c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34036),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X34035) != X34033
| c_List_Oupt(X34036,X34035) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X34034),X34033) ) ),
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,X102,X20,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X102))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X102),hAPP(c_Nat_OSuc,X20))) = c_Groups_Ozero__class_Ozero(X10) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X102))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X102),hAPP(c_Nat_OSuc,X20))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X102),X20))),hAPP(X2,X20)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum__op__ivl__Suc]) ).
fof(i_0_5668,plain,
! [X16,X160,X154,X10] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160),X16))
=> ( ~ hBOOL(hAPP(X154,X16))
=> hBOOL(hAPP(X160,X16)) ) ),
inference(fof_simplification,[status(thm)],[fact_sup1E]) ).
fof(i_0_5669,plain,
! [X21322] : c_Int_Opred(c_Int_OBit1(X21322)) = c_Int_OBit0(X21322),
inference(variable_rename,[status(thm)],[fact_pred__Bit1]) ).
fof(i_0_5670,plain,
! [X103,X170,X144] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)),X103)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)),X103) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X170)))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)),X103)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),X103) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X170)))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)),X103)) = 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),X144),X170))),X103) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__number__of__add__left]) ).
fof(i_0_5671,plain,
! [X30115] : c_Transitive__Closure_Otrancl(X30115,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X30115,X30115),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X30115,X30115),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_trancl__empty]) ).
fof(i_0_5672,plain,
! [X34146,X34147,X34148,X34149] :
( ~ class_Groups_Ocomm__monoid__add(X34149)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X34149),X34148),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X34147,X34146))) = hAPP(c_List_Omonoid__add__class_Olistsum(X34149),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X34149),X34148),c_List_Oupt(X34147,X34146))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__set__upt__conv__listsum__nat])]) ).
fof(i_0_5673,plain,
! [X34150,X34151,X34152,X34153] :
( ~ class_Groups_Ocomm__monoid__add(X34153)
| hAPP(c_List_Omonoid__add__class_Olistsum(X34153),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X34153),X34152),c_List_Oupt(X34151,X34150))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X34153),X34152),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X34151,X34150))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_interv__listsum__conv__setsum__set__nat])]) ).
fof(i_0_5674,plain,
! [X16,X160,X154,X10] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160),X16))
=> ~ ( hBOOL(hAPP(X154,X16))
=> ~ hBOOL(hAPP(X160,X16)) ) ),
inference(fof_simplification,[status(thm)],[fact_inf1E]) ).
fof(i_0_5675,plain,
! [X33518,X33519,X33520] : hAPP(c_List_Orotate1(X33520),hAPP(c_List_Orotate(X33520,X33519),X33518)) = hAPP(c_List_Orotate(X33520,X33519),hAPP(c_List_Orotate1(X33520),X33518)),
inference(variable_rename,[status(thm)],[fact_rotate1__rotate__swap]) ).
fof(i_0_5676,plain,
! [X21219,X21220] :
( ~ class_Int_Onumber__ring(X21220)
| hAPP(c_Int_Onumber__class_Onumber__of(X21220),c_Int_OBit1(X21219)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21220),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21220),c_Groups_Oone__class_Oone(X21220)),hAPP(c_Int_Onumber__class_Onumber__of(X21220),X21219))),hAPP(c_Int_Onumber__class_Onumber__of(X21220),X21219)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Bit1])]) ).
fof(i_0_5677,plain,
! [X160,X154,X18,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X18),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X18),X160))
=> hBOOL(hAPP(hAPP(c_member(X10),X18),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160))) ) ),
inference(fof_simplification,[status(thm)],[fact_DiffI]) ).
fof(i_0_5678,plain,
! [X21864,X21865,X21866,X21867] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X21867,X21866,X21865,c_Code__Numeral_OSuc__code__numeral(X21864)) = hAPP(hAPP(X21865,X21864),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X21867,X21866,X21865,X21864)),
inference(variable_rename,[status(thm)],[fact_code__numeral_Orecs_I2_J]) ).
fof(i_0_5679,plain,
! [X22793] : c_Code__Numeral_OSuc__code__numeral(X22793) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X22793))),
inference(variable_rename,[status(thm)],[fact_Suc__code__numeral__def]) ).
fof(i_0_5680,plain,
! [X154,X10] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(c_Finite__Set_Ocard(X10),X154) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X10,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X10),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X154) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(c_Finite__Set_Ocard(X10),X154) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_simplification,[status(thm)],[fact_card__def]) ).
fof(i_0_5681,plain,
! [X30250,X30251,X30252] : hAPP(hAPP(c_Relation_Orel__comp(X30252,X30252,X30251),c_Relation_OId(X30252)),X30250) = X30250,
inference(variable_rename,[status(thm)],[fact_Id__O__R]) ).
fof(i_0_5682,plain,
! [X21750,X21751] :
( ~ class_Fields_Ofield(X21751)
| ~ class_Int_Onumber__ring(X21751)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21751),X21750),hAPP(c_Int_Onumber__class_Onumber__of(X21751),c_Int_OBit1(c_Int_OPls))) = X21750 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__numeral__1])]) ).
fof(i_0_5683,plain,
! [X21748,X21749] :
( ~ class_Fields_Ofield(X21749)
| ~ class_Int_Onumber__ring(X21749)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21749),X21748),hAPP(c_Int_Onumber__class_Onumber__of(X21749),c_Int_OBit1(c_Int_OPls))) = X21748 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__Numeral1])]) ).
fof(i_0_5684,plain,
! [X93,X92,X84,X94] :
( class_Lattices_Osemilattice__sup(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X94),X84),X92)),X93))
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X93))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X92),X93)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_le__supE]) ).
fof(i_0_5685,plain,
! [X93,X92,X84,X94] :
( class_Orderings_Olinorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),hAPP(hAPP(c_Orderings_Oord__class_Omax(X94),X84),X92)),X93))
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X84),X93))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X92),X93)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_min__max_Ole__supE]) ).
fof(i_0_5686,plain,
! [X21223,X21224] :
( ~ class_Int_Onumber__ring(X21224)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21224),X21223),hAPP(c_Int_Onumber__class_Onumber__of(X21224),c_Int_OBit1(c_Int_OPls))) = X21223 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__numeral__1__right])]) ).
fof(i_0_5687,plain,
! [X33464,X33465,X33466] :
( X33466 = c_List_Olist_ONil(X33465)
| hAPP(c_List_Ohd(X33465),hAPP(c_List_Orotate(X33465,X33464),X33466)) = hAPP(hAPP(c_List_Onth(X33465),X33466),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X33464,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33465)),X33466))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__rotate__conv__nth])]) ).
fof(i_0_5688,plain,
! [X103,X170,X144] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X144),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)),X103)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X144),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)),X103)) = 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),X144),X170))),X103) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__number__of__mult__left]) ).
fof(i_0_5689,plain,
! [X33534,X33535,X33536] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33536)),X33535)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| hAPP(c_List_Orotate(X33536,X33534),X33535) = X33535 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate__length01])]) ).
fof(i_0_5690,plain,
! [X160,X198,X39,X10] :
( ( hBOOL(hAPP(hAPP(c_member(X10),X39),X198))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X39),X160)),X198) = hAPP(hAPP(c_Set_Oinsert(X10),X39),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X160),X198)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X198))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X39),X160)),X198) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X160),X198) ) ),
inference(fof_simplification,[status(thm)],[fact_Int__insert__left]) ).
fof(i_0_5691,plain,
! [X154,X160,X18,X10] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X10),X18),X160))
=> hBOOL(hAPP(hAPP(c_member(X10),X18),X154)) )
=> hBOOL(hAPP(hAPP(c_member(X10),X18),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160))) ),
inference(fof_simplification,[status(thm)],[fact_UnCI]) ).
fof(i_0_5692,plain,
! [X281,X282,X13,X102,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X102),c_Map_Odom(X10,X13,X282)))
=> hAPP(c_Map_Omap__add(X10,X13,X282,X281),X102) = hAPP(X281,X102) ),
inference(fof_simplification,[status(thm)],[fact_map__add__dom__app__simps_I2_J]) ).
fof(i_0_5693,plain,
! [X282,X281,X13,X102,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X102),c_Map_Odom(X10,X13,X281)))
=> hAPP(c_Map_Omap__add(X10,X13,X282,X281),X102) = hAPP(X282,X102) ),
inference(fof_simplification,[status(thm)],[fact_map__add__dom__app__simps_I3_J]) ).
fof(i_0_5694,plain,
! [X84,X94] :
( class_Rings_Olinordered__ring(X94)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X94),X84),X84)),c_Groups_Ozero__class_Ozero(X94))) ),
inference(fof_simplification,[status(thm)],[fact_not__square__less__zero]) ).
fof(i_0_5695,plain,
! [X21294] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21294)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21294),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21294),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21294)),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,
! [X21318,X21319] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21319))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21318))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21319)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21318)),
inference(variable_rename,[status(thm)],[fact_zdiv__number__of__Bit0]) ).
fof(i_0_5697,plain,
! [X42,X103,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X103)),X42))
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),X42))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X103),X42)) ) ),
inference(fof_simplification,[status(thm)],[fact_add__leE]) ).
fof(i_0_5698,plain,
! [X21296] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21296)),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21296),c_Int_OPls)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21296),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21296)),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I27_J])]) ).
fof(i_0_5699,plain,
! [X21316] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21316)),c_Int_OMin))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21316),c_Int_OMin)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21316),c_Int_OMin))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21316)),c_Int_OMin)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I28_J])]) ).
fof(i_0_5700,plain,
! [X21339] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21339)),c_Int_OMin))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21339),c_Int_OMin)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21339),c_Int_OMin))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21339)),c_Int_OMin)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I11_J])]) ).
fof(i_0_5701,plain,
! [X21302] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21302)),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21302),c_Int_OPls)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21302),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21302)),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I10_J])]) ).
fof(i_0_5702,plain,
! [X21320] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21320))))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21320))) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21320)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21320)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__number__of__Bit0])]) ).
fof(i_0_5703,plain,
! [X30253,X30254] : hAPP(c_Relation_OImage(X30254,X30254,c_Relation_OId(X30254)),X30253) = X30253,
inference(variable_rename,[status(thm)],[fact_Image__Id]) ).
fof(i_0_5704,plain,
! [X154,X160,X16,X10] :
( ( hBOOL(hAPP(hAPP(c_member(X10),X16),X160))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)),X160) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X160))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)),X160) = hAPP(hAPP(c_Set_Oinsert(X10),X16),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X154),X160)) ) ),
inference(fof_simplification,[status(thm)],[fact_insert__Diff__if]) ).
fof(i_0_5705,plain,
! [X31789,X31790,X31791,X31792,X31793] : c_Map_Omap__comp(X31793,X31792,X31791,hAPP(c_COMBK(tc_Option_Ooption(X31792),X31793),c_Option_Ooption_ONone(X31792)),X31790,X31789) = c_Option_Ooption_ONone(X31792),
inference(variable_rename,[status(thm)],[fact_map__comp__empty_I2_J]) ).
fof(i_0_5706,plain,
! [X31794,X31795,X31796,X31797,X31798] : c_Map_Omap__comp(X31798,X31797,X31796,X31795,hAPP(c_COMBK(tc_Option_Ooption(X31798),X31796),c_Option_Ooption_ONone(X31798)),X31794) = c_Option_Ooption_ONone(X31797),
inference(variable_rename,[status(thm)],[fact_map__comp__empty_I1_J]) ).
fof(i_0_5707,plain,
! [X21156,X21157] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21157),X21156))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X21157)),X21156)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X21157)),X21156))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21157),X21156)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__pred__less])]) ).
fof(i_0_5708,plain,
! [X21342] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X21342)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X21342)),
inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I6_J]) ).
fof(i_0_5709,plain,
! [X21084,X21085] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21085)))
| hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21085)),X21084)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X21084) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21085)))
| hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21085)),X21084)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X21085))),X21084) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5185])]) ).
fof(i_0_5710,plain,
! [X76,X77,X20,X75,X54,X38] :
( ~ hBOOL(hAPP(X38,X54))
=> ( c_Natural_Oevaln(X75,X54,X20,X77)
=> c_Natural_Oevaln(c_Com_Ocom_OCond(X38,X76,X75),X54,X20,X77) ) ),
inference(fof_simplification,[status(thm)],[fact_evaln_OIfFalse]) ).
fof(i_0_5711,plain,
! [X97,X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X42))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X97),X42) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X97),X42) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42)),X42)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_div__if]) ).
fof(i_0_5712,plain,
! [X97,X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X42))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X97),X42) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42)),X42)) ) ),
inference(fof_simplification,[status(thm)],[fact_div__geq]) ).
fof(i_0_5713,plain,
! [X42] : ~ 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,X42))))),
inference(fof_simplification,[status(thm)],[fact_not__zle__0__negative]) ).
fof(i_0_5714,plain,
! [X30228,X30229] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30229,X30229),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X30229,X30228)),c_Relation_OId(X30229)) = c_Transitive__Closure_Ortrancl(X30229,X30228),
inference(variable_rename,[status(thm)],[fact_rtrancl__reflcl__absorb]) ).
fof(i_0_5715,plain,
! [X34046,X34047] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34047),X34046))
| c_List_Oupt(X34047,hAPP(c_Nat_OSuc,X34046)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X34047,X34046)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X34046),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,
! [X34044,X34045] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34045),X34044))
| c_List_Oupt(X34045,hAPP(c_Nat_OSuc,X34044)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X34045,X34044)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X34044),c_List_Olist_ONil(tc_Nat_Onat))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34045),X34044))
| c_List_Oupt(X34045,hAPP(c_Nat_OSuc,X34044)) = 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,
! [X160,X154,X39,X10] :
( ( hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),X160)) = hAPP(hAPP(c_Set_Oinsert(X10),X39),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) ) ),
inference(fof_simplification,[status(thm)],[fact_Int__insert__right]) ).
fof(i_0_5718,plain,
! [X1,X154,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1),X154) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13,X10,c_Groups_Oplus__class_Oplus(X13)),X1),c_Groups_Ozero__class_Ozero(X13)),X154) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1),X154) = c_Groups_Ozero__class_Ozero(X13) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum_OF__eq]) ).
fof(i_0_5719,plain,
! [X1,X154,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),X154) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13,X10,c_Groups_Otimes__class_Otimes(X13)),X1),c_Groups_Oone__class_Oone(X13)),X154) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),X154) = c_Groups_Oone__class_Oone(X13) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setprod_OF__eq]) ).
fof(i_0_5720,plain,
! [X298,X297,X94,X42] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)))
=> hAPP(hAPP(c_List_Onth(X94),hAPP(hAPP(c_List_Oappend(X94),X297),X298)),X42) = hAPP(hAPP(c_List_Onth(X94),X297),X42) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297)))
=> hAPP(hAPP(c_List_Onth(X94),hAPP(hAPP(c_List_Oappend(X94),X297),X298)),X42) = hAPP(hAPP(c_List_Onth(X94),X298),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X94)),X297))) ) ),
inference(fof_simplification,[status(thm)],[fact_nth__append]) ).
fof(i_0_5721,plain,
! [X154,X18,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X18),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X154)))
<=> ~ hBOOL(hAPP(hAPP(c_member(X10),X18),X154)) ),
inference(fof_simplification,[status(thm)],[fact_Compl__iff]) ).
fof(i_0_5722,plain,
! [X154,X18,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X18),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X154)))
=> ~ hBOOL(hAPP(hAPP(c_member(X10),X18),X154)) ),
inference(fof_simplification,[status(thm)],[fact_ComplD]) ).
fof(i_0_5723,plain,
! [X154,X18,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X18),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X154)))
=> ~ hBOOL(hAPP(hAPP(c_member(X10),X18),X154)) ),
inference(fof_simplification,[status(thm)],[fact_ComplE]) ).
fof(i_0_5724,plain,
! [X21886] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X21886)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21886)),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,
! [X144,X80,X10] :
( ( class_Int_Onumber(X10)
& class_Orderings_Oord(X10) )
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X80)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X144)))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X80)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X144)) = hAPP(c_Int_Onumber__class_Onumber__of(X10),X144) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X80)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X144)))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X80)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X144)) = hAPP(c_Int_Onumber__class_Onumber__of(X10),X80) ) ) ),
inference(fof_simplification,[status(thm)],[fact_max__number__of]) ).
fof(i_0_5726,plain,
! [X144,X80,X10] :
( ( class_Int_Onumber(X10)
& class_Orderings_Oord(X10) )
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X80)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X144)))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X80)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X144)) = hAPP(c_Int_Onumber__class_Onumber__of(X10),X80) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X80)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X144)))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X80)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X144)) = hAPP(c_Int_Onumber__class_Onumber__of(X10),X144) ) ) ),
inference(fof_simplification,[status(thm)],[fact_min__number__of]) ).
fof(i_0_5727,plain,
! [X119,X120] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X120),X119)),X120)),
inference(fof_simplification,[status(thm)],[fact_not__add__less1]) ).
fof(i_0_5728,plain,
! [X120,X119] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X119),X120)),X120)),
inference(fof_simplification,[status(thm)],[fact_not__add__less2]) ).
fof(i_0_5729,plain,
! [X289,X290,X16,X10] :
( ( hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
=> c_List_Oremove1(X10,X16,hAPP(hAPP(c_List_Oappend(X10),X290),X289)) = hAPP(hAPP(c_List_Oappend(X10),c_List_Oremove1(X10,X16,X290)),X289) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
=> c_List_Oremove1(X10,X16,hAPP(hAPP(c_List_Oappend(X10),X290),X289)) = hAPP(hAPP(c_List_Oappend(X10),X290),c_List_Oremove1(X10,X16,X289)) ) ),
inference(fof_simplification,[status(thm)],[fact_remove1__append]) ).
fof(i_0_5730,plain,
! [X21136] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X21136))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21136) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21136) != 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(X21136)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__number__of__pred__iff__0])]) ).
fof(i_0_5731,plain,
! [X16,X2,X10] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X10,X2,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),X16)),
inference(fof_simplification,[status(thm)],[fact_empty__fold1SetE]) ).
fof(i_0_5732,plain,
! [X21193,X21194] :
( ( c_Int_OBit1(X21194) != c_Int_OBit1(X21193)
| X21194 = X21193 )
& ( X21194 != X21193
| c_Int_OBit1(X21194) = c_Int_OBit1(X21193) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I51_J])]) ).
fof(i_0_5733,plain,
! [X102,X13,X154,X16,X10] :
( ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Map_Orestrict__map(X10,X13,X102,X154),X16) = hAPP(X102,X16) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Map_Orestrict__map(X10,X13,X102,X154),X16) = c_Option_Ooption_ONone(X13) ) ),
inference(fof_simplification,[status(thm)],[fact_restrict__map__def]) ).
fof(i_0_5734,plain,
! [X38,X39,X19] :
( hBOOL(hAPP(X19,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X39),X38)))
<=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X39),X38))
& ~ hBOOL(hAPP(X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X164] :
( X39 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X38),X164)
& ~ hBOOL(hAPP(X19,X164)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__diff__split__asm]) ).
fof(i_0_5735,plain,
! [X290,X16,X10] :
( hBOOL(hAPP(c_List_Odistinct(X10),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290)))
<=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
& hBOOL(hAPP(c_List_Odistinct(X10),X290)) ) ),
inference(fof_simplification,[status(thm)],[fact_distinct_Osimps_I2_J]) ).
fof(i_0_5736,plain,
! [X2,X13,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Map_Odom(X10,X13,X2)))
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))))
=> ? [X3] : hAPP(X2,X3) = c_Option_Ooption_ONone(X13) ) ),
inference(fof_simplification,[status(thm)],[fact_finite__map__freshness]) ).
fof(i_0_5737,plain,
! [X33504,X33505,X33506] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33506)),hAPP(c_List_Orotate(X33506,X33505),X33504)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33506)),X33504),
inference(variable_rename,[status(thm)],[fact_length__rotate]) ).
fof(i_0_5738,plain,
! [X154,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = X154 ),
inference(fof_simplification,[status(thm)],[fact_Diff__insert__absorb]) ).
fof(i_0_5739,plain,
! [X2,X39,X225,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X225))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X225))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),hAPP(hAPP(c_Set_Oinsert(X10),X39),X225)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(X2,X39)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),X225)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum__insert]) ).
fof(i_0_5740,plain,
! [X1,X16,X154,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(X1,X16)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1),X154)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum_Oinsert]) ).
fof(i_0_5741,plain,
! [X1,X16,X154,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),hAPP(X1,X16)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),X154)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setprod_Oinsert]) ).
fof(i_0_5742,plain,
! [X2,X39,X154,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),hAPP(hAPP(c_Set_Oinsert(X10),X39),X154)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),hAPP(X2,X39)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),X154)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setprod__insert]) ).
fof(i_0_5743,plain,
! [X34071,X34072,X34073] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),X34073),c_List_Oupt(X34072,X34071)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34072),X34073),X34071),
inference(variable_rename,[status(thm)],[fact_drop__upt]) ).
fof(i_0_5744,plain,
! [X290,X19,X10] :
( hAPP(c_List_Ofilter(X10,X19),X290) = c_List_Olist_ONil(X10)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X290)))
=> ~ hBOOL(hAPP(X19,X3)) ) ),
inference(fof_simplification,[status(thm)],[fact_filter__empty__conv]) ).
fof(i_0_5745,plain,
! [X97,X42] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X42)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X97)))),
inference(fof_simplification,[status(thm)],[fact_not__int__zless__negative]) ).
fof(i_0_5746,plain,
! [X33483,X33484,X33485] : hAPP(c_List_Oset(X33485),hAPP(c_List_Orotate(X33485,X33484),X33483)) = hAPP(c_List_Oset(X33485),X33483),
inference(variable_rename,[status(thm)],[fact_set__rotate]) ).
fof(i_0_5747,plain,
! [X10,X154,X16,X160] :
( ( ~ hBOOL(hAPP(X160,X16))
=> hBOOL(hAPP(X154,X16)) )
=> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X154),X160),X16)) ),
inference(fof_simplification,[status(thm)],[fact_sup1CI]) ).
fof(i_0_5748,plain,
! [X329,X330,X290,X19,X10] :
( c_List_Opartition(X10,X19,X290) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X330),X329)
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X330)))
=> hBOOL(hAPP(X19,X3)) )
& ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X329)))
=> ~ hBOOL(hAPP(X19,X3)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_partition__P]) ).
fof(i_0_5749,plain,
! [X30116,X30117] : hAPP(c_Relation_ODomain(X30117,X30117),c_Transitive__Closure_Otrancl(X30117,X30116)) = hAPP(c_Relation_ODomain(X30117,X30117),X30116),
inference(variable_rename,[status(thm)],[fact_trancl__domain]) ).
fof(i_0_5750,plain,
! [X30118,X30119] : hAPP(c_Relation_ORange(X30119,X30119),c_Transitive__Closure_Otrancl(X30119,X30118)) = hAPP(c_Relation_ORange(X30119,X30119),X30118),
inference(variable_rename,[status(thm)],[fact_trancl__range]) ).
fof(i_0_5751,plain,
! [X174,X168] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X174)))
<=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X168),X174))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X168),c_Int_OPls)) ) ),
inference(fof_simplification,[status(thm)],[fact_le__nat__number__of]) ).
fof(i_0_5752,plain,
! [X104,X105,X93] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X93),X105))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X105),X93)) )
=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X105),X104))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X104),X105)) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X93),X104))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X104),X93)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Oless__trans]) ).
fof(i_0_5753,plain,
! [X21289,X21290] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X21290)),c_Int_OBit0(X21289)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X21290),X21289)),
inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I7_J]) ).
fof(i_0_5754,plain,
! [X21284,X21285] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X21285)),c_Int_OBit0(X21284)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21285),X21284)),
inference(variable_rename,[status(thm)],[fact_add__Bit0__Bit0]) ).
fof(i_0_5755,plain,
! [X16,X154,X225,X2,X10] :
( c_Finite__Set_Ofolding__one(X10,X2,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(X225,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,X2),X16),X154) ) ) ),
inference(fof_simplification,[status(thm)],[fact_folding__one_Oeq__fold_H]) ).
fof(i_0_5756,plain,
! [X16] :
~ ! [X90] :
( X16 = hAPP(c_Int_OAbs__Integ,X90)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X90),c_Int_OInteg)) ),
inference(fof_simplification,[status(thm)],[fact_Abs__Integ__cases]) ).
fof(i_0_5757,plain,
! [X34110,X34111] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34111),X34110))
| c_List_Oupt(X34111,X34110) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X34111),c_List_Oupt(hAPP(c_Nat_OSuc,X34111),X34110)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34111),X34110))
| c_List_Oupt(X34111,X34110) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5187])]) ).
fof(i_0_5758,plain,
! [X34108,X34109] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34109),X34108))
| c_List_Oupt(X34109,X34108) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X34109),c_List_Oupt(hAPP(c_Nat_OSuc,X34109),X34108)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__conv__Cons])]) ).
fof(i_0_5759,plain,
! [X31711,X31712,X31713,X31714,X31715,X31716,X31717] :
( hAPP(X31717,X31716) != hAPP(c_Option_Ooption_OSome(X31715),X31714)
| c_Map_Omap__comp(X31715,X31713,X31712,X31711,X31717,X31716) = hAPP(X31711,X31714) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__comp__simps_I2_J])]) ).
fof(i_0_5760,plain,
! [X290,X2,X10,X16,X19,X13] :
( class_Orderings_Olinorder(X13)
=> ( ~ hBOOL(hAPP(X19,X16))
=> hAPP(c_List_Ofilter(X10,X19),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X13,X2),X16),X290)) = hAPP(c_List_Ofilter(X10,X19),X290) ) ),
inference(fof_simplification,[status(thm)],[fact_filter__insort__triv]) ).
fof(i_0_5761,plain,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omin(X10)),X16),X154) ) ) ),
inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Oeq__fold_H]) ).
fof(i_0_5762,plain,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omax(X10)),X16),X154) ) ) ),
inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Oeq__fold_H]) ).
fof(i_0_5763,plain,
! [X102,X73] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X73)),X102))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X73),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X102))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73))
=> X102 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__dvd__iff]) ).
fof(i_0_5764,plain,
! [X154,X10] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X154),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),
inference(fof_simplification,[status(thm)],[fact_not__psubset__empty]) ).
fof(i_0_5765,plain,
! [X102,X13,X154,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Map_Orestrict__map(X10,X13,X102,X154),X16) = c_Option_Ooption_ONone(X13) ),
inference(fof_simplification,[status(thm)],[fact_restrict__out]) ).
fof(i_0_5766,plain,
! [X39,X154,X10] :
( class_Groups_Oab__semigroup__mult(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),hAPP(hAPP(c_Set_Oinsert(X10),X39),X154)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Groups_Otimes__class_Otimes(X10)),X39),X154) ) ) ),
inference(fof_simplification,[status(thm)],[fact_fold1__eq__fold]) ).
fof(i_0_5767,plain,
! [X21327,X21328] :
( ~ class_Int_Onumber__ring(X21328)
| hAPP(c_Int_Onumber__class_Onumber__of(X21328),c_Int_OBit0(X21327)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21328),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21328),c_Groups_Ozero__class_Ozero(X21328)),hAPP(c_Int_Onumber__class_Onumber__of(X21328),X21327))),hAPP(c_Int_Onumber__class_Onumber__of(X21328),X21327)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Bit0])]) ).
fof(i_0_5768,plain,
! [X34141,X34142] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X34142),hAPP(c_List_Onth(X34142),X34141)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34142)),X34141))) = X34141,
inference(variable_rename,[status(thm)],[fact_map__nth]) ).
fof(i_0_5769,plain,
! [X92,X84,X93,X94] :
( class_Lattices_Osemilattice__inf(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X94),X84),X92)))
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X84))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X92)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_le__infE]) ).
fof(i_0_5770,plain,
! [X92,X84,X93,X94] :
( class_Orderings_Olinorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),hAPP(hAPP(c_Orderings_Oord__class_Omin(X94),X84),X92)))
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X84))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X92)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_min__max_Ole__infE]) ).
fof(i_0_5771,plain,
! [X290,X16,X10] :
( ( hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_List_Oremove1(X10,X16,X290)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_List_Oremove1(X10,X16,X290)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X290) ) ),
inference(fof_simplification,[status(thm)],[fact_length__remove1]) ).
fof(i_0_5772,plain,
! [X160,X198,X39,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X198))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X39),X160)),X198) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X160),X198) ),
inference(fof_simplification,[status(thm)],[fact_Int__insert__left__if0]) ).
fof(i_0_5773,plain,
! [X21832,X21833] :
( ( X21833 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| c_Code__Numeral_Onat__of__aux(X21833,X21832) = X21832 )
& ( X21833 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| c_Code__Numeral_Onat__of__aux(X21833,X21832) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X21833),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,X21832)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__of__aux__code])]) ).
fof(i_0_5774,plain,
! [X22786,X22787] : c_Code__Numeral_Onat__of__aux(X22787,X22786) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X22787)),X22786),
inference(variable_rename,[status(thm)],[fact_nat__of__aux__def]) ).
fof(i_0_5775,plain,
! [X30098,X30099] :
( ~ c_Wellfounded_Owf(X30099,X30098)
| c_Wellfounded_Owf(X30099,c_Transitive__Closure_Otrancl(X30099,X30098)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__trancl])]) ).
fof(i_0_5776,plain,
! [X30247,X30248,X30249] : hAPP(hAPP(c_Relation_Orel__comp(X30249,X30248,X30248),X30247),c_Relation_OId(X30248)) = X30247,
inference(variable_rename,[status(thm)],[fact_R__O__Id]) ).
fof(i_0_5777,plain,
! [X31734,X31735,X31736,X31737,X31738,X31739] :
( hAPP(X31739,X31738) != c_Option_Ooption_ONone(X31737)
| c_Map_Omap__comp(X31737,X31736,X31735,X31734,X31739,X31738) = c_Option_Ooption_ONone(X31736) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__comp__simps_I1_J])]) ).
fof(i_0_5778,plain,
! [X30176,X30177] : c_Transitive__Closure_Otrancl(X30177,X30176) = hAPP(hAPP(c_Relation_Orel__comp(X30177,X30177,X30177),c_Transitive__Closure_Ortrancl(X30177,X30176)),X30176),
inference(variable_rename,[status(thm)],[fact_trancl__unfold__right]) ).
fof(i_0_5779,plain,
! [X30184,X30185] : c_Transitive__Closure_Ortrancl(X30185,c_Transitive__Closure_Otrancl(X30185,X30184)) = c_Transitive__Closure_Ortrancl(X30185,X30184),
inference(variable_rename,[status(thm)],[fact_trancl__rtrancl__absorb]) ).
fof(i_0_5780,plain,
! [X34226] : c_List_Oconcat(X34226,c_List_Olist_ONil(tc_List_Olist(X34226))) = c_List_Olist_ONil(X34226),
inference(variable_rename,[status(thm)],[fact_concat_Osimps_I1_J]) ).
fof(i_0_5781,plain,
! [X38,X39] :
( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X39,X38) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
<=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X39),X38)) ),
inference(fof_simplification,[status(thm)],[fact_dvd_OatLeastatMost__empty__iff]) ).
fof(i_0_5782,plain,
! [X38,X39] :
( 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),X39,X38)
<=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X39),X38)) ),
inference(fof_simplification,[status(thm)],[fact_dvd_OatLeastatMost__empty__iff2]) ).
fof(i_0_5783,plain,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> c_Big__Operators_Olinorder__class_OMin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omin(X10)),X16),X154) ) ) ),
inference(fof_simplification,[status(thm)],[fact_Min_Oeq__fold_H]) ).
fof(i_0_5784,plain,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> c_Big__Operators_Olinorder__class_OMax(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omax(X10)),X16),X154) ) ) ),
inference(fof_simplification,[status(thm)],[fact_Max_Oeq__fold_H]) ).
fof(i_0_5785,plain,
! [X16,X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__inf__class_Oinf(X10)),X16),X154) ) ) ),
inference(fof_simplification,[status(thm)],[fact_Inf__fin_Oeq__fold_H]) ).
fof(i_0_5786,plain,
! [X16,X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__sup__class_Osup(X10)),X16),X154) ) ) ),
inference(fof_simplification,[status(thm)],[fact_Sup__fin_Oeq__fold_H]) ).
fof(i_0_5787,plain,
! [X174,X168] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X174)
<=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X168)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X174)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X168)))
=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X174)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X168) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X174)))
=> X168 = X174 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_eq__nat__number__of]) ).
fof(i_0_5788,plain,
! [X93,X94] :
( ( class_Int_Onumber__ring(X94)
& class_Rings_Olinordered__idom(X94) )
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),X93)),c_Groups_Ozero__class_Ozero(X94)))
=> hAPP(c_Groups_Oabs__class_Oabs(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),X93)) = hAPP(c_Groups_Ouminus__class_Ouminus(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),X93)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),X93)),c_Groups_Ozero__class_Ozero(X94)))
=> hAPP(c_Groups_Oabs__class_Oabs(X94),hAPP(c_Int_Onumber__class_Onumber__of(X94),X93)) = hAPP(c_Int_Onumber__class_Onumber__of(X94),X93) ) ) ),
inference(fof_simplification,[status(thm)],[fact_abs__number__of]) ).
fof(i_0_5789,plain,
! [X30332] : hAPP(c_Relation_Oconverse(X30332,X30332),c_Relation_OId(X30332)) = c_Relation_OId(X30332),
inference(variable_rename,[status(thm)],[fact_converse__Id]) ).
fof(i_0_5790,plain,
! [X170,X144] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X170)))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X170)))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X170))) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_mod__nat__number__of]) ).
fof(i_0_5791,plain,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X16),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X154)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Oinsert]) ).
fof(i_0_5792,plain,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X16),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X154)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Oinsert]) ).
fof(i_0_5793,plain,
! [X21287,X21288] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(X21288)),X21287) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21288),X21287)),
inference(variable_rename,[status(thm)],[fact_mult__Bit0]) ).
fof(i_0_5794,plain,
! [X104,X105,X93] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X93),X105))
=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X105),X104))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X104),X105)) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X93),X104))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X104),X93)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Ole__less__trans]) ).
fof(i_0_5795,plain,
! [X104,X105,X93] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X93),X105))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X105),X93)) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X105),X104))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X93),X104))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X104),X93)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Oless__le__trans]) ).
fof(i_0_5796,plain,
! [X133,X144] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X133)) = 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),X133)) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X133)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X133))) ) ),
inference(fof_simplification,[status(thm)],[fact_power__nat__number__of__number__of]) ).
fof(i_0_5797,plain,
! [X170,X144] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X170))) ) ),
inference(fof_simplification,[status(thm)],[fact_div__nat__number__of]) ).
fof(i_0_5798,plain,
! [X16,X154,X10] :
( class_Groups_Oab__semigroup__mult(X10)
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X16),hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),X154)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_fold1__insert]) ).
fof(i_0_5799,plain,
! [X39,X38] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X38),X39))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X39),X38)) )
=> c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X39,X38) = 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,
! [X21153,X21154] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X21154))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21153)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21154)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21153),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X21154))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__number__of])]) ).
fof(i_0_5801,plain,
! [X20,X19] :
( ~ hBOOL(hAPP(X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(X19,X20))
=> ? [X124] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X124),X20))
& ! [X152] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X152),X124))
=> ~ hBOOL(hAPP(X19,X152)) )
& hBOOL(hAPP(X19,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X124),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_ex__least__nat__less]) ).
fof(i_0_5802,plain,
! [X34157,X34158] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X34158,X34157) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X34158),hAPP(c_Nat_OSuc,X34157))),
inference(variable_rename,[status(thm)],[fact_greaterThanAtMost__upt]) ).
fof(i_0_5803,plain,
! [X21295] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X21295)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X21295)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X21295))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X21295))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I21_J])]) ).
fof(i_0_5804,plain,
! [X21301] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X21301)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X21301)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X21301))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X21301))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I4_J])]) ).
fof(i_0_5805,plain,
! [X21340] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X21340)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X21340)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X21340))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X21340))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I25_J])]) ).
fof(i_0_5806,plain,
! [X21317] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X21317)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X21317)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X21317))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X21317))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I8_J])]) ).
fof(i_0_5807,plain,
! [X160,X154,X39,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X154))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),hAPP(hAPP(c_Set_Oinsert(X10),X39),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X154),X160) ),
inference(fof_simplification,[status(thm)],[fact_Int__insert__right__if0]) ).
fof(i_0_5808,plain,
! [X33531,X33532,X33533] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X33533,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33532)),X33531)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_List_Orotate(X33532,X33533),X33531) = X33531 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate__id])]) ).
fof(i_0_5809,plain,
! [X33476,X33477,X33478] :
( ( hAPP(c_List_Orotate(X33478,X33477),X33476) != c_List_Olist_ONil(X33478)
| X33476 = c_List_Olist_ONil(X33478) )
& ( X33476 != c_List_Olist_ONil(X33478)
| hAPP(c_List_Orotate(X33478,X33477),X33476) = c_List_Olist_ONil(X33478) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate__is__Nil__conv])]) ).
fof(i_0_5810,plain,
! [X113,X163] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X163),X113))
=> c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X113,X163) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X163),X113))
=> c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X113,X163) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),X113),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X113),c_Groups_Oone__class_Oone(tc_Int_Oint)),X163)) ) ),
inference(fof_simplification,[status(thm)],[fact_simp__from__to]) ).
fof(i_0_5811,plain,
! [X21347,X21348] :
( ~ class_Int_Onumber__ring(X21348)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21348),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21348),c_Groups_Oone__class_Oone(X21348)),c_Groups_Oone__class_Oone(X21348))),hAPP(c_Int_Onumber__class_Onumber__of(X21348),X21347)) = hAPP(c_Int_Onumber__class_Onumber__of(X21348),c_Int_OBit0(X21347)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__number__of__Bit0])]) ).
fof(i_0_5812,plain,
! [X38,X160,X39,X10] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X160))
=> X39 = X38 )
=> hBOOL(hAPP(hAPP(c_member(X10),X39),hAPP(hAPP(c_Set_Oinsert(X10),X38),X160))) ),
inference(fof_simplification,[status(thm)],[fact_insertCI]) ).
fof(i_0_5813,plain,
! [X21210] : c_Int_OBit1(X21210) = 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)),X21210)),X21210),
inference(variable_rename,[status(thm)],[fact_Bit1__def]) ).
fof(i_0_5814,plain,
! [X22897,X22898,X22899,X22900,X22901,X22902] : hAPP(hAPP(c_Product__Type_Ointernal__split(X22902,X22901,X22900),X22899),hAPP(hAPP(c_Product__Type_OPair(X22902,X22901),X22898),X22897)) = hAPP(hAPP(X22899,X22898),X22897),
inference(variable_rename,[status(thm)],[fact_internal__split__conv]) ).
fof(i_0_5815,plain,
! [X22894,X22895,X22896] : c_Product__Type_Ointernal__split(X22896,X22895,X22894) = c_Product__Type_Oprod_Oprod__case(X22896,X22895,X22894),
inference(variable_rename,[status(thm)],[fact_internal__split__def]) ).
fof(i_0_5816,plain,
! [X154,X18,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X18),X154))
=> hBOOL(hAPP(hAPP(c_member(X10),X18),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X154))) ),
inference(fof_simplification,[status(thm)],[fact_ComplI]) ).
fof(i_0_5817,plain,
! [X13,X154,X18,X10] :
( ( hBOOL(hAPP(hAPP(c_member(X10),X18),X154))
=> hAPP(c_Set_Ovimage(X13,X10,hAPP(c_COMBK(X10,X13),X18)),X154) = c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X18),X154))
=> hAPP(c_Set_Ovimage(X13,X10,hAPP(c_COMBK(X10,X13),X18)),X154) = c_Orderings_Obot__class_Obot(tc_fun(X13,tc_HOL_Obool)) ) ),
inference(fof_simplification,[status(thm)],[fact_vimage__const]) ).
fof(i_0_5818,plain,
! [X16,X154,X225,X2,X10] :
( c_Finite__Set_Ofolding__one(X10,X2,X225)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> hAPP(X225,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(X2,X16),hAPP(X225,X154)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_folding__one_Oinsert]) ).
fof(i_0_5819,plain,
! [X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X97))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X97),X42))
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X42),X97)) ) ),
inference(fof_simplification,[status(thm)],[fact_zdvd__not__zless]) ).
fof(i_0_5820,plain,
! [X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X97))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42))
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X42),X97)) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__dvd__not__less]) ).
fof(i_0_5821,plain,
! [X34131,X34132] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(X34132,X34131)) = c_List_Oupt(hAPP(c_Nat_OSuc,X34132),hAPP(c_Nat_OSuc,X34131)),
inference(variable_rename,[status(thm)],[fact_map__Suc__upt]) ).
fof(i_0_5822,plain,
! [X92,X84] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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)),X92))
=> c_Divides_Odivmod__int(X84,X92) = c_Divides_OposDivAlg(X84,X92) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X92))
=> ( ( X84 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odivmod__int(X84,X92) = 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)) )
& ( X84 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odivmod__int(X84,X92) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X84),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X92))) ) ) ) ) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X84))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X92))
=> c_Divides_Odivmod__int(X84,X92) = c_Divides_OnegDivAlg(X84,X92) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X92))
=> c_Divides_Odivmod__int(X84,X92) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X84),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X92))) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_divmod__int__def]) ).
fof(i_0_5823,plain,
! [X30288] : c_Relation_Orefl__on(X30288,c_Orderings_Otop__class_Otop(tc_fun(X30288,tc_HOL_Obool)),c_Relation_OId(X30288)),
inference(variable_rename,[status(thm)],[fact_refl__Id]) ).
fof(i_0_5824,plain,
! [X21226] :
( ~ class_Int_Onumber__ring(X21226)
| hAPP(c_Int_Onumber__class_Onumber__of(X21226),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X21226) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_numeral__1__eq__1])]) ).
fof(i_0_5825,plain,
! [X21225] :
( ~ class_Int_Onumber__ring(X21225)
| c_Groups_Oone__class_Oone(X21225) = hAPP(c_Int_Onumber__class_Onumber__of(X21225),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,
! [X20,X102] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)),X102)) ),
inference(fof_simplification,[status(thm)],[fact_not__less__eq__eq]) ).
fof(i_0_5827,plain,
! [X84,X94] :
( class_Groups_Oordered__ab__group__add__abs(X94)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(c_Groups_Oabs__class_Oabs(X94),X84)),c_Groups_Ozero__class_Ozero(X94))) ),
inference(fof_simplification,[status(thm)],[fact_abs__not__less__zero]) ).
fof(i_0_5828,plain,
! [X97,X94] :
( class_Rings_Olinordered__semidom(X94)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),X97)),c_Groups_Ozero__class_Ozero(X94))) ),
inference(fof_simplification,[status(thm)],[fact_of__nat__less__0__iff]) ).
fof(i_0_5829,plain,
! [X21323,X21324] :
( ( ~ c_Int_Oiszero(X21324,hAPP(c_Int_Onumber__class_Onumber__of(X21324),c_Int_OBit0(X21323)))
| c_Int_Oiszero(X21324,hAPP(c_Int_Onumber__class_Onumber__of(X21324),X21323))
| ~ class_Int_Onumber__ring(X21324)
| ~ class_Int_Oring__char__0(X21324) )
& ( ~ c_Int_Oiszero(X21324,hAPP(c_Int_Onumber__class_Onumber__of(X21324),X21323))
| c_Int_Oiszero(X21324,hAPP(c_Int_Onumber__class_Onumber__of(X21324),c_Int_OBit0(X21323)))
| ~ class_Int_Onumber__ring(X21324)
| ~ class_Int_Oring__char__0(X21324) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__number__of__Bit0])])]) ).
fof(i_0_5830,plain,
! [X170,X144] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X144),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X144),c_Int_OPls))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X170),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X170),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X144),X170)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_add__nat__number__of]) ).
fof(i_0_5831,plain,
! [X42,X144] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),X42) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X42) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),X42) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)),X42)) ) ),
inference(fof_simplification,[status(thm)],[fact_power__nat__number__of]) ).
fof(i_0_5832,plain,
! [X21311] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X21311)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X21311)),
inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I3_J]) ).
fof(i_0_5833,plain,
! [X143,X121,X103] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X103),X121))
=> c_Random_Ominus__shift(X143,X103,X121) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X143),X103)),X121) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X103),X121))
=> c_Random_Ominus__shift(X143,X103,X121) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X103),X121) ) ),
inference(fof_simplification,[status(thm)],[fact_minus__shift__def]) ).
fof(i_0_5834,axiom,
! [X101,X20,X19] :
( hBOOL(hAPP(X19,c_Divides_Odiv__class_Omod(tc_Int_Oint,X20,X101)))
<=> epred1_3(X19,X20,X101) ),
inference(apply_def,[status(thm)],[fact_split__zmod,c_0_5188]) ).
fof(i_0_5835,plain,
! [X119,X120] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X120),X119))
=> c_List_Oupto(X120,X119) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X120),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X120),c_Groups_Oone__class_Oone(tc_Int_Oint)),X119)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X120),X119))
=> c_List_Oupto(X120,X119) = c_List_Olist_ONil(tc_Int_Oint) ) ),
inference(fof_simplification,[status(thm)],[fact_upto_Osimps]) ).
fof(i_0_5836,plain,
! [X21280,X21281] : c_Int_OBit0(X21281) != c_Int_OBit1(X21280),
inference(variable_rename,[status(thm)],[fact_rel__simps_I49_J]) ).
fof(i_0_5837,plain,
! [X21282,X21283] : c_Int_OBit1(X21283) != c_Int_OBit0(X21282),
inference(variable_rename,[status(thm)],[fact_rel__simps_I50_J]) ).
fof(i_0_5838,plain,
! [X21889,X21890] : c_Divides_Odivmod__nat(X21890,X21889) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X21890),X21889)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21890,X21889)),
inference(variable_rename,[status(thm)],[fact_divmod__nat__div__mod]) ).
fof(i_0_5839,plain,
! [X21856,X21857,X21858,X21859] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X21859,X21858,X21857,c_Code__Numeral_OSuc__code__numeral(X21856)) = hAPP(X21857,X21856),
inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I5_J]) ).
fof(i_0_5840,plain,
! [X34164,X34165] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X34165,X34164) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X34165),X34164)),
inference(variable_rename,[status(thm)],[fact_greaterThanLessThan__upt]) ).
fof(i_0_5841,plain,
! [X103,X94] :
( class_Rings_Oring__1(X94)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X103),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Int_Oring__1__class_Oof__int(X94),X103) = hAPP(c_Groups_Ouminus__class_Ouminus(X94),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X103)))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X103),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Int_Oring__1__class_Oof__int(X94),X103) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),hAPP(c_Int_Onat,X103)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_of__int__of__nat]) ).
fof(i_0_5842,plain,
! [X74,X75,X38] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X38,X75,X74)))
=> ~ ( hBOOL(hAPP(c_Com_OWT,X75))
=> ~ hBOOL(hAPP(c_Com_OWT,X74)) ) ),
inference(fof_simplification,[status(thm)],[fact_WTs__elim__cases_I5_J]) ).
fof(i_0_5843,plain,
! [X30286] : hAPP(c_Relation_ODomain(X30286,X30286),c_Relation_OId(X30286)) = c_Orderings_Otop__class_Otop(tc_fun(X30286,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Domain__Id]) ).
fof(i_0_5844,plain,
! [X30287] : hAPP(c_Relation_ORange(X30287,X30287),c_Relation_OId(X30287)) = c_Orderings_Otop__class_Otop(tc_fun(X30287,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Range__Id]) ).
fof(i_0_5845,plain,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X16),c_Big__Operators_Olinorder__class_OMin(X10,X154)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_Min_Oinsert]) ).
fof(i_0_5846,plain,
! [X16,X154,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X16),c_Big__Operators_Olinorder__class_OMax(X10,X154)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_Max_Oinsert]) ).
fof(i_0_5847,plain,
! [X16,X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X16),c_Big__Operators_Olattice__class_OInf__fin(X10,X154)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_Inf__fin_Oinsert]) ).
fof(i_0_5848,plain,
! [X16,X154,X10] :
( class_Lattices_Olattice(X10)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( X154 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X16),c_Big__Operators_Olattice__class_OSup__fin(X10,X154)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_Sup__fin_Oinsert]) ).
fof(i_0_5849,plain,
! [X30182,X30183] : c_Transitive__Closure_Otrancl(X30183,c_Transitive__Closure_Ortrancl(X30183,X30182)) = c_Transitive__Closure_Ortrancl(X30183,X30182),
inference(variable_rename,[status(thm)],[fact_rtrancl__trancl__absorb]) ).
fof(i_0_5850,plain,
! [X16,X10,X154] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X154))
=> c_List_Osublist(X10,hAPP(hAPP(c_List_Olist_OCons(X10),X16),c_List_Olist_ONil(X10)),X154) = hAPP(hAPP(c_List_Olist_OCons(X10),X16),c_List_Olist_ONil(X10)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X154))
=> c_List_Osublist(X10,hAPP(hAPP(c_List_Olist_OCons(X10),X16),c_List_Olist_ONil(X10)),X154) = c_List_Olist_ONil(X10) ) ),
inference(fof_simplification,[status(thm)],[fact_sublist__singleton]) ).
fof(i_0_5851,plain,
! [X170] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X170)))
=> 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),X170)) = 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),X170)))
=> 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),X170)) = 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),X170))) ) ),
inference(fof_simplification,[status(thm)],[fact_one__mod__nat__number__of]) ).
fof(i_0_5852,plain,
! [X30574] : c_Relation_Osingle__valued(X30574,X30574,c_Relation_OId(X30574)),
inference(variable_rename,[status(thm)],[fact_single__valued__Id]) ).
fof(i_0_5853,plain,
! [X25,X16,X10] :
( class_Orderings_Opreorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X16),X25))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X25))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X25),X16)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(i_0_5854,plain,
! [X16,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X10),X154)) ) ),
inference(fof_simplification,[status(thm)],[fact_card_Oinsert]) ).
fof(i_0_5855,axiom,
! [X101,X20,X19] :
( hBOOL(hAPP(X19,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20),X101)))
<=> epred2_3(X19,X20,X101) ),
inference(apply_def,[status(thm)],[fact_split__zdiv,c_0_5189]) ).
fof(i_0_5856,plain,
! [X160,X154,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X160))
=> ( hAPP(hAPP(c_Set_Oinsert(X10),X16),X154) = hAPP(hAPP(c_Set_Oinsert(X10),X16),X160)
<=> X154 = X160 ) ) ),
inference(fof_simplification,[status(thm)],[fact_insert__ident]) ).
fof(i_0_5857,plain,
! [X16,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(c_Finite__Set_Ocard(X10),X154) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X10),X154)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_card__insert__if]) ).
fof(i_0_5858,plain,
! [X34133,X34134] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34134),X34133))
| c_List_Olast(tc_Nat_Onat,c_List_Oupt(X34134,X34133)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X34133),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,
! [X21860] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X21860)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = X21860,
inference(variable_rename,[status(thm)],[fact_Suc__code__numeral__minus__one]) ).
fof(i_0_5860,plain,
! [X20,X102] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X102),X20))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),hAPP(c_Nat_OSuc,X102))) ),
inference(fof_simplification,[status(thm)],[fact_not__less__eq]) ).
fof(i_0_5861,plain,
! [X34094,X34095] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X34095,X34094))),
inference(variable_rename,[status(thm)],[fact_distinct__upt]) ).
fof(i_0_5862,plain,
! [X30439,X30440] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30440,X30440),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30439) = c_Relation_OId(X30440),
inference(variable_rename,[status(thm)],[fact_relpow_Osimps_I1_J]) ).
fof(i_0_5863,plain,
! [X103] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X103)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(fof_simplification,[status(thm)],[fact_int__less__0__conv]) ).
fof(i_0_5864,plain,
! [X21206] :
( ( c_Int_OMin != c_Int_OBit1(X21206)
| c_Int_OMin = X21206 )
& ( c_Int_OMin != X21206
| c_Int_OMin = c_Int_OBit1(X21206) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I43_J])]) ).
fof(i_0_5865,plain,
! [X21205] :
( ( c_Int_OBit1(X21205) != c_Int_OMin
| X21205 = c_Int_OMin )
& ( X21205 != c_Int_OMin
| c_Int_OBit1(X21205) = c_Int_OMin ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I47_J])]) ).
fof(i_0_5866,plain,
! [X21203] : c_Int_OBit1(X21203) != c_Int_OPls,
inference(variable_rename,[status(thm)],[fact_rel__simps_I46_J]) ).
fof(i_0_5867,plain,
! [X21204] : c_Int_OPls != c_Int_OBit1(X21204),
inference(variable_rename,[status(thm)],[fact_rel__simps_I39_J]) ).
fof(i_0_5868,plain,
! [X144,X94] :
( class_Int_Onumber__ring(X94)
=> ( ( 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),X144)))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)) = hAPP(c_Int_Onumber__class_Onumber__of(X94),X144) )
& ( ~ 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),X144)))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)) = c_Groups_Ozero__class_Ozero(X94) ) ) ),
inference(fof_simplification,[status(thm)],[fact_of__nat__number__of__lemma]) ).
fof(i_0_5869,plain,
! [X16,X154,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),X154))
=> hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Set_Oinsert(X10),X16),X154)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X10),X154)) ) ),
inference(fof_simplification,[status(thm)],[fact_card__insert__disjoint]) ).
fof(i_0_5870,plain,
! [X25,X16,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X25))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X16),X25))
<=> X16 = X25 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv2]) ).
fof(i_0_5871,plain,
! [X10] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X10)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X10),tc_HOL_Obool)))),
inference(fof_simplification,[status(thm)],[fact_infinite__UNIV__listI]) ).
fof(i_0_5872,plain,
! [X18,X54,X38] :
( ~ hBOOL(hAPP(X38,X54))
=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X38,X18)),X54),X54)) ),
inference(fof_simplification,[status(thm)],[fact_evalc_OWhileFalse]) ).
fof(i_0_5873,plain,
! [X92,X84,X94] :
( class_Orderings_Opreorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),X92))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X92),X84)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym_H]) ).
fof(i_0_5874,plain,
! [X105,X93,X94] :
( class_Orderings_Opreorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X105))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X105),X93)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__less]) ).
fof(i_0_5875,plain,
! [X105,X93,X94] :
( class_Orderings_Opreorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X105))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X105),X93)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__not__sym]) ).
fof(i_0_5876,plain,
! [X105,X93,X94] :
( class_Orderings_Opreorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X105))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X105),X93)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym]) ).
fof(i_0_5877,plain,
! [X25,X16,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X25))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X25),X16)) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__le]) ).
fof(i_0_5878,plain,
! [X93,X105,X94] :
( class_Orderings_Olinorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X105),X93))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X105)) ) ),
inference(fof_simplification,[status(thm)],[fact_leD]) ).
fof(i_0_5879,plain,
! [X25,X16,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X16),X25))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X25),X16)) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__less]) ).
fof(i_0_5880,plain,
! [X25,X16,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X16),X25))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X25),X16))
| X16 = X25 ) ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
fof(i_0_5881,plain,
! [X84,X92,X94] :
( class_Orderings_Oorder(X94)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X92),X84))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),X92)) ) ),
inference(fof_simplification,[status(thm)],[fact_xt1_I9_J]) ).
fof(i_0_5882,plain,
! [X170,X144] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X144),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X144),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X170)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X144),X170)) ) ),
inference(fof_simplification,[status(thm)],[fact_mult__nat__number__of]) ).
fof(i_0_5883,plain,
! [X34077,X34078] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34078),X34077))
| hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(X34078,X34077)) = X34078 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__upt])]) ).
fof(i_0_5884,plain,
! [X18,X10] : ~ hBOOL(hAPP(hAPP(c_member(X10),X18),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),
inference(fof_simplification,[status(thm)],[fact_empty__iff]) ).
fof(i_0_5885,plain,
! [X39,X10] : ~ hBOOL(hAPP(hAPP(c_member(X10),X39),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),
inference(fof_simplification,[status(thm)],[fact_emptyE]) ).
fof(i_0_5886,plain,
! [X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),hAPP(c_Nat_OSuc,X42)))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),X42))
=> X97 = hAPP(c_Nat_OSuc,X42) ) ),
inference(fof_simplification,[status(thm)],[fact_le__SucE]) ).
fof(i_0_5887,plain,
! [X34143,X34144] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X34144,X34143) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X34144,hAPP(c_Nat_OSuc,X34143))),
inference(variable_rename,[status(thm)],[fact_atLeastAtMost__upt]) ).
fof(i_0_5888,plain,
! [X20,X102] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20))
=> hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X102),hAPP(c_Nat_OSuc,X20)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X20),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X102),X20)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X102),X20))
=> hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X102),hAPP(c_Nat_OSuc,X20)) = 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,
! [X290,X10,X16,X19] :
( ( hBOOL(hAPP(X19,X16))
=> hAPP(c_List_Ofilter(X10,X19),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290)) = hAPP(hAPP(c_List_Olist_OCons(X10),X16),hAPP(c_List_Ofilter(X10,X19),X290)) )
& ( ~ hBOOL(hAPP(X19,X16))
=> hAPP(c_List_Ofilter(X10,X19),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X290)) = hAPP(c_List_Ofilter(X10,X19),X290) ) ),
inference(fof_simplification,[status(thm)],[fact_filter_Osimps_I2_J]) ).
fof(i_0_5890,plain,
! [X102,X20] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X102))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),hAPP(c_Nat_OSuc,X102)))
<=> X20 = X102 ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__less__Suc__eq]) ).
fof(i_0_5891,plain,
! [X97,X42] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),X97))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_OSuc,X97)))
=> X97 = X42 ) ),
inference(fof_simplification,[status(thm)],[fact_less__antisym]) ).
fof(i_0_5892,plain,
! [X42,X97] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),hAPP(c_Nat_OSuc,X42)))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42))
=> X97 = X42 ) ),
inference(fof_simplification,[status(thm)],[fact_less__SucE]) ).
fof(i_0_5893,plain,
! [X22009,X22010] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22010,X22009),c_Divides_Odivmod__nat(X22010,X22009))),
inference(variable_rename,[status(thm)],[fact_divmod__nat__rel__divmod__nat]) ).
fof(i_0_5894,plain,
! [X21848] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X21848)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),X21848)),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,
! [X34173] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X34173) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X34173))),
inference(variable_rename,[status(thm)],[fact_atMost__upto]) ).
fof(i_0_5896,plain,
! [X21161] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21161),c_Int_OPls))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21161)),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),X21161),c_Int_OPls))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21161)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X21161)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5190])]) ).
fof(i_0_5897,plain,
! [X21130] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21130),c_Int_OPls))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21130)),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),X21130),c_Int_OPls))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21130)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X21130)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5191])]) ).
fof(i_0_5898,plain,
! [X21179,X21180] :
( ~ class_Int_Onumber__ring(X21180)
| hAPP(c_Int_Onumber__class_Onumber__of(X21180),c_Int_Opred(X21179)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21180),hAPP(c_Groups_Ouminus__class_Ouminus(X21180),c_Groups_Oone__class_Oone(X21180))),hAPP(c_Int_Onumber__class_Onumber__of(X21180),X21179)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__pred])]) ).
fof(i_0_5899,plain,
! [X20,X18,X54,X38] :
( ~ hBOOL(hAPP(X38,X54))
=> c_Natural_Oevaln(c_Com_Ocom_OWhile(X38,X18),X54,X20,X54) ),
inference(fof_simplification,[status(thm)],[fact_evaln_OWhileFalse]) ).
fof(i_0_5900,plain,
! [X38,X39,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(X10,X39,X38)
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),X38)) ) ),
inference(fof_simplification,[status(thm)],[fact_atLeastatMost__empty__iff2]) ).
fof(i_0_5901,plain,
! [X162,X101,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X101,X162)
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X101),X162)) ) ),
inference(fof_simplification,[status(thm)],[fact_greaterThanAtMost__empty__iff2]) ).
fof(i_0_5902,plain,
! [X38,X39,X10] :
( class_Orderings_Oorder(X10)
=> ( c_SetInterval_Oord__class_OatLeastAtMost(X10,X39,X38) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X39),X38)) ) ),
inference(fof_simplification,[status(thm)],[fact_atLeastatMost__empty__iff]) ).
fof(i_0_5903,plain,
! [X162,X101,X10] :
( class_Orderings_Oorder(X10)
=> ( c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X101,X162) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X101),X162)) ) ),
inference(fof_simplification,[status(thm)],[fact_greaterThanAtMost__empty__iff]) ).
fof(i_0_5904,plain,
! [X25,X16] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X16),X25))
<=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X16),X25))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25),X16)) )
| X16 = X25 ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Ole__less]) ).
fof(i_0_5905,plain,
! [X25,X16] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X16),X25))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25),X16)) )
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X16),X25))
& X16 != X25 ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Oless__le]) ).
fof(i_0_5906,plain,
! [X92,X84] :
( X84 != X92
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X84),X92))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X84),X92))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X92),X84)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Oneq__le__trans]) ).
fof(i_0_5907,plain,
! [X105,X93] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X93),X105))
=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X93),X105))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X105),X93)) )
| X93 = X105 ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Ole__imp__less__or__eq]) ).
fof(i_0_5908,plain,
! [X92,X84] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X84),X92))
=> ( X84 != X92
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X84),X92))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X92),X84)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Ole__neq__trans]) ).
fof(i_0_5909,plain,
! [X21883,X21884] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21884),X21883))
| c_Divides_Odivmod__nat(X21884,X21883) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21884) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__base])]) ).
fof(i_0_5910,plain,
! [X10,X160,X154] :
( X154 = X160
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X154),X160))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X160),X154)) ) ),
inference(fof_simplification,[status(thm)],[fact_equalityE]) ).
fof(i_0_5911,plain,
! [X42] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X42)),X42)),
inference(fof_simplification,[status(thm)],[fact_Suc__n__not__le__n]) ).
fof(i_0_5912,plain,
! [X103,X121] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X121))
=> c_SMT_Oz3div(X103,X121) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X103),X121) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X121))
=> c_SMT_Oz3div(X103,X121) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X103),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X121))) ) ),
inference(fof_simplification,[status(thm)],[fact_z3div__def]) ).
fof(i_0_5913,plain,
! [X42,X97] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X97,X42) = X97 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X97,X42) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42),X42) ) ),
inference(fof_simplification,[status(thm)],[fact_mod__if]) ).
fof(i_0_5914,plain,
! [X42,X97] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X97,X42) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42),X42) ),
inference(fof_simplification,[status(thm)],[fact_mod__geq]) ).
fof(i_0_5915,plain,
! [X25,X16,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X16),X25))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X25))
<=> X16 = X25 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv1]) ).
fof(i_0_5916,plain,
! [X38,X39,X10] :
( class_Orderings_Oorder(X10)
=> ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X39),X38) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),X38)) ) ),
inference(fof_simplification,[status(thm)],[fact_atLeastLessThan__empty__iff]) ).
fof(i_0_5917,plain,
! [X38,X39,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X39),X38)
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X39),X38)) ) ),
inference(fof_simplification,[status(thm)],[fact_atLeastLessThan__empty__iff2]) ).
fof(i_0_5918,plain,
! [X21131] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21131),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),X21131)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21131),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),X21131)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X21131)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5192])]) ).
fof(i_0_5919,plain,
! [X21852,X21853] :
( ( c_Code__Numeral_OSuc__code__numeral(X21853) != c_Code__Numeral_OSuc__code__numeral(X21852)
| X21853 = X21852 )
& ( X21853 != X21852
| c_Code__Numeral_OSuc__code__numeral(X21853) = c_Code__Numeral_OSuc__code__numeral(X21852) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral_Oinject])]) ).
fof(i_0_5920,plain,
! [X21849] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(X21849)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X21849)),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_5921,plain,
! [X21291] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(X21291)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21291)),
inference(variable_rename,[status(thm)],[fact_minus__Bit0]) ).
fof(i_0_5922,plain,
! [X21086] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21086)))
| hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21086)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21086)))
| hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21086)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X21086)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5193])]) ).
fof(i_0_5923,plain,
! [X154,X10] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X10),X3),X154))
<=> X154 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
inference(fof_simplification,[status(thm)],[fact_all__not__in__conv]) ).
fof(i_0_5924,plain,
! [X290,X16,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X290)))
=> c_List_Oremove1(X10,X16,X290) = X290 ),
inference(fof_simplification,[status(thm)],[fact_remove1__idem]) ).
fof(i_0_5925,plain,
! [X34029,X34030] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(X34030,X34029)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X34029),X34030),
inference(variable_rename,[status(thm)],[fact_length__upt]) ).
fof(i_0_5926,plain,
! [X93,X94] :
( class_Groups_Osgn__if(X94)
=> ( ( X93 = c_Groups_Ozero__class_Ozero(X94)
=> c_Groups_Osgn__class_Osgn(X94,X93) = c_Groups_Ozero__class_Ozero(X94) )
& ( X93 != c_Groups_Ozero__class_Ozero(X94)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X93))
=> c_Groups_Osgn__class_Osgn(X94,X93) = c_Groups_Oone__class_Oone(X94) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Ozero__class_Ozero(X94)),X93))
=> c_Groups_Osgn__class_Osgn(X94,X93) = hAPP(c_Groups_Ouminus__class_Ouminus(X94),c_Groups_Oone__class_Oone(X94)) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_sgn__if]) ).
fof(i_0_5927,plain,
! [X34064,X34065] :
( ( c_List_Oupt(X34065,X34064) != c_List_Olist_ONil(tc_Nat_Onat)
| X34064 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34064),X34065)) )
& ( X34064 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_List_Oupt(X34065,X34064) = c_List_Olist_ONil(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34064),X34065))
| c_List_Oupt(X34065,X34064) = 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_5928,plain,
! [X34062,X34063] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34063),X34062))
| c_List_Oupt(X34062,X34063) = c_List_Olist_ONil(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__conv__Nil])]) ).
fof(i_0_5929,plain,
! [X103,X121] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X121))
=> c_SMT_Oz3mod(X103,X121) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X103,X121) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X121))
=> c_SMT_Oz3mod(X103,X121) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X103,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X121)) ) ),
inference(fof_simplification,[status(thm)],[fact_z3mod__def]) ).
fof(i_0_5930,plain,
! [X84,X94] :
( class_Groups_Oabs__if(X94)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),c_Groups_Ozero__class_Ozero(X94)))
=> hAPP(c_Groups_Oabs__class_Oabs(X94),X84) = hAPP(c_Groups_Ouminus__class_Ouminus(X94),X84) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X84),c_Groups_Ozero__class_Ozero(X94)))
=> hAPP(c_Groups_Oabs__class_Oabs(X94),X84) = X84 ) ) ),
inference(fof_simplification,[status(thm)],[fact_abs__if]) ).
fof(i_0_5931,plain,
! [X94] :
( class_Rings_Olinordered__semidom(X94)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),c_Groups_Oone__class_Oone(X94)),c_Groups_Ozero__class_Ozero(X94))) ),
inference(fof_simplification,[status(thm)],[fact_not__one__le__zero]) ).
fof(i_0_5932,plain,
! [X94] :
( class_Rings_Olinordered__semidom(X94)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),c_Groups_Oone__class_Oone(X94)),c_Groups_Ozero__class_Ozero(X94))) ),
inference(fof_simplification,[status(thm)],[fact_not__one__less__zero]) ).
fof(i_0_5933,plain,
! [X42,X97] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X42))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X42)) = X97 ),
inference(fof_simplification,[status(thm)],[fact_add__diff__inverse]) ).
fof(i_0_5934,plain,
! [X34145] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X34145) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X34145)),
inference(variable_rename,[status(thm)],[fact_atLeast__upt]) ).
fof(i_0_5935,plain,
! [X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> ( X93 != X105
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X105))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X105),X93)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE]) ).
fof(i_0_5936,plain,
! [X16,X25,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X25),X16))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X16),X25))
<=> X16 = X25 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv3]) ).
fof(i_0_5937,plain,
! [X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X105))
=> ( X93 != X105
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X105),X93)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__cases]) ).
fof(i_0_5938,plain,
! [X105,X93,X94] :
( class_Rings_Olinordered__idom(X94)
=> ( X93 != X105
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X105))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X105),X93)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).
fof(i_0_5939,plain,
! [X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X93),X105))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X105),X93)) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__le__cases]) ).
fof(i_0_5940,plain,
! [X105,X93,X94] :
( class_Orderings_Olinorder(X94)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X105))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X105),X93)) ) ),
inference(fof_simplification,[status(thm)],[fact_leI]) ).
fof(i_0_5941,plain,
! [X93,X105,X94] :
( class_Orderings_Olinorder(X94)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X94),X105),X93))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X105)) ) ),
inference(fof_simplification,[status(thm)],[fact_not__leE]) ).
fof(i_0_5942,plain,
! [X34086,X34087] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X34087,X34086)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34087),X34086),
inference(variable_rename,[status(thm)],[fact_set__upt]) ).
fof(i_0_5943,plain,
! [X34084,X34085] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X34085),X34084) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X34085,X34084)),
inference(variable_rename,[status(thm)],[fact_atLeastLessThan__upt]) ).
fof(i_0_5944,plain,
! [X21146] : c_Int_Osucc(c_Int_Opred(X21146)) = X21146,
inference(variable_rename,[status(thm)],[fact_succ__pred]) ).
fof(i_0_5945,plain,
! [X21128,X21129] :
( ~ class_Int_Onumber__ring(X21129)
| hAPP(c_Int_Onumber__class_Onumber__of(X21129),c_Int_Osucc(X21128)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21129),c_Groups_Oone__class_Oone(X21129)),hAPP(c_Int_Onumber__class_Onumber__of(X21129),X21128)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__succ])]) ).
fof(i_0_5946,plain,
! [X39,X10,X154] :
( X154 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
=> ~ hBOOL(hAPP(hAPP(c_member(X10),X39),X154)) ),
inference(fof_simplification,[status(thm)],[fact_equals0D]) ).
fof(i_0_5947,plain,
! [X16] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X16))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16)) ),
inference(fof_simplification,[status(thm)],[fact_not__neg__eq__ge__0]) ).
fof(i_0_5948,plain,
! [X102,X131] :
( hAPP(c_Int_Onat,X131) = X102
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X131))
=> X131 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X102) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X131))
=> X102 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__eq__iff]) ).
fof(i_0_5949,plain,
! [X131,X102] :
( X102 = hAPP(c_Int_Onat,X131)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X131))
=> X131 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X102) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X131))
=> X102 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__eq__iff2]) ).
fof(i_0_5950,plain,
! [X104] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X104))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X104)) = X104 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X104))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X104)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(fof_simplification,[status(thm)],[fact_int__nat__eq]) ).
fof(i_0_5951,plain,
! [X93,X105] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X105),X93))
=> c_Nat__Transfer_Otsub(X93,X105) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X93),X105) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X105),X93))
=> c_Nat__Transfer_Otsub(X93,X105) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(fof_simplification,[status(thm)],[fact_tsub__def]) ).
fof(i_0_5952,plain,
! [X144,X94] :
( class_Int_Onumber__ring(X94)
=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)) = c_Groups_Ozero__class_Ozero(X94) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X94),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)) = hAPP(c_Int_Onumber__class_Onumber__of(X94),X144) ) ) ),
inference(fof_simplification,[status(thm)],[fact_of__nat__number__of__eq]) ).
fof(i_0_5953,plain,
! [X22330,X22331] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X22331,X22330) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X22331,X22330)),
inference(variable_rename,[status(thm)],[fact_mod__nat__def]) ).
fof(i_0_5954,plain,
! [X290,X10,X16,X19] :
( ~ hBOOL(hAPP(X19,X16))
=> c_List_Oremove1(X10,X16,hAPP(c_List_Ofilter(X10,X19),X290)) = hAPP(c_List_Ofilter(X10,X19),X290) ),
inference(fof_simplification,[status(thm)],[fact_remove1__filter__not]) ).
fof(i_0_5955,plain,
! [X22552,X22553] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X22553),X22552) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X22553,X22552)),
inference(variable_rename,[status(thm)],[fact_div__nat__def]) ).
fof(i_0_5956,plain,
! [X144] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144)))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X144)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X144) ) ),
inference(fof_simplification,[status(thm)],[fact_int__nat__number__of]) ).
fof(i_0_5957,plain,
! [X120] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X120),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X120) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X120) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X120),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X120) = X120 ) ),
inference(fof_simplification,[status(thm)],[fact_zabs__def]) ).
fof(i_0_5958,plain,
! [X105,X93] :
( X93 != X105
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X93),X105))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X105),X93)) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__nat]) ).
fof(i_0_5959,plain,
! [X22011,X22012,X22013] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22013,X22012),X22011))
| c_Divides_Odivmod__nat(X22013,X22012) = X22011 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__eq])]) ).
fof(i_0_5960,plain,
! [X120] :
( ( X120 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Groups_Osgn__class_Osgn(tc_Int_Oint,X120) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( X120 != 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)),X120))
=> c_Groups_Osgn__class_Osgn(tc_Int_Oint,X120) = 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)),X120))
=> c_Groups_Osgn__class_Osgn(tc_Int_Oint,X120) = 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_5961,plain,
! [X34099,X34100] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X34100,X34099)),
inference(variable_rename,[status(thm)],[fact_sorted__upt]) ).
fof(i_0_5962,plain,
! [X29567,X29568] : c_Wellfounded_Owf(X29568,hAPP(c_Wellfounded_Omeasure(X29568),X29567)),
inference(variable_rename,[status(thm)],[fact_wf__measure]) ).
fof(i_0_5963,plain,
! [X93,X94] :
( class_Orderings_Opreorder(X94)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X94),X93),X93)) ),
inference(fof_simplification,[status(thm)],[fact_order__less__irrefl]) ).
fof(i_0_5964,plain,
! [X121,X103] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X103),X121))
=> c_Quickcheck_Obeyond(X103,X121) = X121 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X103),X121))
=> c_Quickcheck_Obeyond(X103,X121) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(fof_simplification,[status(thm)],[fact_beyond__def]) ).
fof(i_0_5965,plain,
! [X33527] : c_List_Orotate(X33527,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(X33527)),
inference(variable_rename,[status(thm)],[fact_rotate0]) ).
fof(i_0_5966,plain,
! [X42] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_simplification,[status(thm)],[fact_less__nat__zero__code]) ).
fof(i_0_5967,plain,
! [X42] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_simplification,[status(thm)],[fact_not__less0]) ).
fof(i_0_5968,plain,
! [X42] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_simplification,[status(thm)],[fact_less__zeroE]) ).
fof(i_0_5969,plain,
! [X62,X58] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X58,X62)))
=> ~ ( hBOOL(hAPP(c_Com_OWT,X58))
=> ~ hBOOL(hAPP(c_Com_OWT,X62)) ) ),
inference(fof_simplification,[status(thm)],[fact_WTs__elim__cases_I4_J]) ).
fof(i_0_5970,plain,
! [X21871] : c_Divides_Odivmod__nat(X21871,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)),X21871),
inference(variable_rename,[status(thm)],[fact_divmod__nat__zero]) ).
fof(i_0_5971,plain,
! [X42] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),X42)),
inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).
fof(i_0_5972,plain,
! [X42] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),X42)),
inference(fof_simplification,[status(thm)],[fact_less__not__refl]) ).
fof(i_0_5973,plain,
! [X21268,X21269] :
( ( c_Int_OBit0(X21269) != c_Int_OBit0(X21268)
| X21269 = X21268 )
& ( X21269 != X21268
| c_Int_OBit0(X21269) = c_Int_OBit0(X21268) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I48_J])]) ).
fof(i_0_5974,plain,
! [X2,X154,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X2),X154) = c_Groups_Ozero__class_Ozero(X13) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum__infinite]) ).
fof(i_0_5975,plain,
! [X1,X154,X10,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X13),X1),X154) = c_Groups_Ozero__class_Ozero(X13) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum_Oinfinite]) ).
fof(i_0_5976,plain,
! [X1,X154,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X1),X154) = c_Groups_Oone__class_Oone(X13) ) ),
inference(fof_simplification,[status(thm)],[fact_setprod_Oinfinite]) ).
fof(i_0_5977,plain,
! [X2,X154,X10,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X13),X2),X154) = c_Groups_Oone__class_Oone(X13) ) ),
inference(fof_simplification,[status(thm)],[fact_setprod__infinite]) ).
fof(i_0_5978,plain,
! [X42] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X42))),
inference(fof_simplification,[status(thm)],[fact_not__neg__int]) ).
fof(i_0_5979,plain,
! [X21855] : c_Code__Numeral_OSuc__code__numeral(X21855) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I3_J]) ).
fof(i_0_5980,plain,
! [X21854] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(X21854),
inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I2_J]) ).
fof(i_0_5981,plain,
! [X17,X19] :
( ~ hBOOL(hAPP(hAPP(c_fimplies,X19),X17))
| ~ hBOOL(X19)
| hBOOL(X17) ),
inference(fof_simplification,[status(thm)],[help_c__fimplies__3]) ).
fof(i_0_5982,plain,
! [X154,X10] :
( hAPP(c_Finite__Set_Ocard(X10),X154) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X154 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154)) ) ),
inference(fof_simplification,[status(thm)],[fact_card__eq__0__iff]) ).
fof(i_0_5983,plain,
! [X17,X19] :
( ~ hBOOL(hAPP(hAPP(c_fdisj,X19),X17))
| hBOOL(X19)
| hBOOL(X17) ),
inference(fof_simplification,[status(thm)],[help_c__fdisj__3]) ).
fof(i_0_5984,plain,
! [X17,X19] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X19),X17))
| hBOOL(X19) ),
inference(fof_simplification,[status(thm)],[help_c__fconj__2]) ).
fof(i_0_5985,plain,
! [X17,X19] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X19),X17))
| hBOOL(X17) ),
inference(fof_simplification,[status(thm)],[help_c__fconj__3]) ).
fof(i_0_5986,plain,
! [X19,X10] :
( c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X10),X19)
<=> ! [X3] : ~ hBOOL(hAPP(X19,X3)) ),
inference(fof_simplification,[status(thm)],[fact_empty__Collect__eq]) ).
fof(i_0_5987,plain,
! [X19,X10] :
( hAPP(c_Set_OCollect(X10),X19) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X19,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(i_0_5988,plain,
! [X25,X16] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X16),X25))
| X16 = X25 ),
inference(fof_simplification,[status(thm)],[help_c__fequal__1]) ).
fof(i_0_5989,plain,
! [X22785] : hAPP(c_Code__Numeral_Onat__of,X22785) = c_Code__Numeral_Onat__of__aux(X22785,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_nat__of__code]) ).
fof(i_0_5990,plain,
! [X21124] : c_Int_Osucc(X21124) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21124),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(variable_rename,[status(thm)],[fact_succ__def]) ).
fof(i_0_5991,plain,
! [X21158] : c_Int_Opred(X21158) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X21158),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(variable_rename,[status(thm)],[fact_pred__def]) ).
fof(i_0_5992,plain,
! [X34079] : c_List_Oupt(X34079,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_5993,plain,
! [X17,X19] :
( ~ hBOOL(X19)
| ~ hBOOL(X17)
| hBOOL(hAPP(hAPP(c_fconj,X19),X17)) ),
inference(fof_simplification,[status(thm)],[help_c__fconj__1]) ).
fof(i_0_5994,plain,
! [X21159] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X21159) = c_Int_Opred(X21159),
inference(variable_rename,[status(thm)],[fact_add__Min]) ).
fof(i_0_5995,plain,
! [X94] :
( class_Int_Onumber__ring(X94)
=> ~ c_Int_Oiszero(X94,hAPP(c_Int_Onumber__class_Onumber__of(X94),c_Int_OMin)) ),
inference(fof_simplification,[status(thm)],[fact_nonzero__number__of__Min]) ).
fof(i_0_5996,plain,
! [X17,X19] :
( ~ hBOOL(X19)
| hBOOL(hAPP(hAPP(c_fdisj,X19),X17)) ),
inference(fof_simplification,[status(thm)],[help_c__fdisj__1]) ).
fof(i_0_5997,plain,
! [X19,X17] :
( ~ hBOOL(X17)
| hBOOL(hAPP(hAPP(c_fdisj,X19),X17)) ),
inference(fof_simplification,[status(thm)],[help_c__fdisj__2]) ).
fof(i_0_5998,plain,
! [X19,X17] :
( ~ hBOOL(X17)
| hBOOL(hAPP(hAPP(c_fimplies,X19),X17)) ),
inference(fof_simplification,[status(thm)],[help_c__fimplies__2]) ).
fof(i_0_5999,plain,
! [X93,X10] : ~ c_Option_Ois__none(X10,hAPP(c_Option_Ooption_OSome(X10),X93)),
inference(fof_simplification,[status(thm)],[fact_is__none__code_I2_J]) ).
fof(i_0_6000,plain,
! [X34374] : c_List_Oreturn__list(X34374) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),X34374),
inference(variable_rename,[status(thm)],[fact_return__list__def]) ).
fof(i_0_6001,plain,
! [X21278] :
( ( c_Int_OPls != c_Int_OBit0(X21278)
| c_Int_OPls = X21278 )
& ( c_Int_OPls != X21278
| c_Int_OPls = c_Int_OBit0(X21278) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I38_J])]) ).
fof(i_0_6002,plain,
! [X21279] :
( ( c_Int_OBit0(X21279) != c_Int_OPls
| X21279 = c_Int_OPls )
& ( X21279 != c_Int_OPls
| c_Int_OBit0(X21279) = c_Int_OPls ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I44_J])]) ).
fof(i_0_6003,plain,
! [X21293] : c_Int_OBit0(X21293) != c_Int_OMin,
inference(variable_rename,[status(thm)],[fact_rel__simps_I45_J]) ).
fof(i_0_6004,plain,
! [X21292] : c_Int_OMin != c_Int_OBit0(X21292),
inference(variable_rename,[status(thm)],[fact_rel__simps_I42_J]) ).
fof(i_0_6005,plain,
! [X104] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X104))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X104)) = X104 ),
inference(fof_simplification,[status(thm)],[fact_not__neg__nat]) ).
fof(i_0_6006,plain,
! [X154,X10] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X154))
=> hAPP(c_Finite__Set_Ocard(X10),X154) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(fof_simplification,[status(thm)],[fact_card__infinite]) ).
fof(i_0_6007,plain,
! [X19] :
( ~ hBOOL(hAPP(c_fNot,X19))
| ~ hBOOL(X19) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
fof(i_0_6008,plain,
! [X94] :
( class_Rings_Osemiring__1(X94)
=> ~ c_Int_Oiszero(X94,c_Groups_Oone__class_Oone(X94)) ),
inference(fof_simplification,[status(thm)],[fact_not__iszero__1]) ).
fof(i_0_6009,plain,
! [X19] :
( hBOOL(X19)
| hBOOL(hAPP(c_fNot,X19)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__2]) ).
fof(i_0_6010,plain,
! [X26196,X26197,X26198,X26199,X26200,X26201,X26202,X26203,X26204,X26205,X26206] :
( ( hBOOL(hAPP(hAPP(c_member(X26206),esk171_11(X26196,X26197,X26198,X26199,X26200,X26201,X26202,X26203,X26204,X26205,X26206)),X26205))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X26200,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26206,tc_fun(X26200,tc_HOL_Obool)),X26198),hAPP(hAPP(c_COMBB(tc_fun(X26203,tc_fun(X26200,tc_HOL_Obool)),tc_fun(X26200,tc_HOL_Obool),X26206),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26203,tc_fun(X26200,tc_HOL_Obool)),X26197)),X26199))),X26196))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26203,tc_HOL_Obool)),X26197),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26203),X26202),X26201)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26206,tc_HOL_Obool)),X26198),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26206),X26205),X26204)))
| ~ c_Equiv__Relations_Ocongruent2(X26206,X26203,tc_fun(X26200,tc_HOL_Obool),X26204,X26201,X26199)
| ~ c_Equiv__Relations_Oequiv(X26203,X26202,X26201)
| ~ c_Equiv__Relations_Oequiv(X26206,X26205,X26204) )
& ( hBOOL(hAPP(hAPP(c_member(X26203),esk172_11(X26196,X26197,X26198,X26199,X26200,X26201,X26202,X26203,X26204,X26205,X26206)),X26202))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X26200,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26206,tc_fun(X26200,tc_HOL_Obool)),X26198),hAPP(hAPP(c_COMBB(tc_fun(X26203,tc_fun(X26200,tc_HOL_Obool)),tc_fun(X26200,tc_HOL_Obool),X26206),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26203,tc_fun(X26200,tc_HOL_Obool)),X26197)),X26199))),X26196))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26203,tc_HOL_Obool)),X26197),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26203),X26202),X26201)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26206,tc_HOL_Obool)),X26198),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26206),X26205),X26204)))
| ~ c_Equiv__Relations_Ocongruent2(X26206,X26203,tc_fun(X26200,tc_HOL_Obool),X26204,X26201,X26199)
| ~ c_Equiv__Relations_Oequiv(X26203,X26202,X26201)
| ~ c_Equiv__Relations_Oequiv(X26206,X26205,X26204) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26200,tc_HOL_Obool)),hAPP(hAPP(X26199,esk171_11(X26196,X26197,X26198,X26199,X26200,X26201,X26202,X26203,X26204,X26205,X26206)),esk172_11(X26196,X26197,X26198,X26199,X26200,X26201,X26202,X26203,X26204,X26205,X26206))),X26196))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X26200,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26206,tc_fun(X26200,tc_HOL_Obool)),X26198),hAPP(hAPP(c_COMBB(tc_fun(X26203,tc_fun(X26200,tc_HOL_Obool)),tc_fun(X26200,tc_HOL_Obool),X26206),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26203,tc_fun(X26200,tc_HOL_Obool)),X26197)),X26199))),X26196))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26203,tc_HOL_Obool)),X26197),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26203),X26202),X26201)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26206,tc_HOL_Obool)),X26198),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26206),X26205),X26204)))
| ~ c_Equiv__Relations_Ocongruent2(X26206,X26203,tc_fun(X26200,tc_HOL_Obool),X26204,X26201,X26199)
| ~ c_Equiv__Relations_Oequiv(X26203,X26202,X26201)
| ~ c_Equiv__Relations_Oequiv(X26206,X26205,X26204) ) ),
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,
! [X17695,X17696,X17697,X17698,X17699,X17700,X17701,X17702,X17703,X17704,X17705,X17706] : c_Com_Ocom_Ocom__rec(X17706,X17705,X17704,X17703,X17702,X17701,X17700,X17699,X17698,c_Com_Ocom_OCond(X17697,X17696,X17695)) = hAPP(hAPP(hAPP(hAPP(hAPP(X17701,X17697),X17696),X17695),c_Com_Ocom_Ocom__rec(X17706,X17705,X17704,X17703,X17702,X17701,X17700,X17699,X17698,X17696)),c_Com_Ocom_Ocom__rec(X17706,X17705,X17704,X17703,X17702,X17701,X17700,X17699,X17698,X17695)),
inference(variable_rename,[status(thm)],[fact_com_Orecs_I5_J]) ).
fof(i_0_6012,plain,
! [X17340,X17341,X17342,X17343,X17344,X17345,X17346,X17347,X17348,X17349,X17350] : c_Com_Ocom_Ocom__rec(X17350,X17349,X17348,X17347,X17346,X17345,X17344,X17343,X17342,c_Com_Ocom_OSemi(X17341,X17340)) = hAPP(hAPP(hAPP(hAPP(X17346,X17341),X17340),c_Com_Ocom_Ocom__rec(X17350,X17349,X17348,X17347,X17346,X17345,X17344,X17343,X17342,X17341)),c_Com_Ocom_Ocom__rec(X17350,X17349,X17348,X17347,X17346,X17345,X17344,X17343,X17342,X17340)),
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,
! [X29381,X29382,X29383,X29384,X29385,X29386,X29387] :
( ~ class_Rings_Osemiring__0(X29387)
| ~ c_Fun_Oinj__on(tc_prod(X29386,X29385),X29387,hAPP(c_Product__Type_Oprod_Oprod__case(X29386,X29385,X29387),hAPP(hAPP(c_COMBC(X29386,tc_fun(X29385,X29387),tc_fun(X29385,X29387)),hAPP(hAPP(c_COMBB(tc_fun(X29387,X29387),tc_fun(tc_fun(X29385,X29387),tc_fun(X29385,X29387)),X29386),c_COMBB(X29387,X29387,X29385)),hAPP(hAPP(c_COMBB(X29387,tc_fun(X29387,X29387),X29386),c_Groups_Otimes__class_Otimes(X29387)),X29384))),X29383)),hAPP(hAPP(c_Product__Type_OSigma(X29386,X29385),X29382),hAPP(c_COMBK(tc_fun(X29385,tc_HOL_Obool),X29386),X29381)))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29387),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29386,X29387),X29384),X29382)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29385,X29387),X29383),X29381)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29387,X29387),c_Fun_Oid(X29387)),hAPP(c_Set_OCollect(X29387),hAPP(hAPP(c_COMBB(tc_fun(X29386,tc_HOL_Obool),tc_HOL_Obool,X29387),c_HOL_OEx(X29386)),hAPP(hAPP(c_COMBB(tc_fun(X29386,tc_fun(X29385,tc_HOL_Obool)),tc_fun(X29386,tc_HOL_Obool),X29387),hAPP(c_COMBB(tc_fun(X29385,tc_HOL_Obool),tc_HOL_Obool,X29386),c_HOL_OEx(X29385))),hAPP(hAPP(c_COMBC(X29387,tc_fun(X29386,tc_fun(X29385,tc_HOL_Obool)),tc_fun(X29386,tc_fun(X29385,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29386,tc_fun(tc_fun(X29385,tc_HOL_Obool),tc_fun(X29385,tc_HOL_Obool))),tc_fun(tc_fun(X29386,tc_fun(X29385,tc_HOL_Obool)),tc_fun(X29386,tc_fun(X29385,tc_HOL_Obool))),X29387),c_COMBS(X29386,tc_fun(X29385,tc_HOL_Obool),tc_fun(X29385,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29386,tc_fun(X29385,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X29386,tc_fun(tc_fun(X29385,tc_HOL_Obool),tc_fun(X29385,tc_HOL_Obool))),X29387),hAPP(c_COMBB(tc_fun(X29385,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X29385,tc_HOL_Obool),tc_fun(X29385,tc_HOL_Obool)),X29386),c_COMBS(X29385,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29386,tc_fun(X29385,tc_HOL_Obool)),tc_fun(X29386,tc_fun(X29385,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X29387),hAPP(c_COMBB(tc_fun(X29385,tc_HOL_Obool),tc_fun(X29385,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X29386),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29385),c_fconj))),hAPP(hAPP(c_COMBC(X29387,tc_fun(X29386,tc_fun(X29385,X29387)),tc_fun(X29386,tc_fun(X29385,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29385,X29387),tc_fun(X29385,tc_HOL_Obool)),tc_fun(tc_fun(X29386,tc_fun(X29385,X29387)),tc_fun(X29386,tc_fun(X29385,tc_HOL_Obool))),X29387),c_COMBB(tc_fun(X29385,X29387),tc_fun(X29385,tc_HOL_Obool),X29386)),hAPP(hAPP(c_COMBB(tc_fun(X29387,tc_HOL_Obool),tc_fun(tc_fun(X29385,X29387),tc_fun(X29385,tc_HOL_Obool)),X29387),c_COMBB(X29387,tc_HOL_Obool,X29385)),c_fequal))),hAPP(hAPP(c_COMBC(X29386,tc_fun(X29385,X29387),tc_fun(X29385,X29387)),hAPP(hAPP(c_COMBB(tc_fun(X29387,X29387),tc_fun(tc_fun(X29385,X29387),tc_fun(X29385,X29387)),X29386),c_COMBB(X29387,X29387,X29385)),hAPP(hAPP(c_COMBB(X29387,tc_fun(X29387,X29387),X29386),c_Groups_Otimes__class_Otimes(X29387)),X29384))),X29383)))))),hAPP(hAPP(c_COMBC(X29386,tc_fun(X29385,tc_HOL_Obool),tc_fun(X29385,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X29385,tc_HOL_Obool),tc_fun(X29385,tc_HOL_Obool)),X29386),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29385)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29386),c_fconj),hAPP(hAPP(c_COMBC(X29386,tc_fun(X29386,tc_HOL_Obool),tc_HOL_Obool),c_member(X29386)),X29382)))),hAPP(hAPP(c_COMBC(X29385,tc_fun(X29385,tc_HOL_Obool),tc_HOL_Obool),c_member(X29385)),X29381))))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__mult__setsum__if__inj])]) ).
fof(i_0_6018,plain,
! [X29457,X29458,X29459,X29460,X29461] : hAPP(hAPP(c_Relation_Orel__comp(X29461,X29460,X29459),X29458),X29457) = hAPP(c_Set_OCollect(tc_prod(X29461,X29459)),hAPP(c_Product__Type_Oprod_Oprod__case(X29461,X29459,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X29459,tc_fun(X29460,tc_HOL_Obool)),tc_fun(X29459,tc_HOL_Obool),X29461),hAPP(c_COMBB(tc_fun(X29460,tc_HOL_Obool),tc_HOL_Obool,X29459),c_HOL_OEx(X29460))),hAPP(hAPP(c_COMBC(X29461,tc_fun(X29459,tc_fun(X29460,tc_HOL_Obool)),tc_fun(X29459,tc_fun(X29460,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29460,tc_HOL_Obool),tc_fun(X29460,tc_HOL_Obool)),tc_fun(tc_fun(X29459,tc_fun(X29460,tc_HOL_Obool)),tc_fun(X29459,tc_fun(X29460,tc_HOL_Obool))),X29461),c_COMBB(tc_fun(X29460,tc_HOL_Obool),tc_fun(X29460,tc_HOL_Obool),X29459)),hAPP(hAPP(c_COMBB(tc_fun(X29460,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X29460,tc_HOL_Obool),tc_fun(X29460,tc_HOL_Obool)),X29461),c_COMBS(X29460,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29460,tc_HOL_Obool),tc_fun(X29460,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X29461),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29460),c_fconj)),hAPP(hAPP(c_COMBC(X29461,tc_fun(tc_prod(X29461,X29460),tc_HOL_Obool),tc_fun(X29460,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29460,tc_fun(tc_fun(tc_prod(X29461,X29460),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29461,X29460),tc_HOL_Obool),tc_fun(X29460,tc_HOL_Obool)),X29461),c_COMBC(X29460,tc_fun(tc_prod(X29461,X29460),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29460,tc_prod(X29461,X29460)),tc_fun(X29460,tc_fun(tc_fun(tc_prod(X29461,X29460),tc_HOL_Obool),tc_HOL_Obool)),X29461),hAPP(c_COMBB(tc_prod(X29461,X29460),tc_fun(tc_fun(tc_prod(X29461,X29460),tc_HOL_Obool),tc_HOL_Obool),X29460),c_member(tc_prod(X29461,X29460)))),c_Product__Type_OPair(X29461,X29460)))),X29458))))),hAPP(hAPP(c_COMBC(X29459,tc_fun(tc_prod(X29460,X29459),tc_HOL_Obool),tc_fun(X29460,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29460,tc_fun(tc_fun(tc_prod(X29460,X29459),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29460,X29459),tc_HOL_Obool),tc_fun(X29460,tc_HOL_Obool)),X29459),c_COMBC(X29460,tc_fun(tc_prod(X29460,X29459),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29460,tc_prod(X29460,X29459)),tc_fun(X29460,tc_fun(tc_fun(tc_prod(X29460,X29459),tc_HOL_Obool),tc_HOL_Obool)),X29459),hAPP(c_COMBB(tc_prod(X29460,X29459),tc_fun(tc_fun(tc_prod(X29460,X29459),tc_HOL_Obool),tc_HOL_Obool),X29460),c_member(tc_prod(X29460,X29459)))),hAPP(c_COMBC(X29460,X29459,tc_prod(X29460,X29459)),c_Product__Type_OPair(X29460,X29459))))),X29457))))),
inference(variable_rename,[status(thm)],[fact_rel__comp__def]) ).
fof(i_0_6019,plain,
! [X29336,X29337,X29338] :
( ~ class_Orderings_Olinorder(X29338)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29338),X29337))
| X29337 = c_Orderings_Obot__class_Obot(tc_fun(X29338,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29338),X29336))
| X29336 = c_Orderings_Obot__class_Obot(tc_fun(X29338,tc_HOL_Obool))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X29338),c_Big__Operators_Olattice_OInf__fin(X29338,c_Orderings_Oord__class_Omin(X29338),X29337)),c_Big__Operators_Olattice_OInf__fin(X29338,c_Orderings_Oord__class_Omin(X29338),X29336)) = c_Big__Operators_Olattice_OInf__fin(X29338,c_Orderings_Oord__class_Omin(X29338),hAPP(c_Set_OCollect(X29338),hAPP(hAPP(c_COMBB(tc_fun(X29338,tc_HOL_Obool),tc_HOL_Obool,X29338),c_HOL_OEx(X29338)),hAPP(hAPP(c_COMBB(tc_fun(X29338,tc_fun(X29338,tc_HOL_Obool)),tc_fun(X29338,tc_HOL_Obool),X29338),hAPP(c_COMBB(tc_fun(X29338,tc_HOL_Obool),tc_HOL_Obool,X29338),c_HOL_OEx(X29338))),hAPP(hAPP(c_COMBC(X29338,tc_fun(X29338,tc_fun(X29338,tc_HOL_Obool)),tc_fun(X29338,tc_fun(X29338,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29338,tc_fun(tc_fun(X29338,tc_HOL_Obool),tc_fun(X29338,tc_HOL_Obool))),tc_fun(tc_fun(X29338,tc_fun(X29338,tc_HOL_Obool)),tc_fun(X29338,tc_fun(X29338,tc_HOL_Obool))),X29338),c_COMBS(X29338,tc_fun(X29338,tc_HOL_Obool),tc_fun(X29338,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29338,tc_fun(X29338,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X29338,tc_fun(tc_fun(X29338,tc_HOL_Obool),tc_fun(X29338,tc_HOL_Obool))),X29338),hAPP(c_COMBB(tc_fun(X29338,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X29338,tc_HOL_Obool),tc_fun(X29338,tc_HOL_Obool)),X29338),c_COMBS(X29338,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29338,tc_fun(X29338,tc_HOL_Obool)),tc_fun(X29338,tc_fun(X29338,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X29338),hAPP(c_COMBB(tc_fun(X29338,tc_HOL_Obool),tc_fun(X29338,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X29338),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29338),c_fconj))),hAPP(hAPP(c_COMBC(X29338,tc_fun(X29338,tc_fun(X29338,X29338)),tc_fun(X29338,tc_fun(X29338,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29338,X29338),tc_fun(X29338,tc_HOL_Obool)),tc_fun(tc_fun(X29338,tc_fun(X29338,X29338)),tc_fun(X29338,tc_fun(X29338,tc_HOL_Obool))),X29338),c_COMBB(tc_fun(X29338,X29338),tc_fun(X29338,tc_HOL_Obool),X29338)),hAPP(hAPP(c_COMBB(tc_fun(X29338,tc_HOL_Obool),tc_fun(tc_fun(X29338,X29338),tc_fun(X29338,tc_HOL_Obool)),X29338),c_COMBB(X29338,tc_HOL_Obool,X29338)),c_fequal))),c_Orderings_Oord__class_Omax(X29338)))))),hAPP(hAPP(c_COMBC(X29338,tc_fun(X29338,tc_HOL_Obool),tc_fun(X29338,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X29338,tc_HOL_Obool),tc_fun(X29338,tc_HOL_Obool)),X29338),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29338)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29338),c_fconj),hAPP(hAPP(c_COMBC(X29338,tc_fun(X29338,tc_HOL_Obool),tc_HOL_Obool),c_member(X29338)),X29337)))),hAPP(hAPP(c_COMBC(X29338,tc_fun(X29338,tc_HOL_Obool),tc_HOL_Obool),c_member(X29338)),X29336))))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf2__distrib])]) ).
fof(i_0_6020,plain,
! [X29378,X29379,X29380] :
( ~ class_Orderings_Olinorder(X29380)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29380),X29379))
| X29379 = c_Orderings_Obot__class_Obot(tc_fun(X29380,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29380),X29378))
| X29378 = c_Orderings_Obot__class_Obot(tc_fun(X29380,tc_HOL_Obool))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X29380),c_Big__Operators_Olattice_OSup__fin(X29380,c_Orderings_Oord__class_Omax(X29380),X29379)),c_Big__Operators_Olattice_OSup__fin(X29380,c_Orderings_Oord__class_Omax(X29380),X29378)) = c_Big__Operators_Olattice_OSup__fin(X29380,c_Orderings_Oord__class_Omax(X29380),hAPP(c_Set_OCollect(X29380),hAPP(hAPP(c_COMBB(tc_fun(X29380,tc_HOL_Obool),tc_HOL_Obool,X29380),c_HOL_OEx(X29380)),hAPP(hAPP(c_COMBB(tc_fun(X29380,tc_fun(X29380,tc_HOL_Obool)),tc_fun(X29380,tc_HOL_Obool),X29380),hAPP(c_COMBB(tc_fun(X29380,tc_HOL_Obool),tc_HOL_Obool,X29380),c_HOL_OEx(X29380))),hAPP(hAPP(c_COMBC(X29380,tc_fun(X29380,tc_fun(X29380,tc_HOL_Obool)),tc_fun(X29380,tc_fun(X29380,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29380,tc_fun(tc_fun(X29380,tc_HOL_Obool),tc_fun(X29380,tc_HOL_Obool))),tc_fun(tc_fun(X29380,tc_fun(X29380,tc_HOL_Obool)),tc_fun(X29380,tc_fun(X29380,tc_HOL_Obool))),X29380),c_COMBS(X29380,tc_fun(X29380,tc_HOL_Obool),tc_fun(X29380,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29380,tc_fun(X29380,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X29380,tc_fun(tc_fun(X29380,tc_HOL_Obool),tc_fun(X29380,tc_HOL_Obool))),X29380),hAPP(c_COMBB(tc_fun(X29380,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X29380,tc_HOL_Obool),tc_fun(X29380,tc_HOL_Obool)),X29380),c_COMBS(X29380,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29380,tc_fun(X29380,tc_HOL_Obool)),tc_fun(X29380,tc_fun(X29380,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X29380),hAPP(c_COMBB(tc_fun(X29380,tc_HOL_Obool),tc_fun(X29380,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X29380),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29380),c_fconj))),hAPP(hAPP(c_COMBC(X29380,tc_fun(X29380,tc_fun(X29380,X29380)),tc_fun(X29380,tc_fun(X29380,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29380,X29380),tc_fun(X29380,tc_HOL_Obool)),tc_fun(tc_fun(X29380,tc_fun(X29380,X29380)),tc_fun(X29380,tc_fun(X29380,tc_HOL_Obool))),X29380),c_COMBB(tc_fun(X29380,X29380),tc_fun(X29380,tc_HOL_Obool),X29380)),hAPP(hAPP(c_COMBB(tc_fun(X29380,tc_HOL_Obool),tc_fun(tc_fun(X29380,X29380),tc_fun(X29380,tc_HOL_Obool)),X29380),c_COMBB(X29380,tc_HOL_Obool,X29380)),c_fequal))),c_Orderings_Oord__class_Omin(X29380)))))),hAPP(hAPP(c_COMBC(X29380,tc_fun(X29380,tc_HOL_Obool),tc_fun(X29380,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X29380,tc_HOL_Obool),tc_fun(X29380,tc_HOL_Obool)),X29380),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29380)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29380),c_fconj),hAPP(hAPP(c_COMBC(X29380,tc_fun(X29380,tc_HOL_Obool),tc_HOL_Obool),c_member(X29380)),X29379)))),hAPP(hAPP(c_COMBC(X29380,tc_fun(X29380,tc_HOL_Obool),tc_HOL_Obool),c_member(X29380)),X29378))))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup2__distrib])]) ).
fof(i_0_6021,plain,
! [X29372,X29373,X29374] :
( ~ class_Lattices_Odistrib__lattice(X29374)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29374),X29373))
| X29373 = c_Orderings_Obot__class_Obot(tc_fun(X29374,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29374),X29372))
| X29372 = c_Orderings_Obot__class_Obot(tc_fun(X29374,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X29374),c_Big__Operators_Olattice__class_OSup__fin(X29374,X29373)),c_Big__Operators_Olattice__class_OSup__fin(X29374,X29372)) = c_Big__Operators_Olattice__class_OSup__fin(X29374,hAPP(c_Set_OCollect(X29374),hAPP(hAPP(c_COMBB(tc_fun(X29374,tc_HOL_Obool),tc_HOL_Obool,X29374),c_HOL_OEx(X29374)),hAPP(hAPP(c_COMBB(tc_fun(X29374,tc_fun(X29374,tc_HOL_Obool)),tc_fun(X29374,tc_HOL_Obool),X29374),hAPP(c_COMBB(tc_fun(X29374,tc_HOL_Obool),tc_HOL_Obool,X29374),c_HOL_OEx(X29374))),hAPP(hAPP(c_COMBC(X29374,tc_fun(X29374,tc_fun(X29374,tc_HOL_Obool)),tc_fun(X29374,tc_fun(X29374,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29374,tc_fun(tc_fun(X29374,tc_HOL_Obool),tc_fun(X29374,tc_HOL_Obool))),tc_fun(tc_fun(X29374,tc_fun(X29374,tc_HOL_Obool)),tc_fun(X29374,tc_fun(X29374,tc_HOL_Obool))),X29374),c_COMBS(X29374,tc_fun(X29374,tc_HOL_Obool),tc_fun(X29374,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29374,tc_fun(X29374,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X29374,tc_fun(tc_fun(X29374,tc_HOL_Obool),tc_fun(X29374,tc_HOL_Obool))),X29374),hAPP(c_COMBB(tc_fun(X29374,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X29374,tc_HOL_Obool),tc_fun(X29374,tc_HOL_Obool)),X29374),c_COMBS(X29374,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29374,tc_fun(X29374,tc_HOL_Obool)),tc_fun(X29374,tc_fun(X29374,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X29374),hAPP(c_COMBB(tc_fun(X29374,tc_HOL_Obool),tc_fun(X29374,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X29374),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29374),c_fconj))),hAPP(hAPP(c_COMBC(X29374,tc_fun(X29374,tc_fun(X29374,X29374)),tc_fun(X29374,tc_fun(X29374,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29374,X29374),tc_fun(X29374,tc_HOL_Obool)),tc_fun(tc_fun(X29374,tc_fun(X29374,X29374)),tc_fun(X29374,tc_fun(X29374,tc_HOL_Obool))),X29374),c_COMBB(tc_fun(X29374,X29374),tc_fun(X29374,tc_HOL_Obool),X29374)),hAPP(hAPP(c_COMBB(tc_fun(X29374,tc_HOL_Obool),tc_fun(tc_fun(X29374,X29374),tc_fun(X29374,tc_HOL_Obool)),X29374),c_COMBB(X29374,tc_HOL_Obool,X29374)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(X29374)))))),hAPP(hAPP(c_COMBC(X29374,tc_fun(X29374,tc_HOL_Obool),tc_fun(X29374,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X29374,tc_HOL_Obool),tc_fun(X29374,tc_HOL_Obool)),X29374),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29374)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29374),c_fconj),hAPP(hAPP(c_COMBC(X29374,tc_fun(X29374,tc_HOL_Obool),tc_HOL_Obool),c_member(X29374)),X29373)))),hAPP(hAPP(c_COMBC(X29374,tc_fun(X29374,tc_HOL_Obool),tc_HOL_Obool),c_member(X29374)),X29372))))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Sup2__distrib])]) ).
fof(i_0_6022,plain,
! [X29366,X29367,X29368] :
( ~ class_Lattices_Odistrib__lattice(X29368)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29368),X29367))
| X29367 = c_Orderings_Obot__class_Obot(tc_fun(X29368,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29368),X29366))
| X29366 = c_Orderings_Obot__class_Obot(tc_fun(X29368,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X29368),c_Big__Operators_Olattice__class_OInf__fin(X29368,X29367)),c_Big__Operators_Olattice__class_OInf__fin(X29368,X29366)) = c_Big__Operators_Olattice__class_OInf__fin(X29368,hAPP(c_Set_OCollect(X29368),hAPP(hAPP(c_COMBB(tc_fun(X29368,tc_HOL_Obool),tc_HOL_Obool,X29368),c_HOL_OEx(X29368)),hAPP(hAPP(c_COMBB(tc_fun(X29368,tc_fun(X29368,tc_HOL_Obool)),tc_fun(X29368,tc_HOL_Obool),X29368),hAPP(c_COMBB(tc_fun(X29368,tc_HOL_Obool),tc_HOL_Obool,X29368),c_HOL_OEx(X29368))),hAPP(hAPP(c_COMBC(X29368,tc_fun(X29368,tc_fun(X29368,tc_HOL_Obool)),tc_fun(X29368,tc_fun(X29368,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29368,tc_fun(tc_fun(X29368,tc_HOL_Obool),tc_fun(X29368,tc_HOL_Obool))),tc_fun(tc_fun(X29368,tc_fun(X29368,tc_HOL_Obool)),tc_fun(X29368,tc_fun(X29368,tc_HOL_Obool))),X29368),c_COMBS(X29368,tc_fun(X29368,tc_HOL_Obool),tc_fun(X29368,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29368,tc_fun(X29368,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X29368,tc_fun(tc_fun(X29368,tc_HOL_Obool),tc_fun(X29368,tc_HOL_Obool))),X29368),hAPP(c_COMBB(tc_fun(X29368,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X29368,tc_HOL_Obool),tc_fun(X29368,tc_HOL_Obool)),X29368),c_COMBS(X29368,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29368,tc_fun(X29368,tc_HOL_Obool)),tc_fun(X29368,tc_fun(X29368,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X29368),hAPP(c_COMBB(tc_fun(X29368,tc_HOL_Obool),tc_fun(X29368,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X29368),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29368),c_fconj))),hAPP(hAPP(c_COMBC(X29368,tc_fun(X29368,tc_fun(X29368,X29368)),tc_fun(X29368,tc_fun(X29368,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29368,X29368),tc_fun(X29368,tc_HOL_Obool)),tc_fun(tc_fun(X29368,tc_fun(X29368,X29368)),tc_fun(X29368,tc_fun(X29368,tc_HOL_Obool))),X29368),c_COMBB(tc_fun(X29368,X29368),tc_fun(X29368,tc_HOL_Obool),X29368)),hAPP(hAPP(c_COMBB(tc_fun(X29368,tc_HOL_Obool),tc_fun(tc_fun(X29368,X29368),tc_fun(X29368,tc_HOL_Obool)),X29368),c_COMBB(X29368,tc_HOL_Obool,X29368)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(X29368)))))),hAPP(hAPP(c_COMBC(X29368,tc_fun(X29368,tc_HOL_Obool),tc_fun(X29368,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X29368,tc_HOL_Obool),tc_fun(X29368,tc_HOL_Obool)),X29368),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29368)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29368),c_fconj),hAPP(hAPP(c_COMBC(X29368,tc_fun(X29368,tc_HOL_Obool),tc_HOL_Obool),c_member(X29368)),X29367)))),hAPP(hAPP(c_COMBC(X29368,tc_fun(X29368,tc_HOL_Obool),tc_HOL_Obool),c_member(X29368)),X29366))))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Inf2__distrib])]) ).
fof(i_0_6023,plain,
! [X17683,X17684,X17685,X17686,X17687,X17688,X17689,X17690,X17691,X17692,X17693,X17694] : c_Com_Ocom_Ocom__rec(X17694,X17693,X17692,X17691,X17690,X17689,X17688,X17687,X17686,c_Com_Ocom_OLocal(X17685,X17684,X17683)) = hAPP(hAPP(hAPP(hAPP(X17691,X17685),X17684),X17683),c_Com_Ocom_Ocom__rec(X17694,X17693,X17692,X17691,X17690,X17689,X17688,X17687,X17686,X17683)),
inference(variable_rename,[status(thm)],[fact_com_Orecs_I3_J]) ).
fof(i_0_6024,plain,
! [X17896,X17897,X17898,X17899,X17900,X17901,X17902,X17903,X17904,X17905,X17906] : c_Com_Ocom_Ocom__rec(X17906,X17905,X17904,X17903,X17902,X17901,X17900,X17899,X17898,c_Com_Ocom_OWhile(X17897,X17896)) = hAPP(hAPP(hAPP(X17900,X17897),X17896),c_Com_Ocom_Ocom__rec(X17906,X17905,X17904,X17903,X17902,X17901,X17900,X17899,X17898,X17896)),
inference(variable_rename,[status(thm)],[fact_com_Orecs_I6_J]) ).
fof(i_0_6025,plain,
! [X32365,X32366,X32367] : c_List_Oset__Cons(X32367,X32366,X32365) = hAPP(c_Set_OCollect(tc_List_Olist(X32367)),hAPP(hAPP(c_COMBB(tc_fun(X32367,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(X32367)),c_HOL_OEx(X32367)),hAPP(hAPP(c_COMBB(tc_fun(X32367,tc_fun(tc_List_Olist(X32367),tc_HOL_Obool)),tc_fun(X32367,tc_HOL_Obool),tc_List_Olist(X32367)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X32367),tc_HOL_Obool),tc_HOL_Obool,X32367),c_HOL_OEx(tc_List_Olist(X32367)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X32367),tc_fun(X32367,tc_fun(tc_List_Olist(X32367),tc_HOL_Obool)),tc_fun(X32367,tc_fun(tc_List_Olist(X32367),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X32367,tc_fun(tc_fun(tc_List_Olist(X32367),tc_HOL_Obool),tc_fun(tc_List_Olist(X32367),tc_HOL_Obool))),tc_fun(tc_fun(X32367,tc_fun(tc_List_Olist(X32367),tc_HOL_Obool)),tc_fun(X32367,tc_fun(tc_List_Olist(X32367),tc_HOL_Obool))),tc_List_Olist(X32367)),c_COMBS(X32367,tc_fun(tc_List_Olist(X32367),tc_HOL_Obool),tc_fun(tc_List_Olist(X32367),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X32367,tc_fun(tc_List_Olist(X32367),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X32367,tc_fun(tc_fun(tc_List_Olist(X32367),tc_HOL_Obool),tc_fun(tc_List_Olist(X32367),tc_HOL_Obool))),tc_List_Olist(X32367)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X32367),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X32367),tc_HOL_Obool),tc_fun(tc_List_Olist(X32367),tc_HOL_Obool)),X32367),c_COMBS(tc_List_Olist(X32367),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X32367,tc_fun(tc_List_Olist(X32367),tc_HOL_Obool)),tc_fun(X32367,tc_fun(tc_List_Olist(X32367),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(X32367)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X32367),tc_HOL_Obool),tc_fun(tc_List_Olist(X32367),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X32367),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X32367)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(X32367),tc_fun(X32367,tc_fun(tc_List_Olist(X32367),tc_List_Olist(X32367))),tc_fun(X32367,tc_fun(tc_List_Olist(X32367),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(X32367),tc_List_Olist(X32367)),tc_fun(tc_List_Olist(X32367),tc_HOL_Obool)),tc_fun(tc_fun(X32367,tc_fun(tc_List_Olist(X32367),tc_List_Olist(X32367))),tc_fun(X32367,tc_fun(tc_List_Olist(X32367),tc_HOL_Obool))),tc_List_Olist(X32367)),c_COMBB(tc_fun(tc_List_Olist(X32367),tc_List_Olist(X32367)),tc_fun(tc_List_Olist(X32367),tc_HOL_Obool),X32367)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X32367),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X32367),tc_List_Olist(X32367)),tc_fun(tc_List_Olist(X32367),tc_HOL_Obool)),tc_List_Olist(X32367)),c_COMBB(tc_List_Olist(X32367),tc_HOL_Obool,tc_List_Olist(X32367))),c_fequal))),c_List_Olist_OCons(X32367)))))),hAPP(hAPP(c_COMBC(X32367,tc_fun(tc_List_Olist(X32367),tc_HOL_Obool),tc_fun(tc_List_Olist(X32367),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X32367),tc_HOL_Obool),tc_fun(tc_List_Olist(X32367),tc_HOL_Obool)),X32367),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X32367))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X32367),c_fconj),hAPP(hAPP(c_COMBC(X32367,tc_fun(X32367,tc_HOL_Obool),tc_HOL_Obool),c_member(X32367)),X32366)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X32367),tc_fun(tc_List_Olist(X32367),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X32367))),X32365)))))),
inference(variable_rename,[status(thm)],[fact_set__Cons__def]) ).
fof(i_0_6026,plain,
! [X29024,X29025,X29026,X29027,X29028,X29029,X29030,X29031] :
( ( X29029 = hAPP(hAPP(c_Product__Type_OPair(X29031,X29030),hAPP(X29026,esk299_8(X29024,X29025,X29026,X29027,X29028,X29029,X29030,X29031))),hAPP(X29025,esk300_8(X29024,X29025,X29026,X29027,X29028,X29029,X29030,X29031)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29031,X29030)),X29029),hAPP(c_Set_Oimage(tc_prod(X29028,X29027),tc_prod(X29031,X29030),c_Product__Type_Omap__pair(X29028,X29031,X29027,X29030,X29026,X29025)),X29024))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29028,X29027)),hAPP(hAPP(c_Product__Type_OPair(X29028,X29027),esk299_8(X29024,X29025,X29026,X29027,X29028,X29029,X29030,X29031)),esk300_8(X29024,X29025,X29026,X29027,X29028,X29029,X29030,X29031))),X29024))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29031,X29030)),X29029),hAPP(c_Set_Oimage(tc_prod(X29028,X29027),tc_prod(X29031,X29030),c_Product__Type_Omap__pair(X29028,X29031,X29027,X29030,X29026,X29025)),X29024))) ) ),
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,
! [X23032,X23033,X23034,X23035,X23036,X23037,X23038,X23039] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X23039,X23038,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X23039)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X23039),X23037),hAPP(c_Com_Ocom_OBODY,X23036)),hAPP(hAPP(c_COMBC(X23039,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)),X23039),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X23035)),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,X23034)))),X23033)),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(X23039),tc_HOL_Obool))))
| c_Hoare__Mirabelle_Ohoare__derivs(X23039,X23038,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X23039)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X23039),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),X23039),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,X23034)))),hAPP(hAPP(c_COMBC(X23039,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)),X23039),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X23037)),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))),X23032)))),c_Com_Ocom_OCall(X23033,X23036,X23032)),X23035)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X23039),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,
! [X31425,X31426,X31427,X31428,X31429,X31430,X31431,X31432] :
( ( hBOOL(hAPP(hAPP(c_member(X31428),esk404_8(X31425,X31426,X31427,X31428,X31429,X31430,X31431,X31432)),X31427))
| ~ hBOOL(hAPP(hAPP(c_member(X31428),X31425),X31427))
| hAPP(c_Set_Oimage(X31432,X31431,X31430),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31428,tc_fun(X31432,tc_HOL_Obool)),X31427),X31426)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31428,tc_fun(X31431,tc_HOL_Obool)),X31427),hAPP(hAPP(c_COMBB(tc_fun(X31432,tc_HOL_Obool),tc_fun(X31431,tc_HOL_Obool),X31428),c_Set_Oimage(X31432,X31431,X31430)),X31426))
| ~ c_Fun_Oinj__on(X31432,X31431,X31430,X31429) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31432,tc_HOL_Obool)),hAPP(X31426,esk404_8(X31425,X31426,X31427,X31428,X31429,X31430,X31431,X31432))),X31429))
| ~ hBOOL(hAPP(hAPP(c_member(X31428),X31425),X31427))
| hAPP(c_Set_Oimage(X31432,X31431,X31430),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31428,tc_fun(X31432,tc_HOL_Obool)),X31427),X31426)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31428,tc_fun(X31431,tc_HOL_Obool)),X31427),hAPP(hAPP(c_COMBB(tc_fun(X31432,tc_HOL_Obool),tc_fun(X31431,tc_HOL_Obool),X31428),c_Set_Oimage(X31432,X31431,X31430)),X31426))
| ~ c_Fun_Oinj__on(X31432,X31431,X31430,X31429) ) ),
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,
! [X17296,X17297,X17298,X17299,X17300,X17301,X17302,X17303,X17304,X17305,X17306,X17307] : c_Com_Ocom_Ocom__rec(X17307,X17306,X17305,X17304,X17303,X17302,X17301,X17300,X17299,c_Com_Ocom_OCall(X17298,X17297,X17296)) = hAPP(hAPP(hAPP(X17299,X17298),X17297),X17296),
inference(variable_rename,[status(thm)],[fact_com_Orecs_I8_J]) ).
fof(i_0_6033,plain,
! [X17471,X17472,X17473,X17474,X17475,X17476,X17477,X17478,X17479,X17480,X17481,X17482] : c_Com_Ocom_Ocom__case(X17482,X17481,X17480,X17479,X17478,X17477,X17476,X17475,X17474,c_Com_Ocom_OLocal(X17473,X17472,X17471)) = hAPP(hAPP(hAPP(X17479,X17473),X17472),X17471),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I66_J]) ).
fof(i_0_6034,plain,
! [X17459,X17460,X17461,X17462,X17463,X17464,X17465,X17466,X17467,X17468,X17469,X17470] : c_Com_Ocom_Ocom__case(X17470,X17469,X17468,X17467,X17466,X17465,X17464,X17463,X17462,c_Com_Ocom_OCond(X17461,X17460,X17459)) = hAPP(hAPP(hAPP(X17465,X17461),X17460),X17459),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I68_J]) ).
fof(i_0_6035,plain,
! [X17233,X17234,X17235,X17236,X17237,X17238,X17239,X17240,X17241,X17242,X17243,X17244] : c_Com_Ocom_Ocom__case(X17244,X17243,X17242,X17241,X17240,X17239,X17238,X17237,X17236,c_Com_Ocom_OCall(X17235,X17234,X17233)) = hAPP(hAPP(hAPP(X17236,X17235),X17234),X17233),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I71_J]) ).
fof(i_0_6036,plain,
! [X17308,X17309,X17310,X17311,X17312,X17313,X17314,X17315,X17316,X17317,X17318] : c_Com_Ocom_Ocom__rec(X17318,X17317,X17316,X17315,X17314,X17313,X17312,X17311,X17310,c_Com_Ocom_OAss(X17309,X17308)) = hAPP(hAPP(X17316,X17309),X17308),
inference(variable_rename,[status(thm)],[fact_com_Orecs_I2_J]) ).
fof(i_0_6037,plain,
! [X17769,X17770,X17771,X17772,X17773,X17774,X17775,X17776,X17777,X17778,X17779] : c_Com_Ocom_Ocom__case(X17779,X17778,X17777,X17776,X17775,X17774,X17773,X17772,X17771,c_Com_Ocom_OWhile(X17770,X17769)) = hAPP(hAPP(X17773,X17770),X17769),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I69_J]) ).
fof(i_0_6038,plain,
! [X17319,X17320,X17321,X17322,X17323,X17324,X17325,X17326,X17327,X17328,X17329] : c_Com_Ocom_Ocom__case(X17329,X17328,X17327,X17326,X17325,X17324,X17323,X17322,X17321,c_Com_Ocom_OSemi(X17320,X17319)) = hAPP(hAPP(X17325,X17320),X17319),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I67_J]) ).
fof(i_0_6039,plain,
! [X17222,X17223,X17224,X17225,X17226,X17227,X17228,X17229,X17230,X17231,X17232] : c_Com_Ocom_Ocom__case(X17232,X17231,X17230,X17229,X17228,X17227,X17226,X17225,X17224,c_Com_Ocom_OAss(X17223,X17222)) = hAPP(hAPP(X17230,X17223),X17222),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I65_J]) ).
fof(i_0_6040,plain,
! [X17405,X17406,X17407,X17408,X17409,X17410,X17411,X17412,X17413,X17414] : c_Com_Ocom_Ocom__rec(X17414,X17413,X17412,X17411,X17410,X17409,X17408,X17407,X17406,hAPP(c_Com_Ocom_OBODY,X17405)) = hAPP(X17407,X17405),
inference(variable_rename,[status(thm)],[fact_com_Orecs_I7_J]) ).
fof(i_0_6041,plain,
! [X17168,X17169,X17170,X17171,X17172,X17173,X17174,X17175,X17176,X17177] : c_Com_Ocom_Ocom__case(X17177,X17176,X17175,X17174,X17173,X17172,X17171,X17170,X17169,hAPP(c_Com_Ocom_OBODY,X17168)) = hAPP(X17170,X17168),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I70_J]) ).
fof(i_0_6042,plain,
! [X17287,X17288,X17289,X17290,X17291,X17292,X17293,X17294,X17295] : c_Com_Ocom_Ocom__rec(X17295,X17294,X17293,X17292,X17291,X17290,X17289,X17288,X17287,c_Com_Ocom_OSKIP) = X17294,
inference(variable_rename,[status(thm)],[fact_com_Orecs_I1_J]) ).
fof(i_0_6043,plain,
! [X17213,X17214,X17215,X17216,X17217,X17218,X17219,X17220,X17221] : c_Com_Ocom_Ocom__case(X17221,X17220,X17219,X17218,X17217,X17216,X17215,X17214,X17213,c_Com_Ocom_OSKIP) = X17220,
inference(variable_rename,[status(thm)],[fact_com_Osimps_I64_J]) ).
fof(i_0_6044,plain,
! [X25131,X25132,X25133,X25134,X25135,X25136] :
( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25136,tc_fun(X25135,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X25136,tc_fun(tc_prod(X25136,X25135),tc_HOL_Obool),tc_fun(X25135,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25135,tc_fun(tc_fun(tc_prod(X25136,X25135),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X25136,X25135),tc_HOL_Obool),tc_fun(X25135,tc_HOL_Obool)),X25136),c_COMBC(X25135,tc_fun(tc_prod(X25136,X25135),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25135,tc_prod(X25136,X25135)),tc_fun(X25135,tc_fun(tc_fun(tc_prod(X25136,X25135),tc_HOL_Obool),tc_HOL_Obool)),X25136),hAPP(c_COMBB(tc_prod(X25136,X25135),tc_fun(tc_fun(tc_prod(X25136,X25135),tc_HOL_Obool),tc_HOL_Obool),X25135),c_member(tc_prod(X25136,X25135)))),c_Product__Type_OPair(X25136,X25135)))),X25134)),hAPP(hAPP(c_COMBC(X25136,tc_fun(tc_prod(X25136,X25135),tc_HOL_Obool),tc_fun(X25135,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25135,tc_fun(tc_fun(tc_prod(X25136,X25135),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X25136,X25135),tc_HOL_Obool),tc_fun(X25135,tc_HOL_Obool)),X25136),c_COMBC(X25135,tc_fun(tc_prod(X25136,X25135),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25135,tc_prod(X25136,X25135)),tc_fun(X25135,tc_fun(tc_fun(tc_prod(X25136,X25135),tc_HOL_Obool),tc_HOL_Obool)),X25136),hAPP(c_COMBB(tc_prod(X25136,X25135),tc_fun(tc_fun(tc_prod(X25136,X25135),tc_HOL_Obool),tc_HOL_Obool),X25135),c_member(tc_prod(X25136,X25135)))),c_Product__Type_OPair(X25136,X25135)))),X25133)),X25132),X25131))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X25136,X25135)),hAPP(hAPP(c_Product__Type_OPair(X25136,X25135),X25132),X25131)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X25136,X25135),tc_HOL_Obool)),X25134),X25133))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X25136,X25135)),hAPP(hAPP(c_Product__Type_OPair(X25136,X25135),X25132),X25131)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X25136,X25135),tc_HOL_Obool)),X25134),X25133)))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25136,tc_fun(X25135,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X25136,tc_fun(tc_prod(X25136,X25135),tc_HOL_Obool),tc_fun(X25135,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25135,tc_fun(tc_fun(tc_prod(X25136,X25135),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X25136,X25135),tc_HOL_Obool),tc_fun(X25135,tc_HOL_Obool)),X25136),c_COMBC(X25135,tc_fun(tc_prod(X25136,X25135),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25135,tc_prod(X25136,X25135)),tc_fun(X25135,tc_fun(tc_fun(tc_prod(X25136,X25135),tc_HOL_Obool),tc_HOL_Obool)),X25136),hAPP(c_COMBB(tc_prod(X25136,X25135),tc_fun(tc_fun(tc_prod(X25136,X25135),tc_HOL_Obool),tc_HOL_Obool),X25135),c_member(tc_prod(X25136,X25135)))),c_Product__Type_OPair(X25136,X25135)))),X25134)),hAPP(hAPP(c_COMBC(X25136,tc_fun(tc_prod(X25136,X25135),tc_HOL_Obool),tc_fun(X25135,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25135,tc_fun(tc_fun(tc_prod(X25136,X25135),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X25136,X25135),tc_HOL_Obool),tc_fun(X25135,tc_HOL_Obool)),X25136),c_COMBC(X25135,tc_fun(tc_prod(X25136,X25135),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25135,tc_prod(X25136,X25135)),tc_fun(X25135,tc_fun(tc_fun(tc_prod(X25136,X25135),tc_HOL_Obool),tc_HOL_Obool)),X25136),hAPP(c_COMBB(tc_prod(X25136,X25135),tc_fun(tc_fun(tc_prod(X25136,X25135),tc_HOL_Obool),tc_HOL_Obool),X25135),c_member(tc_prod(X25136,X25135)))),c_Product__Type_OPair(X25136,X25135)))),X25133)),X25132),X25131)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Int__eq2])]) ).
fof(i_0_6045,plain,
! [X24199,X24200,X24201,X24202,X24203,X24204] :
( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24204,tc_fun(X24203,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X24204,tc_fun(tc_prod(X24204,X24203),tc_HOL_Obool),tc_fun(X24203,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24203,tc_fun(tc_fun(tc_prod(X24204,X24203),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X24204,X24203),tc_HOL_Obool),tc_fun(X24203,tc_HOL_Obool)),X24204),c_COMBC(X24203,tc_fun(tc_prod(X24204,X24203),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24203,tc_prod(X24204,X24203)),tc_fun(X24203,tc_fun(tc_fun(tc_prod(X24204,X24203),tc_HOL_Obool),tc_HOL_Obool)),X24204),hAPP(c_COMBB(tc_prod(X24204,X24203),tc_fun(tc_fun(tc_prod(X24204,X24203),tc_HOL_Obool),tc_HOL_Obool),X24203),c_member(tc_prod(X24204,X24203)))),c_Product__Type_OPair(X24204,X24203)))),X24202)),hAPP(hAPP(c_COMBC(X24204,tc_fun(tc_prod(X24204,X24203),tc_HOL_Obool),tc_fun(X24203,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24203,tc_fun(tc_fun(tc_prod(X24204,X24203),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X24204,X24203),tc_HOL_Obool),tc_fun(X24203,tc_HOL_Obool)),X24204),c_COMBC(X24203,tc_fun(tc_prod(X24204,X24203),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24203,tc_prod(X24204,X24203)),tc_fun(X24203,tc_fun(tc_fun(tc_prod(X24204,X24203),tc_HOL_Obool),tc_HOL_Obool)),X24204),hAPP(c_COMBB(tc_prod(X24204,X24203),tc_fun(tc_fun(tc_prod(X24204,X24203),tc_HOL_Obool),tc_HOL_Obool),X24203),c_member(tc_prod(X24204,X24203)))),c_Product__Type_OPair(X24204,X24203)))),X24201)),X24200),X24199))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X24204,X24203)),hAPP(hAPP(c_Product__Type_OPair(X24204,X24203),X24200),X24199)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X24204,X24203),tc_HOL_Obool)),X24202),X24201))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24204,X24203)),hAPP(hAPP(c_Product__Type_OPair(X24204,X24203),X24200),X24199)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X24204,X24203),tc_HOL_Obool)),X24202),X24201)))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24204,tc_fun(X24203,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X24204,tc_fun(tc_prod(X24204,X24203),tc_HOL_Obool),tc_fun(X24203,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24203,tc_fun(tc_fun(tc_prod(X24204,X24203),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X24204,X24203),tc_HOL_Obool),tc_fun(X24203,tc_HOL_Obool)),X24204),c_COMBC(X24203,tc_fun(tc_prod(X24204,X24203),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24203,tc_prod(X24204,X24203)),tc_fun(X24203,tc_fun(tc_fun(tc_prod(X24204,X24203),tc_HOL_Obool),tc_HOL_Obool)),X24204),hAPP(c_COMBB(tc_prod(X24204,X24203),tc_fun(tc_fun(tc_prod(X24204,X24203),tc_HOL_Obool),tc_HOL_Obool),X24203),c_member(tc_prod(X24204,X24203)))),c_Product__Type_OPair(X24204,X24203)))),X24202)),hAPP(hAPP(c_COMBC(X24204,tc_fun(tc_prod(X24204,X24203),tc_HOL_Obool),tc_fun(X24203,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24203,tc_fun(tc_fun(tc_prod(X24204,X24203),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X24204,X24203),tc_HOL_Obool),tc_fun(X24203,tc_HOL_Obool)),X24204),c_COMBC(X24203,tc_fun(tc_prod(X24204,X24203),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24203,tc_prod(X24204,X24203)),tc_fun(X24203,tc_fun(tc_fun(tc_prod(X24204,X24203),tc_HOL_Obool),tc_HOL_Obool)),X24204),hAPP(c_COMBB(tc_prod(X24204,X24203),tc_fun(tc_fun(tc_prod(X24204,X24203),tc_HOL_Obool),tc_HOL_Obool),X24203),c_member(tc_prod(X24204,X24203)))),c_Product__Type_OPair(X24204,X24203)))),X24201)),X24200),X24199)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Un__eq2])]) ).
fof(i_0_6046,plain,
! [X32198,X32199] : c_List_Olenlex(X32199,X32198) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X32199),tc_List_Olist(X32199))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X32199),tc_List_Olist(X32199),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(X32199),tc_fun(tc_List_Olist(X32199),tc_HOL_Obool),tc_fun(tc_List_Olist(X32199),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X32199),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X32199),tc_HOL_Obool),tc_fun(tc_List_Olist(X32199),tc_HOL_Obool)),tc_List_Olist(X32199)),c_COMBS(tc_List_Olist(X32199),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X32199),tc_HOL_Obool),tc_fun(tc_List_Olist(X32199),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X32199)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X32199)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X32199),tc_fun(tc_List_Olist(X32199),tc_Nat_Onat),tc_fun(tc_List_Olist(X32199),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X32199),tc_Nat_Onat),tc_fun(tc_List_Olist(X32199),tc_HOL_Obool)),tc_List_Olist(X32199)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X32199))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X32199)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X32199))))),c_Nat_Osize__class_Osize(tc_List_Olist(X32199)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(X32199),tc_fun(tc_List_Olist(X32199),tc_HOL_Obool),tc_fun(tc_List_Olist(X32199),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X32199),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X32199),tc_HOL_Obool),tc_fun(tc_List_Olist(X32199),tc_HOL_Obool)),tc_List_Olist(X32199)),c_COMBS(tc_List_Olist(X32199),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X32199),tc_HOL_Obool),tc_fun(tc_List_Olist(X32199),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X32199)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X32199)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X32199),tc_fun(tc_List_Olist(X32199),tc_Nat_Onat),tc_fun(tc_List_Olist(X32199),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X32199),tc_Nat_Onat),tc_fun(tc_List_Olist(X32199),tc_HOL_Obool)),tc_List_Olist(X32199)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X32199))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X32199)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X32199))))),c_Nat_Osize__class_Osize(tc_List_Olist(X32199)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X32199),tc_fun(tc_prod(tc_List_Olist(X32199),tc_List_Olist(X32199)),tc_HOL_Obool),tc_fun(tc_List_Olist(X32199),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X32199),tc_fun(tc_fun(tc_prod(tc_List_Olist(X32199),tc_List_Olist(X32199)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X32199),tc_List_Olist(X32199)),tc_HOL_Obool),tc_fun(tc_List_Olist(X32199),tc_HOL_Obool)),tc_List_Olist(X32199)),c_COMBC(tc_List_Olist(X32199),tc_fun(tc_prod(tc_List_Olist(X32199),tc_List_Olist(X32199)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X32199),tc_prod(tc_List_Olist(X32199),tc_List_Olist(X32199))),tc_fun(tc_List_Olist(X32199),tc_fun(tc_fun(tc_prod(tc_List_Olist(X32199),tc_List_Olist(X32199)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(X32199)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X32199),tc_List_Olist(X32199)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X32199),tc_List_Olist(X32199)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X32199)),c_member(tc_prod(tc_List_Olist(X32199),tc_List_Olist(X32199))))),c_Product__Type_OPair(tc_List_Olist(X32199),tc_List_Olist(X32199))))),c_List_Olex(X32199,X32198)))))),
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,
! [X30974,X30975,X30976,X30977,X30978,X30979] :
( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30979,tc_fun(X30978,tc_fun(X30977,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X30979,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X30978,X30977),tc_HOL_Obool),tc_fun(X30978,tc_fun(X30977,tc_HOL_Obool)),X30979),hAPP(c_COMBC(X30978,tc_fun(tc_prod(X30978,X30977),tc_HOL_Obool),tc_fun(X30977,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30977,tc_fun(tc_fun(tc_prod(X30978,X30977),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X30978,X30977),tc_HOL_Obool),tc_fun(X30977,tc_HOL_Obool)),X30978),c_COMBC(X30977,tc_fun(tc_prod(X30978,X30977),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30977,tc_prod(X30978,X30977)),tc_fun(X30977,tc_fun(tc_fun(tc_prod(X30978,X30977),tc_HOL_Obool),tc_HOL_Obool)),X30978),hAPP(c_COMBB(tc_prod(X30978,X30977),tc_fun(tc_fun(tc_prod(X30978,X30977),tc_HOL_Obool),tc_HOL_Obool),X30977),c_member(tc_prod(X30978,X30977)))),c_Product__Type_OPair(X30978,X30977))))),X30976)),X30975),X30974))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30978,X30977)),hAPP(hAPP(c_Product__Type_OPair(X30978,X30977),X30975),X30974)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30979,tc_fun(tc_prod(X30978,X30977),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X30979,tc_HOL_Obool))),X30976))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30978,X30977)),hAPP(hAPP(c_Product__Type_OPair(X30978,X30977),X30975),X30974)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30979,tc_fun(tc_prod(X30978,X30977),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X30979,tc_HOL_Obool))),X30976)))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30979,tc_fun(X30978,tc_fun(X30977,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X30979,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X30978,X30977),tc_HOL_Obool),tc_fun(X30978,tc_fun(X30977,tc_HOL_Obool)),X30979),hAPP(c_COMBC(X30978,tc_fun(tc_prod(X30978,X30977),tc_HOL_Obool),tc_fun(X30977,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30977,tc_fun(tc_fun(tc_prod(X30978,X30977),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X30978,X30977),tc_HOL_Obool),tc_fun(X30977,tc_HOL_Obool)),X30978),c_COMBC(X30977,tc_fun(tc_prod(X30978,X30977),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30977,tc_prod(X30978,X30977)),tc_fun(X30977,tc_fun(tc_fun(tc_prod(X30978,X30977),tc_HOL_Obool),tc_HOL_Obool)),X30978),hAPP(c_COMBB(tc_prod(X30978,X30977),tc_fun(tc_fun(tc_prod(X30978,X30977),tc_HOL_Obool),tc_HOL_Obool),X30977),c_member(tc_prod(X30978,X30977)))),c_Product__Type_OPair(X30978,X30977))))),X30976)),X30975),X30974)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__INT__eq2])]) ).
fof(i_0_6051,plain,
! [X28316,X28317,X28318,X28319,X28320,X28321] :
( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28321,tc_fun(X28320,tc_fun(X28319,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X28321,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X28320,X28319),tc_HOL_Obool),tc_fun(X28320,tc_fun(X28319,tc_HOL_Obool)),X28321),hAPP(c_COMBC(X28320,tc_fun(tc_prod(X28320,X28319),tc_HOL_Obool),tc_fun(X28319,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28319,tc_fun(tc_fun(tc_prod(X28320,X28319),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28320,X28319),tc_HOL_Obool),tc_fun(X28319,tc_HOL_Obool)),X28320),c_COMBC(X28319,tc_fun(tc_prod(X28320,X28319),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28319,tc_prod(X28320,X28319)),tc_fun(X28319,tc_fun(tc_fun(tc_prod(X28320,X28319),tc_HOL_Obool),tc_HOL_Obool)),X28320),hAPP(c_COMBB(tc_prod(X28320,X28319),tc_fun(tc_fun(tc_prod(X28320,X28319),tc_HOL_Obool),tc_HOL_Obool),X28319),c_member(tc_prod(X28320,X28319)))),c_Product__Type_OPair(X28320,X28319))))),X28318)),X28317),X28316))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X28320,X28319)),hAPP(hAPP(c_Product__Type_OPair(X28320,X28319),X28317),X28316)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28321,tc_fun(tc_prod(X28320,X28319),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X28321,tc_HOL_Obool))),X28318))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28320,X28319)),hAPP(hAPP(c_Product__Type_OPair(X28320,X28319),X28317),X28316)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28321,tc_fun(tc_prod(X28320,X28319),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X28321,tc_HOL_Obool))),X28318)))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28321,tc_fun(X28320,tc_fun(X28319,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X28321,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X28320,X28319),tc_HOL_Obool),tc_fun(X28320,tc_fun(X28319,tc_HOL_Obool)),X28321),hAPP(c_COMBC(X28320,tc_fun(tc_prod(X28320,X28319),tc_HOL_Obool),tc_fun(X28319,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28319,tc_fun(tc_fun(tc_prod(X28320,X28319),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28320,X28319),tc_HOL_Obool),tc_fun(X28319,tc_HOL_Obool)),X28320),c_COMBC(X28319,tc_fun(tc_prod(X28320,X28319),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28319,tc_prod(X28320,X28319)),tc_fun(X28319,tc_fun(tc_fun(tc_prod(X28320,X28319),tc_HOL_Obool),tc_HOL_Obool)),X28320),hAPP(c_COMBB(tc_prod(X28320,X28319),tc_fun(tc_fun(tc_prod(X28320,X28319),tc_HOL_Obool),tc_HOL_Obool),X28319),c_member(tc_prod(X28320,X28319)))),c_Product__Type_OPair(X28320,X28319))))),X28318)),X28317),X28316)) ) ),
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,
! [X26187,X26188,X26189,X26190,X26191,X26192,X26193] :
( ( hBOOL(hAPP(hAPP(c_member(X26193),esk169_7(X26187,X26188,X26189,X26190,X26191,X26192,X26193)),X26192))
| X26188 = X26187
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26193,tc_HOL_Obool)),X26187),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26193),X26192),X26191)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26193,tc_HOL_Obool)),X26188),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26193),X26192),X26191)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26193,tc_fun(X26190,tc_HOL_Obool)),X26188),X26189) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26193,tc_fun(X26190,tc_HOL_Obool)),X26187),X26189)
| ~ c_Equiv__Relations_Ocongruent(X26193,tc_fun(X26190,tc_HOL_Obool),X26191,X26189)
| ~ c_Equiv__Relations_Oequiv(X26193,X26192,X26191) )
& ( hBOOL(hAPP(hAPP(c_member(X26193),esk170_7(X26187,X26188,X26189,X26190,X26191,X26192,X26193)),X26192))
| X26188 = X26187
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26193,tc_HOL_Obool)),X26187),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26193),X26192),X26191)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26193,tc_HOL_Obool)),X26188),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26193),X26192),X26191)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26193,tc_fun(X26190,tc_HOL_Obool)),X26188),X26189) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26193,tc_fun(X26190,tc_HOL_Obool)),X26187),X26189)
| ~ c_Equiv__Relations_Ocongruent(X26193,tc_fun(X26190,tc_HOL_Obool),X26191,X26189)
| ~ c_Equiv__Relations_Oequiv(X26193,X26192,X26191) )
& ( hAPP(X26189,esk169_7(X26187,X26188,X26189,X26190,X26191,X26192,X26193)) = hAPP(X26189,esk170_7(X26187,X26188,X26189,X26190,X26191,X26192,X26193))
| X26188 = X26187
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26193,tc_HOL_Obool)),X26187),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26193),X26192),X26191)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26193,tc_HOL_Obool)),X26188),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26193),X26192),X26191)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26193,tc_fun(X26190,tc_HOL_Obool)),X26188),X26189) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26193,tc_fun(X26190,tc_HOL_Obool)),X26187),X26189)
| ~ c_Equiv__Relations_Ocongruent(X26193,tc_fun(X26190,tc_HOL_Obool),X26191,X26189)
| ~ c_Equiv__Relations_Oequiv(X26193,X26192,X26191) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26193,X26193)),hAPP(hAPP(c_Product__Type_OPair(X26193,X26193),esk169_7(X26187,X26188,X26189,X26190,X26191,X26192,X26193)),esk170_7(X26187,X26188,X26189,X26190,X26191,X26192,X26193))),X26191))
| X26188 = X26187
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26193,tc_HOL_Obool)),X26187),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26193),X26192),X26191)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26193,tc_HOL_Obool)),X26188),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26193),X26192),X26191)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26193,tc_fun(X26190,tc_HOL_Obool)),X26188),X26189) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26193,tc_fun(X26190,tc_HOL_Obool)),X26187),X26189)
| ~ c_Equiv__Relations_Ocongruent(X26193,tc_fun(X26190,tc_HOL_Obool),X26191,X26189)
| ~ c_Equiv__Relations_Oequiv(X26193,X26192,X26191) ) ),
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,
! [X24221,X24222,X24223,X24224,X24225] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X24225,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X24225),tc_HOL_Obool)),X24224),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X24225),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X24225,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X24225)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X24225,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X24225))),hAPP(hAPP(c_COMBB(tc_fun(X24225,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X24225,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X24225))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X24225)),X24223)),c_Com_Ocom_OBODY)),X24222)),X24221)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X24225),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X24225,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X24225)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X24225,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X24225))),hAPP(hAPP(c_COMBB(tc_fun(X24225,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X24225,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X24225))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X24225)),X24223)),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))),X24222)),X24221))
| c_Hoare__Mirabelle_Ohoare__derivs(X24225,X24224,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X24225),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X24225,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X24225)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X24225,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X24225))),hAPP(hAPP(c_COMBB(tc_fun(X24225,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X24225,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X24225))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X24225)),X24223)),c_Com_Ocom_OBODY)),X24222)),X24221)) ),
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,
! [X29348,X29349,X29350,X29351] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29351),hAPP(c_Set_OCollect(X29351),X29350)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29349),hAPP(c_Set_OCollect(X29349),hAPP(hAPP(c_COMBB(tc_fun(X29351,tc_HOL_Obool),tc_HOL_Obool,X29349),c_HOL_OEx(X29351)),hAPP(hAPP(c_COMBC(X29349,tc_fun(X29351,tc_HOL_Obool),tc_fun(X29351,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29351,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X29351,tc_HOL_Obool),tc_fun(X29351,tc_HOL_Obool)),X29349),c_COMBS(X29351,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29351,tc_HOL_Obool),tc_fun(X29351,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X29349),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29351),c_fconj)),hAPP(hAPP(c_COMBC(X29349,tc_fun(X29351,X29349),tc_fun(X29351,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29349,tc_HOL_Obool),tc_fun(tc_fun(X29351,X29349),tc_fun(X29351,tc_HOL_Obool)),X29349),c_COMBB(X29349,tc_HOL_Obool,X29351)),c_fequal)),X29348)))),X29350))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__image__set])]) ).
fof(i_0_6059,plain,
! [X30078,X30079,X30080,X30081,X30082,X30083,X30084,X30085] :
( ( hBOOL(hAPP(hAPP(c_member(X30084),esk364_8(X30078,X30079,X30080,X30081,X30082,X30083,X30084,X30085)),X30081))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X30083,X30085),X30078),X30080) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X30084,X30085),X30079),X30081)
| X30080 != hAPP(c_Set_Oimage(X30084,X30083,X30082),X30081)
| ~ c_Fun_Oinj__on(X30084,X30083,X30082,X30081)
| ~ class_Groups_Ocomm__monoid__add(X30085) )
& ( hAPP(X30079,esk364_8(X30078,X30079,X30080,X30081,X30082,X30083,X30084,X30085)) != hAPP(X30078,hAPP(X30082,esk364_8(X30078,X30079,X30080,X30081,X30082,X30083,X30084,X30085)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X30083,X30085),X30078),X30080) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X30084,X30085),X30079),X30081)
| X30080 != hAPP(c_Set_Oimage(X30084,X30083,X30082),X30081)
| ~ c_Fun_Oinj__on(X30084,X30083,X30082,X30081)
| ~ class_Groups_Ocomm__monoid__add(X30085) ) ),
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,
! [X23400,X23401,X23402,X23403,X23404,X23405,X23406,X23407] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X23407,X23406,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X23407)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X23407),X23405),X23404),hAPP(hAPP(c_COMBC(X23407,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)),X23407),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X23403)),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(X23402))),hAPP(hAPP(c_Natural_Ogetlocs,X23401),X23402))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X23407),tc_HOL_Obool))))
| c_Hoare__Mirabelle_Ohoare__derivs(X23407,X23406,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X23407)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X23407),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),X23407),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,X23401)))),hAPP(hAPP(c_COMBC(X23407,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)),X23407),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X23405)),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(X23402))),X23400)))),c_Com_Ocom_OLocal(X23402,X23400,X23404)),X23403)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X23407),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,
! [X28057,X28058,X28059,X28060,X28061,X28062,X28063,X28064] :
( ( hBOOL(hAPP(hAPP(c_member(X28063),esk265_8(X28057,X28058,X28059,X28060,X28061,X28062,X28063,X28064)),X28060))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28062,X28064),X28057),X28059) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28063,X28064),X28058),X28060)
| X28059 != hAPP(c_Set_Oimage(X28063,X28062,X28061),X28060)
| ~ c_Fun_Oinj__on(X28063,X28062,X28061,X28060)
| ~ class_Groups_Ocomm__monoid__mult(X28064) )
& ( hAPP(X28058,esk265_8(X28057,X28058,X28059,X28060,X28061,X28062,X28063,X28064)) != hAPP(hAPP(c_Fun_Ocomp(X28062,X28064,X28063,X28057),X28061),esk265_8(X28057,X28058,X28059,X28060,X28061,X28062,X28063,X28064))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28062,X28064),X28057),X28059) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28063,X28064),X28058),X28060)
| X28059 != hAPP(c_Set_Oimage(X28063,X28062,X28061),X28060)
| ~ c_Fun_Oinj__on(X28063,X28062,X28061,X28060)
| ~ class_Groups_Ocomm__monoid__mult(X28064) ) ),
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,
! [X30087,X30088,X30089,X30090,X30091,X30092,X30093,X30094] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30093),X30091),esk365_8(X30087,X30088,X30089,X30090,X30091,X30092,X30093,X30094)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X30093,X30094),X30088),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X30093,X30092),X30090)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X30093,X30094),X30087),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X30093,X30091),X30089))
| X30090 != X30089
| X30092 != X30091
| ~ class_Groups_Ocomm__monoid__add(X30094)
| ~ class_Orderings_Oord(X30093) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X30093),esk365_8(X30087,X30088,X30089,X30090,X30091,X30092,X30093,X30094)),X30089))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X30093,X30094),X30088),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X30093,X30092),X30090)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X30093,X30094),X30087),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X30093,X30091),X30089))
| X30090 != X30089
| X30092 != X30091
| ~ class_Groups_Ocomm__monoid__add(X30094)
| ~ class_Orderings_Oord(X30093) )
& ( hAPP(X30088,esk365_8(X30087,X30088,X30089,X30090,X30091,X30092,X30093,X30094)) != hAPP(X30087,esk365_8(X30087,X30088,X30089,X30090,X30091,X30092,X30093,X30094))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X30093,X30094),X30088),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X30093,X30092),X30090)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X30093,X30094),X30087),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X30093,X30091),X30089))
| X30090 != X30089
| X30092 != X30091
| ~ class_Groups_Ocomm__monoid__add(X30094)
| ~ class_Orderings_Oord(X30093) ) ),
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,
! [X26154] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26154) = 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,X26154)),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,
! [X23023,X23024,X23025,X23026,X23027,X23028,X23029] :
( ( hBOOL(hAPP(hAPP(X23029,esk99_7(X23023,X23024,X23025,X23026,X23027,X23028,X23029)),esk98_7(X23023,X23024,X23025,X23026,X23027,X23028,X23029)))
| hBOOL(hAPP(X23025,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X23028,X23027,X23023),X23024),X23026)))
| ~ hBOOL(hAPP(hAPP(X23029,hAPP(c_Product__Type_Osnd(X23028,X23027),X23026)),hAPP(c_Product__Type_Ofst(X23028,X23027),X23026))) )
& ( ~ hBOOL(hAPP(X23025,hAPP(hAPP(X23024,esk98_7(X23023,X23024,X23025,X23026,X23027,X23028,X23029)),esk99_7(X23023,X23024,X23025,X23026,X23027,X23028,X23029))))
| hBOOL(hAPP(X23025,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X23028,X23027,X23023),X23024),X23026)))
| ~ hBOOL(hAPP(hAPP(X23029,hAPP(c_Product__Type_Osnd(X23028,X23027),X23026)),hAPP(c_Product__Type_Ofst(X23028,X23027),X23026))) ) ),
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,
! [X24197,X24198] : c_FunDef_Orp__inv__image(X24198,X24197) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(X24198,X24198),tc_HOL_Obool),tc_fun(tc_prod(X24198,X24198),tc_HOL_Obool),tc_fun(tc_fun(X24197,X24198),tc_prod(tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool),tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(X24198,X24198),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X24198,X24198),tc_HOL_Obool),tc_fun(tc_fun(X24197,X24198),tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X24198,X24198),tc_HOL_Obool),tc_fun(tc_fun(X24197,X24198),tc_prod(tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool),tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(X24197,X24198),tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool)),tc_fun(tc_fun(X24197,X24198),tc_prod(tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool),tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(X24198,X24198),tc_HOL_Obool),tc_fun(tc_fun(X24197,X24198),tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X24198,X24198),tc_HOL_Obool),tc_fun(tc_fun(X24197,X24198),tc_prod(tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool),tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool))))),tc_fun(tc_prod(X24198,X24198),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(X24197,X24198),tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool)),tc_fun(tc_fun(X24197,X24198),tc_prod(tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool),tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool))),tc_fun(tc_prod(X24198,X24198),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X24197,X24198),tc_fun(tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool),tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(X24197,X24198),tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool)),tc_fun(tc_fun(X24197,X24198),tc_prod(tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool),tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool)))),tc_fun(tc_prod(X24198,X24198),tc_HOL_Obool)),c_COMBS(tc_fun(X24197,X24198),tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool),tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X24197,X24198),tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool)),tc_fun(tc_fun(X24197,X24198),tc_fun(tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool),tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool)))),tc_fun(tc_prod(X24198,X24198),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool),tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool))),tc_fun(X24197,X24198)),c_Product__Type_OPair(tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool),tc_fun(tc_prod(X24197,X24197),tc_HOL_Obool)))),c_Relation_Oinv__image(X24198,X24197))))),c_Relation_Oinv__image(X24198,X24197))),
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,
! [X29319,X29320,X29321,X29322] : hAPP(hAPP(c_Relation_Oinv__image(X29322,X29321),X29320),X29319) = hAPP(c_Set_OCollect(tc_prod(X29321,X29321)),hAPP(c_Product__Type_Oprod_Oprod__case(X29321,X29321,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X29321,tc_fun(tc_prod(X29322,X29322),tc_HOL_Obool),tc_fun(X29321,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29321,tc_fun(tc_fun(tc_prod(X29322,X29322),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29322,X29322),tc_HOL_Obool),tc_fun(X29321,tc_HOL_Obool)),X29321),c_COMBC(X29321,tc_fun(tc_prod(X29322,X29322),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29321,tc_prod(X29322,X29322)),tc_fun(X29321,tc_fun(tc_fun(tc_prod(X29322,X29322),tc_HOL_Obool),tc_HOL_Obool)),X29321),hAPP(c_COMBB(tc_prod(X29322,X29322),tc_fun(tc_fun(tc_prod(X29322,X29322),tc_HOL_Obool),tc_HOL_Obool),X29321),c_member(tc_prod(X29322,X29322)))),hAPP(hAPP(c_COMBC(X29321,tc_fun(X29321,X29322),tc_fun(X29321,tc_prod(X29322,X29322))),hAPP(hAPP(c_COMBB(tc_fun(X29322,tc_prod(X29322,X29322)),tc_fun(tc_fun(X29321,X29322),tc_fun(X29321,tc_prod(X29322,X29322))),X29321),c_COMBB(X29322,tc_prod(X29322,X29322),X29321)),hAPP(hAPP(c_COMBB(X29322,tc_fun(X29322,tc_prod(X29322,X29322)),X29321),c_Product__Type_OPair(X29322,X29322)),X29319))),X29319)))),X29320))),
inference(variable_rename,[status(thm)],[fact_inv__image__def]) ).
fof(i_0_6072,plain,
! [X32507,X32508,X32509,X32510] : hAPP(c_List_Oset(tc_prod(X32510,X32509)),hAPP(hAPP(c_List_Ozip(X32510,X32509),X32508),X32507)) = hAPP(c_Set_OCollect(tc_prod(X32510,X32509)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X32510,X32509)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X32510,X32509),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(X32510,X32509)),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(X32510,X32509)),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(X32510,X32509),tc_fun(tc_Nat_Onat,tc_prod(X32510,X32509)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X32510,X32509),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(X32510,X32509)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X32510,X32509)),c_COMBB(tc_prod(X32510,X32509),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X32509,tc_prod(X32510,X32509)),hAPP(hAPP(c_COMBB(X32510,tc_fun(X32509,tc_prod(X32510,X32509)),tc_Nat_Onat),c_Product__Type_OPair(X32510,X32509)),hAPP(c_List_Onth(X32510),X32508))),hAPP(c_List_Onth(X32509),X32507)))))),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(X32510)),X32508)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32509)),X32507)))))),
inference(variable_rename,[status(thm)],[fact_set__zip]) ).
fof(i_0_6073,plain,
! [X23743,X23744,X23745,X23746] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23746,tc_fun(X23745,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X23746,tc_fun(tc_prod(X23746,X23745),tc_HOL_Obool),tc_fun(X23745,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23745,tc_fun(tc_fun(tc_prod(X23746,X23745),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X23746,X23745),tc_HOL_Obool),tc_fun(X23745,tc_HOL_Obool)),X23746),c_COMBC(X23745,tc_fun(tc_prod(X23746,X23745),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23745,tc_prod(X23746,X23745)),tc_fun(X23745,tc_fun(tc_fun(tc_prod(X23746,X23745),tc_HOL_Obool),tc_HOL_Obool)),X23746),hAPP(c_COMBB(tc_prod(X23746,X23745),tc_fun(tc_fun(tc_prod(X23746,X23745),tc_HOL_Obool),tc_HOL_Obool),X23745),c_member(tc_prod(X23746,X23745)))),c_Product__Type_OPair(X23746,X23745)))),X23744)),hAPP(hAPP(c_COMBC(X23746,tc_fun(tc_prod(X23746,X23745),tc_HOL_Obool),tc_fun(X23745,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23745,tc_fun(tc_fun(tc_prod(X23746,X23745),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X23746,X23745),tc_HOL_Obool),tc_fun(X23745,tc_HOL_Obool)),X23746),c_COMBC(X23745,tc_fun(tc_prod(X23746,X23745),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23745,tc_prod(X23746,X23745)),tc_fun(X23745,tc_fun(tc_fun(tc_prod(X23746,X23745),tc_HOL_Obool),tc_HOL_Obool)),X23746),hAPP(c_COMBB(tc_prod(X23746,X23745),tc_fun(tc_fun(tc_prod(X23746,X23745),tc_HOL_Obool),tc_HOL_Obool),X23745),c_member(tc_prod(X23746,X23745)))),c_Product__Type_OPair(X23746,X23745)))),X23743)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X23746,X23745),tc_HOL_Obool)),X23744),X23743)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X23746,X23745),tc_HOL_Obool)),X23744),X23743))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23746,tc_fun(X23745,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X23746,tc_fun(tc_prod(X23746,X23745),tc_HOL_Obool),tc_fun(X23745,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23745,tc_fun(tc_fun(tc_prod(X23746,X23745),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X23746,X23745),tc_HOL_Obool),tc_fun(X23745,tc_HOL_Obool)),X23746),c_COMBC(X23745,tc_fun(tc_prod(X23746,X23745),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23745,tc_prod(X23746,X23745)),tc_fun(X23745,tc_fun(tc_fun(tc_prod(X23746,X23745),tc_HOL_Obool),tc_HOL_Obool)),X23746),hAPP(c_COMBB(tc_prod(X23746,X23745),tc_fun(tc_fun(tc_prod(X23746,X23745),tc_HOL_Obool),tc_HOL_Obool),X23745),c_member(tc_prod(X23746,X23745)))),c_Product__Type_OPair(X23746,X23745)))),X23744)),hAPP(hAPP(c_COMBC(X23746,tc_fun(tc_prod(X23746,X23745),tc_HOL_Obool),tc_fun(X23745,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23745,tc_fun(tc_fun(tc_prod(X23746,X23745),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X23746,X23745),tc_HOL_Obool),tc_fun(X23745,tc_HOL_Obool)),X23746),c_COMBC(X23745,tc_fun(tc_prod(X23746,X23745),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23745,tc_prod(X23746,X23745)),tc_fun(X23745,tc_fun(tc_fun(tc_prod(X23746,X23745),tc_HOL_Obool),tc_HOL_Obool)),X23746),hAPP(c_COMBB(tc_prod(X23746,X23745),tc_fun(tc_fun(tc_prod(X23746,X23745),tc_HOL_Obool),tc_HOL_Obool),X23745),c_member(tc_prod(X23746,X23745)))),c_Product__Type_OPair(X23746,X23745)))),X23743))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq2])]) ).
fof(i_0_6074,plain,
! [X29355,X29356] : hAPP(c_Set_OPow(X29356),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X29356,tc_HOL_Obool)),X29355)) = hAPP(c_Set_OCollect(tc_fun(X29356,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29356,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X29356,tc_HOL_Obool)),c_HOL_OEx(tc_fun(X29356,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X29356,tc_HOL_Obool),tc_fun(tc_fun(X29356,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X29356,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29356,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X29356,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X29356,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X29356,tc_HOL_Obool)),c_COMBS(tc_fun(X29356,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29356,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X29356,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X29356,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X29356,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(X29356,tc_HOL_Obool),tc_fun(tc_fun(X29356,tc_HOL_Obool),tc_fun(X29356,tc_HOL_Obool)),tc_fun(tc_fun(X29356,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29356,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X29356,tc_HOL_Obool),tc_fun(X29356,tc_HOL_Obool)),tc_fun(tc_fun(X29356,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X29356,tc_HOL_Obool)),c_COMBB(tc_fun(X29356,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X29356,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(X29356,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29356,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X29356,tc_HOL_Obool)),hAPP(c_member(tc_fun(X29356,tc_HOL_Obool)),X29355)),c_Set_OPow(X29356))))),
inference(variable_rename,[status(thm)],[fact_Pow__Compl]) ).
fof(i_0_6075,plain,
! [X33654,X33655,X33656,X33657,X33658] : c_Map_Omap__upds(X33658,X33657,X33656,X33655,X33654) = hAPP(c_List_Ofoldl(tc_fun(X33658,tc_Option_Ooption(X33657)),tc_prod(X33658,X33657),hAPP(hAPP(c_COMBB(tc_fun(X33658,tc_fun(X33657,tc_fun(X33658,tc_Option_Ooption(X33657)))),tc_fun(tc_prod(X33658,X33657),tc_fun(X33658,tc_Option_Ooption(X33657))),tc_fun(X33658,tc_Option_Ooption(X33657))),c_Product__Type_Oprod_Oprod__case(X33658,X33657,tc_fun(X33658,tc_Option_Ooption(X33657)))),hAPP(hAPP(c_COMBC(tc_fun(X33658,tc_Option_Ooption(X33657)),tc_fun(X33657,tc_Option_Ooption(X33657)),tc_fun(X33658,tc_fun(X33657,tc_fun(X33658,tc_Option_Ooption(X33657))))),hAPP(hAPP(c_COMBB(tc_fun(X33658,tc_fun(tc_fun(X33657,tc_Option_Ooption(X33657)),tc_fun(X33657,tc_fun(X33658,tc_Option_Ooption(X33657))))),tc_fun(tc_fun(X33657,tc_Option_Ooption(X33657)),tc_fun(X33658,tc_fun(X33657,tc_fun(X33658,tc_Option_Ooption(X33657))))),tc_fun(X33658,tc_Option_Ooption(X33657))),c_COMBC(X33658,tc_fun(X33657,tc_Option_Ooption(X33657)),tc_fun(X33657,tc_fun(X33658,tc_Option_Ooption(X33657))))),hAPP(hAPP(c_COMBB(tc_fun(X33658,tc_fun(tc_Option_Ooption(X33657),tc_fun(X33658,tc_Option_Ooption(X33657)))),tc_fun(X33658,tc_fun(tc_fun(X33657,tc_Option_Ooption(X33657)),tc_fun(X33657,tc_fun(X33658,tc_Option_Ooption(X33657))))),tc_fun(X33658,tc_Option_Ooption(X33657))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X33657),tc_fun(X33658,tc_Option_Ooption(X33657))),tc_fun(tc_fun(X33657,tc_Option_Ooption(X33657)),tc_fun(X33657,tc_fun(X33658,tc_Option_Ooption(X33657)))),X33658),c_COMBB(tc_Option_Ooption(X33657),tc_fun(X33658,tc_Option_Ooption(X33657)),X33657))),c_Fun_Ofun__upd(X33658,tc_Option_Ooption(X33657))))),c_Option_Ooption_OSome(X33657))),X33656),hAPP(hAPP(c_List_Ozip(X33658,X33657),X33655),X33654)),
inference(variable_rename,[status(thm)],[fact_map__upds__fold__map__upd]) ).
fof(i_0_6076,plain,
! [X26209,X26210,X26211,X26212,X26213,X26214,X26215] :
( ( hBOOL(hAPP(hAPP(c_member(X26215),esk173_7(X26209,X26210,X26211,X26212,X26213,X26214,X26215)),X26214))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X26212,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26215,tc_fun(X26212,tc_HOL_Obool)),X26210),X26211)),X26209))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26215,tc_HOL_Obool)),X26210),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26215),X26214),X26213)))
| ~ c_Equiv__Relations_Ocongruent(X26215,tc_fun(X26212,tc_HOL_Obool),X26213,X26211)
| ~ c_Equiv__Relations_Oequiv(X26215,X26214,X26213) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26212,tc_HOL_Obool)),hAPP(X26211,esk173_7(X26209,X26210,X26211,X26212,X26213,X26214,X26215))),X26209))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X26212,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26215,tc_fun(X26212,tc_HOL_Obool)),X26210),X26211)),X26209))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26215,tc_HOL_Obool)),X26210),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26215),X26214),X26213)))
| ~ c_Equiv__Relations_Ocongruent(X26215,tc_fun(X26212,tc_HOL_Obool),X26213,X26211)
| ~ c_Equiv__Relations_Oequiv(X26215,X26214,X26213) ) ),
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,
! [X31219,X31220,X31221,X31222,X31223,X31224,X31225,X31226,X31227,X31228,X31229,X31230,X31231,X31232,X31233] :
( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31225,tc_fun(X31224,tc_fun(X31223,tc_HOL_Obool))),X31222),X31221),X31220),X31219))
| ~ hBOOL(hAPP(hAPP(c_member(X31225),X31226),X31222))
| hBOOL(hAPP(hAPP(hAPP(X31221,X31226),X31220),X31219)) )
& ( hBOOL(hAPP(hAPP(c_member(X31233),esk398_7(X31227,X31228,X31229,X31230,X31231,X31232,X31233)),X31230))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31233,tc_fun(X31232,tc_fun(X31231,tc_HOL_Obool))),X31230),X31229),X31228),X31227)) )
& ( ~ hBOOL(hAPP(hAPP(hAPP(X31229,esk398_7(X31227,X31228,X31229,X31230,X31231,X31232,X31233)),X31228),X31227))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31233,tc_fun(X31232,tc_fun(X31231,tc_HOL_Obool))),X31230),X31229),X31228),X31227)) ) ),
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,
! [X29339,X29340,X29341] :
( ~ class_Orderings_Olinorder(X29341)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29341),X29340))
| X29340 = c_Orderings_Obot__class_Obot(tc_fun(X29341,tc_HOL_Obool))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X29341),X29339),c_Big__Operators_Olattice_OInf__fin(X29341,c_Orderings_Oord__class_Omin(X29341),X29340)) = c_Big__Operators_Olattice_OInf__fin(X29341,c_Orderings_Oord__class_Omin(X29341),hAPP(c_Set_OCollect(X29341),hAPP(hAPP(c_COMBB(tc_fun(X29341,tc_HOL_Obool),tc_HOL_Obool,X29341),c_HOL_OEx(X29341)),hAPP(hAPP(c_COMBC(X29341,tc_fun(X29341,tc_HOL_Obool),tc_fun(X29341,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29341,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X29341,tc_HOL_Obool),tc_fun(X29341,tc_HOL_Obool)),X29341),c_COMBS(X29341,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29341,tc_HOL_Obool),tc_fun(X29341,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X29341),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29341),c_fconj)),hAPP(hAPP(c_COMBC(X29341,tc_fun(X29341,X29341),tc_fun(X29341,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29341,tc_HOL_Obool),tc_fun(tc_fun(X29341,X29341),tc_fun(X29341,tc_HOL_Obool)),X29341),c_COMBB(X29341,tc_HOL_Obool,X29341)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(X29341),X29339))))),hAPP(hAPP(c_COMBC(X29341,tc_fun(X29341,tc_HOL_Obool),tc_HOL_Obool),c_member(X29341)),X29340))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf1__distrib])]) ).
fof(i_0_6079,plain,
! [X29375,X29376,X29377] :
( ~ class_Orderings_Olinorder(X29377)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29377),X29376))
| X29376 = c_Orderings_Obot__class_Obot(tc_fun(X29377,tc_HOL_Obool))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X29377),X29375),c_Big__Operators_Olattice_OSup__fin(X29377,c_Orderings_Oord__class_Omax(X29377),X29376)) = c_Big__Operators_Olattice_OSup__fin(X29377,c_Orderings_Oord__class_Omax(X29377),hAPP(c_Set_OCollect(X29377),hAPP(hAPP(c_COMBB(tc_fun(X29377,tc_HOL_Obool),tc_HOL_Obool,X29377),c_HOL_OEx(X29377)),hAPP(hAPP(c_COMBC(X29377,tc_fun(X29377,tc_HOL_Obool),tc_fun(X29377,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29377,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X29377,tc_HOL_Obool),tc_fun(X29377,tc_HOL_Obool)),X29377),c_COMBS(X29377,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29377,tc_HOL_Obool),tc_fun(X29377,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X29377),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29377),c_fconj)),hAPP(hAPP(c_COMBC(X29377,tc_fun(X29377,X29377),tc_fun(X29377,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29377,tc_HOL_Obool),tc_fun(tc_fun(X29377,X29377),tc_fun(X29377,tc_HOL_Obool)),X29377),c_COMBB(X29377,tc_HOL_Obool,X29377)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(X29377),X29375))))),hAPP(hAPP(c_COMBC(X29377,tc_fun(X29377,tc_HOL_Obool),tc_HOL_Obool),c_member(X29377)),X29376))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup1__distrib])]) ).
fof(i_0_6080,plain,
! [X29369,X29370,X29371] :
( ~ class_Lattices_Odistrib__lattice(X29371)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29371),X29370))
| X29370 = c_Orderings_Obot__class_Obot(tc_fun(X29371,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X29371),X29369),c_Big__Operators_Olattice__class_OSup__fin(X29371,X29370)) = c_Big__Operators_Olattice__class_OSup__fin(X29371,hAPP(c_Set_OCollect(X29371),hAPP(hAPP(c_COMBB(tc_fun(X29371,tc_HOL_Obool),tc_HOL_Obool,X29371),c_HOL_OEx(X29371)),hAPP(hAPP(c_COMBC(X29371,tc_fun(X29371,tc_HOL_Obool),tc_fun(X29371,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29371,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X29371,tc_HOL_Obool),tc_fun(X29371,tc_HOL_Obool)),X29371),c_COMBS(X29371,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29371,tc_HOL_Obool),tc_fun(X29371,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X29371),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29371),c_fconj)),hAPP(hAPP(c_COMBC(X29371,tc_fun(X29371,X29371),tc_fun(X29371,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29371,tc_HOL_Obool),tc_fun(tc_fun(X29371,X29371),tc_fun(X29371,tc_HOL_Obool)),X29371),c_COMBB(X29371,tc_HOL_Obool,X29371)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X29371),X29369))))),hAPP(hAPP(c_COMBC(X29371,tc_fun(X29371,tc_HOL_Obool),tc_HOL_Obool),c_member(X29371)),X29370))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Sup1__distrib])]) ).
fof(i_0_6081,plain,
! [X29363,X29364,X29365] :
( ~ class_Lattices_Odistrib__lattice(X29365)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29365),X29364))
| X29364 = c_Orderings_Obot__class_Obot(tc_fun(X29365,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X29365),X29363),c_Big__Operators_Olattice__class_OInf__fin(X29365,X29364)) = c_Big__Operators_Olattice__class_OInf__fin(X29365,hAPP(c_Set_OCollect(X29365),hAPP(hAPP(c_COMBB(tc_fun(X29365,tc_HOL_Obool),tc_HOL_Obool,X29365),c_HOL_OEx(X29365)),hAPP(hAPP(c_COMBC(X29365,tc_fun(X29365,tc_HOL_Obool),tc_fun(X29365,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29365,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X29365,tc_HOL_Obool),tc_fun(X29365,tc_HOL_Obool)),X29365),c_COMBS(X29365,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29365,tc_HOL_Obool),tc_fun(X29365,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X29365),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29365),c_fconj)),hAPP(hAPP(c_COMBC(X29365,tc_fun(X29365,X29365),tc_fun(X29365,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29365,tc_HOL_Obool),tc_fun(tc_fun(X29365,X29365),tc_fun(X29365,tc_HOL_Obool)),X29365),c_COMBB(X29365,tc_HOL_Obool,X29365)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(X29365),X29363))))),hAPP(hAPP(c_COMBC(X29365,tc_fun(X29365,tc_HOL_Obool),tc_HOL_Obool),c_member(X29365)),X29364))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Inf1__distrib])]) ).
fof(i_0_6082,plain,
! [X29357,X29358,X29359] :
( ~ class_Groups_Olinordered__ab__semigroup__add(X29359)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29359),X29358))
| X29358 = c_Orderings_Obot__class_Obot(tc_fun(X29359,tc_HOL_Obool))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X29359),X29357),c_Big__Operators_Olinorder__class_OMin(X29359,X29358)) = c_Big__Operators_Olinorder__class_OMin(X29359,hAPP(c_Set_OCollect(X29359),hAPP(hAPP(c_COMBB(tc_fun(X29359,tc_HOL_Obool),tc_HOL_Obool,X29359),c_HOL_OEx(X29359)),hAPP(hAPP(c_COMBC(X29359,tc_fun(X29359,tc_HOL_Obool),tc_fun(X29359,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29359,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X29359,tc_HOL_Obool),tc_fun(X29359,tc_HOL_Obool)),X29359),c_COMBS(X29359,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29359,tc_HOL_Obool),tc_fun(X29359,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X29359),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29359),c_fconj)),hAPP(hAPP(c_COMBC(X29359,tc_fun(X29359,X29359),tc_fun(X29359,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29359,tc_HOL_Obool),tc_fun(tc_fun(X29359,X29359),tc_fun(X29359,tc_HOL_Obool)),X29359),c_COMBB(X29359,tc_HOL_Obool,X29359)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X29359),X29357))))),hAPP(hAPP(c_COMBC(X29359,tc_fun(X29359,tc_HOL_Obool),tc_HOL_Obool),c_member(X29359)),X29358))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__Min__commute])]) ).
fof(i_0_6083,plain,
! [X29360,X29361,X29362] :
( ~ class_Groups_Olinordered__ab__semigroup__add(X29362)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29362),X29361))
| X29361 = c_Orderings_Obot__class_Obot(tc_fun(X29362,tc_HOL_Obool))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X29362),X29360),c_Big__Operators_Olinorder__class_OMax(X29362,X29361)) = c_Big__Operators_Olinorder__class_OMax(X29362,hAPP(c_Set_OCollect(X29362),hAPP(hAPP(c_COMBB(tc_fun(X29362,tc_HOL_Obool),tc_HOL_Obool,X29362),c_HOL_OEx(X29362)),hAPP(hAPP(c_COMBC(X29362,tc_fun(X29362,tc_HOL_Obool),tc_fun(X29362,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29362,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X29362,tc_HOL_Obool),tc_fun(X29362,tc_HOL_Obool)),X29362),c_COMBS(X29362,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29362,tc_HOL_Obool),tc_fun(X29362,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X29362),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29362),c_fconj)),hAPP(hAPP(c_COMBC(X29362,tc_fun(X29362,X29362),tc_fun(X29362,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29362,tc_HOL_Obool),tc_fun(tc_fun(X29362,X29362),tc_fun(X29362,tc_HOL_Obool)),X29362),c_COMBB(X29362,tc_HOL_Obool,X29362)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X29362),X29360))))),hAPP(hAPP(c_COMBC(X29362,tc_fun(X29362,tc_HOL_Obool),tc_HOL_Obool),c_member(X29362)),X29361))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__Max__commute])]) ).
fof(i_0_6084,plain,
! [X32891,X32892,X32893,X32894,X32895] :
( ( X32895 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| hAPP(c_Lazy__Sequence_Oanamorph(X32894,X32893,X32892,X32895),X32891) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32893),X32894),c_List_Olist_ONil(X32893)),X32891) )
& ( X32895 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| hAPP(c_Lazy__Sequence_Oanamorph(X32894,X32893,X32892,X32895),X32891) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(X32893),X32894),tc_prod(X32893,X32894),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32893),X32894),c_List_Olist_ONil(X32893)),X32891),hAPP(c_Product__Type_Oprod_Oprod__case(X32893,X32894,tc_prod(tc_List_Olist(X32893),X32894)),hAPP(hAPP(c_COMBC(X32893,tc_fun(X32894,tc_prod(tc_List_Olist(X32893),X32894)),tc_fun(X32894,tc_prod(tc_List_Olist(X32893),X32894))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(X32893),X32894),tc_prod(tc_List_Olist(X32893),X32894)),tc_fun(tc_fun(X32894,tc_prod(tc_List_Olist(X32893),X32894)),tc_fun(X32894,tc_prod(tc_List_Olist(X32893),X32894))),X32893),c_COMBB(tc_prod(tc_List_Olist(X32893),X32894),tc_prod(tc_List_Olist(X32893),X32894),X32894)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X32893),tc_fun(X32894,tc_prod(tc_List_Olist(X32893),X32894))),tc_fun(tc_prod(tc_List_Olist(X32893),X32894),tc_prod(tc_List_Olist(X32893),X32894)),X32893),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X32893),X32894,tc_prod(tc_List_Olist(X32893),X32894))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X32893),tc_List_Olist(X32893)),tc_fun(tc_List_Olist(X32893),tc_fun(X32894,tc_prod(tc_List_Olist(X32893),X32894))),X32893),hAPP(c_COMBB(tc_List_Olist(X32893),tc_fun(X32894,tc_prod(tc_List_Olist(X32893),X32894)),tc_List_Olist(X32893)),c_Product__Type_OPair(tc_List_Olist(X32893),X32894))),c_List_Olist_OCons(X32893))))),c_Lazy__Sequence_Oanamorph(X32894,X32893,X32892,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X32895),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(X32892,X32891)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_anamorph_Osimps])]) ).
fof(i_0_6085,plain,
! [X32237,X32238,X32239,X32240,X32241,X32242,X32243,X32244,X32245] :
( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32240)),X32239) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32240)),X32238)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32240),tc_List_Olist(X32240))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32240),tc_List_Olist(X32240)),X32239),X32238)),c_List_Olistrel(X32240,X32237))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32240,X32240)),X32241),hAPP(c_List_Oset(tc_prod(X32240,X32240)),hAPP(hAPP(c_List_Ozip(X32240,X32240),X32239),X32238))))
| hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X32240,X32240,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X32240,tc_fun(tc_prod(X32240,X32240),tc_HOL_Obool),tc_fun(X32240,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32240,tc_fun(tc_fun(tc_prod(X32240,X32240),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X32240,X32240),tc_HOL_Obool),tc_fun(X32240,tc_HOL_Obool)),X32240),c_COMBC(X32240,tc_fun(tc_prod(X32240,X32240),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32240,tc_prod(X32240,X32240)),tc_fun(X32240,tc_fun(tc_fun(tc_prod(X32240,X32240),tc_HOL_Obool),tc_HOL_Obool)),X32240),hAPP(c_COMBB(tc_prod(X32240,X32240),tc_fun(tc_fun(tc_prod(X32240,X32240),tc_HOL_Obool),tc_HOL_Obool),X32240),c_member(tc_prod(X32240,X32240)))),c_Product__Type_OPair(X32240,X32240)))),X32237)),X32241))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32240),tc_List_Olist(X32240))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32240),tc_List_Olist(X32240)),X32239),X32238)),c_List_Olistrel(X32240,X32237))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32245,X32245)),esk443_4(X32242,X32243,X32244,X32245)),hAPP(c_List_Oset(tc_prod(X32245,X32245)),hAPP(hAPP(c_List_Ozip(X32245,X32245),X32244),X32243))))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32245)),X32244) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32245)),X32243)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32245),tc_List_Olist(X32245))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32245),tc_List_Olist(X32245)),X32244),X32243)),c_List_Olistrel(X32245,X32242))) )
& ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X32245,X32245,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X32245,tc_fun(tc_prod(X32245,X32245),tc_HOL_Obool),tc_fun(X32245,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32245,tc_fun(tc_fun(tc_prod(X32245,X32245),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X32245,X32245),tc_HOL_Obool),tc_fun(X32245,tc_HOL_Obool)),X32245),c_COMBC(X32245,tc_fun(tc_prod(X32245,X32245),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32245,tc_prod(X32245,X32245)),tc_fun(X32245,tc_fun(tc_fun(tc_prod(X32245,X32245),tc_HOL_Obool),tc_HOL_Obool)),X32245),hAPP(c_COMBB(tc_prod(X32245,X32245),tc_fun(tc_fun(tc_prod(X32245,X32245),tc_HOL_Obool),tc_HOL_Obool),X32245),c_member(tc_prod(X32245,X32245)))),c_Product__Type_OPair(X32245,X32245)))),X32242)),esk443_4(X32242,X32243,X32244,X32245)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32245)),X32244) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32245)),X32243)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32245),tc_List_Olist(X32245))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32245),tc_List_Olist(X32245)),X32244),X32243)),c_List_Olistrel(X32245,X32242))) ) ),
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,
! [X29828,X29829,X29830,X29831] :
( ( ~ hBOOL(hAPP(c_Predicate_ODomainP(X29831,X29830,hAPP(hAPP(c_COMBC(X29831,tc_fun(tc_prod(X29831,X29830),tc_HOL_Obool),tc_fun(X29830,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29830,tc_fun(tc_fun(tc_prod(X29831,X29830),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29831,X29830),tc_HOL_Obool),tc_fun(X29830,tc_HOL_Obool)),X29831),c_COMBC(X29830,tc_fun(tc_prod(X29831,X29830),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29830,tc_prod(X29831,X29830)),tc_fun(X29830,tc_fun(tc_fun(tc_prod(X29831,X29830),tc_HOL_Obool),tc_HOL_Obool)),X29831),hAPP(c_COMBB(tc_prod(X29831,X29830),tc_fun(tc_fun(tc_prod(X29831,X29830),tc_HOL_Obool),tc_HOL_Obool),X29830),c_member(tc_prod(X29831,X29830)))),c_Product__Type_OPair(X29831,X29830)))),X29829)),X29828))
| hBOOL(hAPP(hAPP(c_member(X29831),X29828),hAPP(c_Relation_ODomain(X29831,X29830),X29829))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X29831),X29828),hAPP(c_Relation_ODomain(X29831,X29830),X29829)))
| hBOOL(hAPP(c_Predicate_ODomainP(X29831,X29830,hAPP(hAPP(c_COMBC(X29831,tc_fun(tc_prod(X29831,X29830),tc_HOL_Obool),tc_fun(X29830,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29830,tc_fun(tc_fun(tc_prod(X29831,X29830),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29831,X29830),tc_HOL_Obool),tc_fun(X29830,tc_HOL_Obool)),X29831),c_COMBC(X29830,tc_fun(tc_prod(X29831,X29830),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29830,tc_prod(X29831,X29830)),tc_fun(X29830,tc_fun(tc_fun(tc_prod(X29831,X29830),tc_HOL_Obool),tc_HOL_Obool)),X29831),hAPP(c_COMBB(tc_prod(X29831,X29830),tc_fun(tc_fun(tc_prod(X29831,X29830),tc_HOL_Obool),tc_HOL_Obool),X29830),c_member(tc_prod(X29831,X29830)))),c_Product__Type_OPair(X29831,X29830)))),X29829)),X29828)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainP__Domain__eq])]) ).
fof(i_0_6087,plain,
! [X29728,X29729,X29730,X29731] :
( ( ~ hBOOL(hAPP(c_Predicate_ORangeP(X29731,X29730,hAPP(hAPP(c_COMBC(X29731,tc_fun(tc_prod(X29731,X29730),tc_HOL_Obool),tc_fun(X29730,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29730,tc_fun(tc_fun(tc_prod(X29731,X29730),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29731,X29730),tc_HOL_Obool),tc_fun(X29730,tc_HOL_Obool)),X29731),c_COMBC(X29730,tc_fun(tc_prod(X29731,X29730),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29730,tc_prod(X29731,X29730)),tc_fun(X29730,tc_fun(tc_fun(tc_prod(X29731,X29730),tc_HOL_Obool),tc_HOL_Obool)),X29731),hAPP(c_COMBB(tc_prod(X29731,X29730),tc_fun(tc_fun(tc_prod(X29731,X29730),tc_HOL_Obool),tc_HOL_Obool),X29730),c_member(tc_prod(X29731,X29730)))),c_Product__Type_OPair(X29731,X29730)))),X29729)),X29728))
| hBOOL(hAPP(hAPP(c_member(X29730),X29728),hAPP(c_Relation_ORange(X29731,X29730),X29729))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X29730),X29728),hAPP(c_Relation_ORange(X29731,X29730),X29729)))
| hBOOL(hAPP(c_Predicate_ORangeP(X29731,X29730,hAPP(hAPP(c_COMBC(X29731,tc_fun(tc_prod(X29731,X29730),tc_HOL_Obool),tc_fun(X29730,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29730,tc_fun(tc_fun(tc_prod(X29731,X29730),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29731,X29730),tc_HOL_Obool),tc_fun(X29730,tc_HOL_Obool)),X29731),c_COMBC(X29730,tc_fun(tc_prod(X29731,X29730),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29730,tc_prod(X29731,X29730)),tc_fun(X29730,tc_fun(tc_fun(tc_prod(X29731,X29730),tc_HOL_Obool),tc_HOL_Obool)),X29731),hAPP(c_COMBB(tc_prod(X29731,X29730),tc_fun(tc_fun(tc_prod(X29731,X29730),tc_HOL_Obool),tc_HOL_Obool),X29730),c_member(tc_prod(X29731,X29730)))),c_Product__Type_OPair(X29731,X29730)))),X29729)),X29728)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeP__Range__eq])]) ).
fof(i_0_6088,plain,
! [X24482,X24483,X24484] :
( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X24484,hAPP(hAPP(c_COMBC(X24484,tc_fun(tc_prod(X24484,X24484),tc_HOL_Obool),tc_fun(X24484,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24484,tc_fun(tc_fun(tc_prod(X24484,X24484),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X24484,X24484),tc_HOL_Obool),tc_fun(X24484,tc_HOL_Obool)),X24484),c_COMBC(X24484,tc_fun(tc_prod(X24484,X24484),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24484,tc_prod(X24484,X24484)),tc_fun(X24484,tc_fun(tc_fun(tc_prod(X24484,X24484),tc_HOL_Obool),tc_HOL_Obool)),X24484),hAPP(c_COMBB(tc_prod(X24484,X24484),tc_fun(tc_fun(tc_prod(X24484,X24484),tc_HOL_Obool),tc_HOL_Obool),X24484),c_member(tc_prod(X24484,X24484)))),c_Product__Type_OPair(X24484,X24484)))),X24483)),X24482))
| hBOOL(hAPP(hAPP(c_member(X24484),X24482),c_Wellfounded_Oacc(X24484,X24483))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X24484),X24482),c_Wellfounded_Oacc(X24484,X24483)))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X24484,hAPP(hAPP(c_COMBC(X24484,tc_fun(tc_prod(X24484,X24484),tc_HOL_Obool),tc_fun(X24484,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24484,tc_fun(tc_fun(tc_prod(X24484,X24484),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X24484,X24484),tc_HOL_Obool),tc_fun(X24484,tc_HOL_Obool)),X24484),c_COMBC(X24484,tc_fun(tc_prod(X24484,X24484),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24484,tc_prod(X24484,X24484)),tc_fun(X24484,tc_fun(tc_fun(tc_prod(X24484,X24484),tc_HOL_Obool),tc_HOL_Obool)),X24484),hAPP(c_COMBB(tc_prod(X24484,X24484),tc_fun(tc_fun(tc_prod(X24484,X24484),tc_HOL_Obool),tc_HOL_Obool),X24484),c_member(tc_prod(X24484,X24484)))),c_Product__Type_OPair(X24484,X24484)))),X24483)),X24482)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__acc__eq])]) ).
fof(i_0_6089,plain,
! [X23821,X23822,X23823,X23824,X23825,X23826,X23827,X23830,X23831,X23832,X23833,X23834,X23835,X23836,X23837,X23838] :
( ( hAPP(hAPP(X23825,X23822),X23821) = hAPP(hAPP(X23825,esk109_7(X23821,X23822,X23823,X23824,X23825,X23826,X23827)),esk110_7(X23821,X23822,X23823,X23824,X23825,X23826,X23827))
| X23823 = c_Orderings_Obot__class_Obot(tc_fun(X23827,tc_HOL_Obool))
| ~ c_Nitpick_Ofold__graph_H(X23827,X23826,X23825,X23824,X23823,hAPP(hAPP(X23825,X23822),X23821)) )
& ( hBOOL(hAPP(hAPP(c_member(X23827),esk109_7(X23821,X23822,X23823,X23824,X23825,X23826,X23827)),X23823))
| X23823 = c_Orderings_Obot__class_Obot(tc_fun(X23827,tc_HOL_Obool))
| ~ c_Nitpick_Ofold__graph_H(X23827,X23826,X23825,X23824,X23823,hAPP(hAPP(X23825,X23822),X23821)) )
& ( c_Nitpick_Ofold__graph_H(X23827,X23826,X23825,X23824,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23827,tc_HOL_Obool)),X23823),hAPP(hAPP(c_Set_Oinsert(X23827),esk109_7(X23821,X23822,X23823,X23824,X23825,X23826,X23827)),c_Orderings_Obot__class_Obot(tc_fun(X23827,tc_HOL_Obool)))),esk110_7(X23821,X23822,X23823,X23824,X23825,X23826,X23827))
| X23823 = c_Orderings_Obot__class_Obot(tc_fun(X23827,tc_HOL_Obool))
| ~ c_Nitpick_Ofold__graph_H(X23827,X23826,X23825,X23824,X23823,hAPP(hAPP(X23825,X23822),X23821)) )
& ( hAPP(hAPP(X23825,X23822),X23821) = hAPP(hAPP(X23825,esk109_7(X23821,X23822,X23823,X23824,X23825,X23826,X23827)),esk110_7(X23821,X23822,X23823,X23824,X23825,X23826,X23827))
| hAPP(hAPP(X23825,X23822),X23821) = X23824
| ~ c_Nitpick_Ofold__graph_H(X23827,X23826,X23825,X23824,X23823,hAPP(hAPP(X23825,X23822),X23821)) )
& ( hBOOL(hAPP(hAPP(c_member(X23827),esk109_7(X23821,X23822,X23823,X23824,X23825,X23826,X23827)),X23823))
| hAPP(hAPP(X23825,X23822),X23821) = X23824
| ~ c_Nitpick_Ofold__graph_H(X23827,X23826,X23825,X23824,X23823,hAPP(hAPP(X23825,X23822),X23821)) )
& ( c_Nitpick_Ofold__graph_H(X23827,X23826,X23825,X23824,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23827,tc_HOL_Obool)),X23823),hAPP(hAPP(c_Set_Oinsert(X23827),esk109_7(X23821,X23822,X23823,X23824,X23825,X23826,X23827)),c_Orderings_Obot__class_Obot(tc_fun(X23827,tc_HOL_Obool)))),esk110_7(X23821,X23822,X23823,X23824,X23825,X23826,X23827))
| hAPP(hAPP(X23825,X23822),X23821) = X23824
| ~ c_Nitpick_Ofold__graph_H(X23827,X23826,X23825,X23824,X23823,hAPP(hAPP(X23825,X23822),X23821)) )
& ( X23832 != c_Orderings_Obot__class_Obot(tc_fun(X23836,tc_HOL_Obool))
| hAPP(hAPP(X23834,X23831),X23830) != X23833
| c_Nitpick_Ofold__graph_H(X23836,X23835,X23834,X23833,X23832,hAPP(hAPP(X23834,X23831),X23830)) )
& ( hAPP(hAPP(X23834,X23831),X23830) != hAPP(hAPP(X23834,X23837),X23838)
| ~ hBOOL(hAPP(hAPP(c_member(X23836),X23837),X23832))
| ~ c_Nitpick_Ofold__graph_H(X23836,X23835,X23834,X23833,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23836,tc_HOL_Obool)),X23832),hAPP(hAPP(c_Set_Oinsert(X23836),X23837),c_Orderings_Obot__class_Obot(tc_fun(X23836,tc_HOL_Obool)))),X23838)
| c_Nitpick_Ofold__graph_H(X23836,X23835,X23834,X23833,X23832,hAPP(hAPP(X23834,X23831),X23830)) ) ),
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,
! [X26217,X26218,X26219,X26220,X26221,X26222,X26223,X26225,X26226,X26227,X26228,X26229,X26230,X26231,X26232] :
( ( hBOOL(hAPP(hAPP(c_member(X26223),esk174_7(X26217,X26218,X26219,X26220,X26221,X26222,X26223)),X26220))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26223,tc_fun(X26222,tc_fun(X26221,tc_HOL_Obool))),X26220),X26219),X26218),X26217)) )
& ( hBOOL(hAPP(hAPP(hAPP(X26219,esk174_7(X26217,X26218,X26219,X26220,X26221,X26222,X26223)),X26218),X26217))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26223,tc_fun(X26222,tc_fun(X26221,tc_HOL_Obool))),X26220),X26219),X26218),X26217)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X26231),X26232),X26228))
| ~ hBOOL(hAPP(hAPP(hAPP(X26227,X26232),X26226),X26225))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26231,tc_fun(X26230,tc_fun(X26229,tc_HOL_Obool))),X26228),X26227),X26226),X26225)) ) ),
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,
! [X33947,X33948,X33949,X33950] : c_List_Opartition(X33950,X33949,hAPP(hAPP(c_List_Olist_OCons(X33950),X33948),X33947)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X33950),tc_List_Olist(X33950),tc_prod(tc_List_Olist(X33950),tc_List_Olist(X33950))),hAPP(hAPP(c_COMBS(tc_List_Olist(X33950),tc_fun(tc_List_Olist(X33950),tc_prod(tc_List_Olist(X33950),tc_List_Olist(X33950))),tc_fun(tc_List_Olist(X33950),tc_prod(tc_List_Olist(X33950),tc_List_Olist(X33950)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X33950),tc_fun(tc_prod(tc_List_Olist(X33950),tc_List_Olist(X33950)),tc_prod(tc_List_Olist(X33950),tc_List_Olist(X33950)))),tc_fun(tc_fun(tc_List_Olist(X33950),tc_prod(tc_List_Olist(X33950),tc_List_Olist(X33950))),tc_fun(tc_List_Olist(X33950),tc_prod(tc_List_Olist(X33950),tc_List_Olist(X33950)))),tc_List_Olist(X33950)),c_COMBS(tc_List_Olist(X33950),tc_prod(tc_List_Olist(X33950),tc_List_Olist(X33950)),tc_prod(tc_List_Olist(X33950),tc_List_Olist(X33950)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X33950),tc_prod(tc_List_Olist(X33950),tc_List_Olist(X33950))),tc_fun(tc_List_Olist(X33950),tc_fun(tc_prod(tc_List_Olist(X33950),tc_List_Olist(X33950)),tc_prod(tc_List_Olist(X33950),tc_List_Olist(X33950)))),tc_List_Olist(X33950)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X33950),tc_List_Olist(X33950)),tc_fun(tc_prod(tc_List_Olist(X33950),tc_List_Olist(X33950)),tc_prod(tc_List_Olist(X33950),tc_List_Olist(X33950))),tc_List_Olist(X33950)),hAPP(c_If(tc_prod(tc_List_Olist(X33950),tc_List_Olist(X33950))),hAPP(X33949,X33948)))),hAPP(hAPP(c_COMBB(tc_List_Olist(X33950),tc_fun(tc_List_Olist(X33950),tc_prod(tc_List_Olist(X33950),tc_List_Olist(X33950))),tc_List_Olist(X33950)),c_Product__Type_OPair(tc_List_Olist(X33950),tc_List_Olist(X33950))),hAPP(c_List_Olist_OCons(X33950),X33948))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X33950),tc_fun(tc_List_Olist(X33950),tc_List_Olist(X33950)),tc_fun(tc_List_Olist(X33950),tc_prod(tc_List_Olist(X33950),tc_List_Olist(X33950)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X33950),tc_prod(tc_List_Olist(X33950),tc_List_Olist(X33950))),tc_fun(tc_fun(tc_List_Olist(X33950),tc_List_Olist(X33950)),tc_fun(tc_List_Olist(X33950),tc_prod(tc_List_Olist(X33950),tc_List_Olist(X33950)))),tc_List_Olist(X33950)),c_COMBB(tc_List_Olist(X33950),tc_prod(tc_List_Olist(X33950),tc_List_Olist(X33950)),tc_List_Olist(X33950))),c_Product__Type_OPair(tc_List_Olist(X33950),tc_List_Olist(X33950)))),hAPP(c_List_Olist_OCons(X33950),X33948)))),c_List_Opartition(X33950,X33949,X33947)),
inference(variable_rename,[status(thm)],[fact_partition_Osimps_I2_J]) ).
fof(i_0_6092,plain,
! [X23317,X23318,X23319,X23320,X23321] : c_Hoare__Mirabelle_Ohoare__derivs(X23321,X23320,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X23321)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X23321),hAPP(hAPP(c_COMBC(X23321,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)),X23321),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X23319)),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),X23318)),X23317))),c_Com_Ocom_OAss(X23318,X23317)),X23319)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X23321),tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_Ass]) ).
fof(i_0_6093,plain,
! [X23312,X23313,X23314,X23315,X23316] : c_Hoare__Mirabelle_Ohoare__derivs(X23316,X23315,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X23316)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X23316),hAPP(hAPP(c_COMBC(X23316,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)),X23316),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X23314)),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),X23313)),X23312))),c_Com_Ocom_OAss(X23313,X23312)),X23314)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X23316),tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_hoare__derivs_Oequations_I8_J]) ).
fof(i_0_6094,plain,
! [X32266,X32267,X32268] : hAPP(c_List_Olexn(X32268,X32267),hAPP(c_Nat_OSuc,X32266)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(X32268),tc_List_Olist(X32268)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(X32268,tc_List_Olist(X32268)),tc_prod(X32268,tc_List_Olist(X32268))),tc_prod(tc_List_Olist(X32268),tc_List_Olist(X32268)),c_Product__Type_Omap__pair(tc_prod(X32268,tc_List_Olist(X32268)),tc_List_Olist(X32268),tc_prod(X32268,tc_List_Olist(X32268)),tc_List_Olist(X32268),hAPP(c_Product__Type_Oprod_Oprod__case(X32268,tc_List_Olist(X32268),tc_List_Olist(X32268)),c_List_Olist_OCons(X32268)),hAPP(c_Product__Type_Oprod_Oprod__case(X32268,tc_List_Olist(X32268),tc_List_Olist(X32268)),c_List_Olist_OCons(X32268)))),c_Wellfounded_Olex__prod(X32268,tc_List_Olist(X32268),X32267,hAPP(c_List_Olexn(X32268,X32267),X32266)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X32268),tc_List_Olist(X32268))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X32268),tc_List_Olist(X32268),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X32268),tc_fun(tc_List_Olist(X32268),tc_HOL_Obool),tc_fun(tc_List_Olist(X32268),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X32268),tc_HOL_Obool),tc_fun(tc_List_Olist(X32268),tc_HOL_Obool)),tc_List_Olist(X32268)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X32268))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X32268)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X32268),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X32268)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X32268)))),hAPP(c_Nat_OSuc,X32266))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X32268),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X32268)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X32268)))),hAPP(c_Nat_OSuc,X32266)))))),
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,
! [X32587,X32588,X32589] : hAPP(c_List_Oset(X32589),c_List_Osublist(X32589,X32588,X32587)) = hAPP(c_Set_OCollect(X32589),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X32589),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X32589,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)),X32589),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)),X32589),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X32589,tc_fun(tc_Nat_Onat,X32589),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32589,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X32589),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X32589),c_COMBB(X32589,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X32589),X32588))))),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(X32589)),X32588)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X32587))))),
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,
! [X29540,X29541,X29542,X29543,X29544,X29545,X29546] :
( ( ~ c_Predicate_Opred__comp(X29546,X29545,X29544,hAPP(hAPP(c_COMBC(X29546,tc_fun(tc_prod(X29546,X29545),tc_HOL_Obool),tc_fun(X29545,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29545,tc_fun(tc_fun(tc_prod(X29546,X29545),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29546,X29545),tc_HOL_Obool),tc_fun(X29545,tc_HOL_Obool)),X29546),c_COMBC(X29545,tc_fun(tc_prod(X29546,X29545),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29545,tc_prod(X29546,X29545)),tc_fun(X29545,tc_fun(tc_fun(tc_prod(X29546,X29545),tc_HOL_Obool),tc_HOL_Obool)),X29546),hAPP(c_COMBB(tc_prod(X29546,X29545),tc_fun(tc_fun(tc_prod(X29546,X29545),tc_HOL_Obool),tc_HOL_Obool),X29545),c_member(tc_prod(X29546,X29545)))),c_Product__Type_OPair(X29546,X29545)))),X29543),hAPP(hAPP(c_COMBC(X29545,tc_fun(tc_prod(X29545,X29544),tc_HOL_Obool),tc_fun(X29544,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29544,tc_fun(tc_fun(tc_prod(X29545,X29544),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29545,X29544),tc_HOL_Obool),tc_fun(X29544,tc_HOL_Obool)),X29545),c_COMBC(X29544,tc_fun(tc_prod(X29545,X29544),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29544,tc_prod(X29545,X29544)),tc_fun(X29544,tc_fun(tc_fun(tc_prod(X29545,X29544),tc_HOL_Obool),tc_HOL_Obool)),X29545),hAPP(c_COMBB(tc_prod(X29545,X29544),tc_fun(tc_fun(tc_prod(X29545,X29544),tc_HOL_Obool),tc_HOL_Obool),X29544),c_member(tc_prod(X29545,X29544)))),c_Product__Type_OPair(X29545,X29544)))),X29542),X29541,X29540)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X29546,X29544)),hAPP(hAPP(c_Product__Type_OPair(X29546,X29544),X29541),X29540)),hAPP(hAPP(c_Relation_Orel__comp(X29546,X29545,X29544),X29543),X29542))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29546,X29544)),hAPP(hAPP(c_Product__Type_OPair(X29546,X29544),X29541),X29540)),hAPP(hAPP(c_Relation_Orel__comp(X29546,X29545,X29544),X29543),X29542)))
| c_Predicate_Opred__comp(X29546,X29545,X29544,hAPP(hAPP(c_COMBC(X29546,tc_fun(tc_prod(X29546,X29545),tc_HOL_Obool),tc_fun(X29545,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29545,tc_fun(tc_fun(tc_prod(X29546,X29545),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29546,X29545),tc_HOL_Obool),tc_fun(X29545,tc_HOL_Obool)),X29546),c_COMBC(X29545,tc_fun(tc_prod(X29546,X29545),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29545,tc_prod(X29546,X29545)),tc_fun(X29545,tc_fun(tc_fun(tc_prod(X29546,X29545),tc_HOL_Obool),tc_HOL_Obool)),X29546),hAPP(c_COMBB(tc_prod(X29546,X29545),tc_fun(tc_fun(tc_prod(X29546,X29545),tc_HOL_Obool),tc_HOL_Obool),X29545),c_member(tc_prod(X29546,X29545)))),c_Product__Type_OPair(X29546,X29545)))),X29543),hAPP(hAPP(c_COMBC(X29545,tc_fun(tc_prod(X29545,X29544),tc_HOL_Obool),tc_fun(X29544,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29544,tc_fun(tc_fun(tc_prod(X29545,X29544),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29545,X29544),tc_HOL_Obool),tc_fun(X29544,tc_HOL_Obool)),X29545),c_COMBC(X29544,tc_fun(tc_prod(X29545,X29544),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29544,tc_prod(X29545,X29544)),tc_fun(X29544,tc_fun(tc_fun(tc_prod(X29545,X29544),tc_HOL_Obool),tc_HOL_Obool)),X29545),hAPP(c_COMBB(tc_prod(X29545,X29544),tc_fun(tc_fun(tc_prod(X29545,X29544),tc_HOL_Obool),tc_HOL_Obool),X29544),c_member(tc_prod(X29545,X29544)))),c_Product__Type_OPair(X29545,X29544)))),X29542),X29541,X29540) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__comp__rel__comp__eq])]) ).
fof(i_0_6103,plain,
! [X29388,X29389,X29390,X29391,X29392,X29393] :
( ( hBOOL(hAPP(hAPP(c_member(X29391),esk313_6(X29388,X29389,X29390,X29391,X29392,X29393)),X29390))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29393,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X29391,tc_HOL_Obool),tc_Nat_Onat,X29393),c_Finite__Set_Ocard(X29391)),hAPP(hAPP(c_COMBB(tc_fun(X29391,tc_HOL_Obool),tc_fun(X29391,tc_HOL_Obool),X29393),c_Set_OCollect(X29391)),hAPP(hAPP(c_COMBB(tc_fun(X29391,tc_HOL_Obool),tc_fun(X29391,tc_HOL_Obool),X29393),hAPP(c_COMBS(X29391,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29391),c_fconj),hAPP(hAPP(c_COMBC(X29391,tc_fun(X29391,tc_HOL_Obool),tc_HOL_Obool),c_member(X29391)),X29390)))),X29389)))),X29392) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29391,tc_Nat_Onat),X29388),X29390)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29391),X29390))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29393),X29392)) )
& ( hAPP(c_Finite__Set_Ocard(X29393),hAPP(c_Set_OCollect(X29393),hAPP(hAPP(c_COMBS(X29393,tc_HOL_Obool,tc_HOL_Obool),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,X29391,tc_HOL_Obool),X29389),esk313_6(X29388,X29389,X29390,X29391,X29392,X29393))))) != hAPP(X29388,esk313_6(X29388,X29389,X29390,X29391,X29392,X29393))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29393,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X29391,tc_HOL_Obool),tc_Nat_Onat,X29393),c_Finite__Set_Ocard(X29391)),hAPP(hAPP(c_COMBB(tc_fun(X29391,tc_HOL_Obool),tc_fun(X29391,tc_HOL_Obool),X29393),c_Set_OCollect(X29391)),hAPP(hAPP(c_COMBB(tc_fun(X29391,tc_HOL_Obool),tc_fun(X29391,tc_HOL_Obool),X29393),hAPP(c_COMBS(X29391,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29391),c_fconj),hAPP(hAPP(c_COMBC(X29391,tc_fun(X29391,tc_HOL_Obool),tc_HOL_Obool),c_member(X29391)),X29390)))),X29389)))),X29392) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29391,tc_Nat_Onat),X29388),X29390)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29391),X29390))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29393),X29392)) ) ),
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,
! [X32579,X32580] : hAPP(c_List_Oset(X32580),X32579) = hAPP(c_Set_OCollect(X32580),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X32580),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X32580,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)),X32580),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)),X32580),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X32580,tc_fun(tc_Nat_Onat,X32580),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32580,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X32580),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X32580),c_COMBB(X32580,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X32580),X32579))))),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(X32580)),X32579))))),
inference(variable_rename,[status(thm)],[fact_set__conv__nth]) ).
fof(i_0_6105,plain,
! [X28805,X28806,X28807,X28808] : hAPP(hAPP(c_Product__Type_OSigma(X28808,X28807),X28806),X28805) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28808,tc_fun(tc_prod(X28808,X28807),tc_HOL_Obool)),X28806),hAPP(hAPP(c_COMBS(X28808,tc_fun(X28807,tc_fun(tc_prod(X28808,X28807),tc_HOL_Obool)),tc_fun(tc_prod(X28808,X28807),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28807,tc_HOL_Obool),tc_fun(tc_fun(X28807,tc_fun(tc_prod(X28808,X28807),tc_HOL_Obool)),tc_fun(tc_prod(X28808,X28807),tc_HOL_Obool)),X28808),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28807,tc_fun(tc_prod(X28808,X28807),tc_HOL_Obool))),X28805)),hAPP(hAPP(c_COMBC(X28808,tc_fun(tc_prod(X28808,X28807),tc_HOL_Obool),tc_fun(X28807,tc_fun(tc_prod(X28808,X28807),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X28807,tc_fun(tc_fun(tc_prod(X28808,X28807),tc_HOL_Obool),tc_fun(tc_prod(X28808,X28807),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X28808,X28807),tc_HOL_Obool),tc_fun(X28807,tc_fun(tc_prod(X28808,X28807),tc_HOL_Obool))),X28808),c_COMBC(X28807,tc_fun(tc_prod(X28808,X28807),tc_HOL_Obool),tc_fun(tc_prod(X28808,X28807),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X28807,tc_prod(X28808,X28807)),tc_fun(X28807,tc_fun(tc_fun(tc_prod(X28808,X28807),tc_HOL_Obool),tc_fun(tc_prod(X28808,X28807),tc_HOL_Obool))),X28808),hAPP(c_COMBB(tc_prod(X28808,X28807),tc_fun(tc_fun(tc_prod(X28808,X28807),tc_HOL_Obool),tc_fun(tc_prod(X28808,X28807),tc_HOL_Obool)),X28807),c_Set_Oinsert(tc_prod(X28808,X28807)))),c_Product__Type_OPair(X28808,X28807)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28808,X28807),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,
! [X29282,X29283,X29284,X29285,X29286,X29287] :
( ( hBOOL(hAPP(hAPP(c_member(X29285),esk311_6(X29282,X29283,X29284,X29285,X29286,X29287)),X29284))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29287,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X29285,tc_HOL_Obool),tc_Nat_Onat,X29287),c_Finite__Set_Ocard(X29285)),hAPP(hAPP(c_COMBB(tc_fun(X29285,tc_HOL_Obool),tc_fun(X29285,tc_HOL_Obool),X29287),c_Set_OCollect(X29285)),hAPP(hAPP(c_COMBB(tc_fun(X29285,tc_HOL_Obool),tc_fun(X29285,tc_HOL_Obool),X29287),hAPP(c_COMBS(X29285,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29285),c_fconj),hAPP(hAPP(c_COMBC(X29285,tc_fun(X29285,tc_HOL_Obool),tc_HOL_Obool),c_member(X29285)),X29284)))),X29283)))),X29286) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29282),hAPP(c_Finite__Set_Ocard(X29285),X29284))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29285),X29284))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29287),X29286)) )
& ( hAPP(c_Finite__Set_Ocard(X29287),hAPP(c_Set_OCollect(X29287),hAPP(hAPP(c_COMBS(X29287,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29287),c_fconj),hAPP(hAPP(c_COMBC(X29287,tc_fun(X29287,tc_HOL_Obool),tc_HOL_Obool),c_member(X29287)),X29286))),hAPP(hAPP(c_COMBC(X29287,X29285,tc_HOL_Obool),X29283),esk311_6(X29282,X29283,X29284,X29285,X29286,X29287))))) != X29282
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29287,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X29285,tc_HOL_Obool),tc_Nat_Onat,X29287),c_Finite__Set_Ocard(X29285)),hAPP(hAPP(c_COMBB(tc_fun(X29285,tc_HOL_Obool),tc_fun(X29285,tc_HOL_Obool),X29287),c_Set_OCollect(X29285)),hAPP(hAPP(c_COMBB(tc_fun(X29285,tc_HOL_Obool),tc_fun(X29285,tc_HOL_Obool),X29287),hAPP(c_COMBS(X29285,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29285),c_fconj),hAPP(hAPP(c_COMBC(X29285,tc_fun(X29285,tc_HOL_Obool),tc_HOL_Obool),c_member(X29285)),X29284)))),X29283)))),X29286) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29282),hAPP(c_Finite__Set_Ocard(X29285),X29284))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29285),X29284))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29287),X29286)) ) ),
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,
! [X29230,X29231,X29232,X29233,X29234,X29235,X29236] :
( ~ class_Groups_Ocomm__monoid__add(X29236)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29235),X29234))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29233),X29232))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29235,X29236),hAPP(hAPP(c_COMBS(X29235,tc_fun(X29233,tc_HOL_Obool),X29236),hAPP(hAPP(c_COMBB(tc_fun(X29233,X29236),tc_fun(tc_fun(X29233,tc_HOL_Obool),X29236),X29235),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29233,X29236)),X29231)),hAPP(hAPP(c_COMBB(tc_fun(X29233,tc_HOL_Obool),tc_fun(X29233,tc_HOL_Obool),X29235),c_Set_OCollect(X29233)),hAPP(hAPP(c_COMBB(tc_fun(X29233,tc_HOL_Obool),tc_fun(X29233,tc_HOL_Obool),X29235),hAPP(c_COMBS(X29233,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29233),c_fconj),hAPP(hAPP(c_COMBC(X29233,tc_fun(X29233,tc_HOL_Obool),tc_HOL_Obool),c_member(X29233)),X29232)))),X29230)))),X29234) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29233,X29236),hAPP(hAPP(c_COMBS(X29233,tc_fun(X29235,tc_HOL_Obool),X29236),hAPP(hAPP(c_COMBB(tc_fun(X29235,X29236),tc_fun(tc_fun(X29235,tc_HOL_Obool),X29236),X29233),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29235,X29236)),hAPP(c_COMBC(X29235,X29233,X29236),X29231))),hAPP(hAPP(c_COMBB(tc_fun(X29235,tc_HOL_Obool),tc_fun(X29235,tc_HOL_Obool),X29233),c_Set_OCollect(X29235)),hAPP(hAPP(c_COMBB(tc_fun(X29235,tc_HOL_Obool),tc_fun(X29235,tc_HOL_Obool),X29233),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(c_COMBC(X29235,X29233,tc_HOL_Obool),X29230))))),X29232) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__setsum__restrict])]) ).
fof(i_0_6109,plain,
! [X30324,X30325,X30326,X30327,X30328] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30328,X30328)),hAPP(hAPP(c_Product__Type_OPair(X30328,X30328),hAPP(X30327,hAPP(c_Nat_OSuc,esk367_5(X30324,X30325,X30326,X30327,X30328)))),hAPP(X30327,esk367_5(X30324,X30325,X30326,X30327,X30328)))),c_Transitive__Closure_Ortrancl(X30328,X30326)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30328,X30328)),hAPP(hAPP(c_Product__Type_OPair(X30328,X30328),hAPP(X30327,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30325),X30324))),hAPP(X30327,X30325))),c_Transitive__Closure_Ortrancl(X30328,X30326))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sequence__trans])])]) ).
fof(i_0_6110,plain,
! [X31652,X31653,X31654,X31655,X31656,X31657] :
( ( X31655 = hAPP(hAPP(c_Product__Type_OPair(X31657,X31656),esk429_6(X31652,X31653,X31654,X31655,X31656,X31657)),esk431_6(X31652,X31653,X31654,X31655,X31656,X31657))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31657,X31656)),X31655),hAPP(hAPP(c_Relation_Orel__comp(X31657,X31654,X31656),X31653),X31652))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X31657,X31654)),hAPP(hAPP(c_Product__Type_OPair(X31657,X31654),esk429_6(X31652,X31653,X31654,X31655,X31656,X31657)),esk430_6(X31652,X31653,X31654,X31655,X31656,X31657))),X31653))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31657,X31656)),X31655),hAPP(hAPP(c_Relation_Orel__comp(X31657,X31654,X31656),X31653),X31652))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X31654,X31656)),hAPP(hAPP(c_Product__Type_OPair(X31654,X31656),esk430_6(X31652,X31653,X31654,X31655,X31656,X31657)),esk431_6(X31652,X31653,X31654,X31655,X31656,X31657))),X31652))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31657,X31656)),X31655),hAPP(hAPP(c_Relation_Orel__comp(X31657,X31654,X31656),X31653),X31652))) ) ),
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,
! [X22274,X22275] : c_Divides_Odivmod__int__rel(X22275,X22274) = 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,X22275))),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),X22274)))))),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)),X22274))),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)),X22274))))),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)),X22274)))),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),X22274))),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,
! [X27215,X27216,X27217,X27218,X27219,X27220,X27221] :
( ~ class_Rings_Osemiring__0(X27221)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27221),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27220,X27221),X27219),X27218)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27217,X27221),X27216),X27215)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27220,X27221),hAPP(hAPP(c_COMBC(X27220,tc_fun(X27217,tc_HOL_Obool),X27221),hAPP(hAPP(c_COMBB(tc_fun(X27217,X27221),tc_fun(tc_fun(X27217,tc_HOL_Obool),X27221),X27220),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27217,X27221)),hAPP(hAPP(c_COMBC(X27220,tc_fun(X27217,X27221),tc_fun(X27217,X27221)),hAPP(hAPP(c_COMBB(tc_fun(X27221,X27221),tc_fun(tc_fun(X27217,X27221),tc_fun(X27217,X27221)),X27220),c_COMBB(X27221,X27221,X27217)),hAPP(hAPP(c_COMBB(X27221,tc_fun(X27221,X27221),X27220),c_Groups_Otimes__class_Otimes(X27221)),X27219))),X27216))),X27215)),X27218) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__product])]) ).
fof(i_0_6113,plain,
! [X28870,X28871,X28872,X28873,X28874,X28875] :
( ( hBOOL(hAPP(hAPP(c_member(X28874),esk288_6(X28870,X28871,X28872,X28873,X28874,X28875)),X28873))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28875,X28874,c_Groups_Otimes__class_Otimes(X28875)),hAPP(hAPP(c_COMBS(X28874,tc_fun(X28872,tc_HOL_Obool),X28875),hAPP(hAPP(c_COMBC(X28874,X28875,tc_fun(tc_fun(X28872,tc_HOL_Obool),X28875)),hAPP(hAPP(c_COMBB(tc_fun(X28872,X28875),tc_fun(X28875,tc_fun(tc_fun(X28872,tc_HOL_Obool),X28875)),X28874),c_Finite__Set_Ofold__image(X28875,X28872,c_Groups_Otimes__class_Otimes(X28875))),X28870)),c_Groups_Oone__class_Oone(X28875))),X28871)),c_Groups_Oone__class_Oone(X28875)),X28873) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28875,tc_prod(X28874,X28872),c_Groups_Otimes__class_Otimes(X28875)),hAPP(c_Product__Type_Oprod_Oprod__case(X28874,X28872,X28875),X28870)),c_Groups_Oone__class_Oone(X28875)),hAPP(hAPP(c_Product__Type_OSigma(X28874,X28872),X28873),X28871))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28874),X28873))
| ~ class_Groups_Ocomm__monoid__mult(X28875) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28872),hAPP(X28871,esk288_6(X28870,X28871,X28872,X28873,X28874,X28875))))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28875,X28874,c_Groups_Otimes__class_Otimes(X28875)),hAPP(hAPP(c_COMBS(X28874,tc_fun(X28872,tc_HOL_Obool),X28875),hAPP(hAPP(c_COMBC(X28874,X28875,tc_fun(tc_fun(X28872,tc_HOL_Obool),X28875)),hAPP(hAPP(c_COMBB(tc_fun(X28872,X28875),tc_fun(X28875,tc_fun(tc_fun(X28872,tc_HOL_Obool),X28875)),X28874),c_Finite__Set_Ofold__image(X28875,X28872,c_Groups_Otimes__class_Otimes(X28875))),X28870)),c_Groups_Oone__class_Oone(X28875))),X28871)),c_Groups_Oone__class_Oone(X28875)),X28873) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X28875,tc_prod(X28874,X28872),c_Groups_Otimes__class_Otimes(X28875)),hAPP(c_Product__Type_Oprod_Oprod__case(X28874,X28872,X28875),X28870)),c_Groups_Oone__class_Oone(X28875)),hAPP(hAPP(c_Product__Type_OSigma(X28874,X28872),X28873),X28871))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28874),X28873))
| ~ class_Groups_Ocomm__monoid__mult(X28875) ) ),
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,
! [X32232,X32233,X32234] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32234),X32233))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X32234)),hAPP(c_Set_OCollect(tc_List_Olist(X32234)),hAPP(hAPP(c_COMBS(tc_List_Olist(X32234),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X32234)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X32234),tc_fun(X32234,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X32234,tc_HOL_Obool),tc_fun(tc_fun(X32234,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X32234)),c_Orderings_Oord__class_Oless__eq(tc_fun(X32234,tc_HOL_Obool))),c_List_Oset(X32234))),X32233))),hAPP(hAPP(c_COMBC(tc_List_Olist(X32234),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X32234)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X32234)))),X32232))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__lists__length__le])]) ).
fof(i_0_6116,plain,
! [X32202,X32203,X32204] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32204),X32203))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X32204)),hAPP(c_Set_OCollect(tc_List_Olist(X32204)),hAPP(hAPP(c_COMBS(tc_List_Olist(X32204),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X32204)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X32204),tc_fun(X32204,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X32204,tc_HOL_Obool),tc_fun(tc_fun(X32204,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X32204)),c_Orderings_Oord__class_Oless__eq(tc_fun(X32204,tc_HOL_Obool))),c_List_Oset(X32204))),X32203))),hAPP(hAPP(c_COMBC(tc_List_Olist(X32204),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X32204)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X32204)))),X32202))))) ),
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,
! [X29110,X29111,X29112,X29113,X29114,X29115,X29116,X29117] :
( ( hBOOL(hAPP(hAPP(c_member(X29116),esk308_7(X29110,X29111,X29112,X29113,X29114,X29115,X29116)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29116,tc_HOL_Obool)),X29111),X29110)))
| hAPP(X29112,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29116,tc_HOL_Obool)),X29111),X29110)) = hAPP(hAPP(X29115,hAPP(X29112,X29111)),hAPP(X29112,X29110))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29116),X29110))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29116),X29111))
| ~ c_Finite__Set_Ofolding__image__simple(X29117,X29116,X29115,X29114,X29113,X29112) )
& ( hAPP(X29113,esk308_7(X29110,X29111,X29112,X29113,X29114,X29115,X29116)) != X29114
| hAPP(X29112,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29116,tc_HOL_Obool)),X29111),X29110)) = hAPP(hAPP(X29115,hAPP(X29112,X29111)),hAPP(X29112,X29110))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29116),X29110))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29116),X29111))
| ~ c_Finite__Set_Ofolding__image__simple(X29117,X29116,X29115,X29114,X29113,X29112) ) ),
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,
! [X26178] : hAPP(c_Int_Onat,X26178) = 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,X26178)),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,
! [X17961,X17962,X17963,X17964,X17965,X17966,X17968,X17969,X17970,X17971,X17972,X17973,X17974] :
( ( hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17961),hAPP(c_Natural_Ogetlocs,X17963))),X17966),hAPP(hAPP(c_Natural_Ogetlocs,X17961),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,esk23_6(X17961,X17962,X17963,X17964,X17965,X17966)),hAPP(c_Natural_Ogetlocs,X17963))),X17966),hAPP(hAPP(c_Natural_Ogetlocs,esk23_6(X17961,X17962,X17963,X17964,X17965,X17966)),c_Com_ORes))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCall(X17966,X17965,X17964),X17963,X17962,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17961),hAPP(c_Natural_Ogetlocs,X17963))),X17966),hAPP(hAPP(c_Natural_Ogetlocs,X17961),c_Com_ORes))) )
& ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X17965),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17963),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X17964,X17963)),X17962,esk23_6(X17961,X17962,X17963,X17964,X17965,X17966))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCall(X17966,X17965,X17964),X17963,X17962,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17961),hAPP(c_Natural_Ogetlocs,X17963))),X17966),hAPP(hAPP(c_Natural_Ogetlocs,X17961),c_Com_ORes))) )
& ( hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17968),hAPP(c_Natural_Ogetlocs,X17970))),X17973),hAPP(hAPP(c_Natural_Ogetlocs,X17968),c_Com_ORes)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17974),hAPP(c_Natural_Ogetlocs,X17970))),X17973),hAPP(hAPP(c_Natural_Ogetlocs,X17974),c_Com_ORes))
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X17972),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17970),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X17971,X17970)),X17969,X17974)
| c_Natural_Oevaln(c_Com_Ocom_OCall(X17973,X17972,X17971),X17970,X17969,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17968),hAPP(c_Natural_Ogetlocs,X17970))),X17973),hAPP(hAPP(c_Natural_Ogetlocs,X17968),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,
! [X17993,X17994,X17995,X17996,X17997,X17998] :
( ( X17993 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,esk26_6(X17993,X17994,X17995,X17996,X17997,X17998)),hAPP(c_Natural_Ogetlocs,X17995))),X17998),hAPP(hAPP(c_Natural_Ogetlocs,esk26_6(X17993,X17994,X17995,X17996,X17997,X17998)),c_Com_ORes))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCall(X17998,X17997,X17996),X17995,X17994,X17993) )
& ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X17997),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17995),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X17996,X17995)),X17994,esk26_6(X17993,X17994,X17995,X17996,X17997,X17998))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCall(X17998,X17997,X17996),X17995,X17994,X17993) ) ),
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,
! [X21461,X21462,X21463,X21464] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21464),esk83_4(X21461,X21462,X21463,X21464)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21461),hAPP(X21462,X21463)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21462,X21464)),X21461))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21464),X21463))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21464),esk82_4(X21461,X21462,X21463,X21464))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk83_4(X21461,X21462,X21463,X21464)),X21463))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21461),hAPP(X21462,X21463)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21462,X21464)),X21461))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21464),X21463))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21464),esk82_4(X21461,X21462,X21463,X21464))) )
& ( hAPP(X21462,esk83_4(X21461,X21462,X21463,X21464)) = X21461
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21461),hAPP(X21462,X21463)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21462,X21464)),X21461))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21464),X21463))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21464),esk82_4(X21461,X21462,X21463,X21464))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21464),esk83_4(X21461,X21462,X21463,X21464)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21461),hAPP(X21462,X21463)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21462,X21464)),X21461))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21464),X21463))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk82_4(X21461,X21462,X21463,X21464)),X21463)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk83_4(X21461,X21462,X21463,X21464)),X21463))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21461),hAPP(X21462,X21463)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21462,X21464)),X21461))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21464),X21463))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk82_4(X21461,X21462,X21463,X21464)),X21463)) )
& ( hAPP(X21462,esk83_4(X21461,X21462,X21463,X21464)) = X21461
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21461),hAPP(X21462,X21463)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21462,X21464)),X21461))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21464),X21463))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk82_4(X21461,X21462,X21463,X21464)),X21463)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21464),esk83_4(X21461,X21462,X21463,X21464)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21461),hAPP(X21462,X21463)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21462,X21464)),X21461))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21464),X21463))
| ~ 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(X21462,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk82_4(X21461,X21462,X21463,X21464)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X21462,esk82_4(X21461,X21462,X21463,X21464))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk83_4(X21461,X21462,X21463,X21464)),X21463))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21461),hAPP(X21462,X21463)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21462,X21464)),X21461))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21464),X21463))
| ~ 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(X21462,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk82_4(X21461,X21462,X21463,X21464)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X21462,esk82_4(X21461,X21462,X21463,X21464))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
& ( hAPP(X21462,esk83_4(X21461,X21462,X21463,X21464)) = X21461
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21461),hAPP(X21462,X21463)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21462,X21464)),X21461))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21464),X21463))
| ~ 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(X21462,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk82_4(X21461,X21462,X21463,X21464)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X21462,esk82_4(X21461,X21462,X21463,X21464))))),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,
! [X30017,X30018,X30019,X30020,X30021,X30022] :
( ( hBOOL(hAPP(hAPP(c_member(X30022),esk352_6(X30017,X30018,X30019,X30020,X30021,X30022)),X30021))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30022,X30019),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X30022,X30019),X30021),X30018)),hAPP(hAPP(c_Product__Type_OSigma(X30022,X30019),X30020),X30017)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30022,tc_HOL_Obool)),X30021),X30020)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30019,tc_HOL_Obool)),hAPP(X30018,esk352_6(X30017,X30018,X30019,X30020,X30021,X30022))),hAPP(X30017,esk352_6(X30017,X30018,X30019,X30020,X30021,X30022))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30022,X30019),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X30022,X30019),X30021),X30018)),hAPP(hAPP(c_Product__Type_OSigma(X30022,X30019),X30020),X30017)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30022,tc_HOL_Obool)),X30021),X30020)) ) ),
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,
! [X30059,X30060,X30061,X30062,X30063,X30064] :
( ( hBOOL(hAPP(hAPP(c_member(X30063),esk360_6(X30059,X30060,X30061,X30062,X30063,X30064)),X30061))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X30064),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X30063,X30064),X30060),X30061)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X30063,X30064),X30059),X30062)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30063,tc_HOL_Obool)),X30061),X30062))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30063),X30062))
| ~ class_Rings_Ocomm__semiring__1(X30064) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X30064),hAPP(X30060,esk360_6(X30059,X30060,X30061,X30062,X30063,X30064))),hAPP(X30059,esk360_6(X30059,X30060,X30061,X30062,X30063,X30064))))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X30064),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X30063,X30064),X30060),X30061)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X30063,X30064),X30059),X30062)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30063,tc_HOL_Obool)),X30061),X30062))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30063),X30062))
| ~ class_Rings_Ocomm__semiring__1(X30064) ) ),
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,
! [X29960,X29961,X29962,X29963,X29964,X29965] :
( ( X29965 = hAPP(hAPP(c_Product__Type_OPair(X29964,X29963),esk345_6(X29960,X29961,X29962,X29963,X29964,X29965)),esk346_6(X29960,X29961,X29962,X29963,X29964,X29965))
| hBOOL(hAPP(hAPP(c_member(X29962),X29961),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29964,X29963,tc_fun(X29962,tc_HOL_Obool)),X29960),X29965))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X29962),X29961),hAPP(hAPP(X29960,esk345_6(X29960,X29961,X29962,X29963,X29964,X29965)),esk346_6(X29960,X29961,X29962,X29963,X29964,X29965))))
| hBOOL(hAPP(hAPP(c_member(X29962),X29961),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29964,X29963,tc_fun(X29962,tc_HOL_Obool)),X29960),X29965))) ) ),
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,
! [X25125,X25126] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25125),X25126))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25126),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)))),X25125))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25126),X25125))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25126),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)))),X25125))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25125),X25126))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25126),X25125))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25126),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)))),X25125))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5224])])]) ).
fof(i_0_6129,plain,
! [X25127,X25128] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25128),X25127))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25128),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)))),X25127))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25127),X25128))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25128),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)))),X25127))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25128),X25127))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25127),X25128))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25128),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)))),X25127))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5225])])]) ).
fof(i_0_6130,plain,
! [X30430,X30431,X30432] : hAPP(c_Relation_Oconverse(X30432,X30431),X30430) = hAPP(c_Set_OCollect(tc_prod(X30431,X30432)),hAPP(c_Product__Type_Oprod_Oprod__case(X30431,X30432,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X30431,tc_fun(tc_prod(X30432,X30431),tc_HOL_Obool),tc_fun(X30432,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30432,tc_fun(tc_fun(tc_prod(X30432,X30431),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X30432,X30431),tc_HOL_Obool),tc_fun(X30432,tc_HOL_Obool)),X30431),c_COMBC(X30432,tc_fun(tc_prod(X30432,X30431),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30432,tc_prod(X30432,X30431)),tc_fun(X30432,tc_fun(tc_fun(tc_prod(X30432,X30431),tc_HOL_Obool),tc_HOL_Obool)),X30431),hAPP(c_COMBB(tc_prod(X30432,X30431),tc_fun(tc_fun(tc_prod(X30432,X30431),tc_HOL_Obool),tc_HOL_Obool),X30432),c_member(tc_prod(X30432,X30431)))),hAPP(c_COMBC(X30432,X30431,tc_prod(X30432,X30431)),c_Product__Type_OPair(X30432,X30431))))),X30430))),
inference(variable_rename,[status(thm)],[fact_converse__def]) ).
fof(i_0_6131,plain,
! [X32469,X32470,X32471,X32472] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32471),X32470))
| c_Nitpick_Osetsum_H(X32471,X32472,X32469,X32470) = hAPP(c_List_Omonoid__add__class_Olistsum(X32472),hAPP(hAPP(c_List_Omap(X32471,X32472),X32469),c_Hilbert__Choice_OEps(tc_List_Olist(X32471),hAPP(hAPP(c_COMBS(tc_List_Olist(X32471),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X32471)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X32471),tc_fun(X32471,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X32471,tc_HOL_Obool),tc_fun(tc_fun(X32471,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X32471)),c_fequal),c_List_Oset(X32471))),X32470))),c_List_Odistinct(X32471)))))
| ~ class_Groups_Ocomm__monoid__add(X32472) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X32471),X32470))
| c_Nitpick_Osetsum_H(X32471,X32472,X32469,X32470) = c_Groups_Ozero__class_Ozero(X32472)
| ~ class_Groups_Ocomm__monoid__add(X32472) ) ),
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,
! [X29273,X29274] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29274))
| 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)),X29274))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X29273))))) = 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)),X29274))),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,X29273))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__less__Suc])]) ).
fof(i_0_6137,plain,
! [X29257,X29258,X29259,X29260,X29261,X29262] :
( ~ class_Groups_Ocomm__monoid__add(X29262)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29261),X29260))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29261,X29262),X29259),X29260) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29258,X29262),hAPP(hAPP(c_COMBB(tc_fun(X29261,tc_HOL_Obool),X29262,X29258),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29261,X29262),X29259)),hAPP(hAPP(c_COMBB(tc_fun(X29261,tc_HOL_Obool),tc_fun(X29261,tc_HOL_Obool),X29258),c_Set_OCollect(X29261)),hAPP(hAPP(c_COMBB(tc_fun(X29261,tc_HOL_Obool),tc_fun(X29261,tc_HOL_Obool),X29258),hAPP(c_COMBS(X29261,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29261),c_fconj),hAPP(hAPP(c_COMBC(X29261,tc_fun(X29261,tc_HOL_Obool),tc_HOL_Obool),c_member(X29261)),X29260)))),hAPP(c_COMBC(X29261,X29258,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X29258,tc_fun(X29258,tc_HOL_Obool),X29261),c_fequal),X29257)))))),hAPP(c_Set_Oimage(X29261,X29258,X29257),X29260)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__image__gen])]) ).
fof(i_0_6138,plain,
! [X29894,X29895,X29896,X29897,X29898,X29899,X29900,X29901] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29896,X29896)),X29897),X29894))
| hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29896,X29896,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X29896,tc_fun(X29896,tc_HOL_Obool),tc_fun(X29896,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X29896,tc_HOL_Obool),tc_fun(X29896,tc_HOL_Obool)),X29896),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29896)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29896),c_fconj),hAPP(hAPP(c_COMBC(X29896,tc_fun(X29896,tc_HOL_Obool),tc_HOL_Obool),c_member(X29896)),X29895)))),hAPP(hAPP(c_COMBC(X29896,tc_fun(X29896,tc_HOL_Obool),tc_HOL_Obool),c_member(X29896)),X29895))),X29897))
| ~ c_Relation_Orefl__on(X29896,X29895,X29894) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X29896),X29898),X29895))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X29896,X29896)),hAPP(hAPP(c_Product__Type_OPair(X29896,X29896),X29898),X29898)),X29894))
| ~ c_Relation_Orefl__on(X29896,X29895,X29894) )
& ( hBOOL(hAPP(hAPP(c_member(X29901),esk331_3(X29899,X29900,X29901)),X29900))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X29901,X29901)),esk330_3(X29899,X29900,X29901)),X29899))
| c_Relation_Orefl__on(X29901,X29900,X29899) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29901,X29901)),hAPP(hAPP(c_Product__Type_OPair(X29901,X29901),esk331_3(X29899,X29900,X29901)),esk331_3(X29899,X29900,X29901))),X29899))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X29901,X29901)),esk330_3(X29899,X29900,X29901)),X29899))
| c_Relation_Orefl__on(X29901,X29900,X29899) )
& ( hBOOL(hAPP(hAPP(c_member(X29901),esk331_3(X29899,X29900,X29901)),X29900))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29901,X29901,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X29901,tc_fun(X29901,tc_HOL_Obool),tc_fun(X29901,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X29901,tc_HOL_Obool),tc_fun(X29901,tc_HOL_Obool)),X29901),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29901)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29901),c_fconj),hAPP(hAPP(c_COMBC(X29901,tc_fun(X29901,tc_HOL_Obool),tc_HOL_Obool),c_member(X29901)),X29900)))),hAPP(hAPP(c_COMBC(X29901,tc_fun(X29901,tc_HOL_Obool),tc_HOL_Obool),c_member(X29901)),X29900))),esk330_3(X29899,X29900,X29901)))
| c_Relation_Orefl__on(X29901,X29900,X29899) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29901,X29901)),hAPP(hAPP(c_Product__Type_OPair(X29901,X29901),esk331_3(X29899,X29900,X29901)),esk331_3(X29899,X29900,X29901))),X29899))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29901,X29901,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X29901,tc_fun(X29901,tc_HOL_Obool),tc_fun(X29901,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X29901,tc_HOL_Obool),tc_fun(X29901,tc_HOL_Obool)),X29901),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29901)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29901),c_fconj),hAPP(hAPP(c_COMBC(X29901,tc_fun(X29901,tc_HOL_Obool),tc_HOL_Obool),c_member(X29901)),X29900)))),hAPP(hAPP(c_COMBC(X29901,tc_fun(X29901,tc_HOL_Obool),tc_HOL_Obool),c_member(X29901)),X29900))),esk330_3(X29899,X29900,X29901)))
| c_Relation_Orefl__on(X29901,X29900,X29899) ) ),
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,
! [X22992,X22993,X22994,X22995] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X22995),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
| c_Random__Sequence_ORandom(X22994,X22993,X22995,X22992) = 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(X22994)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X22994)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X22995),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
| c_Random__Sequence_ORandom(X22994,X22993,X22995,X22992) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X22994,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(X22994)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(X22993,X22992)),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(X22994)))),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(X22994)))),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(X22994)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(X22994,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(X22994)))),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(X22994)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(X22994,X22993,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X22995),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X22992))),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(X22994)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X22994))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X22994)))),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(X22994)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(X22994,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(X22994)))),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(X22994)))),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(X22994))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X22994)))),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(X22994)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X22994)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X22994))))),tc_prod(X22994,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(X22994)),hAPP(hAPP(c_COMBB(X22994,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X22994)))),tc_prod(X22994,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(X22994)),c_Product__Type_Ofst(X22994,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,
! [X32897,X32898,X32899,X32900,X32901] : hAPP(hAPP(c_List_Ozip(X32901,X32900),X32899),hAPP(hAPP(c_List_Olist_OCons(X32900),X32898),X32897)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X32901,X32900)),X32901,c_List_Olist_ONil(tc_prod(X32901,X32900)),hAPP(hAPP(c_COMBC(X32901,tc_fun(tc_List_Olist(X32901),tc_List_Olist(tc_prod(X32901,X32900))),tc_fun(tc_List_Olist(X32901),tc_List_Olist(tc_prod(X32901,X32900)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X32901,X32900)),tc_List_Olist(tc_prod(X32901,X32900))),tc_fun(tc_fun(tc_List_Olist(X32901),tc_List_Olist(tc_prod(X32901,X32900))),tc_fun(tc_List_Olist(X32901),tc_List_Olist(tc_prod(X32901,X32900)))),X32901),c_COMBB(tc_List_Olist(tc_prod(X32901,X32900)),tc_List_Olist(tc_prod(X32901,X32900)),tc_List_Olist(X32901))),hAPP(hAPP(c_COMBB(tc_prod(X32901,X32900),tc_fun(tc_List_Olist(tc_prod(X32901,X32900)),tc_List_Olist(tc_prod(X32901,X32900))),X32901),c_List_Olist_OCons(tc_prod(X32901,X32900))),hAPP(hAPP(c_COMBC(X32901,X32900,tc_prod(X32901,X32900)),c_Product__Type_OPair(X32901,X32900)),X32898)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X32901),tc_List_Olist(X32900),tc_List_Olist(tc_prod(X32901,X32900))),c_List_Ozip(X32901,X32900)),X32897))),X32899),
inference(variable_rename,[status(thm)],[fact_zip__Cons]) ).
fof(i_0_6144,plain,
! [X24211,X24212,X24213,X24214] :
( ( ~ c_Wellfounded_Omax__extp(X24214,hAPP(hAPP(c_COMBC(X24214,tc_fun(tc_prod(X24214,X24214),tc_HOL_Obool),tc_fun(X24214,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24214,tc_fun(tc_fun(tc_prod(X24214,X24214),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X24214,X24214),tc_HOL_Obool),tc_fun(X24214,tc_HOL_Obool)),X24214),c_COMBC(X24214,tc_fun(tc_prod(X24214,X24214),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24214,tc_prod(X24214,X24214)),tc_fun(X24214,tc_fun(tc_fun(tc_prod(X24214,X24214),tc_HOL_Obool),tc_HOL_Obool)),X24214),hAPP(c_COMBB(tc_prod(X24214,X24214),tc_fun(tc_fun(tc_prod(X24214,X24214),tc_HOL_Obool),tc_HOL_Obool),X24214),c_member(tc_prod(X24214,X24214)))),c_Product__Type_OPair(X24214,X24214)))),X24213),X24212,X24211)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X24214,tc_HOL_Obool),tc_fun(X24214,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X24214,tc_HOL_Obool),tc_fun(X24214,tc_HOL_Obool)),X24212),X24211)),c_Wellfounded_Omax__ext(X24214,X24213))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X24214,tc_HOL_Obool),tc_fun(X24214,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X24214,tc_HOL_Obool),tc_fun(X24214,tc_HOL_Obool)),X24212),X24211)),c_Wellfounded_Omax__ext(X24214,X24213)))
| c_Wellfounded_Omax__extp(X24214,hAPP(hAPP(c_COMBC(X24214,tc_fun(tc_prod(X24214,X24214),tc_HOL_Obool),tc_fun(X24214,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24214,tc_fun(tc_fun(tc_prod(X24214,X24214),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X24214,X24214),tc_HOL_Obool),tc_fun(X24214,tc_HOL_Obool)),X24214),c_COMBC(X24214,tc_fun(tc_prod(X24214,X24214),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24214,tc_prod(X24214,X24214)),tc_fun(X24214,tc_fun(tc_fun(tc_prod(X24214,X24214),tc_HOL_Obool),tc_HOL_Obool)),X24214),hAPP(c_COMBB(tc_prod(X24214,X24214),tc_fun(tc_fun(tc_prod(X24214,X24214),tc_HOL_Obool),tc_HOL_Obool),X24214),c_member(tc_prod(X24214,X24214)))),c_Product__Type_OPair(X24214,X24214)))),X24213),X24212,X24211) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__extp__max__ext__eq])]) ).
fof(i_0_6145,plain,
! [X32262,X32263,X32264,X32265] :
( ( ~ c_List_Olistrelp(X32265,hAPP(hAPP(c_COMBC(X32265,tc_fun(tc_prod(X32265,X32265),tc_HOL_Obool),tc_fun(X32265,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32265,tc_fun(tc_fun(tc_prod(X32265,X32265),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X32265,X32265),tc_HOL_Obool),tc_fun(X32265,tc_HOL_Obool)),X32265),c_COMBC(X32265,tc_fun(tc_prod(X32265,X32265),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32265,tc_prod(X32265,X32265)),tc_fun(X32265,tc_fun(tc_fun(tc_prod(X32265,X32265),tc_HOL_Obool),tc_HOL_Obool)),X32265),hAPP(c_COMBB(tc_prod(X32265,X32265),tc_fun(tc_fun(tc_prod(X32265,X32265),tc_HOL_Obool),tc_HOL_Obool),X32265),c_member(tc_prod(X32265,X32265)))),c_Product__Type_OPair(X32265,X32265)))),X32264),X32263,X32262)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32265),tc_List_Olist(X32265))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32265),tc_List_Olist(X32265)),X32263),X32262)),c_List_Olistrel(X32265,X32264))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32265),tc_List_Olist(X32265))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32265),tc_List_Olist(X32265)),X32263),X32262)),c_List_Olistrel(X32265,X32264)))
| c_List_Olistrelp(X32265,hAPP(hAPP(c_COMBC(X32265,tc_fun(tc_prod(X32265,X32265),tc_HOL_Obool),tc_fun(X32265,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32265,tc_fun(tc_fun(tc_prod(X32265,X32265),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X32265,X32265),tc_HOL_Obool),tc_fun(X32265,tc_HOL_Obool)),X32265),c_COMBC(X32265,tc_fun(tc_prod(X32265,X32265),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32265,tc_prod(X32265,X32265)),tc_fun(X32265,tc_fun(tc_fun(tc_prod(X32265,X32265),tc_HOL_Obool),tc_HOL_Obool)),X32265),hAPP(c_COMBB(tc_prod(X32265,X32265),tc_fun(tc_fun(tc_prod(X32265,X32265),tc_HOL_Obool),tc_HOL_Obool),X32265),c_member(tc_prod(X32265,X32265)))),c_Product__Type_OPair(X32265,X32265)))),X32264),X32263,X32262) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp__listrel__eq])]) ).
fof(i_0_6146,plain,
! [X28797,X28798,X28799,X28800,X28801,X28802,X28803,X28804] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(X28804,X28803),tc_fun(tc_prod(X28802,X28801),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28804,X28803),X28800),hAPP(c_COMBK(tc_fun(X28803,tc_HOL_Obool),X28804),X28799))),hAPP(c_Product__Type_Oprod_Oprod__case(X28804,X28803,tc_fun(tc_prod(X28802,X28801),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X28804,tc_fun(X28803,tc_fun(X28802,tc_fun(X28801,tc_HOL_Obool))),tc_fun(X28803,tc_fun(tc_prod(X28802,X28801),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X28802,tc_fun(X28801,tc_HOL_Obool)),tc_fun(tc_prod(X28802,X28801),tc_HOL_Obool)),tc_fun(tc_fun(X28803,tc_fun(X28802,tc_fun(X28801,tc_HOL_Obool))),tc_fun(X28803,tc_fun(tc_prod(X28802,X28801),tc_HOL_Obool))),X28804),c_COMBB(tc_fun(X28802,tc_fun(X28801,tc_HOL_Obool)),tc_fun(tc_prod(X28802,X28801),tc_HOL_Obool),X28803)),hAPP(hAPP(c_COMBB(tc_fun(X28802,tc_HOL_Obool),tc_fun(tc_fun(X28802,tc_fun(X28801,tc_HOL_Obool)),tc_fun(tc_prod(X28802,X28801),tc_HOL_Obool)),X28804),c_Product__Type_OSigma(X28802,X28801)),X28798))),hAPP(hAPP(c_COMBB(tc_fun(X28801,tc_HOL_Obool),tc_fun(X28802,tc_fun(X28801,tc_HOL_Obool)),X28803),c_COMBK(tc_fun(X28801,tc_HOL_Obool),X28802)),X28797)))) = hAPP(hAPP(c_Product__Type_OSigma(X28802,X28801),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28804,tc_fun(X28802,tc_HOL_Obool)),X28800),X28798)),hAPP(c_COMBK(tc_fun(X28801,tc_HOL_Obool),X28802),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28803,tc_fun(X28801,tc_HOL_Obool)),X28799),X28797))),
inference(variable_rename,[status(thm)],[fact_UN__Times__distrib]) ).
fof(i_0_6147,plain,
! [X28340,X28341] :
( ( ~ c_Equiv__Relations_Oequiv(X28341,c_Orderings_Otop__class_Otop(tc_fun(X28341,tc_HOL_Obool)),X28340)
| c_Equiv__Relations_Oequivp(X28341,hAPP(hAPP(c_COMBC(X28341,tc_fun(tc_prod(X28341,X28341),tc_HOL_Obool),tc_fun(X28341,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28341,tc_fun(tc_fun(tc_prod(X28341,X28341),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28341,X28341),tc_HOL_Obool),tc_fun(X28341,tc_HOL_Obool)),X28341),c_COMBC(X28341,tc_fun(tc_prod(X28341,X28341),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28341,tc_prod(X28341,X28341)),tc_fun(X28341,tc_fun(tc_fun(tc_prod(X28341,X28341),tc_HOL_Obool),tc_HOL_Obool)),X28341),hAPP(c_COMBB(tc_prod(X28341,X28341),tc_fun(tc_fun(tc_prod(X28341,X28341),tc_HOL_Obool),tc_HOL_Obool),X28341),c_member(tc_prod(X28341,X28341)))),c_Product__Type_OPair(X28341,X28341)))),X28340)) )
& ( ~ c_Equiv__Relations_Oequivp(X28341,hAPP(hAPP(c_COMBC(X28341,tc_fun(tc_prod(X28341,X28341),tc_HOL_Obool),tc_fun(X28341,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28341,tc_fun(tc_fun(tc_prod(X28341,X28341),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28341,X28341),tc_HOL_Obool),tc_fun(X28341,tc_HOL_Obool)),X28341),c_COMBC(X28341,tc_fun(tc_prod(X28341,X28341),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28341,tc_prod(X28341,X28341)),tc_fun(X28341,tc_fun(tc_fun(tc_prod(X28341,X28341),tc_HOL_Obool),tc_HOL_Obool)),X28341),hAPP(c_COMBB(tc_prod(X28341,X28341),tc_fun(tc_fun(tc_prod(X28341,X28341),tc_HOL_Obool),tc_HOL_Obool),X28341),c_member(tc_prod(X28341,X28341)))),c_Product__Type_OPair(X28341,X28341)))),X28340))
| c_Equiv__Relations_Oequiv(X28341,c_Orderings_Otop__class_Otop(tc_fun(X28341,tc_HOL_Obool)),X28340) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__equiv])]) ).
fof(i_0_6148,plain,
! [X29823,X29824] :
( ( ~ c_Wellfounded_OwfP(X29824,hAPP(hAPP(c_COMBC(X29824,tc_fun(tc_prod(X29824,X29824),tc_HOL_Obool),tc_fun(X29824,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29824,tc_fun(tc_fun(tc_prod(X29824,X29824),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29824,X29824),tc_HOL_Obool),tc_fun(X29824,tc_HOL_Obool)),X29824),c_COMBC(X29824,tc_fun(tc_prod(X29824,X29824),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29824,tc_prod(X29824,X29824)),tc_fun(X29824,tc_fun(tc_fun(tc_prod(X29824,X29824),tc_HOL_Obool),tc_HOL_Obool)),X29824),hAPP(c_COMBB(tc_prod(X29824,X29824),tc_fun(tc_fun(tc_prod(X29824,X29824),tc_HOL_Obool),tc_HOL_Obool),X29824),c_member(tc_prod(X29824,X29824)))),c_Product__Type_OPair(X29824,X29824)))),X29823))
| c_Wellfounded_Owf(X29824,X29823) )
& ( ~ c_Wellfounded_Owf(X29824,X29823)
| c_Wellfounded_OwfP(X29824,hAPP(hAPP(c_COMBC(X29824,tc_fun(tc_prod(X29824,X29824),tc_HOL_Obool),tc_fun(X29824,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29824,tc_fun(tc_fun(tc_prod(X29824,X29824),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29824,X29824),tc_HOL_Obool),tc_fun(X29824,tc_HOL_Obool)),X29824),c_COMBC(X29824,tc_fun(tc_prod(X29824,X29824),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29824,tc_prod(X29824,X29824)),tc_fun(X29824,tc_fun(tc_fun(tc_prod(X29824,X29824),tc_HOL_Obool),tc_HOL_Obool)),X29824),hAPP(c_COMBB(tc_prod(X29824,X29824),tc_fun(tc_fun(tc_prod(X29824,X29824),tc_HOL_Obool),tc_HOL_Obool),X29824),c_member(tc_prod(X29824,X29824)))),c_Product__Type_OPair(X29824,X29824)))),X29823)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__wf__eq])]) ).
fof(i_0_6149,plain,
! [X23707,X23708,X23709,X23710] :
( ( hAPP(hAPP(c_COMBC(X23710,tc_fun(tc_prod(X23710,X23709),tc_HOL_Obool),tc_fun(X23709,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23709,tc_fun(tc_fun(tc_prod(X23710,X23709),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X23710,X23709),tc_HOL_Obool),tc_fun(X23709,tc_HOL_Obool)),X23710),c_COMBC(X23709,tc_fun(tc_prod(X23710,X23709),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23709,tc_prod(X23710,X23709)),tc_fun(X23709,tc_fun(tc_fun(tc_prod(X23710,X23709),tc_HOL_Obool),tc_HOL_Obool)),X23710),hAPP(c_COMBB(tc_prod(X23710,X23709),tc_fun(tc_fun(tc_prod(X23710,X23709),tc_HOL_Obool),tc_HOL_Obool),X23709),c_member(tc_prod(X23710,X23709)))),c_Product__Type_OPair(X23710,X23709)))),X23708) != hAPP(hAPP(c_COMBC(X23710,tc_fun(tc_prod(X23710,X23709),tc_HOL_Obool),tc_fun(X23709,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23709,tc_fun(tc_fun(tc_prod(X23710,X23709),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X23710,X23709),tc_HOL_Obool),tc_fun(X23709,tc_HOL_Obool)),X23710),c_COMBC(X23709,tc_fun(tc_prod(X23710,X23709),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23709,tc_prod(X23710,X23709)),tc_fun(X23709,tc_fun(tc_fun(tc_prod(X23710,X23709),tc_HOL_Obool),tc_HOL_Obool)),X23710),hAPP(c_COMBB(tc_prod(X23710,X23709),tc_fun(tc_fun(tc_prod(X23710,X23709),tc_HOL_Obool),tc_HOL_Obool),X23709),c_member(tc_prod(X23710,X23709)))),c_Product__Type_OPair(X23710,X23709)))),X23707)
| X23708 = X23707 )
& ( X23708 != X23707
| hAPP(hAPP(c_COMBC(X23710,tc_fun(tc_prod(X23710,X23709),tc_HOL_Obool),tc_fun(X23709,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23709,tc_fun(tc_fun(tc_prod(X23710,X23709),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X23710,X23709),tc_HOL_Obool),tc_fun(X23709,tc_HOL_Obool)),X23710),c_COMBC(X23709,tc_fun(tc_prod(X23710,X23709),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23709,tc_prod(X23710,X23709)),tc_fun(X23709,tc_fun(tc_fun(tc_prod(X23710,X23709),tc_HOL_Obool),tc_HOL_Obool)),X23710),hAPP(c_COMBB(tc_prod(X23710,X23709),tc_fun(tc_fun(tc_prod(X23710,X23709),tc_HOL_Obool),tc_HOL_Obool),X23709),c_member(tc_prod(X23710,X23709)))),c_Product__Type_OPair(X23710,X23709)))),X23708) = hAPP(hAPP(c_COMBC(X23710,tc_fun(tc_prod(X23710,X23709),tc_HOL_Obool),tc_fun(X23709,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23709,tc_fun(tc_fun(tc_prod(X23710,X23709),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X23710,X23709),tc_HOL_Obool),tc_fun(X23709,tc_HOL_Obool)),X23710),c_COMBC(X23709,tc_fun(tc_prod(X23710,X23709),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23709,tc_prod(X23710,X23709)),tc_fun(X23709,tc_fun(tc_fun(tc_prod(X23710,X23709),tc_HOL_Obool),tc_HOL_Obool)),X23710),hAPP(c_COMBB(tc_prod(X23710,X23709),tc_fun(tc_fun(tc_prod(X23710,X23709),tc_HOL_Obool),tc_HOL_Obool),X23709),c_member(tc_prod(X23710,X23709)))),c_Product__Type_OPair(X23710,X23709)))),X23707) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq2])]) ).
fof(i_0_6150,plain,
! [X29968,X29969,X29970,X29971,X29972,X29973] :
( ( X29968 = hAPP(hAPP(c_Product__Type_OPair(X29971,X29970),esk347_6(X29968,X29969,X29970,X29971,X29972,X29973)),esk348_6(X29968,X29969,X29970,X29971,X29972,X29973))
| ~ hBOOL(hAPP(hAPP(c_member(X29973),X29972),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29971,X29970,tc_fun(X29973,tc_HOL_Obool)),X29969),X29968))) )
& ( hBOOL(hAPP(hAPP(c_member(X29973),X29972),hAPP(hAPP(X29969,esk347_6(X29968,X29969,X29970,X29971,X29972,X29973)),esk348_6(X29968,X29969,X29970,X29971,X29972,X29973))))
| ~ hBOOL(hAPP(hAPP(c_member(X29973),X29972),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29971,X29970,tc_fun(X29973,tc_HOL_Obool)),X29969),X29968))) ) ),
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,
! [X32058,X32059,X32060,X32061,X32062,X32063,X32064,X32065] : hAPP(hAPP(c_List_Omap(tc_prod(X32065,X32064),X32063),X32062),hAPP(hAPP(c_List_Ozip(X32065,X32064),X32061),hAPP(hAPP(c_List_Omap(X32060,X32064),X32059),X32058))) = hAPP(hAPP(c_List_Omap(tc_prod(X32065,X32060),X32063),hAPP(c_Product__Type_Oprod_Oprod__case(X32065,X32060,X32063),hAPP(hAPP(c_COMBB(tc_fun(X32060,tc_prod(X32065,X32064)),tc_fun(X32060,X32063),X32065),hAPP(c_COMBB(tc_prod(X32065,X32064),X32063,X32060),X32062)),hAPP(hAPP(c_COMBC(X32065,tc_fun(X32060,X32064),tc_fun(X32060,tc_prod(X32065,X32064))),hAPP(hAPP(c_COMBB(tc_fun(X32064,tc_prod(X32065,X32064)),tc_fun(tc_fun(X32060,X32064),tc_fun(X32060,tc_prod(X32065,X32064))),X32065),c_COMBB(X32064,tc_prod(X32065,X32064),X32060)),c_Product__Type_OPair(X32065,X32064))),X32059)))),hAPP(hAPP(c_List_Ozip(X32065,X32060),X32061),X32058)),
inference(variable_rename,[status(thm)],[fact_map__zip__map2]) ).
fof(i_0_6152,plain,
! [X30834,X30835,X30836,X30837,X30838,X30839,X30840] :
( ( X30835 = hAPP(hAPP(X30838,X30834),esk390_7(X30834,X30835,X30836,X30837,X30838,X30839,X30840))
| ~ hBOOL(hAPP(hAPP(c_member(X30840),X30834),X30836))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X30840,X30839,X30838,X30837,X30836),X30835))
| ~ c_Finite__Set_Ofun__left__comm(X30840,X30839,X30838) )
& ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X30840,X30839,X30838,X30837,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30840,tc_HOL_Obool)),X30836),hAPP(hAPP(c_Set_Oinsert(X30840),X30834),c_Orderings_Obot__class_Obot(tc_fun(X30840,tc_HOL_Obool))))),esk390_7(X30834,X30835,X30836,X30837,X30838,X30839,X30840)))
| ~ hBOOL(hAPP(hAPP(c_member(X30840),X30834),X30836))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X30840,X30839,X30838,X30837,X30836),X30835))
| ~ c_Finite__Set_Ofun__left__comm(X30840,X30839,X30838) ) ),
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,
! [X31468,X31469,X31470,X31471,X31472,X31473,X31474] :
( ( X31468 = hAPP(hAPP(X31472,X31470),esk414_7(X31468,X31469,X31470,X31471,X31472,X31473,X31474))
| hBOOL(hAPP(hAPP(c_member(X31474),X31470),X31469))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X31474,X31473,X31472,X31471,hAPP(hAPP(c_Set_Oinsert(X31474),X31470),X31469)),X31468))
| ~ c_Finite__Set_Ofun__left__comm(X31474,X31473,X31472) )
& ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X31474,X31473,X31472,X31471,X31469),esk414_7(X31468,X31469,X31470,X31471,X31472,X31473,X31474)))
| hBOOL(hAPP(hAPP(c_member(X31474),X31470),X31469))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X31474,X31473,X31472,X31471,hAPP(hAPP(c_Set_Oinsert(X31474),X31470),X31469)),X31468))
| ~ c_Finite__Set_Ofun__left__comm(X31474,X31473,X31472) ) ),
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,
! [X31813,X31814,X31815,X31816,X31817] : c_Map_Omap__of(X31817,X31816,hAPP(hAPP(c_List_Omap(tc_prod(X31817,X31815),tc_prod(X31817,X31816)),hAPP(c_Product__Type_Oprod_Oprod__case(X31817,X31815,tc_prod(X31817,X31816)),hAPP(hAPP(c_COMBC(X31817,tc_fun(X31815,X31816),tc_fun(X31815,tc_prod(X31817,X31816))),hAPP(hAPP(c_COMBB(tc_fun(X31816,tc_prod(X31817,X31816)),tc_fun(tc_fun(X31815,X31816),tc_fun(X31815,tc_prod(X31817,X31816))),X31817),c_COMBB(X31816,tc_prod(X31817,X31816),X31815)),c_Product__Type_OPair(X31817,X31816))),X31814))),X31813)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(X31815),tc_Option_Ooption(X31816),X31817,hAPP(c_Option_Omap(X31815,X31816),X31814)),c_Map_Omap__of(X31817,X31815,X31813)),
inference(variable_rename,[status(thm)],[fact_map__of__map]) ).
fof(i_0_6155,plain,
! [X32915,X32916,X32917,X32918,X32919] : hAPP(hAPP(c_List_Ozip(X32919,X32918),hAPP(hAPP(c_List_Olist_OCons(X32919),X32917),X32916)),X32915) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X32919,X32918)),X32918,c_List_Olist_ONil(tc_prod(X32919,X32918)),hAPP(hAPP(c_COMBC(X32918,tc_fun(tc_List_Olist(X32918),tc_List_Olist(tc_prod(X32919,X32918))),tc_fun(tc_List_Olist(X32918),tc_List_Olist(tc_prod(X32919,X32918)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X32919,X32918)),tc_List_Olist(tc_prod(X32919,X32918))),tc_fun(tc_fun(tc_List_Olist(X32918),tc_List_Olist(tc_prod(X32919,X32918))),tc_fun(tc_List_Olist(X32918),tc_List_Olist(tc_prod(X32919,X32918)))),X32918),c_COMBB(tc_List_Olist(tc_prod(X32919,X32918)),tc_List_Olist(tc_prod(X32919,X32918)),tc_List_Olist(X32918))),hAPP(hAPP(c_COMBB(tc_prod(X32919,X32918),tc_fun(tc_List_Olist(tc_prod(X32919,X32918)),tc_List_Olist(tc_prod(X32919,X32918))),X32918),c_List_Olist_OCons(tc_prod(X32919,X32918))),hAPP(c_Product__Type_OPair(X32919,X32918),X32917)))),hAPP(c_List_Ozip(X32919,X32918),X32916))),X32915),
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,
! [X29889,X29890,X29891,X29892] :
( ( hBOOL(hAPP(hAPP(c_member(X29892),esk329_4(X29889,X29890,X29891,X29892)),X29891))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29890),hAPP(c_Set_Oimage(X29892,X29890,X29889),X29891)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29892),X29891)) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29892),hAPP(c_Set_OCollect(X29892),hAPP(hAPP(c_COMBS(X29892,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29892),c_fconj),hAPP(hAPP(c_COMBC(X29892,tc_fun(X29892,tc_HOL_Obool),tc_HOL_Obool),c_member(X29892)),X29891))),hAPP(hAPP(c_COMBC(X29892,X29890,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X29890,tc_fun(X29890,tc_HOL_Obool),X29892),c_fequal),X29889)),hAPP(X29889,esk329_4(X29889,X29890,X29891,X29892)))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29890),hAPP(c_Set_Oimage(X29892,X29890,X29889),X29891)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29892),X29891)) ) ),
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,
! [X29661,X29662,X29663,X29664] :
( ( hBOOL(hAPP(X29664,esk320_4(X29661,X29662,X29663,X29664)))
| c_Wellfounded_Owf(X29661,hAPP(c_Set_OCollect(tc_prod(X29661,X29661)),hAPP(c_Product__Type_Oprod_Oprod__case(X29661,X29661,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X29661,tc_HOL_Obool),tc_fun(X29661,tc_HOL_Obool),X29661),hAPP(c_COMBS(X29661,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29661),c_fconj),X29664))),hAPP(hAPP(c_COMBC(X29661,tc_fun(X29661,X29661),tc_fun(X29661,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29661,tc_HOL_Obool),tc_fun(tc_fun(X29661,X29661),tc_fun(X29661,tc_HOL_Obool)),X29661),c_COMBB(X29661,tc_HOL_Obool,X29661)),c_fequal)),X29662))))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X29663,hAPP(X29662,esk320_4(X29661,X29662,X29663,X29664)))),hAPP(X29663,esk320_4(X29661,X29662,X29663,X29664))))
| c_Wellfounded_Owf(X29661,hAPP(c_Set_OCollect(tc_prod(X29661,X29661)),hAPP(c_Product__Type_Oprod_Oprod__case(X29661,X29661,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X29661,tc_HOL_Obool),tc_fun(X29661,tc_HOL_Obool),X29661),hAPP(c_COMBS(X29661,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29661),c_fconj),X29664))),hAPP(hAPP(c_COMBC(X29661,tc_fun(X29661,X29661),tc_fun(X29661,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29661,tc_HOL_Obool),tc_fun(tc_fun(X29661,X29661),tc_fun(X29661,tc_HOL_Obool)),X29661),c_COMBB(X29661,tc_HOL_Obool,X29661)),c_fequal)),X29662))))) ) ),
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,
! [X29534,X29535,X29536] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29536,X29536),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X29536,X29536,X29536),X29535),X29534)),X29535))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X29536,tc_HOL_Obool),tc_fun(X29536,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X29536,tc_HOL_Obool),tc_fun(X29536,tc_HOL_Obool),tc_fun(X29536,tc_HOL_Obool)),c_Wellfounded_Omax__ext(X29536,X29535)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X29536,tc_HOL_Obool),tc_fun(X29536,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(X29536,X29534)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X29536,tc_HOL_Obool),tc_fun(X29536,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X29536,tc_HOL_Obool),tc_fun(X29536,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X29536,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X29536,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X29536,tc_HOL_Obool),tc_fun(X29536,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(X29536,X29535))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ext__compat])]) ).
fof(i_0_6163,plain,
! [X29537,X29538,X29539] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29539,X29539),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X29539,X29539,X29539),X29538),X29537)),X29538))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X29539,tc_HOL_Obool),tc_fun(X29539,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X29539,tc_HOL_Obool),tc_fun(X29539,tc_HOL_Obool),tc_fun(X29539,tc_HOL_Obool)),c_Wellfounded_Omin__ext(X29539,X29538)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X29539,tc_HOL_Obool),tc_fun(X29539,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(X29539,X29537)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X29539,tc_HOL_Obool),tc_fun(X29539,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X29539,tc_HOL_Obool),tc_fun(X29539,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X29539,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X29539,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X29539,tc_HOL_Obool),tc_fun(X29539,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(X29539,X29538))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__ext__compat])]) ).
fof(i_0_6164,plain,
! [X27990,X27991,X27992,X27993,X27994,X27995,X27996] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X27996,X27995,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X27996)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X27996),c_Hoare__Mirabelle_Opeek__and(X27996,X27994,X27993)),X27992),X27991)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X27996),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X27996,X27995,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X27996)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X27996),c_Hoare__Mirabelle_Opeek__and(X27996,X27994,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X27993))),X27990),X27991)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X27996),tc_HOL_Obool))))
| c_Hoare__Mirabelle_Ohoare__derivs(X27996,X27995,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X27996)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X27996),X27994),c_Com_Ocom_OCond(X27993,X27992,X27990)),X27991)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X27996),tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hoare__derivs_OIf])]) ).
cnf(i_0_6165,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)))),esk495_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5240]) ).
cnf(i_0_6166,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)))),esk494_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_5241]) ).
fof(i_0_6167,plain,
! [X29252,X29253,X29254,X29255,X29256] :
( ~ class_Groups_Ocomm__monoid__add(X29256)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29255),X29254))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29255,X29256),X29253),hAPP(c_Set_OCollect(X29255),hAPP(hAPP(c_COMBS(X29255,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29255),c_fconj),hAPP(hAPP(c_COMBC(X29255,tc_fun(X29255,tc_HOL_Obool),tc_HOL_Obool),c_member(X29255)),X29254))),hAPP(hAPP(c_COMBC(X29255,tc_fun(X29255,tc_HOL_Obool),tc_HOL_Obool),c_member(X29255)),X29252)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29255,X29256),hAPP(hAPP(c_COMBC(X29255,X29256,X29256),hAPP(hAPP(c_COMBS(X29255,X29256,tc_fun(X29256,X29256)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X29256,tc_fun(X29256,X29256)),X29255),c_If(X29256)),hAPP(hAPP(c_COMBC(X29255,tc_fun(X29255,tc_HOL_Obool),tc_HOL_Obool),c_member(X29255)),X29252))),X29253)),c_Groups_Ozero__class_Ozero(X29256))),X29254) ),
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,
! [X32088,X32089,X32090,X32091,X32092,X32093,X32094,X32095] : hAPP(hAPP(c_List_Ozip(X32095,X32094),hAPP(hAPP(c_List_Omap(X32093,X32095),X32092),X32091)),hAPP(hAPP(c_List_Omap(X32090,X32094),X32089),X32088)) = hAPP(hAPP(c_List_Omap(tc_prod(X32093,X32090),tc_prod(X32095,X32094)),hAPP(c_Product__Type_Oprod_Oprod__case(X32093,X32090,tc_prod(X32095,X32094)),hAPP(hAPP(c_COMBC(X32093,tc_fun(X32090,X32094),tc_fun(X32090,tc_prod(X32095,X32094))),hAPP(hAPP(c_COMBB(tc_fun(X32094,tc_prod(X32095,X32094)),tc_fun(tc_fun(X32090,X32094),tc_fun(X32090,tc_prod(X32095,X32094))),X32093),c_COMBB(X32094,tc_prod(X32095,X32094),X32090)),hAPP(hAPP(c_COMBB(X32095,tc_fun(X32094,tc_prod(X32095,X32094)),X32093),c_Product__Type_OPair(X32095,X32094)),X32092))),X32089))),hAPP(hAPP(c_List_Ozip(X32093,X32090),X32091),X32088)),
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,
! [X29318] : c_Wellfounded_Ofinite__psubset(X29318) = hAPP(c_Set_OCollect(tc_prod(tc_fun(X29318,tc_HOL_Obool),tc_fun(X29318,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(X29318,tc_HOL_Obool),tc_fun(X29318,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X29318,tc_HOL_Obool),tc_fun(tc_fun(X29318,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X29318,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29318,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X29318,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X29318,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X29318,tc_HOL_Obool)),c_COMBS(tc_fun(X29318,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29318,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X29318,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X29318,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X29318,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(X29318,tc_HOL_Obool))))),c_Finite__Set_Ofinite(X29318)))),
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,
! [X32235,X32236] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32236),X32235))
| c_Nitpick_Ocard_H(X32236,X32235) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32236)),c_Hilbert__Choice_OEps(tc_List_Olist(X32236),hAPP(hAPP(c_COMBS(tc_List_Olist(X32236),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X32236)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X32236),tc_fun(X32236,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X32236,tc_HOL_Obool),tc_fun(tc_fun(X32236,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X32236)),c_fequal),c_List_Oset(X32236))),X32235))),c_List_Odistinct(X32236)))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X32236),X32235))
| c_Nitpick_Ocard_H(X32236,X32235) = 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,
! [X29119,X29120] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29120))
| 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)),X29120))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X29119)))) = 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)),X29120))),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,X29119))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5250])]) ).
fof(i_0_6179,plain,
! [X28923,X28924,X28925,X28926,X28927,X28928,X28929,X28930,X28931] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28931,X28930)),hAPP(hAPP(c_Product__Type_OPair(X28931,X28930),X28929),X28928)),X28927))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X28926,X28925)),hAPP(hAPP(c_Product__Type_OPair(X28926,X28925),hAPP(X28924,X28929)),hAPP(X28923,X28928))),hAPP(c_Set_Oimage(tc_prod(X28931,X28930),tc_prod(X28926,X28925),c_Product__Type_Omap__pair(X28931,X28926,X28930,X28925,X28924,X28923)),X28927))) ),
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,
! [X22959,X22960,X22961,X22962,X22963,X22964,X22965] : c_New__Random__Sequence_Oneg__decr__bind(X22965,X22964,X22963,X22962,X22961,X22960,X22959) = c_New__DSequence_Oneg__decr__bind(X22965,X22964,hAPP(hAPP(hAPP(X22963,X22961),X22960),X22959),hAPP(hAPP(c_COMBC(X22965,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(X22964)))),hAPP(hAPP(c_COMBC(X22965,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(X22964))))),hAPP(hAPP(c_COMBC(X22965,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(X22964)))))),X22962),X22961)),X22960)),X22959)),
inference(variable_rename,[status(thm)],[fact_New__Random__Sequence_Oneg__decr__bind__def]) ).
fof(i_0_6183,plain,
! [X31138,X31139,X31140,X31141] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31141,tc_fun(X31140,tc_HOL_Obool)),X31139),X31138) = hAPP(c_Set_OCollect(X31140),hAPP(hAPP(c_COMBB(tc_fun(X31141,tc_HOL_Obool),tc_HOL_Obool,X31140),c_HOL_OAll(X31141)),hAPP(hAPP(c_COMBB(tc_fun(X31141,tc_HOL_Obool),tc_fun(X31141,tc_HOL_Obool),X31140),hAPP(c_COMBS(X31141,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X31141),c_fimplies),hAPP(hAPP(c_COMBC(X31141,tc_fun(X31141,tc_HOL_Obool),tc_HOL_Obool),c_member(X31141)),X31139)))),hAPP(hAPP(c_COMBC(X31140,tc_fun(X31141,tc_fun(X31140,tc_HOL_Obool)),tc_fun(X31141,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X31140,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X31141,tc_fun(X31140,tc_HOL_Obool)),tc_fun(X31141,tc_HOL_Obool)),X31140),c_COMBB(tc_fun(X31140,tc_HOL_Obool),tc_HOL_Obool,X31141)),c_member(X31140))),X31138)))),
inference(variable_rename,[status(thm)],[fact_INTER__def]) ).
fof(i_0_6184,plain,
! [X29915,X29916,X29917,X29918,X29919,X29920,X29921,X29922,X29923] :
( ( ~ c_Equiv__Relations_Ocongruent(X29918,X29917,X29916,X29915)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29918,X29918)),X29919),X29916))
| hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29918,X29918,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X29918,tc_fun(X29918,X29917),tc_fun(X29918,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29917,tc_HOL_Obool),tc_fun(tc_fun(X29918,X29917),tc_fun(X29918,tc_HOL_Obool)),X29918),c_COMBB(X29917,tc_HOL_Obool,X29918)),hAPP(hAPP(c_COMBB(X29917,tc_fun(X29917,tc_HOL_Obool),X29918),c_fequal),X29915))),X29915)),X29919)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29923,X29923)),esk333_4(X29920,X29921,X29922,X29923)),X29921))
| c_Equiv__Relations_Ocongruent(X29923,X29922,X29921,X29920) )
& ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29923,X29923,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X29923,tc_fun(X29923,X29922),tc_fun(X29923,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29922,tc_HOL_Obool),tc_fun(tc_fun(X29923,X29922),tc_fun(X29923,tc_HOL_Obool)),X29923),c_COMBB(X29922,tc_HOL_Obool,X29923)),hAPP(hAPP(c_COMBB(X29922,tc_fun(X29922,tc_HOL_Obool),X29923),c_fequal),X29920))),X29920)),esk333_4(X29920,X29921,X29922,X29923)))
| c_Equiv__Relations_Ocongruent(X29923,X29922,X29921,X29920) ) ),
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,
! [X29342,X29343,X29344,X29345,X29346] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29343),hAPP(c_Set_OCollect(X29343),hAPP(hAPP(c_COMBB(tc_fun(X29345,tc_HOL_Obool),tc_HOL_Obool,X29343),c_HOL_OEx(X29345)),hAPP(hAPP(c_COMBB(tc_fun(X29345,tc_HOL_Obool),tc_fun(X29345,tc_HOL_Obool),X29343),hAPP(c_COMBS(X29345,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29345),c_fconj),X29344))),X29342)))))
| ~ hBOOL(hAPP(X29344,X29346))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29343),hAPP(c_Set_OCollect(X29343),hAPP(hAPP(c_COMBC(X29343,X29345,tc_HOL_Obool),X29342),X29346))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29345),hAPP(c_Set_OCollect(X29345),X29344))) )
& ( hBOOL(hAPP(X29344,esk312_4(X29342,X29343,X29344,X29345)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29343),hAPP(c_Set_OCollect(X29343),hAPP(hAPP(c_COMBB(tc_fun(X29345,tc_HOL_Obool),tc_HOL_Obool,X29343),c_HOL_OEx(X29345)),hAPP(hAPP(c_COMBB(tc_fun(X29345,tc_HOL_Obool),tc_fun(X29345,tc_HOL_Obool),X29343),hAPP(c_COMBS(X29345,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29345),c_fconj),X29344))),X29342)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29345),hAPP(c_Set_OCollect(X29345),X29344))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29343),hAPP(c_Set_OCollect(X29343),hAPP(hAPP(c_COMBC(X29343,X29345,tc_HOL_Obool),X29342),esk312_4(X29342,X29343,X29344,X29345)))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29343),hAPP(c_Set_OCollect(X29343),hAPP(hAPP(c_COMBB(tc_fun(X29345,tc_HOL_Obool),tc_HOL_Obool,X29343),c_HOL_OEx(X29345)),hAPP(hAPP(c_COMBB(tc_fun(X29345,tc_HOL_Obool),tc_fun(X29345,tc_HOL_Obool),X29343),hAPP(c_COMBS(X29345,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29345),c_fconj),X29344))),X29342)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29345),hAPP(c_Set_OCollect(X29345),X29344))) ) ),
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,
! [X28884,X28885,X28886,X28887,X28888,X28889] :
( ( hBOOL(hAPP(hAPP(c_member(X28888),esk290_6(X28884,X28885,X28886,X28887,X28888,X28889)),X28887))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28888,X28889),hAPP(hAPP(c_COMBS(X28888,tc_fun(X28886,tc_HOL_Obool),X28889),hAPP(hAPP(c_COMBB(tc_fun(X28886,X28889),tc_fun(tc_fun(X28886,tc_HOL_Obool),X28889),X28888),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28886,X28889)),X28884)),X28885)),X28887) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X28888,X28886),X28889),hAPP(c_Product__Type_Oprod_Oprod__case(X28888,X28886,X28889),X28884)),hAPP(hAPP(c_Product__Type_OSigma(X28888,X28886),X28887),X28885))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28888),X28887))
| ~ class_Groups_Ocomm__monoid__add(X28889) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28886),hAPP(X28885,esk290_6(X28884,X28885,X28886,X28887,X28888,X28889))))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28888,X28889),hAPP(hAPP(c_COMBS(X28888,tc_fun(X28886,tc_HOL_Obool),X28889),hAPP(hAPP(c_COMBB(tc_fun(X28886,X28889),tc_fun(tc_fun(X28886,tc_HOL_Obool),X28889),X28888),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28886,X28889)),X28884)),X28885)),X28887) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X28888,X28886),X28889),hAPP(c_Product__Type_Oprod_Oprod__case(X28888,X28886,X28889),X28884)),hAPP(hAPP(c_Product__Type_OSigma(X28888,X28886),X28887),X28885))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28888),X28887))
| ~ class_Groups_Ocomm__monoid__add(X28889) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Sigma])])])]) ).
fof(i_0_6187,plain,
! [X28877,X28878,X28879,X28880,X28881,X28882] :
( ( hBOOL(hAPP(hAPP(c_member(X28881),esk289_6(X28877,X28878,X28879,X28880,X28881,X28882)),X28880))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28881,X28882),hAPP(hAPP(c_COMBS(X28881,tc_fun(X28879,tc_HOL_Obool),X28882),hAPP(hAPP(c_COMBB(tc_fun(X28879,X28882),tc_fun(tc_fun(X28879,tc_HOL_Obool),X28882),X28881),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28879,X28882)),X28877)),X28878)),X28880) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X28881,X28879),X28882),hAPP(c_Product__Type_Oprod_Oprod__case(X28881,X28879,X28882),X28877)),hAPP(hAPP(c_Product__Type_OSigma(X28881,X28879),X28880),X28878))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28881),X28880))
| ~ class_Groups_Ocomm__monoid__mult(X28882) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28879),hAPP(X28878,esk289_6(X28877,X28878,X28879,X28880,X28881,X28882))))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28881,X28882),hAPP(hAPP(c_COMBS(X28881,tc_fun(X28879,tc_HOL_Obool),X28882),hAPP(hAPP(c_COMBB(tc_fun(X28879,X28882),tc_fun(tc_fun(X28879,tc_HOL_Obool),X28882),X28881),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28879,X28882)),X28877)),X28878)),X28880) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X28881,X28879),X28882),hAPP(c_Product__Type_Oprod_Oprod__case(X28881,X28879,X28882),X28877)),hAPP(hAPP(c_Product__Type_OSigma(X28881,X28879),X28880),X28878))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28881),X28880))
| ~ class_Groups_Ocomm__monoid__mult(X28882) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__Sigma])])])]) ).
fof(i_0_6188,plain,
! [X27347,X27348,X27349,X27350,X27351] :
( ~ class_Groups_Ocomm__monoid__add(X27351)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27350),X27349))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27350,X27351),X27348),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27350,tc_HOL_Obool)),X27349),X27347)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27350,X27351),hAPP(hAPP(c_COMBC(X27350,X27351,X27351),hAPP(hAPP(c_COMBS(X27350,X27351,tc_fun(X27351,X27351)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X27351,tc_fun(X27351,X27351)),X27350),c_If(X27351)),hAPP(hAPP(c_COMBC(X27350,tc_fun(X27350,tc_HOL_Obool),tc_HOL_Obool),c_member(X27350)),X27347))),X27348)),c_Groups_Ozero__class_Ozero(X27351))),X27349) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__restrict__set])]) ).
fof(i_0_6189,plain,
! [X28505,X28506,X28507,X28508,X28509,X28510] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X28510),X28507),X28508))
| hAPP(c_Set_Ovimage(X28506,X28510,hAPP(hAPP(c_COMBC(X28506,X28510,X28510),hAPP(hAPP(c_COMBC(X28506,X28510,tc_fun(X28510,X28510)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X28510,tc_fun(X28510,X28510)),X28506),c_If(X28510)),hAPP(hAPP(c_COMBC(X28506,tc_fun(X28506,tc_HOL_Obool),tc_HOL_Obool),c_member(X28506)),X28505))),X28509)),X28507)),X28508) = c_Orderings_Otop__class_Otop(tc_fun(X28506,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X28510),X28509),X28508)) )
& ( hBOOL(hAPP(hAPP(c_member(X28510),X28507),X28508))
| hAPP(c_Set_Ovimage(X28506,X28510,hAPP(hAPP(c_COMBC(X28506,X28510,X28510),hAPP(hAPP(c_COMBC(X28506,X28510,tc_fun(X28510,X28510)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X28510,tc_fun(X28510,X28510)),X28506),c_If(X28510)),hAPP(hAPP(c_COMBC(X28506,tc_fun(X28506,tc_HOL_Obool),tc_HOL_Obool),c_member(X28506)),X28505))),X28509)),X28507)),X28508) = X28505
| ~ hBOOL(hAPP(hAPP(c_member(X28510),X28509),X28508)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X28510),X28507),X28508))
| hAPP(c_Set_Ovimage(X28506,X28510,hAPP(hAPP(c_COMBC(X28506,X28510,X28510),hAPP(hAPP(c_COMBC(X28506,X28510,tc_fun(X28510,X28510)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X28510,tc_fun(X28510,X28510)),X28506),c_If(X28510)),hAPP(hAPP(c_COMBC(X28506,tc_fun(X28506,tc_HOL_Obool),tc_HOL_Obool),c_member(X28506)),X28505))),X28509)),X28507)),X28508) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28506,tc_HOL_Obool)),X28505)
| hBOOL(hAPP(hAPP(c_member(X28510),X28509),X28508)) )
& ( hBOOL(hAPP(hAPP(c_member(X28510),X28507),X28508))
| hAPP(c_Set_Ovimage(X28506,X28510,hAPP(hAPP(c_COMBC(X28506,X28510,X28510),hAPP(hAPP(c_COMBC(X28506,X28510,tc_fun(X28510,X28510)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X28510,tc_fun(X28510,X28510)),X28506),c_If(X28510)),hAPP(hAPP(c_COMBC(X28506,tc_fun(X28506,tc_HOL_Obool),tc_HOL_Obool),c_member(X28506)),X28505))),X28509)),X28507)),X28508) = c_Orderings_Obot__class_Obot(tc_fun(X28506,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X28510),X28509),X28508)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5253])])]) ).
fof(i_0_6190,plain,
! [X28322,X28323,X28324,X28325] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28325,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X28325,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk270_4(X28322,X28323,X28324,X28325))),X28324)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X28325,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),esk270_4(X28322,X28323,X28324,X28325)),X28323))),X28322)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28325,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X28325,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X28324)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X28325,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X28322))) ),
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,
! [X22946,X22947,X22948,X22949,X22950,X22951,X22952] : c_New__Random__Sequence_Opos__decr__bind(X22952,X22951,X22950,X22949,X22948,X22947,X22946) = c_New__DSequence_Opos__decr__bind(X22952,X22951,hAPP(hAPP(hAPP(X22950,X22948),X22947),X22946),hAPP(hAPP(c_COMBC(X22952,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X22951))),hAPP(hAPP(c_COMBC(X22952,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(X22951)))),hAPP(hAPP(c_COMBC(X22952,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(X22951))))),X22949),X22948)),X22947)),X22946)),
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,
! [X28592,X28593,X28594,X28595,X28596,X28597] : hAPP(c_Set_Oimage(X28597,tc_prod(X28596,X28595),hAPP(hAPP(c_COMBS(X28597,X28595,tc_prod(X28596,X28595)),hAPP(hAPP(c_COMBB(X28596,tc_fun(X28595,tc_prod(X28596,X28595)),X28597),c_Product__Type_OPair(X28596,X28595)),X28594)),X28593)),X28592) = hAPP(hAPP(c_Product__Type_OSigma(X28596,X28595),hAPP(c_Set_Oimage(X28597,X28596,X28594),X28592)),hAPP(hAPP(c_COMBB(tc_fun(X28597,tc_HOL_Obool),tc_fun(X28595,tc_HOL_Obool),X28596),c_Set_Oimage(X28597,X28595,X28593)),hAPP(hAPP(c_COMBC(X28596,tc_fun(X28597,tc_HOL_Obool),tc_fun(X28597,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28597,tc_HOL_Obool),tc_fun(tc_fun(X28597,tc_HOL_Obool),tc_fun(X28597,tc_HOL_Obool)),X28596),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28597,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X28596,tc_HOL_Obool),tc_fun(X28597,tc_HOL_Obool),X28596),c_Set_Ovimage(X28597,X28596,X28594)),hAPP(hAPP(c_COMBC(X28596,tc_fun(X28596,tc_HOL_Obool),tc_fun(X28596,tc_HOL_Obool)),c_Set_Oinsert(X28596)),c_Orderings_Obot__class_Obot(tc_fun(X28596,tc_HOL_Obool)))))),X28592))),
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,
! [X31263,X31264] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31264)
| c_Complete__Lattice_OSup__class_OSup(X31264,X31263) = c_Complete__Lattice_OInf__class_OInf(X31264,hAPP(c_Set_OCollect(X31264),hAPP(hAPP(c_COMBB(tc_fun(X31264,tc_HOL_Obool),tc_HOL_Obool,X31264),c_HOL_OAll(X31264)),hAPP(hAPP(c_COMBB(tc_fun(X31264,tc_HOL_Obool),tc_fun(X31264,tc_HOL_Obool),X31264),hAPP(c_COMBS(X31264,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X31264),c_fimplies),hAPP(hAPP(c_COMBC(X31264,tc_fun(X31264,tc_HOL_Obool),tc_HOL_Obool),c_member(X31264)),X31263)))),hAPP(c_COMBC(X31264,X31264,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X31264)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__Inf])]) ).
fof(i_0_6201,plain,
! [X27535,X27536,X27537,X27538,X27539,X27540] :
( ( hBOOL(hAPP(hAPP(c_member(X27539),esk253_6(X27535,X27536,X27537,X27538,X27539,X27540)),X27538))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27539,X27540),X27537),X27538) != X27536
| ~ hBOOL(hAPP(hAPP(c_member(X27539),X27535),X27538))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27540),hAPP(X27537,X27535)),X27536))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27539),X27538))
| ~ class_Groups_Oordered__ab__group__add(X27540) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27540),c_Groups_Ozero__class_Ozero(X27540)),hAPP(X27537,esk253_6(X27535,X27536,X27537,X27538,X27539,X27540))))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27539,X27540),X27537),X27538) != X27536
| ~ hBOOL(hAPP(hAPP(c_member(X27539),X27535),X27538))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27540),hAPP(X27537,X27535)),X27536))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27539),X27538))
| ~ class_Groups_Oordered__ab__group__add(X27540) ) ),
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,
! [X25560,X25561,X25562,X25563,X25564,X25565] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25564),X25562),X25563))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25564,X25565),hAPP(hAPP(c_COMBC(X25564,X25565,X25565),hAPP(hAPP(c_COMBS(X25564,X25565,tc_fun(X25565,X25565)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X25565,tc_fun(X25565,X25565)),X25564),c_If(X25565)),hAPP(hAPP(c_COMBC(X25564,X25564,tc_HOL_Obool),c_fequal),X25562))),X25561)),X25560)),X25563) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25565),hAPP(X25561,X25562)),hAPP(hAPP(c_Power_Opower__class_Opower(X25565),X25560),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25564),X25563)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25564),X25563))
| ~ class_Groups_Ocomm__monoid__mult(X25565) )
& ( hBOOL(hAPP(hAPP(c_member(X25564),X25562),X25563))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25564,X25565),hAPP(hAPP(c_COMBC(X25564,X25565,X25565),hAPP(hAPP(c_COMBS(X25564,X25565,tc_fun(X25565,X25565)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X25565,tc_fun(X25565,X25565)),X25564),c_If(X25565)),hAPP(hAPP(c_COMBC(X25564,X25564,tc_HOL_Obool),c_fequal),X25562))),X25561)),X25560)),X25563) = hAPP(hAPP(c_Power_Opower__class_Opower(X25565),X25560),hAPP(c_Finite__Set_Ocard(X25564),X25563))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25564),X25563))
| ~ class_Groups_Ocomm__monoid__mult(X25565) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5261])])]) ).
fof(i_0_6203,plain,
! [X27284,X27285,X27286,X27287,X27288] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X27287),X27285),X27286))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27287,X27288),hAPP(hAPP(c_COMBC(X27287,X27288,X27288),hAPP(hAPP(c_COMBS(X27287,X27288,tc_fun(X27288,X27288)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X27288,tc_fun(X27288,X27288)),X27287),c_If(X27288)),hAPP(hAPP(c_COMBC(X27287,X27287,tc_HOL_Obool),c_fequal),X27285))),X27284)),c_Groups_Ozero__class_Ozero(X27288))),X27286) = hAPP(X27284,X27285)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27287),X27286))
| ~ class_Groups_Ocomm__monoid__add(X27288) )
& ( hBOOL(hAPP(hAPP(c_member(X27287),X27285),X27286))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27287,X27288),hAPP(hAPP(c_COMBC(X27287,X27288,X27288),hAPP(hAPP(c_COMBS(X27287,X27288,tc_fun(X27288,X27288)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X27288,tc_fun(X27288,X27288)),X27287),c_If(X27288)),hAPP(hAPP(c_COMBC(X27287,X27287,tc_HOL_Obool),c_fequal),X27285))),X27284)),c_Groups_Ozero__class_Ozero(X27288))),X27286) = c_Groups_Ozero__class_Ozero(X27288)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27287),X27286))
| ~ class_Groups_Ocomm__monoid__add(X27288) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5262])])]) ).
fof(i_0_6204,plain,
! [X25696,X25697,X25698,X25699,X25700] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25699),X25697),X25698))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25699,X25700),hAPP(hAPP(c_COMBC(X25699,X25700,X25700),hAPP(hAPP(c_COMBS(X25699,X25700,tc_fun(X25700,X25700)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X25700,tc_fun(X25700,X25700)),X25699),c_If(X25700)),hAPP(hAPP(c_COMBC(X25699,X25699,tc_HOL_Obool),c_fequal),X25697))),X25696)),c_Groups_Oone__class_Oone(X25700))),X25698) = hAPP(X25696,X25697)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25699),X25698))
| ~ class_Groups_Ocomm__monoid__mult(X25700) )
& ( hBOOL(hAPP(hAPP(c_member(X25699),X25697),X25698))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25699,X25700),hAPP(hAPP(c_COMBC(X25699,X25700,X25700),hAPP(hAPP(c_COMBS(X25699,X25700,tc_fun(X25700,X25700)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X25700,tc_fun(X25700,X25700)),X25699),c_If(X25700)),hAPP(hAPP(c_COMBC(X25699,X25699,tc_HOL_Obool),c_fequal),X25697))),X25696)),c_Groups_Oone__class_Oone(X25700))),X25698) = c_Groups_Oone__class_Oone(X25700)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25699),X25698))
| ~ class_Groups_Ocomm__monoid__mult(X25700) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5263])])]) ).
fof(i_0_6205,plain,
! [X31265,X31266] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31266)
| c_Complete__Lattice_OInf__class_OInf(X31266,X31265) = c_Complete__Lattice_OSup__class_OSup(X31266,hAPP(c_Set_OCollect(X31266),hAPP(hAPP(c_COMBB(tc_fun(X31266,tc_HOL_Obool),tc_HOL_Obool,X31266),c_HOL_OAll(X31266)),hAPP(hAPP(c_COMBB(tc_fun(X31266,tc_HOL_Obool),tc_fun(X31266,tc_HOL_Obool),X31266),hAPP(c_COMBS(X31266,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X31266),c_fimplies),hAPP(hAPP(c_COMBC(X31266,tc_fun(X31266,tc_HOL_Obool),tc_HOL_Obool),c_member(X31266)),X31265)))),c_Orderings_Oord__class_Oless__eq(X31266))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__Sup])]) ).
fof(i_0_6206,plain,
! [X26059,X26060,X26061,X26062,X26063,X26064,X26065] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26065,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26064,tc_fun(X26065,tc_HOL_Obool)),X26063),X26062)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26061,tc_fun(X26065,tc_HOL_Obool)),X26060),X26059)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26064,tc_fun(X26065,tc_HOL_Obool)),X26063),hAPP(hAPP(c_COMBB(tc_fun(X26061,tc_fun(X26065,tc_HOL_Obool)),tc_fun(X26065,tc_HOL_Obool),X26064),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26061,tc_fun(X26065,tc_HOL_Obool)),X26060)),hAPP(hAPP(c_COMBC(X26064,tc_fun(X26061,tc_fun(X26065,tc_HOL_Obool)),tc_fun(X26061,tc_fun(X26065,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X26065,tc_HOL_Obool),tc_fun(X26065,tc_HOL_Obool)),tc_fun(tc_fun(X26061,tc_fun(X26065,tc_HOL_Obool)),tc_fun(X26061,tc_fun(X26065,tc_HOL_Obool))),X26064),c_COMBB(tc_fun(X26065,tc_HOL_Obool),tc_fun(X26065,tc_HOL_Obool),X26061)),hAPP(hAPP(c_COMBB(tc_fun(X26065,tc_HOL_Obool),tc_fun(tc_fun(X26065,tc_HOL_Obool),tc_fun(X26065,tc_HOL_Obool)),X26064),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26065,tc_HOL_Obool))),X26062))),X26059))),
inference(variable_rename,[status(thm)],[fact_Int__UN__distrib2]) ).
fof(i_0_6207,plain,
! [X31116,X31117,X31118,X31119,X31120,X31121,X31122] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31122,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31121,tc_fun(X31122,tc_HOL_Obool)),X31120),X31119)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31118,tc_fun(X31122,tc_HOL_Obool)),X31117),X31116)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31121,tc_fun(X31122,tc_HOL_Obool)),X31120),hAPP(hAPP(c_COMBB(tc_fun(X31118,tc_fun(X31122,tc_HOL_Obool)),tc_fun(X31122,tc_HOL_Obool),X31121),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31118,tc_fun(X31122,tc_HOL_Obool)),X31117)),hAPP(hAPP(c_COMBC(X31121,tc_fun(X31118,tc_fun(X31122,tc_HOL_Obool)),tc_fun(X31118,tc_fun(X31122,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X31122,tc_HOL_Obool),tc_fun(X31122,tc_HOL_Obool)),tc_fun(tc_fun(X31118,tc_fun(X31122,tc_HOL_Obool)),tc_fun(X31118,tc_fun(X31122,tc_HOL_Obool))),X31121),c_COMBB(tc_fun(X31122,tc_HOL_Obool),tc_fun(X31122,tc_HOL_Obool),X31118)),hAPP(hAPP(c_COMBB(tc_fun(X31122,tc_HOL_Obool),tc_fun(tc_fun(X31122,tc_HOL_Obool),tc_fun(X31122,tc_HOL_Obool)),X31121),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31122,tc_HOL_Obool))),X31119))),X31116))),
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,
! [X22977,X22978,X22979,X22980,X22981,X22982,X22983] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(X22983,X22982,X22981,X22980),X22979),X22978),X22977) = c_New__DSequence_Oneg__bind(X22983,X22982,hAPP(hAPP(hAPP(X22981,X22979),X22978),X22977),hAPP(hAPP(c_COMBC(X22983,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(X22982)))),hAPP(hAPP(c_COMBC(X22983,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(X22982))))),hAPP(hAPP(c_COMBC(X22983,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(X22982)))))),X22980),X22979)),X22978)),X22977)),
inference(variable_rename,[status(thm)],[fact_neg__bind__def]) ).
fof(i_0_6213,plain,
! [X33195,X33196,X33197,X33198,X33199] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33199),tc_List_Olist(X33199))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33199),tc_List_Olist(X33199)),hAPP(hAPP(c_List_Oappend(X33199),X33198),X33197)),hAPP(hAPP(c_List_Oappend(X33199),X33198),X33196))),c_List_Olexord(X33199,X33195)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X33199,X33199)),hAPP(hAPP(c_Product__Type_OPair(X33199,X33199),esk463_5(X33195,X33196,X33197,X33198,X33199)),esk463_5(X33195,X33196,X33197,X33198,X33199))),X33195))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33199),tc_List_Olist(X33199))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33199),tc_List_Olist(X33199)),X33197),X33196)),c_List_Olexord(X33199,X33195))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5268])])]) ).
fof(i_0_6214,plain,
! [X31346,X31347] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X31347,tc_HOL_Obool),X31346) = hAPP(c_Set_OCollect(X31347),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X31347,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X31347),c_HOL_OAll(tc_fun(X31347,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X31347,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X31347,tc_HOL_Obool),tc_HOL_Obool),X31347),hAPP(c_COMBS(tc_fun(X31347,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(X31347,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(X31347,tc_HOL_Obool),tc_fun(tc_fun(X31347,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X31347,tc_HOL_Obool))),X31346)))),c_member(X31347)))),
inference(variable_rename,[status(thm)],[fact_Inter__eq]) ).
fof(i_0_6215,plain,
! [X30601,X30602,X30603,X30604,X30605] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30605,X30605)),hAPP(hAPP(c_Product__Type_OPair(X30605,X30605),esk382_5(X30601,X30602,X30603,X30604,X30605)),X30603)),c_Transitive__Closure_Ortrancl(X30605,X30602)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30605,X30605)),hAPP(hAPP(c_Product__Type_OPair(X30605,X30605),X30604),X30603)),c_Transitive__Closure_Ortrancl(X30605,X30602)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30605,X30605)),hAPP(hAPP(c_Product__Type_OPair(X30605,X30605),X30604),X30603)),c_Transitive__Closure_Ortrancl(X30605,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30605,X30605),tc_HOL_Obool)),X30602),X30601)))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30605,X30605)),hAPP(hAPP(c_Product__Type_OPair(X30605,X30605),esk383_5(X30601,X30602,X30603,X30604,X30605)),esk382_5(X30601,X30602,X30603,X30604,X30605))),X30601))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30605,X30605)),hAPP(hAPP(c_Product__Type_OPair(X30605,X30605),X30604),X30603)),c_Transitive__Closure_Ortrancl(X30605,X30602)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30605,X30605)),hAPP(hAPP(c_Product__Type_OPair(X30605,X30605),X30604),X30603)),c_Transitive__Closure_Ortrancl(X30605,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30605,X30605),tc_HOL_Obool)),X30602),X30601)))) )
& ( esk383_5(X30601,X30602,X30603,X30604,X30605) != esk382_5(X30601,X30602,X30603,X30604,X30605)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30605,X30605)),hAPP(hAPP(c_Product__Type_OPair(X30605,X30605),X30604),X30603)),c_Transitive__Closure_Ortrancl(X30605,X30602)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30605,X30605)),hAPP(hAPP(c_Product__Type_OPair(X30605,X30605),X30604),X30603)),c_Transitive__Closure_Ortrancl(X30605,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30605,X30605),tc_HOL_Obool)),X30602),X30601)))) ) ),
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_6216,plain,
! [X30556,X30557,X30558,X30559,X30560] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30560,X30560)),hAPP(hAPP(c_Product__Type_OPair(X30560,X30560),X30559),esk377_5(X30556,X30557,X30558,X30559,X30560))),c_Transitive__Closure_Ortrancl(X30560,X30557)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30560,X30560)),hAPP(hAPP(c_Product__Type_OPair(X30560,X30560),X30559),X30558)),c_Transitive__Closure_Ortrancl(X30560,X30557)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30560,X30560)),hAPP(hAPP(c_Product__Type_OPair(X30560,X30560),X30559),X30558)),c_Transitive__Closure_Ortrancl(X30560,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30560,X30560),tc_HOL_Obool)),X30557),X30556)))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30560,X30560)),hAPP(hAPP(c_Product__Type_OPair(X30560,X30560),esk377_5(X30556,X30557,X30558,X30559,X30560)),esk378_5(X30556,X30557,X30558,X30559,X30560))),X30556))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30560,X30560)),hAPP(hAPP(c_Product__Type_OPair(X30560,X30560),X30559),X30558)),c_Transitive__Closure_Ortrancl(X30560,X30557)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30560,X30560)),hAPP(hAPP(c_Product__Type_OPair(X30560,X30560),X30559),X30558)),c_Transitive__Closure_Ortrancl(X30560,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30560,X30560),tc_HOL_Obool)),X30557),X30556)))) )
& ( esk377_5(X30556,X30557,X30558,X30559,X30560) != esk378_5(X30556,X30557,X30558,X30559,X30560)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30560,X30560)),hAPP(hAPP(c_Product__Type_OPair(X30560,X30560),X30559),X30558)),c_Transitive__Closure_Ortrancl(X30560,X30557)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30560,X30560)),hAPP(hAPP(c_Product__Type_OPair(X30560,X30560),X30559),X30558)),c_Transitive__Closure_Ortrancl(X30560,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30560,X30560),tc_HOL_Obool)),X30557),X30556)))) ) ),
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_6217,plain,
! [X32102,X32103,X32104,X32105,X32106,X32107] : hAPP(hAPP(c_List_Ozip(X32107,X32106),X32105),hAPP(hAPP(c_List_Omap(X32104,X32106),X32103),X32102)) = hAPP(hAPP(c_List_Omap(tc_prod(X32107,X32104),tc_prod(X32107,X32106)),hAPP(c_Product__Type_Oprod_Oprod__case(X32107,X32104,tc_prod(X32107,X32106)),hAPP(hAPP(c_COMBC(X32107,tc_fun(X32104,X32106),tc_fun(X32104,tc_prod(X32107,X32106))),hAPP(hAPP(c_COMBB(tc_fun(X32106,tc_prod(X32107,X32106)),tc_fun(tc_fun(X32104,X32106),tc_fun(X32104,tc_prod(X32107,X32106))),X32107),c_COMBB(X32106,tc_prod(X32107,X32106),X32104)),c_Product__Type_OPair(X32107,X32106))),X32103))),hAPP(hAPP(c_List_Ozip(X32107,X32104),X32105),X32102)),
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,
! [X21095,X21096,X21097] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk81_3(X21095,X21096,X21097)),X21097))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21095),hAPP(X21096,X21097)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21096,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X21095))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk80_3(X21095,X21096,X21097)),X21097)) )
& ( hAPP(X21096,esk81_3(X21095,X21096,X21097)) = X21095
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21095),hAPP(X21096,X21097)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21096,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X21095))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk80_3(X21095,X21096,X21097)),X21097)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk81_3(X21095,X21096,X21097)),X21097))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21095),hAPP(X21096,X21097)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21096,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X21095))
| ~ 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(X21096,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk80_3(X21095,X21096,X21097)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X21096,esk80_3(X21095,X21096,X21097))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
& ( hAPP(X21096,esk81_3(X21095,X21096,X21097)) = X21095
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21095),hAPP(X21096,X21097)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21096,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X21095))
| ~ 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(X21096,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk80_3(X21095,X21096,X21097)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X21096,esk80_3(X21095,X21096,X21097))))),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,
! [X21090,X21091,X21092] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk79_3(X21090,X21091,X21092)),X21092))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21090),hAPP(X21091,X21092)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21091,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X21090))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk78_3(X21090,X21091,X21092)),X21092)) )
& ( hAPP(X21091,esk79_3(X21090,X21091,X21092)) = X21090
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21090),hAPP(X21091,X21092)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21091,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X21090))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk78_3(X21090,X21091,X21092)),X21092)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk79_3(X21090,X21091,X21092)),X21092))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21090),hAPP(X21091,X21092)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21091,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X21090))
| ~ 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(X21091,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk78_3(X21090,X21091,X21092)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X21091,esk78_3(X21090,X21091,X21092))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
& ( hAPP(X21091,esk79_3(X21090,X21091,X21092)) = X21090
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21090),hAPP(X21091,X21092)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21091,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X21090))
| ~ 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(X21091,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk78_3(X21090,X21091,X21092)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X21091,esk78_3(X21090,X21091,X21092))))),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,
! [X30534,X30535,X30536,X30537,X30538] :
( ( X30535 = hAPP(c_Nat_OSuc,esk373_5(X30534,X30535,X30536,X30537,X30538))
| X30535 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30538,X30538)),hAPP(hAPP(c_Product__Type_OPair(X30538,X30538),X30537),X30536)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30538,X30538),tc_HOL_Obool),X30535),X30534))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30538,X30538)),hAPP(hAPP(c_Product__Type_OPair(X30538,X30538),X30537),esk372_5(X30534,X30535,X30536,X30537,X30538))),X30534))
| X30535 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30538,X30538)),hAPP(hAPP(c_Product__Type_OPair(X30538,X30538),X30537),X30536)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30538,X30538),tc_HOL_Obool),X30535),X30534))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30538,X30538)),hAPP(hAPP(c_Product__Type_OPair(X30538,X30538),esk372_5(X30534,X30535,X30536,X30537,X30538)),X30536)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30538,X30538),tc_HOL_Obool),esk373_5(X30534,X30535,X30536,X30537,X30538)),X30534)))
| X30535 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30538,X30538)),hAPP(hAPP(c_Product__Type_OPair(X30538,X30538),X30537),X30536)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30538,X30538),tc_HOL_Obool),X30535),X30534))) )
& ( X30535 = hAPP(c_Nat_OSuc,esk373_5(X30534,X30535,X30536,X30537,X30538))
| X30537 = X30536
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30538,X30538)),hAPP(hAPP(c_Product__Type_OPair(X30538,X30538),X30537),X30536)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30538,X30538),tc_HOL_Obool),X30535),X30534))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30538,X30538)),hAPP(hAPP(c_Product__Type_OPair(X30538,X30538),X30537),esk372_5(X30534,X30535,X30536,X30537,X30538))),X30534))
| X30537 = X30536
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30538,X30538)),hAPP(hAPP(c_Product__Type_OPair(X30538,X30538),X30537),X30536)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30538,X30538),tc_HOL_Obool),X30535),X30534))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30538,X30538)),hAPP(hAPP(c_Product__Type_OPair(X30538,X30538),esk372_5(X30534,X30535,X30536,X30537,X30538)),X30536)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30538,X30538),tc_HOL_Obool),esk373_5(X30534,X30535,X30536,X30537,X30538)),X30534)))
| X30537 = X30536
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30538,X30538)),hAPP(hAPP(c_Product__Type_OPair(X30538,X30538),X30537),X30536)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30538,X30538),tc_HOL_Obool),X30535),X30534))) ) ),
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,
! [X31684,X31685,X31686,X31687] :
( ~ class_Smallcheck_Osmall(X31687)
| ~ class_Smallcheck_Osmall(X31686)
| hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(X31686,X31687)),X31685),X31684) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(X31686),hAPP(hAPP(c_COMBC(X31686,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(X31687,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))),X31686),c_Smallcheck_Osmall__class_Osmall(X31687)),hAPP(hAPP(c_COMBB(tc_fun(X31687,tc_prod(X31686,X31687)),tc_fun(X31687,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),X31686),hAPP(c_COMBB(tc_prod(X31686,X31687),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),X31687),X31685)),c_Product__Type_OPair(X31686,X31687)))),X31684)),X31684) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_small__prod__def])]) ).
cnf(i_0_6225,plain,
( hAPP(X1,esk435_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),esk435_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,
! [X28379,X28380,X28381,X28382] :
( ~ c_Fun_Oinj__on(X28382,X28381,X28380,c_Orderings_Otop__class_Otop(tc_fun(X28382,tc_HOL_Obool)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28382,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X28382,X28381,X28380),hAPP(hAPP(c_Set_Oinsert(X28381),X28379),c_Orderings_Obot__class_Obot(tc_fun(X28381,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X28382),c_HOL_OThe(X28382,hAPP(hAPP(c_COMBC(X28382,X28381,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X28381,tc_fun(X28381,tc_HOL_Obool),X28382),c_fequal),X28380)),X28379))),c_Orderings_Obot__class_Obot(tc_fun(X28382,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__vimage__singleton])]) ).
fof(i_0_6229,plain,
! [X23012,X23013,X23014,X23015,X23016,X23017,X23018] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(X23018,X23017,X23016,X23015),X23014),X23013),X23012) = c_New__DSequence_Opos__bind(X23018,X23017,hAPP(hAPP(hAPP(X23016,X23014),X23013),X23012),hAPP(hAPP(c_COMBC(X23018,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X23017))),hAPP(hAPP(c_COMBC(X23018,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(X23017)))),hAPP(hAPP(c_COMBC(X23018,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(X23017))))),X23015),X23014)),X23013)),X23012)),
inference(variable_rename,[status(thm)],[fact_pos__bind__def]) ).
fof(i_0_6230,plain,
! [X17975,X17976,X17977,X17978,X17979,X17981,X17982,X17983,X17984,X17985,X17986] :
( ( hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17975),hAPP(c_Natural_Ogetlocs,X17976))),X17979),hAPP(hAPP(c_Natural_Ogetlocs,X17975),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,esk24_5(X17975,X17976,X17977,X17978,X17979)),hAPP(c_Natural_Ogetlocs,X17976))),X17979),hAPP(hAPP(c_Natural_Ogetlocs,esk24_5(X17975,X17976,X17977,X17978,X17979)),c_Com_ORes))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(X17979,X17978,X17977)),X17976),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17975),hAPP(c_Natural_Ogetlocs,X17976))),X17979),hAPP(hAPP(c_Natural_Ogetlocs,X17975),c_Com_ORes)))) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X17978)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17976),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X17977,X17976))),esk24_5(X17975,X17976,X17977,X17978,X17979)))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(X17979,X17978,X17977)),X17976),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17975),hAPP(c_Natural_Ogetlocs,X17976))),X17979),hAPP(hAPP(c_Natural_Ogetlocs,X17975),c_Com_ORes)))) )
& ( hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17981),hAPP(c_Natural_Ogetlocs,X17982))),X17985),hAPP(hAPP(c_Natural_Ogetlocs,X17981),c_Com_ORes)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17986),hAPP(c_Natural_Ogetlocs,X17982))),X17985),hAPP(hAPP(c_Natural_Ogetlocs,X17986),c_Com_ORes))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X17984)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17982),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X17983,X17982))),X17986))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(X17985,X17984,X17983)),X17982),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17981),hAPP(c_Natural_Ogetlocs,X17982))),X17985),hAPP(hAPP(c_Natural_Ogetlocs,X17981),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,
! [X25238,X25239] :
( ( 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)))),X25239,X25238) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25239),X25238))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25238),X25239)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25239),X25238))
| 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)))),X25239,X25238) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25238),X25239))
| 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)))),X25239,X25238) = 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,
! [X25236,X25237] :
( ( 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)))),X25237,X25236) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25237),X25236))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25236),X25237)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25237),X25236))
| 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)))),X25237,X25236) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25236),X25237))
| 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)))),X25237,X25236) = 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,
! [X25210,X25211] :
( ( 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)))),X25211,X25210)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25211),X25210))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25210),X25211)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25211),X25210))
| 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)))),X25211,X25210) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25210),X25211))
| 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)))),X25211,X25210) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5275])])]) ).
fof(i_0_6234,plain,
! [X25240,X25241] :
( ( 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)))),X25241,X25240)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25241),X25240))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25240),X25241)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25241),X25240))
| 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)))),X25241,X25240) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25240),X25241))
| 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)))),X25241,X25240) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5276])])]) ).
fof(i_0_6235,plain,
! [X29325,X29326,X29327,X29328] : c_Nitpick_Oprod(X29328,X29327,X29326,X29325) = hAPP(c_Set_OCollect(tc_prod(X29328,X29327)),hAPP(c_Product__Type_Oprod_Oprod__case(X29328,X29327,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X29328,tc_fun(X29327,tc_HOL_Obool),tc_fun(X29327,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X29327,tc_HOL_Obool),tc_fun(X29327,tc_HOL_Obool)),X29328),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29327)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29328),c_fconj),hAPP(hAPP(c_COMBC(X29328,tc_fun(X29328,tc_HOL_Obool),tc_HOL_Obool),c_member(X29328)),X29326)))),hAPP(hAPP(c_COMBC(X29327,tc_fun(X29327,tc_HOL_Obool),tc_HOL_Obool),c_member(X29327)),X29325)))),
inference(variable_rename,[status(thm)],[fact_Nitpick_Oprod__def]) ).
fof(i_0_6236,plain,
! [X23486,X23487,X23488,X23489] :
( ~ class_Orderings_Oorder(X23489)
| ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X23489,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)))),X23488)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23487),X23486))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23486),X23487))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23489),hAPP(X23488,X23487)),hAPP(X23488,X23486))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5277])]) ).
fof(i_0_6237,plain,
! [X23539,X23540] :
( ~ class_Orderings_Oorder(X23540)
| ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X23540,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)))),X23539)
| c_Orderings_Oorder_Omono(tc_Nat_Onat,X23540,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23539) ),
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,
! [X28957,X28958,X28959,X28960,X28961,X28962,X28963,X28964,X28965,X28966,X28967] : hAPP(c_Product__Type_Omap__pair(X28967,X28966,X28965,X28964,X28963,X28962),hAPP(c_Product__Type_Omap__pair(X28961,X28967,X28960,X28965,X28959,X28958),X28957)) = hAPP(c_Product__Type_Omap__pair(X28961,X28966,X28960,X28964,hAPP(c_Fun_Ocomp(X28967,X28966,X28961,X28963),X28959),hAPP(c_Fun_Ocomp(X28965,X28964,X28960,X28962),X28958)),X28957),
inference(variable_rename,[status(thm)],[fact_map__pair_Ocompositionality]) ).
fof(i_0_6240,plain,
! [X24394,X24395,X24396,X24397] :
( ( ~ 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),X24397),X24396)),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),X24395),X24394)),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),X24397),X24394)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24395),X24396))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24397),X24394)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24395),X24396)))
| 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),X24397),X24396)),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),X24395),X24394)),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,
! [X24425,X24426,X24427,X24428] :
( ( ~ 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),X24428),X24427)),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),X24426),X24425)),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),X24428),X24425)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24426),X24427))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24428),X24425)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24426),X24427)))
| 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),X24428),X24427)),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),X24426),X24425)),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,
! [X28009,X28010,X28011,X28012,X28013,X28014] :
( ( hBOOL(hAPP(hAPP(c_member(X28013),esk263_6(X28009,X28010,X28011,X28012,X28013,X28014)),X28012))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28009,X28014),X28010),hAPP(c_Set_Oimage(X28013,X28009,X28011),X28012)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28013,X28014),hAPP(c_Fun_Ocomp(X28009,X28014,X28013,X28010),X28011)),X28012)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28013),X28012))
| ~ class_Groups_Ocomm__monoid__add(X28014) )
& ( hBOOL(hAPP(hAPP(c_member(X28013),esk264_6(X28009,X28010,X28011,X28012,X28013,X28014)),X28012))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28009,X28014),X28010),hAPP(c_Set_Oimage(X28013,X28009,X28011),X28012)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28013,X28014),hAPP(c_Fun_Ocomp(X28009,X28014,X28013,X28010),X28011)),X28012)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28013),X28012))
| ~ class_Groups_Ocomm__monoid__add(X28014) )
& ( esk263_6(X28009,X28010,X28011,X28012,X28013,X28014) != esk264_6(X28009,X28010,X28011,X28012,X28013,X28014)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28009,X28014),X28010),hAPP(c_Set_Oimage(X28013,X28009,X28011),X28012)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28013,X28014),hAPP(c_Fun_Ocomp(X28009,X28014,X28013,X28010),X28011)),X28012)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28013),X28012))
| ~ class_Groups_Ocomm__monoid__add(X28014) )
& ( hAPP(X28011,esk263_6(X28009,X28010,X28011,X28012,X28013,X28014)) = hAPP(X28011,esk264_6(X28009,X28010,X28011,X28012,X28013,X28014))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28009,X28014),X28010),hAPP(c_Set_Oimage(X28013,X28009,X28011),X28012)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28013,X28014),hAPP(c_Fun_Ocomp(X28009,X28014,X28013,X28010),X28011)),X28012)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28013),X28012))
| ~ class_Groups_Ocomm__monoid__add(X28014) )
& ( hAPP(X28010,hAPP(X28011,esk263_6(X28009,X28010,X28011,X28012,X28013,X28014))) != c_Groups_Ozero__class_Ozero(X28014)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28009,X28014),X28010),hAPP(c_Set_Oimage(X28013,X28009,X28011),X28012)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28013,X28014),hAPP(c_Fun_Ocomp(X28009,X28014,X28013,X28010),X28011)),X28012)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28013),X28012))
| ~ class_Groups_Ocomm__monoid__add(X28014) ) ),
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,
! [X17987,X17988,X17989,X17990,X17991] :
( ( X17987 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,esk25_5(X17987,X17988,X17989,X17990,X17991)),hAPP(c_Natural_Ogetlocs,X17988))),X17991),hAPP(hAPP(c_Natural_Ogetlocs,esk25_5(X17987,X17988,X17989,X17990,X17991)),c_Com_ORes))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(X17991,X17990,X17989)),X17988),X17987)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X17990)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17988),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X17989,X17988))),esk25_5(X17987,X17988,X17989,X17990,X17991)))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(X17991,X17990,X17989)),X17988),X17987)) ) ),
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,
! [X29237,X29238,X29239,X29240,X29241,X29242] : hAPP(c_Set_Oimage(X29242,X29241,hAPP(hAPP(c_COMBS(X29242,X29241,X29241),hAPP(hAPP(c_COMBS(X29242,X29241,tc_fun(X29241,X29241)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X29241,tc_fun(X29241,X29241)),X29242),c_If(X29241)),X29240)),X29239)),X29238)),X29237) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29241,tc_HOL_Obool)),hAPP(c_Set_Oimage(X29242,X29241,X29239),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29242,tc_HOL_Obool)),X29237),hAPP(c_Set_OCollect(X29242),X29240)))),hAPP(c_Set_Oimage(X29242,X29241,X29238),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29242,tc_HOL_Obool)),X29237),hAPP(c_Set_OCollect(X29242),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29242),c_fNot),X29240))))),
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,
! [X24390,X24391,X24392,X24393] : 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),X24393),X24392)),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),X24391),X24390)),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),X24393),X24391)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24392),X24390))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24393),X24390)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24392),X24391)))),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,
! [X17739,X17740,X17741,X17742,X17743,X17744,X17746,X17747,X17748,X17749,X17750,X17751,X17752] :
( ( hAPP(hAPP(hAPP(c_Natural_Oupdate,X17739),c_Com_Ovname_OLoc(X17744)),hAPP(hAPP(c_Natural_Ogetlocs,X17741),X17744)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,esk15_6(X17739,X17740,X17741,X17742,X17743,X17744)),c_Com_Ovname_OLoc(X17744)),hAPP(hAPP(c_Natural_Ogetlocs,X17741),X17744))
| ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(X17744,X17743,X17742),X17741,X17740,hAPP(hAPP(hAPP(c_Natural_Oupdate,X17739),c_Com_Ovname_OLoc(X17744)),hAPP(hAPP(c_Natural_Ogetlocs,X17741),X17744))) )
& ( c_Natural_Oevaln(X17742,hAPP(hAPP(hAPP(c_Natural_Oupdate,X17741),c_Com_Ovname_OLoc(X17744)),hAPP(X17743,X17741)),X17740,esk15_6(X17739,X17740,X17741,X17742,X17743,X17744))
| ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(X17744,X17743,X17742),X17741,X17740,hAPP(hAPP(hAPP(c_Natural_Oupdate,X17739),c_Com_Ovname_OLoc(X17744)),hAPP(hAPP(c_Natural_Ogetlocs,X17741),X17744))) )
& ( hAPP(hAPP(hAPP(c_Natural_Oupdate,X17746),c_Com_Ovname_OLoc(X17751)),hAPP(hAPP(c_Natural_Ogetlocs,X17748),X17751)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,X17752),c_Com_Ovname_OLoc(X17751)),hAPP(hAPP(c_Natural_Ogetlocs,X17748),X17751))
| ~ c_Natural_Oevaln(X17749,hAPP(hAPP(hAPP(c_Natural_Oupdate,X17748),c_Com_Ovname_OLoc(X17751)),hAPP(X17750,X17748)),X17747,X17752)
| c_Natural_Oevaln(c_Com_Ocom_OLocal(X17751,X17750,X17749),X17748,X17747,hAPP(hAPP(hAPP(c_Natural_Oupdate,X17746),c_Com_Ovname_OLoc(X17751)),hAPP(hAPP(c_Natural_Ogetlocs,X17748),X17751))) ) ),
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,
! [X30052,X30053,X30054,X30055,X30056,X30057] :
( ( hBOOL(hAPP(hAPP(c_member(X30056),esk359_6(X30052,X30053,X30054,X30055,X30056,X30057)),X30055))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X30057,X30056,c_Groups_Otimes__class_Otimes(X30057)),X30054),X30052),X30055) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X30057,X30056,c_Groups_Otimes__class_Otimes(X30057)),X30053),X30052),X30055)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30056),X30055))
| ~ class_Groups_Oab__semigroup__mult(X30057) )
& ( hAPP(X30054,esk359_6(X30052,X30053,X30054,X30055,X30056,X30057)) != hAPP(X30053,esk359_6(X30052,X30053,X30054,X30055,X30056,X30057))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X30057,X30056,c_Groups_Otimes__class_Otimes(X30057)),X30054),X30052),X30055) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X30057,X30056,c_Groups_Otimes__class_Otimes(X30057)),X30053),X30052),X30055)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30056),X30055))
| ~ class_Groups_Oab__semigroup__mult(X30057) ) ),
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,
! [X29591,X29592,X29593,X29594,X29595,X29596,X29597,X29599,X29600,X29601,X29602,X29603,X29604,X29605,X29606] :
( ( hBOOL(hAPP(hAPP(X29594,X29592),esk317_4(X29591,X29592,X29593,X29594)))
| ~ c_Predicate_Opred__comp(X29597,X29596,X29595,X29594,X29593,X29592,X29591) )
& ( hBOOL(hAPP(hAPP(X29593,esk317_4(X29591,X29592,X29593,X29594)),X29591))
| ~ c_Predicate_Opred__comp(X29597,X29596,X29595,X29594,X29593,X29592,X29591) )
& ( ~ hBOOL(hAPP(hAPP(X29602,X29600),X29603))
| ~ hBOOL(hAPP(hAPP(X29601,X29603),X29599))
| c_Predicate_Opred__comp(X29606,X29605,X29604,X29602,X29601,X29600,X29599) ) ),
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,
! [X29655,X29656,X29657,X29658] :
( ~ c_Wellfounded_Owf(X29658,X29657)
| ~ c_Fun_Oinj__on(X29658,X29656,X29655,c_Orderings_Otop__class_Otop(tc_fun(X29658,tc_HOL_Obool)))
| c_Wellfounded_Owf(X29656,hAPP(c_Set_Oimage(tc_prod(X29658,X29658),tc_prod(X29656,X29656),c_Product__Type_Omap__pair(X29658,X29656,X29658,X29656,X29655,X29655)),X29657)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__map__pair__image])]) ).
fof(i_0_6254,plain,
! [X31461,X31462,X31463,X31464,X31465,X31466] :
( ( hBOOL(hAPP(hAPP(c_member(X31465),esk413_6(X31461,X31462,X31463,X31464,X31465,X31466)),X31466))
| c_Fun_Oinj__on(X31464,X31463,X31462,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31465,tc_fun(X31464,tc_HOL_Obool)),X31466),X31461))
| X31466 = c_Orderings_Obot__class_Obot(tc_fun(X31465,tc_HOL_Obool)) )
& ( ~ c_Fun_Oinj__on(X31464,X31463,X31462,hAPP(X31461,esk413_6(X31461,X31462,X31463,X31464,X31465,X31466)))
| c_Fun_Oinj__on(X31464,X31463,X31462,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31465,tc_fun(X31464,tc_HOL_Obool)),X31466),X31461))
| X31466 = c_Orderings_Obot__class_Obot(tc_fun(X31465,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,
! [X17917,X17918,X17919,X17920,X17921,X17922] :
( ( X17917 = hAPP(hAPP(hAPP(c_Natural_Oupdate,esk21_6(X17917,X17918,X17919,X17920,X17921,X17922)),c_Com_Ovname_OLoc(X17922)),hAPP(hAPP(c_Natural_Ogetlocs,X17919),X17922))
| ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(X17922,X17921,X17920),X17919,X17918,X17917) )
& ( c_Natural_Oevaln(X17920,hAPP(hAPP(hAPP(c_Natural_Oupdate,X17919),c_Com_Ovname_OLoc(X17922)),hAPP(X17921,X17919)),X17918,esk21_6(X17917,X17918,X17919,X17920,X17921,X17922))
| ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(X17922,X17921,X17920),X17919,X17918,X17917) ) ),
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,
! [X33724,X33725,X33726,X33727,X33728] :
( ( hBOOL(hAPP(hAPP(c_member(X33727),esk474_5(X33724,X33725,X33726,X33727,X33728)),hAPP(c_List_Oset(X33727),X33726)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X33728),hAPP(c_List_Omonoid__add__class_Olistsum(X33728),hAPP(hAPP(c_List_Omap(X33727,X33728),X33725),X33726))),hAPP(c_List_Omonoid__add__class_Olistsum(X33728),hAPP(hAPP(c_List_Omap(X33727,X33728),X33724),X33726))))
| ~ class_Groups_Omonoid__add(X33728)
| ~ class_Groups_Oordered__ab__semigroup__add(X33728) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X33728),hAPP(X33725,esk474_5(X33724,X33725,X33726,X33727,X33728))),hAPP(X33724,esk474_5(X33724,X33725,X33726,X33727,X33728))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X33728),hAPP(c_List_Omonoid__add__class_Olistsum(X33728),hAPP(hAPP(c_List_Omap(X33727,X33728),X33725),X33726))),hAPP(c_List_Omonoid__add__class_Olistsum(X33728),hAPP(hAPP(c_List_Omap(X33727,X33728),X33724),X33726))))
| ~ class_Groups_Omonoid__add(X33728)
| ~ class_Groups_Oordered__ab__semigroup__add(X33728) ) ),
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,
! [X27594,X27595,X27596,X27597,X27598] :
( ( hBOOL(hAPP(hAPP(c_member(X27597),esk260_5(X27594,X27595,X27596,X27597,X27598)),X27596))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27598),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27597,X27598),X27595),X27596)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27597,X27598),X27594),X27596)))
| X27596 = c_Orderings_Obot__class_Obot(tc_fun(X27597,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27597),X27596))
| ~ class_Groups_Ocomm__monoid__add(X27598)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X27598) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27598),hAPP(X27595,esk260_5(X27594,X27595,X27596,X27597,X27598))),hAPP(X27594,esk260_5(X27594,X27595,X27596,X27597,X27598))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27598),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27597,X27598),X27595),X27596)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27597,X27598),X27594),X27596)))
| X27596 = c_Orderings_Obot__class_Obot(tc_fun(X27597,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27597),X27596))
| ~ class_Groups_Ocomm__monoid__add(X27598)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X27598) ) ),
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,
! [X29267,X29268,X29269,X29270,X29271,X29272] :
( ~ class_Groups_Ocomm__monoid__add(X29272)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29271),X29270))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29271,X29272),hAPP(hAPP(c_COMBS(X29271,X29272,X29272),hAPP(hAPP(c_COMBS(X29271,X29272,tc_fun(X29272,X29272)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X29272,tc_fun(X29272,X29272)),X29271),c_If(X29272)),X29269)),X29268)),X29267)),X29270) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X29272),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29271,X29272),X29268),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29271,tc_HOL_Obool)),X29270),hAPP(c_Set_OCollect(X29271),X29269)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29271,X29272),X29267),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29271,tc_HOL_Obool)),X29270),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X29271,tc_HOL_Obool)),hAPP(c_Set_OCollect(X29271),X29269))))) ),
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,
! [X29077,X29078,X29079,X29080,X29081] :
( ~ c_Finite__Set_Ofolding__one__idem(X29081,X29080,X29079)
| hAPP(X29078,hAPP(hAPP(X29080,esk304_5(X29077,X29078,X29079,X29080,X29081)),esk305_5(X29077,X29078,X29079,X29080,X29081))) != hAPP(hAPP(X29080,hAPP(X29078,esk304_5(X29077,X29078,X29079,X29080,X29081))),hAPP(X29078,esk305_5(X29077,X29078,X29079,X29080,X29081)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29081),X29077))
| X29077 = c_Orderings_Obot__class_Obot(tc_fun(X29081,tc_HOL_Obool))
| hAPP(X29078,hAPP(X29079,X29077)) = hAPP(X29079,hAPP(c_Set_Oimage(X29081,X29081,X29078),X29077)) ),
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),esk491_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),esk491_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),esk491_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),esk491_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),esk87_3(X1,X2,X3)),esk88_3(X1,X2,X3))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk88_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(X1,esk87_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)))),esk88_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,
! [X27279,X27280,X27281,X27282,X27283] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X27282),X27280),X27281))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27282,X27283),hAPP(hAPP(c_COMBC(X27282,X27283,X27283),hAPP(hAPP(c_COMBS(X27282,X27283,tc_fun(X27283,X27283)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X27283,tc_fun(X27283,X27283)),X27282),c_If(X27283)),hAPP(c_fequal,X27280))),X27279)),c_Groups_Ozero__class_Ozero(X27283))),X27281) = hAPP(X27279,X27280)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27282),X27281))
| ~ class_Groups_Ocomm__monoid__add(X27283) )
& ( hBOOL(hAPP(hAPP(c_member(X27282),X27280),X27281))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27282,X27283),hAPP(hAPP(c_COMBC(X27282,X27283,X27283),hAPP(hAPP(c_COMBS(X27282,X27283,tc_fun(X27283,X27283)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X27283,tc_fun(X27283,X27283)),X27282),c_If(X27283)),hAPP(c_fequal,X27280))),X27279)),c_Groups_Ozero__class_Ozero(X27283))),X27281) = c_Groups_Ozero__class_Ozero(X27283)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27282),X27281))
| ~ class_Groups_Ocomm__monoid__add(X27283) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5287])])]) ).
fof(i_0_6269,plain,
! [X25691,X25692,X25693,X25694,X25695] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25694),X25692),X25693))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25694,X25695),hAPP(hAPP(c_COMBC(X25694,X25695,X25695),hAPP(hAPP(c_COMBS(X25694,X25695,tc_fun(X25695,X25695)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X25695,tc_fun(X25695,X25695)),X25694),c_If(X25695)),hAPP(c_fequal,X25692))),X25691)),c_Groups_Oone__class_Oone(X25695))),X25693) = hAPP(X25691,X25692)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25694),X25693))
| ~ class_Groups_Ocomm__monoid__mult(X25695) )
& ( hBOOL(hAPP(hAPP(c_member(X25694),X25692),X25693))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25694,X25695),hAPP(hAPP(c_COMBC(X25694,X25695,X25695),hAPP(hAPP(c_COMBS(X25694,X25695,tc_fun(X25695,X25695)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X25695,tc_fun(X25695,X25695)),X25694),c_If(X25695)),hAPP(c_fequal,X25692))),X25691)),c_Groups_Oone__class_Oone(X25695))),X25693) = c_Groups_Oone__class_Oone(X25695)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25694),X25693))
| ~ class_Groups_Ocomm__monoid__mult(X25695) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5288])])]) ).
fof(i_0_6270,plain,
! [X28978,X28979,X28980,X28981,X28982,X28983,X28984,X28985,X28986,X28987] : hAPP(c_Fun_Ocomp(tc_prod(X28987,X28986),tc_prod(X28985,X28984),tc_prod(X28983,X28982),c_Product__Type_Omap__pair(X28987,X28985,X28986,X28984,X28981,X28980)),c_Product__Type_Omap__pair(X28983,X28987,X28982,X28986,X28979,X28978)) = c_Product__Type_Omap__pair(X28983,X28985,X28982,X28984,hAPP(c_Fun_Ocomp(X28987,X28985,X28983,X28981),X28979),hAPP(c_Fun_Ocomp(X28986,X28984,X28982,X28980),X28978)),
inference(variable_rename,[status(thm)],[fact_map__pair_Ocomp]) ).
fof(i_0_6271,plain,
! [X28968,X28969,X28970,X28971,X28972,X28973,X28974,X28975,X28976,X28977] : c_Product__Type_Omap__pair(X28977,X28976,X28975,X28974,hAPP(c_Fun_Ocomp(X28973,X28976,X28977,X28972),X28971),hAPP(c_Fun_Ocomp(X28970,X28974,X28975,X28969),X28968)) = hAPP(c_Fun_Ocomp(tc_prod(X28973,X28970),tc_prod(X28976,X28974),tc_prod(X28977,X28975),c_Product__Type_Omap__pair(X28973,X28976,X28970,X28974,X28972,X28969)),c_Product__Type_Omap__pair(X28977,X28973,X28975,X28970,X28971,X28968)),
inference(variable_rename,[status(thm)],[fact_map__pair__compose]) ).
fof(i_0_6272,plain,
! [X32594,X32595,X32596,X32597,X32598,X32599,X32600,X32601,X32602] :
( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32597)),X32596) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32597)),X32595)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32597),tc_List_Olist(X32597))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32597),tc_List_Olist(X32597)),X32596),X32595)),c_List_Olistrel(X32597,X32594))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32598),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32597)),X32596)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X32597,X32597)),hAPP(hAPP(c_Product__Type_OPair(X32597,X32597),hAPP(hAPP(c_List_Onth(X32597),X32596),X32598)),hAPP(hAPP(c_List_Onth(X32597),X32595),X32598))),X32594))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32597),tc_List_Olist(X32597))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32597),tc_List_Olist(X32597)),X32596),X32595)),c_List_Olistrel(X32597,X32594))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk455_4(X32599,X32600,X32601,X32602)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32602)),X32601)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32602)),X32601) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32602)),X32600)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32602),tc_List_Olist(X32602))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32602),tc_List_Olist(X32602)),X32601),X32600)),c_List_Olistrel(X32602,X32599))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32602,X32602)),hAPP(hAPP(c_Product__Type_OPair(X32602,X32602),hAPP(hAPP(c_List_Onth(X32602),X32601),esk455_4(X32599,X32600,X32601,X32602))),hAPP(hAPP(c_List_Onth(X32602),X32600),esk455_4(X32599,X32600,X32601,X32602)))),X32599))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32602)),X32601) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32602)),X32600)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32602),tc_List_Olist(X32602))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32602),tc_List_Olist(X32602)),X32601),X32600)),c_List_Olistrel(X32602,X32599))) ) ),
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),esk92_3(X1,X2,X3)),esk93_3(X1,X2,X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk93_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(X1,esk92_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)))),esk93_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,
! [X32368,X32369,X32370,X32371,X32372] :
( ( X32371 = hAPP(hAPP(c_List_Olist_OCons(X32372),esk444_5(X32368,X32369,X32370,X32371,X32372)),esk445_5(X32368,X32369,X32370,X32371,X32372))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32372),tc_List_Olist(X32372))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32372),tc_List_Olist(X32372)),X32371),hAPP(hAPP(c_List_Olist_OCons(X32372),X32370),X32369))),c_List_Olistrel(X32372,X32368))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32372,X32372)),hAPP(hAPP(c_Product__Type_OPair(X32372,X32372),esk444_5(X32368,X32369,X32370,X32371,X32372)),X32370)),X32368))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32372),tc_List_Olist(X32372))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32372),tc_List_Olist(X32372)),X32371),hAPP(hAPP(c_List_Olist_OCons(X32372),X32370),X32369))),c_List_Olistrel(X32372,X32368))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32372),tc_List_Olist(X32372))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32372),tc_List_Olist(X32372)),esk445_5(X32368,X32369,X32370,X32371,X32372)),X32369)),c_List_Olistrel(X32372,X32368)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32372),tc_List_Olist(X32372))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32372),tc_List_Olist(X32372)),X32371),hAPP(hAPP(c_List_Olist_OCons(X32372),X32370),X32369))),c_List_Olistrel(X32372,X32368))) ) ),
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,
! [X30620,X30621,X30622,X30623,X30624] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30624,X30624)),hAPP(hAPP(c_Product__Type_OPair(X30624,X30624),X30623),esk386_5(X30620,X30621,X30622,X30623,X30624))),X30620))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30624,X30624)),hAPP(hAPP(c_Product__Type_OPair(X30624,X30624),X30623),X30622)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30624,X30624),tc_HOL_Obool),hAPP(c_Nat_OSuc,X30621)),X30620))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30624,X30624)),hAPP(hAPP(c_Product__Type_OPair(X30624,X30624),esk386_5(X30620,X30621,X30622,X30623,X30624)),X30622)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30624,X30624),tc_HOL_Obool),X30621),X30620)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30624,X30624)),hAPP(hAPP(c_Product__Type_OPair(X30624,X30624),X30623),X30622)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30624,X30624),tc_HOL_Obool),hAPP(c_Nat_OSuc,X30621)),X30620))) ) ),
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,
! [X30608,X30609,X30610,X30611,X30612] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30612,X30612)),hAPP(hAPP(c_Product__Type_OPair(X30612,X30612),X30611),esk384_5(X30608,X30609,X30610,X30611,X30612))),X30608))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30612,X30612)),hAPP(hAPP(c_Product__Type_OPair(X30612,X30612),X30611),X30610)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30612,X30612),tc_HOL_Obool),hAPP(c_Nat_OSuc,X30609)),X30608))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30612,X30612)),hAPP(hAPP(c_Product__Type_OPair(X30612,X30612),esk384_5(X30608,X30609,X30610,X30611,X30612)),X30610)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30612,X30612),tc_HOL_Obool),X30609),X30608)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30612,X30612)),hAPP(hAPP(c_Product__Type_OPair(X30612,X30612),X30611),X30610)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30612,X30612),tc_HOL_Obool),hAPP(c_Nat_OSuc,X30609)),X30608))) ) ),
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,
! [X30541,X30542,X30543,X30544,X30545] :
( ( X30542 = hAPP(c_Nat_OSuc,esk375_5(X30541,X30542,X30543,X30544,X30545))
| X30542 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30545,X30545)),hAPP(hAPP(c_Product__Type_OPair(X30545,X30545),X30544),X30543)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30545,X30545),tc_HOL_Obool),X30542),X30541))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30545,X30545)),hAPP(hAPP(c_Product__Type_OPair(X30545,X30545),X30544),esk374_5(X30541,X30542,X30543,X30544,X30545))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30545,X30545),tc_HOL_Obool),esk375_5(X30541,X30542,X30543,X30544,X30545)),X30541)))
| X30542 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30545,X30545)),hAPP(hAPP(c_Product__Type_OPair(X30545,X30545),X30544),X30543)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30545,X30545),tc_HOL_Obool),X30542),X30541))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30545,X30545)),hAPP(hAPP(c_Product__Type_OPair(X30545,X30545),esk374_5(X30541,X30542,X30543,X30544,X30545)),X30543)),X30541))
| X30542 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30545,X30545)),hAPP(hAPP(c_Product__Type_OPair(X30545,X30545),X30544),X30543)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30545,X30545),tc_HOL_Obool),X30542),X30541))) )
& ( X30542 = hAPP(c_Nat_OSuc,esk375_5(X30541,X30542,X30543,X30544,X30545))
| X30544 = X30543
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30545,X30545)),hAPP(hAPP(c_Product__Type_OPair(X30545,X30545),X30544),X30543)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30545,X30545),tc_HOL_Obool),X30542),X30541))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30545,X30545)),hAPP(hAPP(c_Product__Type_OPair(X30545,X30545),X30544),esk374_5(X30541,X30542,X30543,X30544,X30545))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30545,X30545),tc_HOL_Obool),esk375_5(X30541,X30542,X30543,X30544,X30545)),X30541)))
| X30544 = X30543
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30545,X30545)),hAPP(hAPP(c_Product__Type_OPair(X30545,X30545),X30544),X30543)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30545,X30545),tc_HOL_Obool),X30542),X30541))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30545,X30545)),hAPP(hAPP(c_Product__Type_OPair(X30545,X30545),esk374_5(X30541,X30542,X30543,X30544,X30545)),X30543)),X30541))
| X30544 = X30543
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30545,X30545)),hAPP(hAPP(c_Product__Type_OPair(X30545,X30545),X30544),X30543)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30545,X30545),tc_HOL_Obool),X30542),X30541))) ) ),
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,
! [X30614,X30615,X30616,X30617,X30618] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30618,X30618)),hAPP(hAPP(c_Product__Type_OPair(X30618,X30618),X30617),esk385_5(X30614,X30615,X30616,X30617,X30618))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30618,X30618),tc_HOL_Obool),X30615),X30614)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30618,X30618)),hAPP(hAPP(c_Product__Type_OPair(X30618,X30618),X30617),X30616)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30618,X30618),tc_HOL_Obool),hAPP(c_Nat_OSuc,X30615)),X30614))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30618,X30618)),hAPP(hAPP(c_Product__Type_OPair(X30618,X30618),esk385_5(X30614,X30615,X30616,X30617,X30618)),X30616)),X30614))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30618,X30618)),hAPP(hAPP(c_Product__Type_OPair(X30618,X30618),X30617),X30616)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30618,X30618),tc_HOL_Obool),hAPP(c_Nat_OSuc,X30615)),X30614))) ) ),
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,
! [X25792,X25793,X25794] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X25794),X25793),X25792) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25794,tc_fun(tc_fun(X25794,tc_HOL_Obool),tc_HOL_Obool)),X25793),hAPP(hAPP(c_COMBC(X25794,tc_fun(tc_fun(X25794,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X25794,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25794,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X25794,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X25794,tc_HOL_Obool),tc_HOL_Obool)),X25794),c_Set_Oinsert(tc_fun(X25794,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X25794,tc_HOL_Obool),tc_fun(X25794,tc_HOL_Obool),X25794),c_Relation_OImage(X25794,X25794,X25792)),hAPP(hAPP(c_COMBC(X25794,tc_fun(X25794,tc_HOL_Obool),tc_fun(X25794,tc_HOL_Obool)),c_Set_Oinsert(X25794)),c_Orderings_Obot__class_Obot(tc_fun(X25794,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X25794,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,
! [X24442,X24443,X24444,X24445,X24446] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X24444,X24446)),hAPP(hAPP(c_Product__Type_OPair(X24444,X24446),esk123_5(X24442,X24443,X24444,X24445,X24446)),X24445)),X24443))
| ~ hBOOL(hAPP(hAPP(c_member(X24446),X24445),hAPP(c_Relation_OImage(X24444,X24446,X24443),X24442))) )
& ( hBOOL(hAPP(hAPP(c_member(X24444),esk123_5(X24442,X24443,X24444,X24445,X24446)),X24442))
| ~ hBOOL(hAPP(hAPP(c_member(X24446),X24445),hAPP(c_Relation_OImage(X24444,X24446,X24443),X24442))) ) ),
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,
! [X24360,X24361,X24362,X24363,X24364,X24366,X24367,X24368,X24369,X24370,X24371] :
( ( hBOOL(hAPP(hAPP(c_member(X24362),esk119_5(X24360,X24361,X24362,X24363,X24364)),X24360))
| ~ hBOOL(hAPP(hAPP(c_member(X24364),X24363),hAPP(c_Relation_OImage(X24362,X24364,X24361),X24360))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X24362,X24364)),hAPP(hAPP(c_Product__Type_OPair(X24362,X24364),esk119_5(X24360,X24361,X24362,X24363,X24364)),X24363)),X24361))
| ~ hBOOL(hAPP(hAPP(c_member(X24364),X24363),hAPP(c_Relation_OImage(X24362,X24364,X24361),X24360))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X24368),X24371),X24366))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24368,X24370)),hAPP(hAPP(c_Product__Type_OPair(X24368,X24370),X24371),X24369)),X24367))
| hBOOL(hAPP(hAPP(c_member(X24370),X24369),hAPP(c_Relation_OImage(X24368,X24370,X24367),X24366))) ) ),
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,
! [X31960,X31961,X31962] :
( ~ hBOOL(hAPP(c_List_Odistinct(X31962),hAPP(hAPP(c_List_Omap(tc_prod(X31962,X31961),X31962),c_Product__Type_Ofst(X31962,X31961)),X31960)))
| hAPP(c_List_Oset(tc_prod(X31962,X31961)),X31960) = hAPP(c_Set_OCollect(tc_prod(X31962,X31961)),hAPP(c_Product__Type_Oprod_Oprod__case(X31962,X31961,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X31962,tc_fun(X31961,tc_Option_Ooption(X31961)),tc_fun(X31961,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X31961),tc_HOL_Obool),tc_fun(tc_fun(X31961,tc_Option_Ooption(X31961)),tc_fun(X31961,tc_HOL_Obool)),X31962),c_COMBB(tc_Option_Ooption(X31961),tc_HOL_Obool,X31961)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X31961),tc_fun(tc_Option_Ooption(X31961),tc_HOL_Obool),X31962),c_fequal),c_Map_Omap__of(X31962,X31961,X31960)))),c_Option_Ooption_OSome(X31961)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__map__of__compr])]) ).
fof(i_0_6305,plain,
! [X25407,X25408,X25409,X25410] :
( ~ c_Finite__Set_Ofolding__one(X25410,X25409,X25408)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25410),X25407))
| X25407 = c_Orderings_Obot__class_Obot(tc_fun(X25410,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X25410),hAPP(hAPP(X25409,esk143_4(X25407,X25408,X25409,X25410)),esk144_4(X25407,X25408,X25409,X25410))),hAPP(hAPP(c_Set_Oinsert(X25410),esk143_4(X25407,X25408,X25409,X25410)),hAPP(hAPP(c_Set_Oinsert(X25410),esk144_4(X25407,X25408,X25409,X25410)),c_Orderings_Obot__class_Obot(tc_fun(X25410,tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_member(X25410),hAPP(X25408,X25407)),X25407)) ),
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,
! [X26550,X26551,X26552,X26553] :
( ~ c_Fun_Oinj__on(X26553,tc_fun(tc_fun(X26553,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X26553,tc_fun(tc_prod(X26553,X26553),tc_HOL_Obool),tc_fun(tc_fun(X26553,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26553,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X26553,X26553),tc_HOL_Obool),tc_fun(tc_fun(X26553,tc_HOL_Obool),tc_HOL_Obool)),X26553),c_Equiv__Relations_Oquotient(X26553)),hAPP(hAPP(c_COMBC(X26553,tc_fun(X26553,tc_HOL_Obool),tc_fun(X26553,tc_HOL_Obool)),c_Set_Oinsert(X26553)),c_Orderings_Obot__class_Obot(tc_fun(X26553,tc_HOL_Obool))))),X26552),X26551)
| ~ hBOOL(hAPP(hAPP(c_member(X26553),X26550),X26551))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(X26553),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26553,tc_HOL_Obool)),X26551),hAPP(hAPP(c_Set_Oinsert(X26553),X26550),c_Orderings_Obot__class_Obot(tc_fun(X26553,tc_HOL_Obool))))),X26552) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(X26553,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26553),X26551),X26552)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26553),hAPP(hAPP(c_Set_Oinsert(X26553),X26550),c_Orderings_Obot__class_Obot(tc_fun(X26553,tc_HOL_Obool)))),X26552)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__diff1])]) ).
fof(i_0_6309,plain,
! [X31087,X31088,X31089,X31090] : hAPP(c_Set_OCollect(X31090),hAPP(hAPP(c_COMBB(tc_fun(X31089,tc_HOL_Obool),tc_HOL_Obool,X31090),c_HOL_OAll(X31089)),hAPP(hAPP(c_COMBB(tc_fun(X31089,tc_HOL_Obool),tc_fun(X31089,tc_HOL_Obool),X31090),hAPP(c_COMBS(X31089,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X31089),c_fimplies),hAPP(hAPP(c_COMBC(X31089,tc_fun(X31089,tc_HOL_Obool),tc_HOL_Obool),c_member(X31089)),X31088)))),X31087))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31089,tc_fun(X31090,tc_HOL_Obool)),X31088),hAPP(hAPP(c_COMBB(tc_fun(X31090,tc_HOL_Obool),tc_fun(X31090,tc_HOL_Obool),X31089),c_Set_OCollect(X31090)),hAPP(c_COMBC(X31090,X31089,tc_HOL_Obool),X31087))),
inference(variable_rename,[status(thm)],[fact_Collect__ball__eq]) ).
fof(i_0_6310,plain,
! [X33175,X33176,X33177,X33178] : c_List_Osublist(X33178,hAPP(hAPP(c_List_Oappend(X33178),X33177),X33176),X33175) = hAPP(hAPP(c_List_Oappend(X33178),c_List_Osublist(X33178,X33177,X33175)),c_List_Osublist(X33178,X33176,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(X33178)),X33177)))),X33175)))),
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,
! [X34000,X34001,X34002,X34003,X34004] : hAPP(hAPP(c_List_Omap(X34004,X34003),X34002),hAPP(c_List_Ofilter(X34004,X34001),X34000)) = c_List_Omap__filter(X34004,X34003,hAPP(hAPP(c_COMBC(X34004,tc_Option_Ooption(X34003),tc_Option_Ooption(X34003)),hAPP(hAPP(c_COMBS(X34004,tc_Option_Ooption(X34003),tc_fun(tc_Option_Ooption(X34003),tc_Option_Ooption(X34003))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X34003),tc_fun(tc_Option_Ooption(X34003),tc_Option_Ooption(X34003))),X34004),c_If(tc_Option_Ooption(X34003))),X34001)),hAPP(hAPP(c_COMBB(X34003,tc_Option_Ooption(X34003),X34004),c_Option_Ooption_OSome(X34003)),X34002))),c_Option_Ooption_ONone(X34003)),X34000),
inference(variable_rename,[status(thm)],[fact_map__filter__map__filter]) ).
fof(i_0_6318,plain,
! [X26418,X26419,X26420] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26420),X26419))
| ~ c_Fun_Oinj__on(X26420,tc_fun(tc_fun(X26420,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X26420,tc_fun(tc_prod(X26420,X26420),tc_HOL_Obool),tc_fun(tc_fun(X26420,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26420,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X26420,X26420),tc_HOL_Obool),tc_fun(tc_fun(X26420,tc_HOL_Obool),tc_HOL_Obool)),X26420),c_Equiv__Relations_Oquotient(X26420)),hAPP(hAPP(c_COMBC(X26420,tc_fun(X26420,tc_HOL_Obool),tc_fun(X26420,tc_HOL_Obool)),c_Set_Oinsert(X26420)),c_Orderings_Obot__class_Obot(tc_fun(X26420,tc_HOL_Obool))))),X26418),X26419)
| hAPP(c_Finite__Set_Ocard(tc_fun(X26420,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X26420),X26419),X26418)) = hAPP(c_Finite__Set_Ocard(X26420),X26419) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__quotient__disjoint])]) ).
fof(i_0_6319,plain,
! [X29243,X29244,X29245,X29246,X29247] : c_Map_Odom(X29247,X29246,hAPP(hAPP(c_COMBS(X29247,tc_Option_Ooption(X29246),tc_Option_Ooption(X29246)),hAPP(hAPP(c_COMBS(X29247,tc_Option_Ooption(X29246),tc_fun(tc_Option_Ooption(X29246),tc_Option_Ooption(X29246))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X29246),tc_fun(tc_Option_Ooption(X29246),tc_Option_Ooption(X29246))),X29247),c_If(tc_Option_Ooption(X29246))),X29245)),X29244)),X29243)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29247,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29247,tc_HOL_Obool)),c_Map_Odom(X29247,X29246,X29244)),hAPP(c_Set_OCollect(X29247),X29245))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29247,tc_HOL_Obool)),c_Map_Odom(X29247,X29246,X29243)),hAPP(c_Set_OCollect(X29247),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29247),c_fNot),X29245)))),
inference(variable_rename,[status(thm)],[fact_dom__if]) ).
fof(i_0_6320,plain,
! [X33954,X33955,X33956,X33957] : c_List_Omap__filter(X33957,X33956,X33955,X33954) = hAPP(hAPP(c_List_Omap(X33957,X33956),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X33956),X33956,X33957,c_Option_Othe(X33956)),X33955)),hAPP(c_List_Ofilter(X33957,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X33957),c_fNot),hAPP(hAPP(c_COMBC(X33957,tc_Option_Ooption(X33956),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X33956),tc_fun(tc_Option_Ooption(X33956),tc_HOL_Obool),X33957),c_fequal),X33955)),c_Option_Ooption_ONone(X33956)))),X33954)),
inference(variable_rename,[status(thm)],[fact_map__filter__def]) ).
fof(i_0_6321,plain,
! [X27447,X27448,X27449,X27450] :
( ~ class_Rings_Ocomm__semiring__1(X27450)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27450),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27450),c_Groups_Oone__class_Oone(X27450)),c_Groups_Oone__class_Oone(X27450))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27450),hAPP(hAPP(c_COMBB(X27450,X27450,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(X27450),X27449)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X27450,X27450),hAPP(hAPP(c_COMBB(X27450,tc_fun(X27450,X27450),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(X27450)),c_Nat_Osemiring__1__class_Oof__nat(X27450))),X27448))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X27447))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27450),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27450),X27447)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27450),X27449),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27450),X27449),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27450),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27450),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X27447),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X27448)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__series__general])]) ).
fof(i_0_6322,plain,
! [X25234,X25235] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25235),X25234))
| 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)))),X25234,X25235) = 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,
! [X25232,X25233] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25233),X25232))
| 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)))),X25232,X25233) = 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,
! [X23564,X23565] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),esk102_2(X23564,X23565)),esk103_2(X23564,X23565)))
| c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X23565,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)))),X23564)
| ~ class_Orderings_Oorder(X23565) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),esk103_2(X23564,X23565)),esk102_2(X23564,X23565)))
| c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X23565,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)))),X23564)
| ~ class_Orderings_Oorder(X23565) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23565),hAPP(X23564,esk102_2(X23564,X23565))),hAPP(X23564,esk103_2(X23564,X23565))))
| c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X23565,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)))),X23564)
| ~ class_Orderings_Oorder(X23565) ) ),
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,
! [X25123,X25124] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25124),X25123))
| 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)))),X25123,X25124) = 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,
! [X29649,X29650] :
( ( c_Wellfounded_Owf(X29650,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X29650,X29650),tc_HOL_Obool),tc_fun(tc_prod(X29650,X29650),tc_HOL_Obool)),X29649))
| ~ c_FunDef_Oreduction__pair(X29650,X29649) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29650,X29650),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X29650,X29650,X29650),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X29650,X29650),tc_HOL_Obool),tc_fun(tc_prod(X29650,X29650),tc_HOL_Obool)),X29649)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X29650,X29650),tc_HOL_Obool),tc_fun(tc_prod(X29650,X29650),tc_HOL_Obool)),X29649))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X29650,X29650),tc_HOL_Obool),tc_fun(tc_prod(X29650,X29650),tc_HOL_Obool)),X29649)))
| ~ c_FunDef_Oreduction__pair(X29650,X29649) )
& ( ~ c_Wellfounded_Owf(X29650,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X29650,X29650),tc_HOL_Obool),tc_fun(tc_prod(X29650,X29650),tc_HOL_Obool)),X29649))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29650,X29650),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X29650,X29650,X29650),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X29650,X29650),tc_HOL_Obool),tc_fun(tc_prod(X29650,X29650),tc_HOL_Obool)),X29649)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X29650,X29650),tc_HOL_Obool),tc_fun(tc_prod(X29650,X29650),tc_HOL_Obool)),X29649))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X29650,X29650),tc_HOL_Obool),tc_fun(tc_prod(X29650,X29650),tc_HOL_Obool)),X29649)))
| c_FunDef_Oreduction__pair(X29650,X29649) ) ),
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,
! [X25994,X25995,X25996,X25997,X25998,X25999,X26000,X26001,X26002,X26003,X26004] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25998,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25997,tc_fun(X25998,tc_HOL_Obool)),X25996),X25995)),X25994))
| ~ hBOOL(hAPP(hAPP(c_member(X25997),X25999),X25996))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25998,tc_HOL_Obool)),hAPP(X25995,X25999)),X25994)) )
& ( hBOOL(hAPP(hAPP(c_member(X26003),esk168_5(X26000,X26001,X26002,X26003,X26004)),X26002))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26004,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26003,tc_fun(X26004,tc_HOL_Obool)),X26002),X26001)),X26000)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26004,tc_HOL_Obool)),hAPP(X26001,esk168_5(X26000,X26001,X26002,X26003,X26004))),X26000))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26004,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26003,tc_fun(X26004,tc_HOL_Obool)),X26002),X26001)),X26000)) ) ),
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,
! [X27457,X27458,X27459,X27460,X27461] :
( ( hBOOL(hAPP(hAPP(c_member(X27460),esk243_5(X27457,X27458,X27459,X27460,X27461)),X27459))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27461),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27460,X27461),X27458),X27459)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27461),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27461),hAPP(c_Finite__Set_Ocard(X27460),X27459))),X27457)))
| ~ class_Groups_Oordered__ab__semigroup__add(X27461)
| ~ class_Rings_Osemiring__1(X27461) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27461),hAPP(X27458,esk243_5(X27457,X27458,X27459,X27460,X27461))),X27457))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27461),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27460,X27461),X27458),X27459)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27461),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27461),hAPP(c_Finite__Set_Ocard(X27460),X27459))),X27457)))
| ~ class_Groups_Oordered__ab__semigroup__add(X27461)
| ~ class_Rings_Osemiring__1(X27461) ) ),
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,
! [X29000,X29001,X29002,X29003,X29004,X29005] : c_Product__Type_Omap__pair(X29005,X29004,X29003,X29002,X29001,X29000) = hAPP(c_Product__Type_Oprod_Oprod__case(X29005,X29003,tc_prod(X29004,X29002)),hAPP(hAPP(c_COMBC(X29005,tc_fun(X29003,X29002),tc_fun(X29003,tc_prod(X29004,X29002))),hAPP(hAPP(c_COMBB(tc_fun(X29002,tc_prod(X29004,X29002)),tc_fun(tc_fun(X29003,X29002),tc_fun(X29003,tc_prod(X29004,X29002))),X29005),c_COMBB(X29002,tc_prod(X29004,X29002),X29003)),hAPP(hAPP(c_COMBB(X29004,tc_fun(X29002,tc_prod(X29004,X29002)),X29005),c_Product__Type_OPair(X29004,X29002)),X29001))),X29000)),
inference(variable_rename,[status(thm)],[fact_map__pair__def]) ).
fof(i_0_6335,plain,
! [X20623,X20624,X20625] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20625))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20624),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),X20624),X20623))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X20625))),X20623)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_decr__lemma])]) ).
fof(i_0_6336,plain,
! [X25937,X25938,X25939,X25940,X25941,X25942] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25941),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25940,X25941),X25939),X25938)),X25937))
| ~ hBOOL(hAPP(hAPP(c_member(X25940),X25942),X25939))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25941),hAPP(X25938,X25942)),X25937))
| ~ class_Complete__Lattice_Ocomplete__lattice(X25941) )
& ( hBOOL(hAPP(hAPP(c_member(X25940),esk163_5(X25937,X25938,X25939,X25940,X25941)),X25939))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25941),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25940,X25941),X25939),X25938)),X25937))
| ~ class_Complete__Lattice_Ocomplete__lattice(X25941) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25941),hAPP(X25938,esk163_5(X25937,X25938,X25939,X25940,X25941))),X25937))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25941),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25940,X25941),X25939),X25938)),X25937))
| ~ class_Complete__Lattice_Ocomplete__lattice(X25941) ) ),
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,
! [X32609,X32610,X32611,X32612,X32614,X32615,X32616,X32617,X32618] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk456_4(X32609,X32610,X32611,X32612)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32612)),X32611)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32612)),X32610))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32612)),X32611)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32612)),X32610)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32612),tc_List_Olist(X32612))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32612),tc_List_Olist(X32612)),X32611),X32610)),c_List_Olexord(X32612,X32609))) )
& ( hAPP(hAPP(c_List_Otake(X32612),esk456_4(X32609,X32610,X32611,X32612)),X32611) = hAPP(hAPP(c_List_Otake(X32612),esk456_4(X32609,X32610,X32611,X32612)),X32610)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32612)),X32611)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32612)),X32610)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32612),tc_List_Olist(X32612))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32612),tc_List_Olist(X32612)),X32611),X32610)),c_List_Olexord(X32612,X32609))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32612,X32612)),hAPP(hAPP(c_Product__Type_OPair(X32612,X32612),hAPP(hAPP(c_List_Onth(X32612),X32611),esk456_4(X32609,X32610,X32611,X32612))),hAPP(hAPP(c_List_Onth(X32612),X32610),esk456_4(X32609,X32610,X32611,X32612)))),X32609))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32612)),X32611)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32612)),X32610)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32612),tc_List_Olist(X32612))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32612),tc_List_Olist(X32612)),X32611),X32610)),c_List_Olexord(X32612,X32609))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk456_4(X32609,X32610,X32611,X32612)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32612)),X32611)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32612)),X32610))))
| hAPP(hAPP(c_List_Otake(X32612),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32612)),X32611)),X32610) = X32611
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32612),tc_List_Olist(X32612))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32612),tc_List_Olist(X32612)),X32611),X32610)),c_List_Olexord(X32612,X32609))) )
& ( hAPP(hAPP(c_List_Otake(X32612),esk456_4(X32609,X32610,X32611,X32612)),X32611) = hAPP(hAPP(c_List_Otake(X32612),esk456_4(X32609,X32610,X32611,X32612)),X32610)
| hAPP(hAPP(c_List_Otake(X32612),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32612)),X32611)),X32610) = X32611
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32612),tc_List_Olist(X32612))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32612),tc_List_Olist(X32612)),X32611),X32610)),c_List_Olexord(X32612,X32609))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32612,X32612)),hAPP(hAPP(c_Product__Type_OPair(X32612,X32612),hAPP(hAPP(c_List_Onth(X32612),X32611),esk456_4(X32609,X32610,X32611,X32612))),hAPP(hAPP(c_List_Onth(X32612),X32610),esk456_4(X32609,X32610,X32611,X32612)))),X32609))
| hAPP(hAPP(c_List_Otake(X32612),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32612)),X32611)),X32610) = X32611
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32612),tc_List_Olist(X32612))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32612),tc_List_Olist(X32612)),X32611),X32610)),c_List_Olexord(X32612,X32609))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32617)),X32616)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32617)),X32615)))
| hAPP(hAPP(c_List_Otake(X32617),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32617)),X32616)),X32615) != X32616
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32617),tc_List_Olist(X32617))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32617),tc_List_Olist(X32617)),X32616),X32615)),c_List_Olexord(X32617,X32614))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32618),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32617)),X32616)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32617)),X32615))))
| hAPP(hAPP(c_List_Otake(X32617),X32618),X32616) != hAPP(hAPP(c_List_Otake(X32617),X32618),X32615)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32617,X32617)),hAPP(hAPP(c_Product__Type_OPair(X32617,X32617),hAPP(hAPP(c_List_Onth(X32617),X32616),X32618)),hAPP(hAPP(c_List_Onth(X32617),X32615),X32618))),X32614))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32617),tc_List_Olist(X32617))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32617),tc_List_Olist(X32617)),X32616),X32615)),c_List_Olexord(X32617,X32614))) ) ),
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,
! [X29550,X29551,X29552,X29553,X29554,X29555,X29556,X29557] :
( ~ hBOOL(hAPP(hAPP(X29557,X29556),X29555))
| ~ hBOOL(hAPP(hAPP(X29554,X29555),X29553))
| c_Predicate_Opred__comp(X29552,X29551,X29550,X29557,X29554,X29556,X29553) ),
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,
! [X29129,X29130,X29131,X29132] : hAPP(c_Set_OCollect(tc_prod(X29132,X29131)),hAPP(c_Product__Type_Oprod_Oprod__case(X29132,X29131,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X29132,tc_fun(X29131,tc_HOL_Obool),tc_fun(X29131,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X29131,tc_HOL_Obool),tc_fun(X29131,tc_HOL_Obool)),X29132),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29131)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29132),c_fconj),X29130))),X29129))) = hAPP(hAPP(c_Product__Type_OSigma(X29132,X29131),hAPP(c_Set_OCollect(X29132),X29130)),hAPP(hAPP(c_COMBB(tc_fun(X29131,tc_HOL_Obool),tc_fun(X29131,tc_HOL_Obool),X29132),c_Set_OCollect(X29131)),X29129)),
inference(variable_rename,[status(thm)],[fact_SetCompr__Sigma__eq]) ).
fof(i_0_6344,plain,
! [X29275,X29276] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29276))
| 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)),X29276))),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,X29275))))) != 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,
! [X30013,X30014,X30015,X30016] : c_Hilbert__Choice_OEps(tc_prod(X30016,X30015),hAPP(c_Product__Type_Oprod_Oprod__case(X30016,X30015,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X30016,tc_fun(X30015,tc_HOL_Obool),tc_fun(X30015,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X30015,tc_HOL_Obool),tc_fun(X30015,tc_HOL_Obool)),X30016),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X30015)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X30016),c_fconj),hAPP(c_fequal,X30014)))),hAPP(c_fequal,X30013)))) = hAPP(hAPP(c_Product__Type_OPair(X30016,X30015),X30014),X30013),
inference(variable_rename,[status(thm)],[fact_Eps__split__eq]) ).
fof(i_0_6346,plain,
! [X22996,X22997,X22998,X22999] : c_HOL_OThe(tc_prod(X22999,X22998),hAPP(c_Product__Type_Oprod_Oprod__case(X22999,X22998,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X22999,tc_fun(X22998,tc_HOL_Obool),tc_fun(X22998,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X22998,tc_HOL_Obool),tc_fun(X22998,tc_HOL_Obool)),X22999),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X22998)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X22999),c_fconj),hAPP(c_fequal,X22997)))),hAPP(c_fequal,X22996)))) = hAPP(hAPP(c_Product__Type_OPair(X22999,X22998),X22997),X22996),
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,
! [X27199,X27200,X27201,X27202,X27203,X27204] :
( ~ class_Groups_Ocomm__monoid__add(X27204)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27203,X27204),hAPP(hAPP(c_COMBC(X27203,tc_fun(X27202,tc_HOL_Obool),X27204),hAPP(hAPP(c_COMBB(tc_fun(X27202,X27204),tc_fun(tc_fun(X27202,tc_HOL_Obool),X27204),X27203),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27202,X27204)),X27201)),X27200)),X27199) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27202,X27204),hAPP(hAPP(c_COMBC(X27202,tc_fun(X27203,tc_HOL_Obool),X27204),hAPP(hAPP(c_COMBB(tc_fun(X27203,X27204),tc_fun(tc_fun(X27203,tc_HOL_Obool),X27204),X27202),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27203,X27204)),hAPP(c_COMBC(X27203,X27202,X27204),X27201))),X27199)),X27200) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__commute])]) ).
fof(i_0_6349,plain,
! [X29133,X29134,X29135,X29136] : hAPP(c_Set_OCollect(tc_prod(X29136,X29135)),hAPP(c_Product__Type_Oprod_Oprod__case(X29136,X29135,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X29136,tc_fun(X29135,tc_HOL_Obool),tc_fun(X29135,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X29135,tc_HOL_Obool),tc_fun(X29135,tc_HOL_Obool)),X29136),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29135)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29136),c_fconj),X29134))),X29133))) = hAPP(hAPP(c_Product__Type_OSigma(X29136,X29135),hAPP(c_Set_OCollect(X29136),X29134)),hAPP(c_COMBK(tc_fun(X29135,tc_HOL_Obool),X29136),hAPP(c_Set_OCollect(X29135),X29133))),
inference(variable_rename,[status(thm)],[fact_Collect__split]) ).
fof(i_0_6350,plain,
! [X26295,X26296,X26297,X26298] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26298),X26297))
| hAPP(c_Set_Oimage(X26298,X26296,X26295),X26297) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(X26296,tc_HOL_Obool),X26298,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26296,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X26298,tc_fun(X26296,tc_HOL_Obool),tc_fun(X26296,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X26296,tc_fun(tc_fun(X26296,tc_HOL_Obool),tc_fun(X26296,tc_HOL_Obool)),X26298),c_Set_Oinsert(X26296)),X26295)),c_Orderings_Obot__class_Obot(tc_fun(X26296,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(X26296,tc_HOL_Obool))),X26297) ),
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,
! [X25521,X25522,X25523,X25524] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25524),X25523))
| ~ hBOOL(hAPP(hAPP(c_member(X25524),X25522),X25523))
| ~ hBOOL(hAPP(hAPP(c_member(X25524),X25521),X25523))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25524),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25524,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25524,tc_HOL_Obool)),X25523),hAPP(hAPP(c_Set_Oinsert(X25524),X25522),c_Orderings_Obot__class_Obot(tc_fun(X25524,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X25524),X25521),c_Orderings_Obot__class_Obot(tc_fun(X25524,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X25524),X25523))) ),
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,
! [X26250,X26251] : c_Relation_OId__on(X26251,X26250) = hAPP(c_Product__Type_Oprod_Oprod__case(X26251,X26251,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X26251,tc_HOL_Obool,tc_fun(X26251,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26251,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(X26251,tc_HOL_Obool)),X26251),c_COMBC(X26251,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26251,tc_HOL_Obool),tc_fun(X26251,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X26251),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X26251),c_fconj)),c_fequal))),X26250)),
inference(variable_rename,[status(thm)],[fact_Id__on__def_H]) ).
fof(i_0_6355,plain,
! [X29330] : c_Int_Oint__ge__less__than(X29330) = 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),X29330)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
inference(variable_rename,[status(thm)],[fact_int__ge__less__than__def]) ).
fof(i_0_6356,plain,
! [X22825,X22826,X22827,X22828,X22829,X22830,X22831,X22832,X22833] : hAPP(hAPP(c_Product__Type_Oscomp(X22833,X22832,X22831,X22830),hAPP(hAPP(c_Product__Type_Oscomp(X22833,X22829,X22828,tc_prod(X22832,X22831)),X22827),X22826)),X22825) = hAPP(hAPP(c_Product__Type_Oscomp(X22833,X22829,X22828,X22830),X22827),hAPP(hAPP(c_COMBC(X22829,tc_fun(X22832,tc_fun(X22831,X22830)),tc_fun(X22828,X22830)),hAPP(hAPP(c_COMBB(tc_fun(X22828,tc_prod(X22832,X22831)),tc_fun(tc_fun(X22832,tc_fun(X22831,X22830)),tc_fun(X22828,X22830)),X22829),c_Product__Type_Oscomp(X22828,X22832,X22831,X22830)),X22826)),X22825)),
inference(variable_rename,[status(thm)],[fact_scomp__scomp]) ).
fof(i_0_6357,plain,
! [X23905,X23906,X23907,X23908] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X23908),X23907))
| ~ 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)),X23906),X23908)),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)),X23905),X23907)),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)),X23906),X23905)),X23907)),c_FunDef_Omax__weak)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wmax__insertI])]) ).
fof(i_0_6358,plain,
! [X23896,X23897,X23898,X23899] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X23899),X23898))
| ~ 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)),X23897),X23899)),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)),X23896),X23898)),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)),X23897),X23896)),X23898)),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,
! [X34019,X34020,X34021,X34022,X34023] :
( ~ class_Orderings_Olinorder(X34023)
| c_List_Olinorder__class_Osorted(X34023,hAPP(hAPP(c_List_Omap(X34022,X34023),X34021),hAPP(c_List_Ofilter(X34022,hAPP(hAPP(c_COMBC(X34022,X34023,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X34023,tc_fun(X34023,tc_HOL_Obool),X34022),c_fequal),X34021)),hAPP(X34020,X34019))),X34019))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__map__same])]) ).
fof(i_0_6362,plain,
! [X32375,X32376,X32377,X32378,X32379] :
( ( X32376 = hAPP(hAPP(c_List_Olist_OCons(X32379),esk446_5(X32375,X32376,X32377,X32378,X32379)),esk447_5(X32375,X32376,X32377,X32378,X32379))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32379),tc_List_Olist(X32379))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32379),tc_List_Olist(X32379)),hAPP(hAPP(c_List_Olist_OCons(X32379),X32378),X32377)),X32376)),c_List_Olistrel(X32379,X32375))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32379,X32379)),hAPP(hAPP(c_Product__Type_OPair(X32379,X32379),X32378),esk446_5(X32375,X32376,X32377,X32378,X32379))),X32375))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32379),tc_List_Olist(X32379))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32379),tc_List_Olist(X32379)),hAPP(hAPP(c_List_Olist_OCons(X32379),X32378),X32377)),X32376)),c_List_Olistrel(X32379,X32375))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32379),tc_List_Olist(X32379))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32379),tc_List_Olist(X32379)),X32377),esk447_5(X32375,X32376,X32377,X32378,X32379))),c_List_Olistrel(X32379,X32375)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32379),tc_List_Olist(X32379))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32379),tc_List_Olist(X32379)),hAPP(hAPP(c_List_Olist_OCons(X32379),X32378),X32377)),X32376)),c_List_Olistrel(X32379,X32375))) ) ),
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,
! [X27997,X27998,X27999,X28000,X28001] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X28001,X28000,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X28001)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X28001),c_Hoare__Mirabelle_Opeek__and(X28001,X27999,X27998)),X27997),X27999)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X28001),tc_HOL_Obool))))
| c_Hoare__Mirabelle_Ohoare__derivs(X28001,X28000,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X28001)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X28001),X27999),c_Com_Ocom_OWhile(X27998,X27997)),c_Hoare__Mirabelle_Opeek__and(X28001,X27999,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X27998)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X28001),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,
! [X30040,X30041,X30042,X30043,X30044,X30046,X30047,X30048,X30049,X30051] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X30043),X30042))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X30043,tc_HOL_Obool),tc_fun(X30043,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X30043,tc_HOL_Obool),tc_fun(X30043,tc_HOL_Obool)),X30042),X30041)),c_Wellfounded_Omax__ext(X30043,X30040))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X30043),X30041))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X30043,tc_HOL_Obool),tc_fun(X30043,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X30043,tc_HOL_Obool),tc_fun(X30043,tc_HOL_Obool)),X30042),X30041)),c_Wellfounded_Omax__ext(X30043,X30040))) )
& ( X30041 != c_Orderings_Obot__class_Obot(tc_fun(X30043,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X30043,tc_HOL_Obool),tc_fun(X30043,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X30043,tc_HOL_Obool),tc_fun(X30043,tc_HOL_Obool)),X30042),X30041)),c_Wellfounded_Omax__ext(X30043,X30040))) )
& ( hBOOL(hAPP(hAPP(c_member(X30043),esk357_5(X30040,X30041,X30042,X30043,X30044)),X30041))
| ~ hBOOL(hAPP(hAPP(c_member(X30043),X30044),X30042))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X30043,tc_HOL_Obool),tc_fun(X30043,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X30043,tc_HOL_Obool),tc_fun(X30043,tc_HOL_Obool)),X30042),X30041)),c_Wellfounded_Omax__ext(X30043,X30040))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30043,X30043)),hAPP(hAPP(c_Product__Type_OPair(X30043,X30043),X30044),esk357_5(X30040,X30041,X30042,X30043,X30044))),X30040))
| ~ hBOOL(hAPP(hAPP(c_member(X30043),X30044),X30042))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X30043,tc_HOL_Obool),tc_fun(X30043,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X30043,tc_HOL_Obool),tc_fun(X30043,tc_HOL_Obool)),X30042),X30041)),c_Wellfounded_Omax__ext(X30043,X30040))) )
& ( hBOOL(hAPP(hAPP(c_member(X30049),esk358_4(X30046,X30047,X30048,X30049)),X30048))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30049),X30048))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30049),X30047))
| X30047 = c_Orderings_Obot__class_Obot(tc_fun(X30049,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X30049,tc_HOL_Obool),tc_fun(X30049,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X30049,tc_HOL_Obool),tc_fun(X30049,tc_HOL_Obool)),X30048),X30047)),c_Wellfounded_Omax__ext(X30049,X30046))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X30049),X30051),X30047))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30049,X30049)),hAPP(hAPP(c_Product__Type_OPair(X30049,X30049),esk358_4(X30046,X30047,X30048,X30049)),X30051)),X30046))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30049),X30048))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30049),X30047))
| X30047 = c_Orderings_Obot__class_Obot(tc_fun(X30049,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X30049,tc_HOL_Obool),tc_fun(X30049,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X30049,tc_HOL_Obool),tc_fun(X30049,tc_HOL_Obool)),X30048),X30047)),c_Wellfounded_Omax__ext(X30049,X30046))) ) ),
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,
! [X29569,X29570,X29571] :
( ( ~ c_Wellfounded_Owf(X29571,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29571,X29571),tc_HOL_Obool)),X29570),X29569))
| c_Wellfounded_Owf(X29571,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29571,X29571),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29571,X29571),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X29571,X29571,X29571),X29570),X29570)),hAPP(hAPP(c_Relation_Orel__comp(X29571,X29571,X29571),X29569),X29570))),X29569)) )
& ( ~ c_Wellfounded_Owf(X29571,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29571,X29571),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29571,X29571),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X29571,X29571,X29571),X29570),X29570)),hAPP(hAPP(c_Relation_Orel__comp(X29571,X29571,X29571),X29569),X29570))),X29569))
| c_Wellfounded_Owf(X29571,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29571,X29571),tc_HOL_Obool)),X29570),X29569)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__union__merge])]) ).
fof(i_0_6368,plain,
! [X29006,X29007,X29008,X29009,X29010,X29011,X29012,X29013,X29014,X29015] :
( hAPP(c_Set_Oimage(X29015,X29014,X29013),X29012) != X29011
| hAPP(c_Set_Oimage(X29010,X29009,X29008),X29007) != X29006
| hAPP(c_Set_Oimage(tc_prod(X29015,X29010),tc_prod(X29014,X29009),c_Product__Type_Omap__pair(X29015,X29014,X29010,X29009,X29013,X29008)),hAPP(hAPP(c_Product__Type_OSigma(X29015,X29010),X29012),hAPP(c_COMBK(tc_fun(X29010,tc_HOL_Obool),X29015),X29007))) = hAPP(hAPP(c_Product__Type_OSigma(X29014,X29009),X29011),hAPP(c_COMBK(tc_fun(X29009,tc_HOL_Obool),X29014),X29006)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__pair__surj__on])]) ).
fof(i_0_6369,plain,
! [X23909,X23910,X23911,X23912] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X23912),X23911))
| ~ 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)),X23912),X23910)),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)),X23911),X23909)),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)),X23911),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X23910),X23909))),c_FunDef_Omin__weak)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wmin__insertI])]) ).
fof(i_0_6370,plain,
! [X23892,X23893,X23894,X23895] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X23895),X23894))
| ~ 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)),X23895),X23893)),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)),X23894),X23892)),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)),X23894),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X23893),X23892))),c_FunDef_Omin__strict)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smin__insertI])]) ).
fof(i_0_6371,plain,
! [X28585,X28586,X28587,X28588,X28589] :
( ( hAPP(hAPP(c_Set_Oinsert(X28589),X28587),X28586) = hAPP(hAPP(c_Set_Oinsert(X28589),esk280_5(X28585,X28586,X28587,X28588,X28589)),esk281_5(X28585,X28586,X28587,X28588,X28589))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X28589,X28588,hAPP(hAPP(c_Set_Oinsert(X28589),X28587),X28586)),X28585)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28589,X28589,X28588,esk280_5(X28585,X28586,X28587,X28588,X28589),esk281_5(X28585,X28586,X28587,X28588,X28589)),X28585))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X28589,X28588,hAPP(hAPP(c_Set_Oinsert(X28589),X28587),X28586)),X28585)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X28589),esk280_5(X28585,X28586,X28587,X28588,X28589)),esk281_5(X28585,X28586,X28587,X28588,X28589)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X28589,X28588,hAPP(hAPP(c_Set_Oinsert(X28589),X28587),X28586)),X28585)) ) ),
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,
! [X28571,X28572,X28573,X28574,X28575,X28578,X28579,X28580,X28581,X28582,X28583,X28584] :
( ( hAPP(hAPP(c_Set_Oinsert(X28575),X28573),X28572) = hAPP(hAPP(c_Set_Oinsert(X28575),esk278_5(X28571,X28572,X28573,X28574,X28575)),esk279_5(X28571,X28572,X28573,X28574,X28575))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X28575,X28574,hAPP(hAPP(c_Set_Oinsert(X28575),X28573),X28572)),X28571)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28575,X28575,X28574,esk278_5(X28571,X28572,X28573,X28574,X28575),esk279_5(X28571,X28572,X28573,X28574,X28575)),X28571))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X28575,X28574,hAPP(hAPP(c_Set_Oinsert(X28575),X28573),X28572)),X28571)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X28575),esk278_5(X28571,X28572,X28573,X28574,X28575)),esk279_5(X28571,X28572,X28573,X28574,X28575)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X28575,X28574,hAPP(hAPP(c_Set_Oinsert(X28575),X28573),X28572)),X28571)) )
& ( hAPP(hAPP(c_Set_Oinsert(X28582),X28580),X28579) != hAPP(hAPP(c_Set_Oinsert(X28582),X28583),X28584)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28582,X28582,X28581,X28583,X28584),X28578))
| hBOOL(hAPP(hAPP(c_member(X28582),X28583),X28584))
| hBOOL(hAPP(c_Finite__Set_Ofold1Set(X28582,X28581,hAPP(hAPP(c_Set_Oinsert(X28582),X28580),X28579)),X28578)) ) ),
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,
! [X33286,X33287,X33288,X33289,X33292,X33293,X33294,X33295,X33296,X33297] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33289,X33289)),hAPP(hAPP(c_Product__Type_OPair(X33289,X33289),hAPP(hAPP(c_List_Onth(X33289),X33288),esk465_4(X33286,X33287,X33288,X33289))),esk464_4(X33286,X33287,X33288,X33289))),X33286))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33289),tc_List_Olist(X33289))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33289),tc_List_Olist(X33289)),X33288),X33287)),c_List_Olistrel1(X33289,X33286))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk465_4(X33286,X33287,X33288,X33289)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33289)),X33288)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33289),tc_List_Olist(X33289))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33289),tc_List_Olist(X33289)),X33288),X33287)),c_List_Olistrel1(X33289,X33286))) )
& ( X33287 = hAPP(hAPP(c_List_Olist__update(X33289,X33288),esk465_4(X33286,X33287,X33288,X33289)),esk464_4(X33286,X33287,X33288,X33289))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33289),tc_List_Olist(X33289))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33289),tc_List_Olist(X33289)),X33288),X33287)),c_List_Olistrel1(X33289,X33286))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33295,X33295)),hAPP(hAPP(c_Product__Type_OPair(X33295,X33295),hAPP(hAPP(c_List_Onth(X33295),X33294),X33297)),X33296)),X33292))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33297),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33295)),X33294)))
| X33293 != hAPP(hAPP(c_List_Olist__update(X33295,X33294),X33297),X33296)
| 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))) ) ),
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,
! [X28917,X28918,X28919,X28920,X28921,X28922] :
( hAPP(c_Set_Oimage(X28922,X28921,X28920),c_Orderings_Otop__class_Otop(tc_fun(X28922,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X28921,tc_HOL_Obool))
| hAPP(c_Set_Oimage(X28919,X28918,X28917),c_Orderings_Otop__class_Otop(tc_fun(X28919,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X28918,tc_HOL_Obool))
| hAPP(c_Set_Oimage(tc_prod(X28922,X28919),tc_prod(X28921,X28918),c_Product__Type_Omap__pair(X28922,X28921,X28919,X28918,X28920,X28917)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X28922,X28919),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X28921,X28918),tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__pair__surj])]) ).
fof(i_0_6375,plain,
! [X30739,X30740,X30741] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30741),X30740))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30741,tc_HOL_Obool)),X30739),X30740) = hAPP(hAPP(c_Finite__Set_Ofold(X30741,tc_fun(X30741,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X30741,tc_HOL_Obool),tc_fun(tc_fun(X30741,tc_HOL_Obool),tc_fun(X30741,tc_HOL_Obool)),X30741),hAPP(c_COMBC(tc_fun(X30741,tc_HOL_Obool),tc_fun(X30741,tc_HOL_Obool),tc_fun(X30741,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X30741,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X30741,tc_fun(X30741,tc_HOL_Obool),tc_fun(X30741,tc_HOL_Obool)),c_Set_Oinsert(X30741)),c_Orderings_Obot__class_Obot(tc_fun(X30741,tc_HOL_Obool))))),X30739),X30740) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__fold__remove])]) ).
fof(i_0_6376,plain,
! [X31695,X31696,X31697,X31698,X31699,X31700,X31701] :
( ~ c_Fun_Oinj__on(X31701,X31700,X31699,c_Orderings_Otop__class_Otop(tc_fun(X31701,tc_HOL_Obool)))
| hAPP(c_Map_Omap__of(X31701,X31698,X31697),X31696) != hAPP(c_Option_Ooption_OSome(X31698),X31695)
| hAPP(c_Map_Omap__of(X31700,X31698,hAPP(hAPP(c_List_Omap(tc_prod(X31701,X31698),tc_prod(X31700,X31698)),hAPP(c_Product__Type_Oprod_Oprod__case(X31701,X31698,tc_prod(X31700,X31698)),hAPP(hAPP(c_COMBB(X31700,tc_fun(X31698,tc_prod(X31700,X31698)),X31701),c_Product__Type_OPair(X31700,X31698)),X31699))),X31697)),hAPP(X31699,X31696)) = hAPP(c_Option_Ooption_OSome(X31698),X31695) ),
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,
! [X28932,X28933,X28934,X28935,X28936,X28937,X28938] : hAPP(c_Product__Type_Ofst(X28938,X28937),hAPP(c_Product__Type_Omap__pair(X28936,X28938,X28935,X28937,X28934,X28933),X28932)) = hAPP(X28934,hAPP(c_Product__Type_Ofst(X28936,X28935),X28932)),
inference(variable_rename,[status(thm)],[fact_fst__map__pair]) ).
fof(i_0_6383,plain,
! [X28939,X28940,X28941,X28942,X28943,X28944,X28945] : hAPP(c_Product__Type_Osnd(X28945,X28944),hAPP(c_Product__Type_Omap__pair(X28943,X28945,X28942,X28944,X28941,X28940),X28939)) = hAPP(X28940,hAPP(c_Product__Type_Osnd(X28943,X28942),X28939)),
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,
! [X33762,X33763,X33764,X33765] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33765,X33765)),hAPP(hAPP(c_Product__Type_OPair(X33765,X33765),esk475_4(X33762,X33763,X33764,X33765)),esk476_4(X33762,X33763,X33764,X33765))),X33764))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33765),tc_List_Olist(X33765))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33765),tc_List_Olist(X33765)),X33763),X33762)),c_List_Olexord(X33765,X33764)))
| X33763 = X33762
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33765),tc_List_Olist(X33765))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33765),tc_List_Olist(X33765)),X33762),X33763)),c_List_Olexord(X33765,X33764))) )
& ( esk475_4(X33762,X33763,X33764,X33765) != esk476_4(X33762,X33763,X33764,X33765)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33765),tc_List_Olist(X33765))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33765),tc_List_Olist(X33765)),X33763),X33762)),c_List_Olexord(X33765,X33764)))
| X33763 = X33762
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33765),tc_List_Olist(X33765))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33765),tc_List_Olist(X33765)),X33762),X33763)),c_List_Olexord(X33765,X33764))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33765,X33765)),hAPP(hAPP(c_Product__Type_OPair(X33765,X33765),esk476_4(X33762,X33763,X33764,X33765)),esk475_4(X33762,X33763,X33764,X33765))),X33764))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33765),tc_List_Olist(X33765))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33765),tc_List_Olist(X33765)),X33763),X33762)),c_List_Olexord(X33765,X33764)))
| X33763 = X33762
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33765),tc_List_Olist(X33765))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33765),tc_List_Olist(X33765)),X33762),X33763)),c_List_Olexord(X33765,X33764))) ) ),
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,
! [X24419,X24420,X24421,X24422] : 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),X24422),X24421)),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),X24420),X24419)),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),X24422),X24420)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24421),X24419))),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,
! [X26233,X26234] : c_Relation_OId__on(X26234,X26233) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26234,tc_fun(tc_prod(X26234,X26234),tc_HOL_Obool)),X26233),hAPP(hAPP(c_COMBC(X26234,tc_fun(tc_prod(X26234,X26234),tc_HOL_Obool),tc_fun(tc_prod(X26234,X26234),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(X26234,X26234),tc_fun(tc_fun(tc_prod(X26234,X26234),tc_HOL_Obool),tc_fun(tc_prod(X26234,X26234),tc_HOL_Obool)),X26234),c_Set_Oinsert(tc_prod(X26234,X26234))),hAPP(hAPP(c_COMBS(X26234,X26234,tc_prod(X26234,X26234)),c_Product__Type_OPair(X26234,X26234)),c_COMBI(X26234)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X26234,X26234),tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_Id__on__def]) ).
fof(i_0_6389,plain,
! [X31688,X31689,X31690,X31691] :
( ( 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)),esk432_4(X31688,X31689,X31690,X31691)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk433_4(X31688,X31689,X31690,X31691)),esk434_4(X31688,X31689,X31690,X31691)))))
| hBOOL(hAPP(hAPP(hAPP(X31688,X31691),X31690),X31689))
| ~ 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)),X31691),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X31690),X31689)))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk433_4(X31688,X31689,X31690,X31691)),esk434_4(X31688,X31689,X31690,X31691)))
| hAPP(esk432_4(X31688,X31689,X31690,X31691),esk434_4(X31688,X31689,X31690,X31691)) != c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
| hBOOL(hAPP(hAPP(hAPP(X31688,esk432_4(X31688,X31689,X31690,X31691)),esk433_4(X31688,X31689,X31690,X31691)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk434_4(X31688,X31689,X31690,X31691)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| hBOOL(hAPP(hAPP(hAPP(X31688,X31691),X31690),X31689))
| ~ 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)),X31691),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X31690),X31689)))) )
& ( ~ hBOOL(hAPP(hAPP(hAPP(X31688,esk432_4(X31688,X31689,X31690,X31691)),esk433_4(X31688,X31689,X31690,X31691)),esk434_4(X31688,X31689,X31690,X31691)))
| hBOOL(hAPP(hAPP(hAPP(X31688,X31691),X31690),X31689))
| ~ 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)),X31691),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X31690),X31689)))) ) ),
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,
! [X32050,X32051,X32052,X32053,X32054,X32055,X32056,X32057] : hAPP(hAPP(c_List_Omap(tc_prod(X32057,X32056),X32055),X32054),hAPP(hAPP(c_List_Ozip(X32057,X32056),hAPP(hAPP(c_List_Omap(X32053,X32057),X32052),X32051)),X32050)) = hAPP(hAPP(c_List_Omap(tc_prod(X32053,X32056),X32055),hAPP(c_Product__Type_Oprod_Oprod__case(X32053,X32056,X32055),hAPP(hAPP(c_COMBB(tc_fun(X32056,tc_prod(X32057,X32056)),tc_fun(X32056,X32055),X32053),hAPP(c_COMBB(tc_prod(X32057,X32056),X32055,X32056),X32054)),hAPP(hAPP(c_COMBB(X32057,tc_fun(X32056,tc_prod(X32057,X32056)),X32053),c_Product__Type_OPair(X32057,X32056)),X32052)))),hAPP(hAPP(c_List_Ozip(X32053,X32056),X32051),X32050)),
inference(variable_rename,[status(thm)],[fact_map__zip__map]) ).
fof(i_0_6394,plain,
! [X32990,X32991,X32992,X32993] : c_List_Osublist(X32993,hAPP(hAPP(c_List_Olist_OCons(X32993),X32992),X32991),X32990) = hAPP(hAPP(c_List_Oappend(X32993),hAPP(hAPP(hAPP(c_If(tc_List_Olist(X32993)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32990)),hAPP(hAPP(c_List_Olist_OCons(X32993),X32992),c_List_Olist_ONil(X32993))),c_List_Olist_ONil(X32993))),c_List_Osublist(X32993,X32991,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)),X32990)))),
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,
! [X29277,X29278,X29279,X29280,X29281] : c_Map_Odom(X29281,X29280,c_Fun_Ooverride__on(X29281,tc_Option_Ooption(X29280),X29279,X29278,X29277)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29281,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29281,tc_HOL_Obool)),c_Map_Odom(X29281,X29280,X29279)),hAPP(c_Set_OCollect(X29281),hAPP(hAPP(c_COMBC(X29281,tc_fun(X29281,tc_HOL_Obool),tc_HOL_Obool),c_member(X29281)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29281,tc_HOL_Obool)),X29277),c_Map_Odom(X29281,X29280,X29278)))))),hAPP(c_Set_OCollect(X29281),hAPP(hAPP(c_COMBC(X29281,tc_fun(X29281,tc_HOL_Obool),tc_HOL_Obool),c_member(X29281)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29281,tc_HOL_Obool)),X29277),c_Map_Odom(X29281,X29280,X29278))))),
inference(variable_rename,[status(thm)],[fact_dom__override__on]) ).
fof(i_0_6397,plain,
! [X34363,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))),c_List_Otranspose(X34366,X34365))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34363),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)))),X34365))))
| hAPP(hAPP(c_List_Onth(X34366),hAPP(hAPP(c_List_Onth(tc_List_Olist(X34366)),c_List_Otranspose(X34366,X34365)),X34364)),X34363) = hAPP(hAPP(c_List_Onth(X34366),hAPP(hAPP(c_List_Onth(tc_List_Olist(X34366)),X34365),X34363)),X34364) ),
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,
! [X30942,X30943,X30944,X30945,X30946,X30948] :
( ( hBOOL(hAPP(hAPP(c_member(X30945),esk391_5(X30942,X30943,X30944,X30945,X30946)),X30944))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X30946),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30945,X30946),X30944),X30943)),X30942))
| ~ class_Complete__Lattice_Ocomplete__lattice(X30946)
| ~ class_Orderings_Olinorder(X30946) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X30946),hAPP(X30943,esk391_5(X30942,X30943,X30944,X30945,X30946))),X30942))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X30946),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30945,X30946),X30944),X30943)),X30942))
| ~ class_Complete__Lattice_Ocomplete__lattice(X30946)
| ~ class_Orderings_Olinorder(X30946) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X30945),X30948),X30944))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X30946),hAPP(X30943,X30948)),X30942))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X30946),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30945,X30946),X30944),X30943)),X30942))
| ~ class_Complete__Lattice_Ocomplete__lattice(X30946)
| ~ class_Orderings_Olinorder(X30946) ) ),
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,
! [X25887,X25888,X25889,X25890,X25891,X25893,X25894,X25895,X25896,X25897,X25898,X25899,X25902] :
( ( hBOOL(hAPP(hAPP(c_member(X25891),esk160_5(X25887,X25888,X25889,X25890,X25891)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25890,tc_fun(X25891,tc_HOL_Obool)),X25889),X25888)))
| ~ hBOOL(hAPP(hAPP(c_member(X25890),X25893),X25889))
| ~ hBOOL(hAPP(hAPP(c_member(X25891),X25894),hAPP(X25888,X25893)))
| hBOOL(hAPP(X25887,X25894)) )
& ( ~ hBOOL(hAPP(X25887,esk160_5(X25887,X25888,X25889,X25890,X25891)))
| ~ hBOOL(hAPP(hAPP(c_member(X25890),X25893),X25889))
| ~ hBOOL(hAPP(hAPP(c_member(X25891),X25894),hAPP(X25888,X25893)))
| hBOOL(hAPP(X25887,X25894)) )
& ( hBOOL(hAPP(hAPP(c_member(X25898),esk161_5(X25895,X25896,X25897,X25898,X25899)),X25897))
| ~ hBOOL(hAPP(hAPP(c_member(X25899),X25902),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25898,tc_fun(X25899,tc_HOL_Obool)),X25897),X25896)))
| hBOOL(hAPP(X25895,X25902)) )
& ( hBOOL(hAPP(hAPP(c_member(X25899),esk162_5(X25895,X25896,X25897,X25898,X25899)),hAPP(X25896,esk161_5(X25895,X25896,X25897,X25898,X25899))))
| ~ hBOOL(hAPP(hAPP(c_member(X25899),X25902),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25898,tc_fun(X25899,tc_HOL_Obool)),X25897),X25896)))
| hBOOL(hAPP(X25895,X25902)) )
& ( ~ hBOOL(hAPP(X25895,esk162_5(X25895,X25896,X25897,X25898,X25899)))
| ~ hBOOL(hAPP(hAPP(c_member(X25899),X25902),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25898,tc_fun(X25899,tc_HOL_Obool)),X25897),X25896)))
| hBOOL(hAPP(X25895,X25902)) ) ),
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,
! [X24205,X24206,X24207,X24208,X24209,X24210] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X24210,tc_HOL_Obool),tc_fun(X24210,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X24210,tc_HOL_Obool),tc_fun(X24210,tc_HOL_Obool)),X24209),X24208)),c_Wellfounded_Omax__ext(X24210,X24207)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X24210,tc_HOL_Obool),tc_fun(X24210,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X24210,tc_HOL_Obool),tc_fun(X24210,tc_HOL_Obool)),X24206),X24205)),c_Wellfounded_Omax__ext(X24210,X24207)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X24210,tc_HOL_Obool),tc_fun(X24210,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X24210,tc_HOL_Obool),tc_fun(X24210,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24210,tc_HOL_Obool)),X24209),X24206)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24210,tc_HOL_Obool)),X24208),X24205))),c_Wellfounded_Omax__ext(X24210,X24207))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ext__additive])]) ).
fof(i_0_6411,plain,
! [X28910,X28911,X28912,X28913,X28914] :
( ( hBOOL(hAPP(hAPP(c_member(X28914),esk297_5(X28910,X28911,X28912,X28913,X28914)),X28911))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28914,X28913)),X28912),hAPP(hAPP(c_Product__Type_OSigma(X28914,X28913),X28911),X28910))) )
& ( hBOOL(hAPP(hAPP(c_member(X28913),esk298_5(X28910,X28911,X28912,X28913,X28914)),hAPP(X28910,esk297_5(X28910,X28911,X28912,X28913,X28914))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28914,X28913)),X28912),hAPP(hAPP(c_Product__Type_OSigma(X28914,X28913),X28911),X28910))) )
& ( X28912 = hAPP(hAPP(c_Product__Type_OPair(X28914,X28913),esk297_5(X28910,X28911,X28912,X28913,X28914)),esk298_5(X28910,X28911,X28912,X28913,X28914))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28914,X28913)),X28912),hAPP(hAPP(c_Product__Type_OSigma(X28914,X28913),X28911),X28910))) ) ),
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,
! [X33566,X33567,X33568,X33569,X33570,X33571,X33572] : hAPP(c_List_Ofoldl(X33572,X33571,X33570,X33569),hAPP(hAPP(c_List_Omap(X33568,X33571),X33567),X33566)) = hAPP(c_List_Ofoldl(X33572,X33568,hAPP(hAPP(c_COMBC(X33572,tc_fun(X33568,X33571),tc_fun(X33568,X33572)),hAPP(hAPP(c_COMBB(tc_fun(X33571,X33572),tc_fun(tc_fun(X33568,X33571),tc_fun(X33568,X33572)),X33572),c_COMBB(X33571,X33572,X33568)),X33570)),X33567),X33569),X33566),
inference(variable_rename,[status(thm)],[fact_foldl__map]) ).
fof(i_0_6413,plain,
! [X29470,X29471,X29472,X29473,X29474,X29475,X29476] : hAPP(hAPP(c_Relation_Orel__comp(X29476,X29475,X29474),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29473,tc_fun(tc_prod(X29476,X29475),tc_HOL_Obool)),X29472),X29471)),X29470) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29473,tc_fun(tc_prod(X29476,X29474),tc_HOL_Obool)),X29472),hAPP(hAPP(c_COMBC(X29473,tc_fun(tc_prod(X29475,X29474),tc_HOL_Obool),tc_fun(tc_prod(X29476,X29474),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X29476,X29475),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X29475,X29474),tc_HOL_Obool),tc_fun(tc_prod(X29476,X29474),tc_HOL_Obool)),X29473),c_Relation_Orel__comp(X29476,X29475,X29474)),X29471)),X29470)),
inference(variable_rename,[status(thm)],[fact_rel__comp__UNION__distrib2]) ).
fof(i_0_6414,plain,
! [X21862,X21863] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21863),c_Int_OPls))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21862)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21863)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21862) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21863),c_Int_OPls))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21862)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21863)) = 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),X21862),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21863)))),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,
! [X29155,X29156,X29157] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X29157),hAPP(c_Set_OCollect(X29157),X29156)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29157),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_fdisj),X29156)),X29155)))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X29157),hAPP(c_Set_OCollect(X29157),X29155)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29157),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_fdisj),X29156)),X29155)))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29157),hAPP(c_Set_OCollect(X29157),X29156)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29157),hAPP(c_Set_OCollect(X29157),X29155)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29157),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_fdisj),X29156)),X29155)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Collect__disjI])])]) ).
fof(i_0_6416,plain,
! [X21899,X21900] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X21900))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X21899)),hAPP(c_Int_Onat,X21900)) = hAPP(c_Int_Onat,X21899) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X21900))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X21899)),hAPP(c_Int_Onat,X21900)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X21899),X21900)),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,
! [X28066,X28067,X28068,X28069,X28070] :
( ~ class_Groups_Oab__semigroup__mult(X28070)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28070,X28070,c_Groups_Otimes__class_Otimes(X28070),X28069,X28068),X28067))
| ~ hBOOL(hAPP(hAPP(c_member(X28070),X28066),X28068))
| hBOOL(hAPP(hAPP(c_member(X28070),X28069),X28068))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28070,X28070,c_Groups_Otimes__class_Otimes(X28070),X28066,hAPP(hAPP(c_Set_Oinsert(X28070),X28069),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28070,tc_HOL_Obool)),X28068),hAPP(hAPP(c_Set_Oinsert(X28070),X28066),c_Orderings_Obot__class_Obot(tc_fun(X28070,tc_HOL_Obool)))))),X28067)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5354])]) ).
fof(i_0_6418,plain,
! [X25877,X25878,X25879,X25880,X25881,X25882,X25883,X25884,X25885,X25886] :
( ~ c_Equiv__Relations_Oequiv(X25886,X25885,X25884)
| ~ c_Equiv__Relations_Oequiv(X25883,X25882,X25881)
| ~ c_Equiv__Relations_Ocongruent2(X25886,X25883,tc_fun(X25880,tc_HOL_Obool),X25884,X25881,X25879)
| ~ hBOOL(hAPP(hAPP(c_member(X25886),X25878),X25885))
| ~ hBOOL(hAPP(hAPP(c_member(X25883),X25877),X25882))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25886,tc_fun(X25880,tc_HOL_Obool)),hAPP(c_Relation_OImage(X25886,X25886,X25884),hAPP(hAPP(c_Set_Oinsert(X25886),X25878),c_Orderings_Obot__class_Obot(tc_fun(X25886,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(X25883,tc_fun(X25880,tc_HOL_Obool)),tc_fun(X25880,tc_HOL_Obool),X25886),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25883,tc_fun(X25880,tc_HOL_Obool)),hAPP(c_Relation_OImage(X25883,X25883,X25881),hAPP(hAPP(c_Set_Oinsert(X25883),X25877),c_Orderings_Obot__class_Obot(tc_fun(X25883,tc_HOL_Obool)))))),X25879)) = hAPP(hAPP(X25879,X25878),X25877) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__equiv__class2])]) ).
fof(i_0_6419,plain,
! [X32382,X32383,X32384] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32384)),c_List_Osublist(X32384,X32383,X32382)) = 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(X32384)),X32383)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X32382)))),
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,
! [X33951,X33952,X33953] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33953)),hAPP(c_List_Ofilter(X33953,X33952),X33951)) = 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(X33953)),X33951)))),hAPP(hAPP(c_COMBB(X33953,tc_HOL_Obool,tc_Nat_Onat),X33952),hAPP(c_List_Onth(X33953),X33951))))),
inference(variable_rename,[status(thm)],[fact_length__filter__conv__card]) ).
fof(i_0_6422,plain,
! [X26263,X26264,X26265,X26266,X26267] :
( ~ class_Groups_Ocomm__monoid__mult(X26267)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26266),X26265))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X26267,X26266,c_Groups_Otimes__class_Otimes(X26267)),hAPP(hAPP(c_COMBS(X26266,X26267,X26267),hAPP(hAPP(c_COMBB(X26267,tc_fun(X26267,X26267),X26266),c_Groups_Otimes__class_Otimes(X26267)),X26264)),X26263)),c_Groups_Oone__class_Oone(X26267)),X26265) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26267),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X26267,X26266,c_Groups_Otimes__class_Otimes(X26267)),X26264),c_Groups_Oone__class_Oone(X26267)),X26265)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X26267,X26266,c_Groups_Otimes__class_Otimes(X26267)),X26263),c_Groups_Oone__class_Oone(X26267)),X26265)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__image__distrib])]) ).
fof(i_0_6423,plain,
! [X33189,X33190,X33191,X33192,X33193,X33194] :
( ( X33193 = X33191
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33194),tc_List_Olist(X33194))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33194),tc_List_Olist(X33194)),X33193),X33191)),c_List_Olistrel1(X33194,X33189)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33194),tc_List_Olist(X33194))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33194),tc_List_Olist(X33194)),hAPP(hAPP(c_List_Oappend(X33194),X33193),hAPP(hAPP(c_List_Olist_OCons(X33194),X33192),c_List_Olist_ONil(X33194)))),hAPP(hAPP(c_List_Oappend(X33194),X33191),hAPP(hAPP(c_List_Olist_OCons(X33194),X33190),c_List_Olist_ONil(X33194))))),c_List_Olistrel1(X33194,X33189))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33194,X33194)),hAPP(hAPP(c_Product__Type_OPair(X33194,X33194),X33192),X33190)),X33189))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33194),tc_List_Olist(X33194))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33194),tc_List_Olist(X33194)),X33193),X33191)),c_List_Olistrel1(X33194,X33189)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33194),tc_List_Olist(X33194))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33194),tc_List_Olist(X33194)),hAPP(hAPP(c_List_Oappend(X33194),X33193),hAPP(hAPP(c_List_Olist_OCons(X33194),X33192),c_List_Olist_ONil(X33194)))),hAPP(hAPP(c_List_Oappend(X33194),X33191),hAPP(hAPP(c_List_Olist_OCons(X33194),X33190),c_List_Olist_ONil(X33194))))),c_List_Olistrel1(X33194,X33189))) )
& ( X33193 = X33191
| X33192 = X33190
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33194),tc_List_Olist(X33194))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33194),tc_List_Olist(X33194)),hAPP(hAPP(c_List_Oappend(X33194),X33193),hAPP(hAPP(c_List_Olist_OCons(X33194),X33192),c_List_Olist_ONil(X33194)))),hAPP(hAPP(c_List_Oappend(X33194),X33191),hAPP(hAPP(c_List_Olist_OCons(X33194),X33190),c_List_Olist_ONil(X33194))))),c_List_Olistrel1(X33194,X33189))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33194,X33194)),hAPP(hAPP(c_Product__Type_OPair(X33194,X33194),X33192),X33190)),X33189))
| X33192 = X33190
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33194),tc_List_Olist(X33194))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33194),tc_List_Olist(X33194)),hAPP(hAPP(c_List_Oappend(X33194),X33193),hAPP(hAPP(c_List_Olist_OCons(X33194),X33192),c_List_Olist_ONil(X33194)))),hAPP(hAPP(c_List_Oappend(X33194),X33191),hAPP(hAPP(c_List_Olist_OCons(X33194),X33190),c_List_Olist_ONil(X33194))))),c_List_Olistrel1(X33194,X33189))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33194),tc_List_Olist(X33194))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33194),tc_List_Olist(X33194)),X33193),X33191)),c_List_Olistrel1(X33194,X33189)))
| X33192 != X33190
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33194),tc_List_Olist(X33194))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33194),tc_List_Olist(X33194)),hAPP(hAPP(c_List_Oappend(X33194),X33193),hAPP(hAPP(c_List_Olist_OCons(X33194),X33192),c_List_Olist_ONil(X33194)))),hAPP(hAPP(c_List_Oappend(X33194),X33191),hAPP(hAPP(c_List_Olist_OCons(X33194),X33190),c_List_Olist_ONil(X33194))))),c_List_Olistrel1(X33194,X33189))) )
& ( X33193 != X33191
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33194,X33194)),hAPP(hAPP(c_Product__Type_OPair(X33194,X33194),X33192),X33190)),X33189))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33194),tc_List_Olist(X33194))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33194),tc_List_Olist(X33194)),hAPP(hAPP(c_List_Oappend(X33194),X33193),hAPP(hAPP(c_List_Olist_OCons(X33194),X33192),c_List_Olist_ONil(X33194)))),hAPP(hAPP(c_List_Oappend(X33194),X33191),hAPP(hAPP(c_List_Olist_OCons(X33194),X33190),c_List_Olist_ONil(X33194))))),c_List_Olistrel1(X33194,X33189))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snoc__listrel1__snoc__iff])])]) ).
fof(i_0_6424,plain,
! [X28327,X28328,X28329,X28330] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X28330,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk271_4(X28327,X28328,X28329,X28330))),X28329) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X28330,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),esk271_4(X28327,X28328,X28329,X28330)),X28328))),X28327)
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X28330,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X28329) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X28330,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X28327) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__finite2__eq])])]) ).
fof(i_0_6425,plain,
! [X28565,X28566,X28567,X28568,X28570] :
( ( hBOOL(hAPP(hAPP(c_member(X28568),esk277_4(X28565,X28566,X28567,X28568)),X28567))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X28568,tc_HOL_Obool),tc_fun(X28568,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X28568,tc_HOL_Obool),tc_fun(X28568,tc_HOL_Obool)),X28567),X28566)),c_Wellfounded_Omax__ext(X28568,X28565)))
| X28566 = c_Orderings_Obot__class_Obot(tc_fun(X28568,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28568),X28566))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28568),X28567)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X28568),X28570),X28566))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28568,X28568)),hAPP(hAPP(c_Product__Type_OPair(X28568,X28568),esk277_4(X28565,X28566,X28567,X28568)),X28570)),X28565))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X28568,tc_HOL_Obool),tc_fun(X28568,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X28568,tc_HOL_Obool),tc_fun(X28568,tc_HOL_Obool)),X28567),X28566)),c_Wellfounded_Omax__ext(X28568,X28565)))
| X28566 = c_Orderings_Obot__class_Obot(tc_fun(X28568,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28568),X28566))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28568),X28567)) ) ),
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,
! [X29352,X29353,X29354] : c_Map_Oran(X29354,X29353,X29352) = hAPP(c_Set_OCollect(X29353),hAPP(hAPP(c_COMBB(tc_fun(X29354,tc_HOL_Obool),tc_HOL_Obool,X29353),c_HOL_OEx(X29354)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X29353),tc_fun(X29354,tc_HOL_Obool),X29353),hAPP(c_COMBC(X29354,tc_Option_Ooption(X29353),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X29353),tc_fun(tc_Option_Ooption(X29353),tc_HOL_Obool),X29354),c_fequal),X29352))),c_Option_Ooption_OSome(X29353)))),
inference(variable_rename,[status(thm)],[fact_ran__def]) ).
fof(i_0_6427,plain,
! [X30074,X30075,X30076] :
( ~ c_Wellfounded_Owf(X30076,X30075)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30076,X30076)),hAPP(hAPP(c_Product__Type_OPair(X30076,X30076),hAPP(X30074,hAPP(c_Nat_OSuc,esk363_3(X30074,X30075,X30076)))),hAPP(X30074,esk363_3(X30074,X30075,X30076)))),X30075)) ),
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,
! [X29634,X29635,X29636,X29638,X29639,X29641] :
( ( ~ c_Wellfounded_Owf(X29635,X29634)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29635,X29635)),hAPP(hAPP(c_Product__Type_OPair(X29635,X29635),hAPP(X29636,hAPP(c_Nat_OSuc,esk318_3(X29634,X29635,X29636)))),hAPP(X29636,esk318_3(X29634,X29635,X29636)))),X29634)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29639,X29639)),hAPP(hAPP(c_Product__Type_OPair(X29639,X29639),hAPP(esk319_2(X29638,X29639),hAPP(c_Nat_OSuc,X29641))),hAPP(esk319_2(X29638,X29639),X29641))),X29638))
| c_Wellfounded_Owf(X29639,X29638) ) ),
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,
! [X26145,X26146,X26147,X26148,X26149,X26150,X26151,X26152,X26153] :
( ~ c_Equiv__Relations_Oequiv(X26153,X26152,X26151)
| ~ c_Equiv__Relations_Oequiv(X26150,X26149,X26148)
| ~ c_Equiv__Relations_Ocongruent2(X26153,X26150,tc_fun(X26147,tc_HOL_Obool),X26151,X26148,X26146)
| ~ hBOOL(hAPP(hAPP(c_member(X26150),X26145),X26149))
| c_Equiv__Relations_Ocongruent(X26153,tc_fun(X26147,tc_HOL_Obool),X26151,hAPP(hAPP(c_COMBB(tc_fun(X26150,tc_fun(X26147,tc_HOL_Obool)),tc_fun(X26147,tc_HOL_Obool),X26153),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26150,tc_fun(X26147,tc_HOL_Obool)),hAPP(c_Relation_OImage(X26150,X26150,X26148),hAPP(hAPP(c_Set_Oinsert(X26150),X26145),c_Orderings_Obot__class_Obot(tc_fun(X26150,tc_HOL_Obool)))))),X26146)) ),
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,
! [X28108,X28109,X28110,X28111,X28112,X28113,X28114] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28114,X28113,X28112,X28111,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28114,tc_HOL_Obool)),X28110),hAPP(hAPP(c_Set_Oinsert(X28114),X28109),c_Orderings_Obot__class_Obot(tc_fun(X28114,tc_HOL_Obool))))),X28108))
| ~ hBOOL(hAPP(hAPP(c_member(X28114),X28109),X28110))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28114,X28113,X28112,X28111,X28110),hAPP(hAPP(X28112,X28109),X28108))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff1__fold__graph])]) ).
fof(i_0_6433,plain,
! [X27529,X27530,X27531,X27532,X27533] :
( ( hBOOL(hAPP(hAPP(c_member(X27532),esk252_5(X27529,X27530,X27531,X27532,X27533)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27532,tc_HOL_Obool)),X27531),X27530)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27533),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27532,X27533),X27529),X27530)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27532,X27533),X27529),X27531)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27532,tc_HOL_Obool)),X27530),X27531))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27532),X27531))
| ~ class_Groups_Ocomm__monoid__add(X27533)
| ~ class_Groups_Oordered__ab__semigroup__add(X27533) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27533),c_Groups_Ozero__class_Ozero(X27533)),hAPP(X27529,esk252_5(X27529,X27530,X27531,X27532,X27533))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27533),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27532,X27533),X27529),X27530)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27532,X27533),X27529),X27531)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27532,tc_HOL_Obool)),X27530),X27531))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27532),X27531))
| ~ class_Groups_Ocomm__monoid__add(X27533)
| ~ class_Groups_Oordered__ab__semigroup__add(X27533) ) ),
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,
! [X27451,X27452,X27453,X27454,X27455] :
( ( hBOOL(hAPP(hAPP(c_member(X27454),esk242_5(X27451,X27452,X27453,X27454,X27455)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27454,tc_HOL_Obool)),X27453),X27452)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27455),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27454,X27455),X27451),X27452)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27454,X27455),X27451),X27453)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27454,tc_HOL_Obool)),X27452),X27453))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27454),X27453))
| ~ class_Groups_Oordered__comm__monoid__add(X27455) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27455),c_Groups_Ozero__class_Ozero(X27455)),hAPP(X27451,esk242_5(X27451,X27452,X27453,X27454,X27455))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27455),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27454,X27455),X27451),X27452)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27454,X27455),X27451),X27453)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27454,tc_HOL_Obool)),X27452),X27453))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27454),X27453))
| ~ class_Groups_Oordered__comm__monoid__add(X27455) ) ),
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,
! [X30980,X30981,X30982,X30983] :
( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30983,tc_fun(X30982,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X30983,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X30982,tc_HOL_Obool),tc_fun(X30982,tc_HOL_Obool),X30983),hAPP(c_COMBC(X30982,tc_fun(X30982,tc_HOL_Obool),tc_HOL_Obool),c_member(X30982))),X30981)),X30980))
| hBOOL(hAPP(hAPP(c_member(X30982),X30980),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30983,tc_fun(X30982,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X30983,tc_HOL_Obool))),X30981))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X30982),X30980),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30983,tc_fun(X30982,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X30983,tc_HOL_Obool))),X30981)))
| hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30983,tc_fun(X30982,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X30983,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X30982,tc_HOL_Obool),tc_fun(X30982,tc_HOL_Obool),X30983),hAPP(c_COMBC(X30982,tc_fun(X30982,tc_HOL_Obool),tc_HOL_Obool),c_member(X30982))),X30981)),X30980)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__INT__eq])]) ).
fof(i_0_6436,plain,
! [X28232,X28233,X28234,X28235] :
( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28235,tc_fun(X28234,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X28235,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X28234,tc_HOL_Obool),tc_fun(X28234,tc_HOL_Obool),X28235),hAPP(c_COMBC(X28234,tc_fun(X28234,tc_HOL_Obool),tc_HOL_Obool),c_member(X28234))),X28233)),X28232))
| hBOOL(hAPP(hAPP(c_member(X28234),X28232),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28235,tc_fun(X28234,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X28235,tc_HOL_Obool))),X28233))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X28234),X28232),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28235,tc_fun(X28234,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X28235,tc_HOL_Obool))),X28233)))
| hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28235,tc_fun(X28234,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X28235,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X28234,tc_HOL_Obool),tc_fun(X28234,tc_HOL_Obool),X28235),hAPP(c_COMBC(X28234,tc_fun(X28234,tc_HOL_Obool),tc_HOL_Obool),c_member(X28234))),X28233)),X28232)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__UN__eq])]) ).
fof(i_0_6437,plain,
! [X20511,X20512,X20513,X20514,X20515,X20516] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20516),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20516),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20516),X20515),X20514)),X20513)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20516),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20516),X20512),X20514)),X20511)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20516),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20516),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20516),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20516),X20515),X20512)),X20514)),X20513)),X20511))
| ~ class_Rings_Oordered__ring(X20516) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20516),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20516),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20516),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20516),X20515),X20512)),X20514)),X20513)),X20511))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20516),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20516),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20516),X20515),X20514)),X20513)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20516),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20516),X20512),X20514)),X20511)))
| ~ class_Rings_Oordered__ring(X20516) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__iff1])])]) ).
fof(i_0_6438,plain,
! [X20523,X20524,X20525,X20526,X20527,X20528] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20528),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20528),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20528),X20527),X20526)),X20525)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20528),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20528),X20524),X20526)),X20523)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20528),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20528),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20528),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20528),X20527),X20524)),X20526)),X20525)),X20523))
| ~ class_Rings_Oordered__ring(X20528) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20528),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20528),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20528),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20528),X20527),X20524)),X20526)),X20525)),X20523))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20528),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20528),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20528),X20527),X20526)),X20525)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20528),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20528),X20524),X20526)),X20523)))
| ~ class_Rings_Oordered__ring(X20528) ) ),
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,
! [X23762,X23763,X23764,X23765,X23766,X23767,X23768] :
( ~ hBOOL(hAPP(hAPP(c_member(X23768),X23767),X23766))
| ~ c_Nitpick_Ofold__graph_H(X23768,X23765,X23764,X23763,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23768,tc_HOL_Obool)),X23766),hAPP(hAPP(c_Set_Oinsert(X23768),X23767),c_Orderings_Obot__class_Obot(tc_fun(X23768,tc_HOL_Obool)))),X23762)
| c_Nitpick_Ofold__graph_H(X23768,X23765,X23764,X23763,X23766,hAPP(hAPP(X23764,X23767),X23762)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__graph_H_Ointros_I2_J])]) ).
fof(i_0_6441,plain,
! [X31047,X31048,X31049,X31050,X31051,X31052,X31053,X31054,X31055,X31056,X31057] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31051,tc_HOL_Obool)),X31050),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31049,tc_fun(X31051,tc_HOL_Obool)),X31048),X31047)))
| ~ hBOOL(hAPP(hAPP(c_member(X31049),X31052),X31048))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31051,tc_HOL_Obool)),X31050),hAPP(X31047,X31052))) )
& ( hBOOL(hAPP(hAPP(c_member(X31055),esk396_5(X31053,X31054,X31055,X31056,X31057)),X31054))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31057,tc_HOL_Obool)),X31056),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31055,tc_fun(X31057,tc_HOL_Obool)),X31054),X31053))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31057,tc_HOL_Obool)),X31056),hAPP(X31053,esk396_5(X31053,X31054,X31055,X31056,X31057))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31057,tc_HOL_Obool)),X31056),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31055,tc_fun(X31057,tc_HOL_Obool)),X31054),X31053))) ) ),
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,
! [X22255,X22256,X22257,X22258] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22258,X22257),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22256),X22255)))
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22258),X22257),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X22255),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22256)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22256)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X22255),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),X22257),X22255))))) ),
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,
! [X30984,X30985,X30986,X30987,X30988,X30989,X30990,X30991,X30992,X30993,X30994] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X30988),X30987),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30986,tc_fun(X30988,tc_HOL_Obool)),X30985),X30984)))
| ~ hBOOL(hAPP(hAPP(c_member(X30986),X30989),X30985))
| hBOOL(hAPP(hAPP(c_member(X30988),X30987),hAPP(X30984,X30989))) )
& ( hBOOL(hAPP(hAPP(c_member(X30992),esk394_5(X30990,X30991,X30992,X30993,X30994)),X30991))
| hBOOL(hAPP(hAPP(c_member(X30994),X30993),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30992,tc_fun(X30994,tc_HOL_Obool)),X30991),X30990))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X30994),X30993),hAPP(X30990,esk394_5(X30990,X30991,X30992,X30993,X30994))))
| hBOOL(hAPP(hAPP(c_member(X30994),X30993),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30992,tc_fun(X30994,tc_HOL_Obool)),X30991),X30990))) ) ),
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,
! [X28849,X28850,X28851,X28852,X28853,X28854] : hAPP(c_Set_Ovimage(X28854,tc_prod(X28853,X28852),X28851),hAPP(hAPP(c_Product__Type_OSigma(X28853,X28852),X28850),hAPP(c_COMBK(tc_fun(X28852,tc_HOL_Obool),X28853),X28849))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28854,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X28854,X28853,hAPP(c_Fun_Ocomp(tc_prod(X28853,X28852),X28853,X28854,c_Product__Type_Ofst(X28853,X28852)),X28851)),X28850)),hAPP(c_Set_Ovimage(X28854,X28852,hAPP(c_Fun_Ocomp(tc_prod(X28853,X28852),X28852,X28854,c_Product__Type_Osnd(X28853,X28852)),X28851)),X28849)),
inference(variable_rename,[status(thm)],[fact_vimage__Times]) ).
fof(i_0_6446,plain,
! [X23839,X23840,X23841,X23842,X23843,X23844,X23845,X23846] :
( ( X23844 = X23842
| hBOOL(hAPP(hAPP(c_member(tc_prod(X23846,X23846)),hAPP(hAPP(c_Product__Type_OPair(X23846,X23846),X23844),X23842)),X23840))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X23846,X23845),tc_prod(X23846,X23845))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X23846,X23845),tc_prod(X23846,X23845)),hAPP(hAPP(c_Product__Type_OPair(X23846,X23845),X23844),X23843)),hAPP(hAPP(c_Product__Type_OPair(X23846,X23845),X23842),X23841))),c_Wellfounded_Olex__prod(X23846,X23845,X23840,X23839))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X23845,X23845)),hAPP(hAPP(c_Product__Type_OPair(X23845,X23845),X23843),X23841)),X23839))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X23846,X23846)),hAPP(hAPP(c_Product__Type_OPair(X23846,X23846),X23844),X23842)),X23840))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X23846,X23845),tc_prod(X23846,X23845))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X23846,X23845),tc_prod(X23846,X23845)),hAPP(hAPP(c_Product__Type_OPair(X23846,X23845),X23844),X23843)),hAPP(hAPP(c_Product__Type_OPair(X23846,X23845),X23842),X23841))),c_Wellfounded_Olex__prod(X23846,X23845,X23840,X23839))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23846,X23846)),hAPP(hAPP(c_Product__Type_OPair(X23846,X23846),X23844),X23842)),X23840))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X23846,X23845),tc_prod(X23846,X23845))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X23846,X23845),tc_prod(X23846,X23845)),hAPP(hAPP(c_Product__Type_OPair(X23846,X23845),X23844),X23843)),hAPP(hAPP(c_Product__Type_OPair(X23846,X23845),X23842),X23841))),c_Wellfounded_Olex__prod(X23846,X23845,X23840,X23839))) )
& ( X23844 != X23842
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23845,X23845)),hAPP(hAPP(c_Product__Type_OPair(X23845,X23845),X23843),X23841)),X23839))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X23846,X23845),tc_prod(X23846,X23845))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X23846,X23845),tc_prod(X23846,X23845)),hAPP(hAPP(c_Product__Type_OPair(X23846,X23845),X23844),X23843)),hAPP(hAPP(c_Product__Type_OPair(X23846,X23845),X23842),X23841))),c_Wellfounded_Olex__prod(X23846,X23845,X23840,X23839))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__lex__prod])])]) ).
fof(i_0_6447,plain,
! [X31207,X31208,X31209,X31210,X31211,X31212,X31213,X31214,X31215,X31216,X31217] :
( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31211,tc_fun(X31210,tc_HOL_Obool)),X31209),X31208),X31207))
| ~ hBOOL(hAPP(hAPP(c_member(X31211),X31212),X31209))
| hBOOL(hAPP(hAPP(X31208,X31212),X31207)) )
& ( hBOOL(hAPP(hAPP(c_member(X31217),esk397_5(X31213,X31214,X31215,X31216,X31217)),X31215))
| hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31217,tc_fun(X31216,tc_HOL_Obool)),X31215),X31214),X31213)) )
& ( ~ hBOOL(hAPP(hAPP(X31214,esk397_5(X31213,X31214,X31215,X31216,X31217)),X31213))
| hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31217,tc_fun(X31216,tc_HOL_Obool)),X31215),X31214),X31213)) ) ),
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,
! [X29228,X29229] : 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),X29229)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X29228))))),
inference(variable_rename,[status(thm)],[fact_finite__M__bounded__by__nat]) ).
fof(i_0_6449,plain,
! [X20626,X20627,X20628] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20628))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20627),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20626),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),X20626),X20627))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X20628)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_incr__lemma])]) ).
fof(i_0_6450,plain,
! [X31040,X31041,X31042,X31043,X31044,X31045] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31044),X31043),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31042,X31044),X31041),X31040)))
| ~ hBOOL(hAPP(hAPP(c_member(X31042),X31045),X31041))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31044),X31043),hAPP(X31040,X31045)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X31044) )
& ( hBOOL(hAPP(hAPP(c_member(X31042),esk395_5(X31040,X31041,X31042,X31043,X31044)),X31041))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31044),X31043),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31042,X31044),X31041),X31040)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X31044) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31044),X31043),hAPP(X31040,esk395_5(X31040,X31041,X31042,X31043,X31044))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31044),X31043),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31042,X31044),X31041),X31040)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X31044) ) ),
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,
! [X27542,X27543,X27544,X27545,X27546] :
( ( hBOOL(hAPP(hAPP(c_member(X27545),esk254_5(X27542,X27543,X27544,X27545,X27546)),X27544))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27545,X27546),X27543),X27544) != c_Groups_Ozero__class_Ozero(X27546)
| ~ hBOOL(hAPP(hAPP(c_member(X27545),X27542),X27544))
| hAPP(X27543,X27542) = c_Groups_Ozero__class_Ozero(X27546)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27545),X27544))
| ~ class_Groups_Oordered__ab__group__add(X27546) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27546),c_Groups_Ozero__class_Ozero(X27546)),hAPP(X27543,esk254_5(X27542,X27543,X27544,X27545,X27546))))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27545,X27546),X27543),X27544) != c_Groups_Ozero__class_Ozero(X27546)
| ~ hBOOL(hAPP(hAPP(c_member(X27545),X27542),X27544))
| hAPP(X27543,X27542) = c_Groups_Ozero__class_Ozero(X27546)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27545),X27544))
| ~ class_Groups_Oordered__ab__group__add(X27546) ) ),
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,
! [X27028,X27029,X27030,X27031,X27032] : hAPP(c_Fun_Othe__inv__into(X27032,X27031,X27030,X27029),X27028) = c_HOL_OThe(X27032,hAPP(hAPP(c_COMBS(X27032,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27032),c_fconj),hAPP(hAPP(c_COMBC(X27032,tc_fun(X27032,tc_HOL_Obool),tc_HOL_Obool),c_member(X27032)),X27030))),hAPP(hAPP(c_COMBC(X27032,X27031,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X27031,tc_fun(X27031,tc_HOL_Obool),X27032),c_fequal),X27029)),X27028))),
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,
! [X33298,X33299,X33300,X33301] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33301,X33301)),hAPP(hAPP(c_Product__Type_OPair(X33301,X33301),esk466_4(X33298,X33299,X33300,X33301)),esk467_4(X33298,X33299,X33300,X33301))),X33298))
| ~ 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))) )
& ( X33300 = hAPP(hAPP(c_List_Oappend(X33301),esk468_4(X33298,X33299,X33300,X33301)),hAPP(hAPP(c_List_Olist_OCons(X33301),esk466_4(X33298,X33299,X33300,X33301)),esk469_4(X33298,X33299,X33300,X33301)))
| ~ 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))) )
& ( X33299 = hAPP(hAPP(c_List_Oappend(X33301),esk468_4(X33298,X33299,X33300,X33301)),hAPP(hAPP(c_List_Olist_OCons(X33301),esk467_4(X33298,X33299,X33300,X33301)),esk469_4(X33298,X33299,X33300,X33301)))
| ~ 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(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1E])])])]) ).
fof(i_0_6456,plain,
! [X27673,X27674,X27675,X27676,X27677,X27678] :
( ~ class_Groups_Ocomm__monoid__add(X27678)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27677),X27676))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27675),X27674))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_sum(X27677,X27675),X27678),X27673),c_Sum__Type_OPlus(X27677,X27675,X27676,X27674)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27678),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27677,X27678),hAPP(c_Fun_Ocomp(tc_sum(X27677,X27675),X27678,X27677,X27673),c_Sum__Type_OInl(X27677,X27675))),X27676)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27675,X27678),hAPP(c_Fun_Ocomp(tc_sum(X27677,X27675),X27678,X27675,X27673),c_Sum__Type_OInr(X27675,X27677))),X27674)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Plus])]) ).
fof(i_0_6457,plain,
! [X30793,X30794,X30795,X30796,X30797,X30798,X30799] :
( ~ c_Finite__Set_Ofun__left__comm(X30799,X30798,X30797)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X30799,X30798,X30797,X30796,X30795),X30794))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X30799,X30798,X30797,X30796,X30795),X30793))
| X30793 = X30794 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__determ])]) ).
fof(i_0_6458,plain,
! [X32412,X32413,X32414,X32415,X32416] :
( ~ class_Groups_Oab__group__add(X32416)
| hAPP(c_List_Omonoid__add__class_Olistsum(X32416),hAPP(hAPP(c_List_Omap(X32415,X32416),hAPP(hAPP(c_COMBS(X32415,X32416,X32416),hAPP(hAPP(c_COMBB(X32416,tc_fun(X32416,X32416),X32415),c_Groups_Ominus__class_Ominus(X32416)),X32414)),X32413)),X32412)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X32416),hAPP(c_List_Omonoid__add__class_Olistsum(X32416),hAPP(hAPP(c_List_Omap(X32415,X32416),X32414),X32412))),hAPP(c_List_Omonoid__add__class_Olistsum(X32416),hAPP(hAPP(c_List_Omap(X32415,X32416),X32413),X32412))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__subtractf])]) ).
fof(i_0_6459,plain,
! [X32427,X32428,X32429,X32430,X32431] :
( ~ class_Groups_Ocomm__monoid__add(X32431)
| hAPP(c_List_Omonoid__add__class_Olistsum(X32431),hAPP(hAPP(c_List_Omap(X32430,X32431),hAPP(hAPP(c_COMBS(X32430,X32431,X32431),hAPP(hAPP(c_COMBB(X32431,tc_fun(X32431,X32431),X32430),c_Groups_Oplus__class_Oplus(X32431)),X32429)),X32428)),X32427)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X32431),hAPP(c_List_Omonoid__add__class_Olistsum(X32431),hAPP(hAPP(c_List_Omap(X32430,X32431),X32429),X32427))),hAPP(c_List_Omonoid__add__class_Olistsum(X32431),hAPP(hAPP(c_List_Omap(X32430,X32431),X32428),X32427))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__addf])]) ).
fof(i_0_6460,plain,
! [X26410,X26411,X26412,X26413] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X26413,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26412,tc_fun(tc_fun(X26413,tc_HOL_Obool),tc_HOL_Obool)),X26411),hAPP(hAPP(c_COMBB(tc_fun(X26413,tc_HOL_Obool),tc_fun(tc_fun(X26413,tc_HOL_Obool),tc_HOL_Obool),X26412),c_Set_OPow(X26413)),X26410))),hAPP(c_Set_OPow(X26413),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26412,tc_fun(X26413,tc_HOL_Obool)),X26411),X26410)))),
inference(variable_rename,[status(thm)],[fact_UN__Pow__subset]) ).
fof(i_0_6461,plain,
! [X20581,X20582,X20583,X20584,X20585] :
( ( ~ 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),X20584),X20583)),X20582)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20585),X20583)),X20581)))
| 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),X20584),X20585)),X20583)),X20582)),X20581))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20585),X20584)) )
& ( ~ 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),X20584),X20585)),X20583)),X20582)),X20581))
| 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),X20584),X20583)),X20582)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20585),X20583)),X20581)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20585),X20584)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff1])])]) ).
fof(i_0_6462,plain,
! [X20603,X20604,X20605,X20606,X20607] :
( ( ~ 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),X20606),X20605)),X20604)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20607),X20605)),X20603)))
| 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),X20606),X20607)),X20605)),X20604)),X20603))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20607),X20606)) )
& ( ~ 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),X20606),X20607)),X20605)),X20604)),X20603))
| 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),X20606),X20605)),X20604)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20607),X20605)),X20603)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20607),X20606)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff1])])]) ).
fof(i_0_6463,plain,
! [X32422,X32423,X32424,X32425,X32426] :
( ~ class_Rings_Osemiring__0(X32426)
| hAPP(c_List_Omonoid__add__class_Olistsum(X32426),hAPP(hAPP(c_List_Omap(X32425,X32426),hAPP(hAPP(c_COMBC(X32425,X32426,X32426),hAPP(hAPP(c_COMBB(X32426,tc_fun(X32426,X32426),X32425),c_Groups_Otimes__class_Otimes(X32426)),X32424)),X32423)),X32422)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X32426),hAPP(c_List_Omonoid__add__class_Olistsum(X32426),hAPP(hAPP(c_List_Omap(X32425,X32426),X32424),X32422))),X32423) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__mult__const])]) ).
fof(i_0_6464,plain,
! [X29329] : c_Int_Oint__ge__less__than2(X29329) = 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),X29329)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
inference(variable_rename,[status(thm)],[fact_int__ge__less__than2__def]) ).
fof(i_0_6465,plain,
! [X26310,X26311,X26312,X26313,X26314] :
( ( hBOOL(hAPP(hAPP(c_member(X26313),esk177_5(X26310,X26311,X26312,X26313,X26314)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26313,tc_HOL_Obool)),X26312),X26311)))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X26314,X26313,c_Groups_Otimes__class_Otimes(X26314)),X26310),c_Groups_Oone__class_Oone(X26314)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26313,tc_HOL_Obool)),X26312),X26311)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26314),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X26314,X26313,c_Groups_Otimes__class_Otimes(X26314)),X26310),c_Groups_Oone__class_Oone(X26314)),X26312)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X26314,X26313,c_Groups_Otimes__class_Otimes(X26314)),X26310),c_Groups_Oone__class_Oone(X26314)),X26311))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26313),X26311))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26313),X26312))
| ~ class_Groups_Ocomm__monoid__mult(X26314) )
& ( hAPP(X26310,esk177_5(X26310,X26311,X26312,X26313,X26314)) != c_Groups_Oone__class_Oone(X26314)
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X26314,X26313,c_Groups_Otimes__class_Otimes(X26314)),X26310),c_Groups_Oone__class_Oone(X26314)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26313,tc_HOL_Obool)),X26312),X26311)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26314),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X26314,X26313,c_Groups_Otimes__class_Otimes(X26314)),X26310),c_Groups_Oone__class_Oone(X26314)),X26312)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X26314,X26313,c_Groups_Otimes__class_Otimes(X26314)),X26310),c_Groups_Oone__class_Oone(X26314)),X26311))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26313),X26311))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26313),X26312))
| ~ class_Groups_Ocomm__monoid__mult(X26314) ) ),
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,
! [X24707,X24708,X24709,X24710] :
( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24710,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X24710,tc_fun(X24710,tc_HOL_Obool),tc_HOL_Obool),c_member(X24710)),X24709)),hAPP(hAPP(c_COMBC(X24710,tc_fun(X24710,tc_HOL_Obool),tc_HOL_Obool),c_member(X24710)),X24708)),X24707))
| hBOOL(hAPP(hAPP(c_member(X24710),X24707),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24710,tc_HOL_Obool)),X24709),X24708))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X24710),X24707),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24710,tc_HOL_Obool)),X24709),X24708)))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24710,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X24710,tc_fun(X24710,tc_HOL_Obool),tc_HOL_Obool),c_member(X24710)),X24709)),hAPP(hAPP(c_COMBC(X24710,tc_fun(X24710,tc_HOL_Obool),tc_HOL_Obool),c_member(X24710)),X24708)),X24707)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Int__eq])]) ).
fof(i_0_6467,plain,
! [X24169,X24170,X24171,X24172] :
( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24172,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X24172,tc_fun(X24172,tc_HOL_Obool),tc_HOL_Obool),c_member(X24172)),X24171)),hAPP(hAPP(c_COMBC(X24172,tc_fun(X24172,tc_HOL_Obool),tc_HOL_Obool),c_member(X24172)),X24170)),X24169))
| hBOOL(hAPP(hAPP(c_member(X24172),X24169),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24172,tc_HOL_Obool)),X24171),X24170))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X24172),X24169),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24172,tc_HOL_Obool)),X24171),X24170)))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24172,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X24172,tc_fun(X24172,tc_HOL_Obool),tc_HOL_Obool),c_member(X24172)),X24171)),hAPP(hAPP(c_COMBC(X24172,tc_fun(X24172,tc_HOL_Obool),tc_HOL_Obool),c_member(X24172)),X24170)),X24169)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Un__eq])]) ).
fof(i_0_6468,plain,
! [X29158,X29159,X29160] : hAPP(hAPP(c_Set_Oinsert(X29160),X29159),hAPP(c_Set_OCollect(X29160),X29158)) = hAPP(c_Set_OCollect(X29160),hAPP(hAPP(c_COMBS(X29160,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29160),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29160),c_fNot),hAPP(hAPP(c_COMBC(X29160,X29160,tc_HOL_Obool),c_fequal),X29159)))),X29158)),
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,
! [X24676,X24677,X24678,X24679,X24680,X24681] :
( ~ c_Equiv__Relations_Oequiv(X24681,X24680,X24679)
| ~ hBOOL(hAPP(hAPP(c_member(X24681),X24678),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24681,tc_HOL_Obool)),hAPP(c_Relation_OImage(X24681,X24681,X24679),hAPP(hAPP(c_Set_Oinsert(X24681),X24677),c_Orderings_Obot__class_Obot(tc_fun(X24681,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X24681,X24681,X24679),hAPP(hAPP(c_Set_Oinsert(X24681),X24676),c_Orderings_Obot__class_Obot(tc_fun(X24681,tc_HOL_Obool)))))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X24681,X24681)),hAPP(hAPP(c_Product__Type_OPair(X24681,X24681),X24677),X24676)),X24679)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__nondisjoint])]) ).
fof(i_0_6471,plain,
! [X22026,X22027,X22028,X22029,X22030,X22031,X22032] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22032,X22031),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X22030),X22029)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22028,X22031),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X22027),X22026)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22031))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22032),X22028),X22031),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),X22030),X22027)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22029),X22026)),X22031))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22029),X22026),X22031)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__add1__eq])]) ).
fof(i_0_6472,plain,
! [X28017,X28018,X28019,X28020] : c_Random__Sequence_Omap(X28020,X28019,X28018,X28017) = c_Random__Sequence_Obind(X28020,X28019,X28017,hAPP(c_Fun_Ocomp(X28019,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(X28019)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),X28020,c_Random__Sequence_Osingle(X28019)),X28018)),
inference(variable_rename,[status(thm)],[fact_Random__Sequence_Omap__def]) ).
fof(i_0_6473,plain,
! [X25763,X25764,X25765,X25766,X25767] :
( ( hBOOL(hAPP(hAPP(c_member(X25766),esk154_5(X25763,X25764,X25765,X25766,X25767)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25766,tc_HOL_Obool)),X25765),X25764)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25766,X25767),X25763),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25766,tc_HOL_Obool)),X25765),X25764)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25767),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25767),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25766,X25767),X25763),X25765)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25766,X25767),X25763),X25764))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25766,X25767),X25763),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25766,tc_HOL_Obool)),X25765),X25764)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25766),X25764))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25766),X25765))
| ~ class_Fields_Ofield(X25767) )
& ( hAPP(X25763,esk154_5(X25763,X25764,X25765,X25766,X25767)) = c_Groups_Ozero__class_Ozero(X25767)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25766,X25767),X25763),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25766,tc_HOL_Obool)),X25765),X25764)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25767),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25767),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25766,X25767),X25763),X25765)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25766,X25767),X25763),X25764))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25766,X25767),X25763),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25766,tc_HOL_Obool)),X25765),X25764)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25766),X25764))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25766),X25765))
| ~ class_Fields_Ofield(X25767) ) ),
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,
! [X22248,X22249,X22250,X22251,X22252,X22253,X22254] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22254,X22253),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22252),X22251)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22250,X22253),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22249),X22248)))
| X22253 = 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),X22254),X22250),X22253),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),X22252),X22249)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22251),X22248)),X22253))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22251),X22248),X22253)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd1__lemma])]) ).
fof(i_0_6475,plain,
! [X28635,X28636,X28637,X28638,X28639,X28640] :
( ~ class_Groups_Ocomm__monoid__add(X28640)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28639,X28640),hAPP(hAPP(c_COMBC(X28639,tc_fun(X28638,tc_HOL_Obool),X28640),hAPP(hAPP(c_COMBB(tc_fun(X28638,X28640),tc_fun(tc_fun(X28638,tc_HOL_Obool),X28640),X28639),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28638,X28640)),X28637)),X28636)),X28635) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X28639,X28638),X28640),hAPP(c_Product__Type_Oprod_Oprod__case(X28639,X28638,X28640),X28637)),hAPP(hAPP(c_Product__Type_OSigma(X28639,X28638),X28635),hAPP(c_COMBK(tc_fun(X28638,tc_HOL_Obool),X28639),X28636))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__cartesian__product])]) ).
fof(i_0_6476,plain,
! [X28654,X28655,X28656,X28657,X28658,X28659] :
( ~ class_Groups_Ocomm__monoid__mult(X28659)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28658,X28659),hAPP(hAPP(c_COMBC(X28658,tc_fun(X28657,tc_HOL_Obool),X28659),hAPP(hAPP(c_COMBB(tc_fun(X28657,X28659),tc_fun(tc_fun(X28657,tc_HOL_Obool),X28659),X28658),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X28657,X28659)),X28656)),X28655)),X28654) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X28658,X28657),X28659),hAPP(c_Product__Type_Oprod_Oprod__case(X28658,X28657,X28659),X28656)),hAPP(hAPP(c_Product__Type_OSigma(X28658,X28657),X28654),hAPP(c_COMBK(tc_fun(X28657,tc_HOL_Obool),X28658),X28655))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__cartesian__product])]) ).
fof(i_0_6477,plain,
! [X31570,X31571,X31572,X31573] :
( ( X31571 = hAPP(hAPP(c_Product__Type_OPair(X31573,X31572),esk428_4(X31570,X31571,X31572,X31573)),esk427_4(X31570,X31571,X31572,X31573))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31573,X31572)),X31571),hAPP(c_Relation_Oconverse(X31572,X31573),X31570))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X31572,X31573)),hAPP(hAPP(c_Product__Type_OPair(X31572,X31573),esk427_4(X31570,X31571,X31572,X31573)),esk428_4(X31570,X31571,X31572,X31573))),X31570))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31573,X31572)),X31571),hAPP(c_Relation_Oconverse(X31572,X31573),X31570))) ) ),
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,
! [X29016,X29017,X29018,X29019,X29020,X29021,X29022,X29023] :
( ~ c_Fun_Oinj__on(X29023,X29022,X29021,X29020)
| ~ c_Fun_Oinj__on(X29019,X29018,X29017,X29016)
| c_Fun_Oinj__on(tc_prod(X29023,X29019),tc_prod(X29022,X29018),c_Product__Type_Omap__pair(X29023,X29022,X29019,X29018,X29021,X29017),hAPP(hAPP(c_Product__Type_OSigma(X29023,X29019),X29020),hAPP(c_COMBK(tc_fun(X29019,tc_HOL_Obool),X29023),X29016))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__pair__inj__on])]) ).
fof(i_0_6479,plain,
! [X21993,X21994,X21995,X21996,X21997] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X21997,X21996),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X21995),X21994)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21996))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21993),X21997),X21996),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),X21993),X21995)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21993),X21994)),X21996))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21993),X21994),X21996)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__mult1__eq])]) ).
fof(i_0_6480,plain,
! [X18547,X18548,X18549,X18550] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18550),hAPP(X18549,X18548)),hAPP(X18549,X18547)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18548),X18547))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18550),hAPP(X18549,esk44_4(X18547,X18548,X18549,X18550))),hAPP(X18549,hAPP(c_Nat_OSuc,esk44_4(X18547,X18548,X18549,X18550)))))
| ~ class_Orderings_Oorder(X18550) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18548),X18547))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18550),hAPP(X18549,X18548)),hAPP(X18549,X18547)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18550),hAPP(X18549,esk44_4(X18547,X18548,X18549,X18550))),hAPP(X18549,hAPP(c_Nat_OSuc,esk44_4(X18547,X18548,X18549,X18550)))))
| ~ class_Orderings_Oorder(X18550) ) ),
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,
! [X18542,X18543,X18544,X18545] :
( ~ class_Orderings_Oorder(X18545)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18545),hAPP(X18544,esk43_4(X18542,X18543,X18544,X18545))),hAPP(X18544,hAPP(c_Nat_OSuc,esk43_4(X18542,X18543,X18544,X18545)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18543),X18542))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18545),hAPP(X18544,X18543)),hAPP(X18544,X18542))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lift__Suc__mono__less])])]) ).
fof(i_0_6482,plain,
! [X28071,X28072,X28073,X28074,X28075] :
( ( hBOOL(hAPP(hAPP(c_member(X28073),esk266_5(X28071,X28072,X28073,X28074,X28075)),X28071))
| ~ hBOOL(hAPP(hAPP(c_member(X28075),X28074),c_Map_Oran(X28073,X28075,c_Map_Orestrict__map(X28073,X28075,X28072,X28071)))) )
& ( hAPP(X28072,esk266_5(X28071,X28072,X28073,X28074,X28075)) = hAPP(c_Option_Ooption_OSome(X28075),X28074)
| ~ hBOOL(hAPP(hAPP(c_member(X28075),X28074),c_Map_Oran(X28073,X28075,c_Map_Orestrict__map(X28073,X28075,X28072,X28071)))) ) ),
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,
! [X22269,X22270,X22271,X22272,X22273] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22273,X22272),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22271),X22270)))
| X22272 = 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),X22269),X22273),X22272),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),X22269),X22271)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22269),X22270)),X22272))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22269),X22270),X22272)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult1__lemma])]) ).
fof(i_0_6484,plain,
! [X27422,X27423,X27424,X27425] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X27424),X27423))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27425),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X27425,X27425),hAPP(hAPP(c_COMBB(X27425,tc_fun(X27425,X27425),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X27425)),X27422)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X27425,tc_Nat_Onat),X27422),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,X27424,X27423)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27425),hAPP(X27422,X27424)),hAPP(X27422,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27423),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Groups_Oab__group__add(X27425) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X27424),X27423))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27425),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X27425,X27425),hAPP(hAPP(c_COMBB(X27425,tc_fun(X27425,X27425),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X27425)),X27422)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X27425,tc_Nat_Onat),X27422),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,X27424,X27423)) = c_Groups_Ozero__class_Ozero(X27425)
| ~ class_Groups_Oab__group__add(X27425) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5364])])]) ).
fof(i_0_6485,plain,
! [X32925,X32926,X32927,X32928,X32929,X32930,X32931] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X32931),X32930),hAPP(c_List_Oset(X32931),hAPP(hAPP(c_List_Otake(X32931),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32929)),X32928)),X32927))))
| c_Map_Omap__upds(X32931,X32929,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X32931,tc_Option_Ooption(X32929)),X32926),X32930),hAPP(c_Option_Ooption_OSome(X32929),X32925)),X32927,X32928) = c_Map_Omap__upds(X32931,X32929,X32926,X32927,X32928) )
& ( hBOOL(hAPP(hAPP(c_member(X32931),X32930),hAPP(c_List_Oset(X32931),hAPP(hAPP(c_List_Otake(X32931),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32929)),X32928)),X32927))))
| c_Map_Omap__upds(X32931,X32929,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X32931,tc_Option_Ooption(X32929)),X32926),X32930),hAPP(c_Option_Ooption_OSome(X32929),X32925)),X32927,X32928) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X32931,tc_Option_Ooption(X32929)),c_Map_Omap__upds(X32931,X32929,X32926,X32927,X32928)),X32930),hAPP(c_Option_Ooption_OSome(X32929),X32925)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5365])]) ).
fof(i_0_6486,plain,
! [X28865,X28866,X28867,X28868] :
( c_Fun_Oinj__on(X28868,tc_prod(X28867,X28868),esk287_4(X28865,X28866,X28867,X28868),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28867,tc_fun(X28868,tc_HOL_Obool)),X28866),X28865))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28867,X28868),tc_HOL_Obool)),hAPP(c_Set_Oimage(X28868,tc_prod(X28867,X28868),esk287_4(X28865,X28866,X28867,X28868)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28867,tc_fun(X28868,tc_HOL_Obool)),X28866),X28865))),hAPP(hAPP(c_Product__Type_OSigma(X28867,X28868),X28866),X28865))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact_Ex__inj__on__UNION__Sigma])]) ).
fof(i_0_6487,plain,
! [X28103,X28104,X28105,X28106,X28107] :
( ~ class_Groups_Oab__semigroup__mult(X28107)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28107,X28107,c_Groups_Otimes__class_Otimes(X28107),X28106,X28105),X28104))
| hBOOL(hAPP(hAPP(c_member(X28107),X28106),X28105))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28107,X28107,c_Groups_Otimes__class_Otimes(X28107),X28103,hAPP(hAPP(c_Set_Oinsert(X28107),X28106),X28105)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X28107),X28103),X28104))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5366])]) ).
fof(i_0_6488,plain,
! [X33987,X33988,X33989,X33990] : hAPP(hAPP(c_List_Omap(tc_prod(X33990,tc_Nat_Onat),X33990),c_Product__Type_Ofst(X33990,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X33990,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X33990,tc_Nat_Onat)),X33989),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(X33990,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(X33990,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(X33990,tc_Nat_Onat),X33988),X33987))) = hAPP(hAPP(c_List_Omap(tc_prod(X33990,tc_Nat_Onat),X33990),c_Product__Type_Ofst(X33990,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X33990,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X33990,tc_Nat_Onat)),X33989),c_Product__Type_Osnd(X33990,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(X33990,tc_Nat_Onat),X33988),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),X33987)))),
inference(variable_rename,[status(thm)],[fact_sublist__shift__lemma__Suc]) ).
fof(i_0_6489,plain,
! [X28994,X28995,X28996,X28997,X28998,X28999] : hAPP(c_Fun_Ocomp(tc_prod(X28999,X28998),X28999,tc_prod(X28997,X28996),c_Product__Type_Ofst(X28999,X28998)),c_Product__Type_Omap__pair(X28997,X28999,X28996,X28998,X28995,X28994)) = hAPP(c_Fun_Ocomp(X28997,X28999,tc_prod(X28997,X28996),X28995),c_Product__Type_Ofst(X28997,X28996)),
inference(variable_rename,[status(thm)],[fact_fst__comp__map__pair]) ).
fof(i_0_6490,plain,
! [X28988,X28989,X28990,X28991,X28992,X28993] : hAPP(c_Fun_Ocomp(tc_prod(X28993,X28992),X28992,tc_prod(X28991,X28990),c_Product__Type_Osnd(X28993,X28992)),c_Product__Type_Omap__pair(X28991,X28993,X28990,X28992,X28989,X28988)) = hAPP(c_Fun_Ocomp(X28990,X28992,tc_prod(X28991,X28990),X28988),c_Product__Type_Osnd(X28991,X28990)),
inference(variable_rename,[status(thm)],[fact_snd__comp__map__pair]) ).
fof(i_0_6491,plain,
! [X30907,X30908,X30909,X30910,X30911,X30912] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30912,tc_fun(X30911,tc_HOL_Obool)),X30910),hAPP(hAPP(c_COMBC(X30912,tc_fun(X30909,tc_fun(X30911,tc_HOL_Obool)),tc_fun(X30911,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30909,tc_HOL_Obool),tc_fun(tc_fun(X30909,tc_fun(X30911,tc_HOL_Obool)),tc_fun(X30911,tc_HOL_Obool)),X30912),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30909,tc_fun(X30911,tc_HOL_Obool))),X30908)),X30907)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30909,tc_fun(X30911,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30912,tc_fun(X30909,tc_HOL_Obool)),X30910),X30908)),X30907),
inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I9_J]) ).
fof(i_0_6492,plain,
! [X25921,X25922,X25923,X25924,X25925,X25926] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25926,tc_fun(X25925,tc_HOL_Obool)),X25924),hAPP(hAPP(c_COMBC(X25926,tc_fun(X25923,tc_fun(X25925,tc_HOL_Obool)),tc_fun(X25925,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25923,tc_HOL_Obool),tc_fun(tc_fun(X25923,tc_fun(X25925,tc_HOL_Obool)),tc_fun(X25925,tc_HOL_Obool)),X25926),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25923,tc_fun(X25925,tc_HOL_Obool))),X25922)),X25921)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25923,tc_fun(X25925,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25926,tc_fun(X25923,tc_HOL_Obool)),X25924),X25922)),X25921),
inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I9_J]) ).
fof(i_0_6493,plain,
! [X30901,X30902,X30903,X30904,X30905,X30906] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30906,tc_fun(X30905,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30904,tc_fun(X30906,tc_HOL_Obool)),X30903),X30902)),X30901) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30904,tc_fun(X30905,tc_HOL_Obool)),X30903),hAPP(hAPP(c_COMBC(X30904,tc_fun(X30906,tc_fun(X30905,tc_HOL_Obool)),tc_fun(X30905,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30906,tc_HOL_Obool),tc_fun(tc_fun(X30906,tc_fun(X30905,tc_HOL_Obool)),tc_fun(X30905,tc_HOL_Obool)),X30904),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30906,tc_fun(X30905,tc_HOL_Obool))),X30902)),X30901)),
inference(variable_rename,[status(thm)],[fact_INT__simps_I9_J]) ).
fof(i_0_6494,plain,
! [X25915,X25916,X25917,X25918,X25919,X25920] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25920,tc_fun(X25919,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25918,tc_fun(X25920,tc_HOL_Obool)),X25917),X25916)),X25915) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25918,tc_fun(X25919,tc_HOL_Obool)),X25917),hAPP(hAPP(c_COMBC(X25918,tc_fun(X25920,tc_fun(X25919,tc_HOL_Obool)),tc_fun(X25919,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25920,tc_HOL_Obool),tc_fun(tc_fun(X25920,tc_fun(X25919,tc_HOL_Obool)),tc_fun(X25919,tc_HOL_Obool)),X25918),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25920,tc_fun(X25919,tc_HOL_Obool))),X25916)),X25915)),
inference(variable_rename,[status(thm)],[fact_UN__simps_I9_J]) ).
fof(i_0_6495,plain,
! [X25909,X25910,X25911,X25912,X25913,X25914] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25914,tc_fun(X25913,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25912,tc_fun(X25914,tc_HOL_Obool)),X25911),X25910)),X25909) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25912,tc_fun(X25913,tc_HOL_Obool)),X25911),hAPP(hAPP(c_COMBC(X25912,tc_fun(X25914,tc_fun(X25913,tc_HOL_Obool)),tc_fun(X25913,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25914,tc_HOL_Obool),tc_fun(tc_fun(X25914,tc_fun(X25913,tc_HOL_Obool)),tc_fun(X25913,tc_HOL_Obool)),X25912),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25914,tc_fun(X25913,tc_HOL_Obool))),X25910)),X25909)),
inference(variable_rename,[status(thm)],[fact_UN__UN__flatten]) ).
fof(i_0_6496,plain,
! [X28096,X28097,X28098,X28099,X28100,X28101,X28102] :
( hBOOL(hAPP(hAPP(c_member(X28102),X28101),X28100))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28102,X28099,X28098,X28097,X28100),X28096))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28102,X28099,X28098,X28097,hAPP(hAPP(c_Set_Oinsert(X28102),X28101),X28100)),hAPP(hAPP(X28098,X28101),X28096))) ),
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),esk436_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,esk436_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,
! [X25927,X25928,X25929,X25930,X25931,X25932,X25933,X25934,X25935,X25936] :
( ~ c_Equiv__Relations_Ocongruent2(X25936,X25935,X25934,X25933,X25932,X25931)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X25936,X25936)),hAPP(hAPP(c_Product__Type_OPair(X25936,X25936),X25930),X25929)),X25933))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X25935,X25935)),hAPP(hAPP(c_Product__Type_OPair(X25935,X25935),X25928),X25927)),X25932))
| hAPP(hAPP(X25931,X25930),X25928) = hAPP(hAPP(X25931,X25929),X25927) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruent2D])]) ).
fof(i_0_6500,plain,
! [X31554,X31555,X31556,X31557,X31558] :
( ( hBOOL(hAPP(hAPP(c_member(X31558),esk425_5(X31554,X31555,X31556,X31557,X31558)),X31557))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31558,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31558,tc_HOL_Obool)),X31557),hAPP(c_Set_OCollect(X31558),X31555))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31558,tc_HOL_Obool)),X31556),hAPP(c_Set_OCollect(X31558),X31554))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31558,tc_HOL_Obool)),X31557),X31556)) )
& ( hBOOL(hAPP(X31555,esk425_5(X31554,X31555,X31556,X31557,X31558)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31558,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31558,tc_HOL_Obool)),X31557),hAPP(c_Set_OCollect(X31558),X31555))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31558,tc_HOL_Obool)),X31556),hAPP(c_Set_OCollect(X31558),X31554))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31558,tc_HOL_Obool)),X31557),X31556)) )
& ( ~ hBOOL(hAPP(X31554,esk425_5(X31554,X31555,X31556,X31557,X31558)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31558,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31558,tc_HOL_Obool)),X31557),hAPP(c_Set_OCollect(X31558),X31555))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31558,tc_HOL_Obool)),X31556),hAPP(c_Set_OCollect(X31558),X31554))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31558,tc_HOL_Obool)),X31557),X31556)) ) ),
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,
! [X32984,X32985,X32986,X32987,X32988,X32989] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32989)),X32988)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32987)),X32986)))
| c_Map_Omap__upds(X32989,X32987,X32985,hAPP(hAPP(c_List_Oappend(X32989),X32988),hAPP(hAPP(c_List_Olist_OCons(X32989),X32984),c_List_Olist_ONil(X32989))),X32986) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X32989,tc_Option_Ooption(X32987)),c_Map_Omap__upds(X32989,X32987,X32985,X32988,X32986)),X32984),hAPP(c_Option_Ooption_OSome(X32987),hAPP(hAPP(c_List_Onth(X32987),X32986),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32989)),X32988)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__upds__append1])]) ).
fof(i_0_6502,plain,
! [X28332,X28333,X28334] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28334,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X28334,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk272_3(X28332,X28333,X28334))),X28333)),X28332))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28334,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X28334,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X28333)),X28332)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__finite__subset])])]) ).
fof(i_0_6503,plain,
! [X29208,X29209,X29210] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29210,tc_HOL_Obool)),X29209),X29208) = hAPP(c_Set_OCollect(X29210),hAPP(hAPP(c_COMBS(X29210,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29210),c_fconj),hAPP(hAPP(c_COMBC(X29210,tc_fun(X29210,tc_HOL_Obool),tc_HOL_Obool),c_member(X29210)),X29209))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29210),c_fNot),hAPP(hAPP(c_COMBC(X29210,tc_fun(X29210,tc_HOL_Obool),tc_HOL_Obool),c_member(X29210)),X29208)))),
inference(variable_rename,[status(thm)],[fact_set__diff__eq]) ).
fof(i_0_6504,plain,
! [X29124,X29125,X29126] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29126),hAPP(c_Set_OCollect(X29126),X29125)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29126),hAPP(c_Set_OCollect(X29126),hAPP(hAPP(c_COMBS(X29126,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29126),c_fconj),X29125)),X29124)))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29126),hAPP(c_Set_OCollect(X29126),X29124)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29126),hAPP(c_Set_OCollect(X29126),hAPP(hAPP(c_COMBS(X29126,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29126),c_fconj),X29125)),X29124)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Collect__conjI])])]) ).
fof(i_0_6505,plain,
! [X17727,X17728,X17729,X17730,X17731,X17733,X17734,X17735,X17736,X17737,X17738] :
( ( hAPP(hAPP(hAPP(c_Natural_Oupdate,X17727),c_Com_Ovname_OLoc(X17731)),hAPP(hAPP(c_Natural_Ogetlocs,X17728),X17731)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,esk14_5(X17727,X17728,X17729,X17730,X17731)),c_Com_Ovname_OLoc(X17731)),hAPP(hAPP(c_Natural_Ogetlocs,X17728),X17731))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(X17731,X17730,X17729)),X17728),hAPP(hAPP(hAPP(c_Natural_Oupdate,X17727),c_Com_Ovname_OLoc(X17731)),hAPP(hAPP(c_Natural_Ogetlocs,X17728),X17731)))) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17729),hAPP(hAPP(hAPP(c_Natural_Oupdate,X17728),c_Com_Ovname_OLoc(X17731)),hAPP(X17730,X17728))),esk14_5(X17727,X17728,X17729,X17730,X17731)))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(X17731,X17730,X17729)),X17728),hAPP(hAPP(hAPP(c_Natural_Oupdate,X17727),c_Com_Ovname_OLoc(X17731)),hAPP(hAPP(c_Natural_Ogetlocs,X17728),X17731)))) )
& ( hAPP(hAPP(hAPP(c_Natural_Oupdate,X17733),c_Com_Ovname_OLoc(X17737)),hAPP(hAPP(c_Natural_Ogetlocs,X17734),X17737)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,X17738),c_Com_Ovname_OLoc(X17737)),hAPP(hAPP(c_Natural_Ogetlocs,X17734),X17737))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17735),hAPP(hAPP(hAPP(c_Natural_Oupdate,X17734),c_Com_Ovname_OLoc(X17737)),hAPP(X17736,X17734))),X17738))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(X17737,X17736,X17735)),X17734),hAPP(hAPP(hAPP(c_Natural_Oupdate,X17733),c_Com_Ovname_OLoc(X17737)),hAPP(hAPP(c_Natural_Ogetlocs,X17734),X17737)))) ) ),
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,
! [X28308,X28309] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X28309,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(X28309,tc_HOL_Obool)),tc_fun(X28309,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(X28309,tc_HOL_Obool)),tc_fun(X28309,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X28309,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X28308)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X28309,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X28308),
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),esk388_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,
! [X28946,X28947,X28948,X28949,X28950,X28951,X28952,X28953] : hAPP(c_Product__Type_Omap__pair(X28953,X28952,X28951,X28950,X28949,X28948),hAPP(hAPP(c_Product__Type_OPair(X28953,X28951),X28947),X28946)) = hAPP(hAPP(c_Product__Type_OPair(X28952,X28950),hAPP(X28949,X28947)),hAPP(X28948,X28946)),
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,
! [X28954,X28955,X28956] : hAPP(c_Product__Type_Omap__pair(X28956,X28956,X28955,X28955,c_COMBI(X28956),c_COMBI(X28955)),X28954) = X28954,
inference(variable_rename,[status(thm)],[fact_map__pair__ident]) ).
fof(i_0_6513,plain,
! [X26904,X26905,X26906,X26907,X26908] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk240_5(X26904,X26905,X26906,X26907,X26908)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26906)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26907),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26908),X26904)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26907),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26908),X26906)),X26904)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26907),X26906)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk241_5(X26904,X26905,X26906,X26907,X26908)),X26905))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26907),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26908),X26904)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26907),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26908),X26906)),X26904)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26907),X26906)) )
& ( X26908 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk241_5(X26904,X26905,X26906,X26907,X26908)),esk240_5(X26904,X26905,X26906,X26907,X26908))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26907),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26908),X26904)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26907),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26908),X26906)),X26904)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26907),X26906)) ) ),
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,
! [X26767,X26768,X26769,X26770,X26771] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk230_5(X26767,X26768,X26769,X26770,X26771)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26769)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26770),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26771),X26767)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26770),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26771),X26769)),X26767)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26770),X26769)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk231_5(X26767,X26768,X26769,X26770,X26771)),X26768))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26770),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26771),X26767)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26770),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26771),X26769)),X26767)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26770),X26769)) )
& ( X26771 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk231_5(X26767,X26768,X26769,X26770,X26771)),esk230_5(X26767,X26768,X26769,X26770,X26771))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26770),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26771),X26767)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26770),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26771),X26769)),X26767)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26770),X26769)) ) ),
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,
! [X32966,X32967,X32968,X32969,X32970,X32971,X32972] :
( hBOOL(hAPP(hAPP(c_member(X32972),X32971),hAPP(c_List_Oset(X32972),X32970)))
| c_Map_Omap__upds(X32972,X32969,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X32972,tc_Option_Ooption(X32969)),X32968),X32971),hAPP(c_Option_Ooption_OSome(X32969),X32967)),X32970,X32966) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X32972,tc_Option_Ooption(X32969)),c_Map_Omap__upds(X32972,X32969,X32968,X32970,X32966)),X32971),hAPP(c_Option_Ooption_OSome(X32969),X32967)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5375])]) ).
fof(i_0_6516,plain,
! [X26897,X26898,X26899,X26900,X26901] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk238_5(X26897,X26898,X26899,X26900,X26901)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26899)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26900),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26901),X26897)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26900),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26901),X26899)),X26897)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26900),X26899)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk239_5(X26897,X26898,X26899,X26900,X26901)),X26898))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26900),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26901),X26897)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26900),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26901),X26899)),X26897)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26900),X26899)) )
& ( X26901 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk239_5(X26897,X26898,X26899,X26900,X26901)),esk238_5(X26897,X26898,X26899,X26900,X26901))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26900),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26901),X26897)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26900),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26901),X26899)),X26897)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26900),X26899)) ) ),
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,
! [X26890,X26891,X26892,X26893,X26894] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk236_5(X26890,X26891,X26892,X26893,X26894)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26892)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26893),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26894),X26890)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26893),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26894),X26892)),X26890)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26893),X26892)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk237_5(X26890,X26891,X26892,X26893,X26894)),X26891))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26893),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26894),X26890)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26893),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26894),X26892)),X26890)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26893),X26892)) )
& ( X26894 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk237_5(X26890,X26891,X26892,X26893,X26894)),esk236_5(X26890,X26891,X26892,X26893,X26894))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26893),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26894),X26890)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26893),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26894),X26892)),X26890)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26893),X26892)) ) ),
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,
! [X25079,X25080,X25081,X25082,X25083,X25084,X25085,X25086] :
( ~ c_Finite__Set_Ofolding__image__simple(X25086,X25085,X25084,X25083,X25082,X25081)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25085),X25080))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25085),X25079))
| hAPP(hAPP(X25084,hAPP(X25081,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25085,tc_HOL_Obool)),X25080),X25079))),hAPP(X25081,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25085,tc_HOL_Obool)),X25080),X25079))) = hAPP(hAPP(X25084,hAPP(X25081,X25080)),hAPP(X25081,X25079)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Ounion__inter])]) ).
fof(i_0_6519,plain,
! [X27523,X27524,X27525,X27526,X27527] :
( ( hBOOL(hAPP(hAPP(c_member(X27526),esk251_5(X27523,X27524,X27525,X27526,X27527)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27526,tc_HOL_Obool)),X27525),X27524)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27526,X27527),X27523),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27526,tc_HOL_Obool)),X27525),X27524)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27527),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27526,X27527),X27523),X27525)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27526,X27527),X27523),X27524))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27526),X27524))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27526),X27525))
| ~ class_Groups_Ocomm__monoid__add(X27527) )
& ( hAPP(X27523,esk251_5(X27523,X27524,X27525,X27526,X27527)) != c_Groups_Ozero__class_Ozero(X27527)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27526,X27527),X27523),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27526,tc_HOL_Obool)),X27525),X27524)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27527),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27526,X27527),X27523),X27525)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27526,X27527),X27523),X27524))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27526),X27524))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27526),X27525))
| ~ class_Groups_Ocomm__monoid__add(X27527) ) ),
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_6520,plain,
! [X27463,X27464,X27465,X27466,X27467] :
( ( hBOOL(hAPP(hAPP(c_member(X27466),esk244_5(X27463,X27464,X27465,X27466,X27467)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27466,tc_HOL_Obool)),X27465),X27464)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27466,X27467),X27463),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27466,tc_HOL_Obool)),X27465),X27464)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27467),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27466,X27467),X27463),X27465)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27466,X27467),X27463),X27464))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27466),X27464))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27466),X27465))
| ~ class_Groups_Ocomm__monoid__add(X27467) )
& ( hAPP(X27463,esk244_5(X27463,X27464,X27465,X27466,X27467)) != c_Groups_Ozero__class_Ozero(X27467)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27466,X27467),X27463),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27466,tc_HOL_Obool)),X27465),X27464)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27467),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27466,X27467),X27463),X27465)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27466,X27467),X27463),X27464))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27466),X27464))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27466),X27465))
| ~ class_Groups_Ocomm__monoid__add(X27467) ) ),
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_6521,plain,
! [X25775,X25776,X25777,X25778,X25779] :
( ( hBOOL(hAPP(hAPP(c_member(X25778),esk156_5(X25775,X25776,X25777,X25778,X25779)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25778,tc_HOL_Obool)),X25777),X25776)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25778,X25779),X25775),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25778,tc_HOL_Obool)),X25777),X25776)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25779),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25778,X25779),X25775),X25777)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25778,X25779),X25775),X25776))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25778),X25776))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25778),X25777))
| ~ class_Groups_Ocomm__monoid__mult(X25779) )
& ( hAPP(X25775,esk156_5(X25775,X25776,X25777,X25778,X25779)) != c_Groups_Oone__class_Oone(X25779)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25778,X25779),X25775),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25778,tc_HOL_Obool)),X25777),X25776)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25779),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25778,X25779),X25775),X25777)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25778,X25779),X25775),X25776))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25778),X25776))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25778),X25777))
| ~ class_Groups_Ocomm__monoid__mult(X25779) ) ),
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_6522,plain,
! [X25769,X25770,X25771,X25772,X25773] :
( ( hBOOL(hAPP(hAPP(c_member(X25772),esk155_5(X25769,X25770,X25771,X25772,X25773)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25772,tc_HOL_Obool)),X25771),X25770)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25772,X25773),X25769),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25772,tc_HOL_Obool)),X25771),X25770)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25773),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25772,X25773),X25769),X25771)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25772,X25773),X25769),X25770))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25772),X25770))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25772),X25771))
| ~ class_Groups_Ocomm__monoid__mult(X25773) )
& ( hAPP(X25769,esk155_5(X25769,X25770,X25771,X25772,X25773)) != c_Groups_Oone__class_Oone(X25773)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25772,X25773),X25769),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25772,tc_HOL_Obool)),X25771),X25770)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25773),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25772,X25773),X25769),X25771)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25772,X25773),X25769),X25770))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25772),X25770))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25772),X25771))
| ~ class_Groups_Ocomm__monoid__mult(X25773) ) ),
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_6523,plain,
! [X29263,X29264,X29265,X29266] : hAPP(c_Relation_OImage(X29266,X29265,X29264),hAPP(hAPP(c_Set_Oinsert(X29266),X29263),c_Orderings_Obot__class_Obot(tc_fun(X29266,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(X29265),hAPP(hAPP(c_COMBC(X29265,tc_fun(tc_prod(X29266,X29265),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X29266,X29265),tc_fun(tc_fun(tc_prod(X29266,X29265),tc_HOL_Obool),tc_HOL_Obool),X29265),c_member(tc_prod(X29266,X29265))),hAPP(c_Product__Type_OPair(X29266,X29265),X29263))),X29264)),
inference(variable_rename,[status(thm)],[fact_Image__singleton]) ).
fof(i_0_6524,plain,
! [X17911,X17912,X17913,X17914,X17915] :
( ( X17911 = hAPP(hAPP(hAPP(c_Natural_Oupdate,esk20_5(X17911,X17912,X17913,X17914,X17915)),c_Com_Ovname_OLoc(X17915)),hAPP(hAPP(c_Natural_Ogetlocs,X17912),X17915))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(X17915,X17914,X17913)),X17912),X17911)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17913),hAPP(hAPP(hAPP(c_Natural_Oupdate,X17912),c_Com_Ovname_OLoc(X17915)),hAPP(X17914,X17912))),esk20_5(X17911,X17912,X17913,X17914,X17915)))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(X17915,X17914,X17913)),X17912),X17911)) ) ),
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,
! [X24581,X24582,X24583,X24584,X24585,X24586,X24587,X24588] :
( ~ c_Finite__Set_Ofolding__image__simple(X24588,X24587,X24586,X24585,X24584,X24583)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24587),X24582))
| ~ hBOOL(hAPP(hAPP(c_member(X24587),X24581),X24582))
| hAPP(X24583,X24582) = hAPP(hAPP(X24586,hAPP(X24584,X24581)),hAPP(X24583,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24587,tc_HOL_Obool)),X24582),hAPP(hAPP(c_Set_Oinsert(X24587),X24581),c_Orderings_Obot__class_Obot(tc_fun(X24587,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oremove])]) ).
fof(i_0_6527,plain,
! [X24273,X24274,X24275,X24276,X24277,X24279,X24280,X24281,X24282,X24283,X24284] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24275,tc_HOL_Obool)),esk117_5(X24273,X24274,X24275,X24276,X24277)),X24273))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24277,tc_HOL_Obool)),X24276),hAPP(c_Set_Oimage(X24275,X24277,X24274),X24273))) )
& ( X24276 = hAPP(c_Set_Oimage(X24275,X24277,X24274),esk117_5(X24273,X24274,X24275,X24276,X24277))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24277,tc_HOL_Obool)),X24276),hAPP(c_Set_Oimage(X24275,X24277,X24274),X24273))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24281,tc_HOL_Obool)),X24284),X24279))
| X24282 != hAPP(c_Set_Oimage(X24281,X24283,X24280),X24284)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24283,tc_HOL_Obool)),X24282),hAPP(c_Set_Oimage(X24281,X24283,X24280),X24279))) ) ),
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,
! [X25951,X25952,X25953,X25954,X25955,X25957,X25958,X25959,X25960,X25961,X25962] :
( ( hBOOL(hAPP(hAPP(c_member(X25953),esk165_5(X25951,X25952,X25953,X25954,X25955)),X25952))
| ~ hBOOL(hAPP(hAPP(c_member(X25955),X25954),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25953,tc_fun(X25955,tc_HOL_Obool)),X25952),X25951))) )
& ( hBOOL(hAPP(hAPP(c_member(X25955),X25954),hAPP(X25951,esk165_5(X25951,X25952,X25953,X25954,X25955))))
| ~ hBOOL(hAPP(hAPP(c_member(X25955),X25954),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25953,tc_fun(X25955,tc_HOL_Obool)),X25952),X25951))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X25959),X25962),X25958))
| ~ hBOOL(hAPP(hAPP(c_member(X25961),X25960),hAPP(X25957,X25962)))
| hBOOL(hAPP(hAPP(c_member(X25961),X25960),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25959,tc_fun(X25961,tc_HOL_Obool)),X25958),X25957))) ) ),
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,
! [X24656,X24657,X24658,X24659,X24660,X24661,X24662,X24663] :
( ~ c_Finite__Set_Ofolding__image__simple(X24663,X24662,X24661,X24660,X24659,X24658)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24662),X24657))
| hAPP(X24658,hAPP(hAPP(c_Set_Oinsert(X24662),X24656),X24657)) = hAPP(hAPP(X24661,hAPP(X24659,X24656)),hAPP(X24658,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24662,tc_HOL_Obool)),X24657),hAPP(hAPP(c_Set_Oinsert(X24662),X24656),c_Orderings_Obot__class_Obot(tc_fun(X24662,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oinsert__remove])]) ).
fof(i_0_6530,plain,
! [X27852,X27853,X27854,X27855,X27856,X27857,X27858] :
( ~ c_Fun_Oinj__on(X27858,X27857,X27856,hAPP(c_Set_Oimage(X27855,X27858,X27854),X27853))
| ~ c_Fun_Oinj__on(X27855,X27858,X27854,X27853)
| ~ hBOOL(hAPP(hAPP(c_member(X27857),X27852),hAPP(c_Set_Oimage(X27858,X27857,X27856),hAPP(c_Set_Oimage(X27855,X27858,X27854),X27853))))
| hAPP(c_Fun_Othe__inv__into(X27855,X27857,X27853,hAPP(c_Fun_Ocomp(X27858,X27857,X27855,X27856),X27854)),X27852) = hAPP(hAPP(c_Fun_Ocomp(X27858,X27855,X27857,c_Fun_Othe__inv__into(X27855,X27858,X27853,X27854)),c_Fun_Othe__inv__into(X27858,X27857,hAPP(c_Set_Oimage(X27855,X27858,X27854),X27853),X27856)),X27852) ),
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,
! [X27558,X27559,X27560,X27561,X27562] :
( ( hBOOL(hAPP(hAPP(c_member(X27561),esk257_5(X27558,X27559,X27560,X27561,X27562)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27561,tc_HOL_Obool)),X27560),X27559)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27561,X27562),X27558),X27559) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27561,X27562),X27558),X27560)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27561,tc_HOL_Obool)),X27559),X27560))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27561),X27560))
| ~ class_Groups_Ocomm__monoid__add(X27562) )
& ( hAPP(X27558,esk257_5(X27558,X27559,X27560,X27561,X27562)) != c_Groups_Ozero__class_Ozero(X27562)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27561,X27562),X27558),X27559) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27561,X27562),X27558),X27560)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27561,tc_HOL_Obool)),X27559),X27560))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27561),X27560))
| ~ class_Groups_Ocomm__monoid__add(X27562) ) ),
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_6533,plain,
! [X27552,X27553,X27554,X27555,X27556] :
( ( hBOOL(hAPP(hAPP(c_member(X27555),esk256_5(X27552,X27553,X27554,X27555,X27556)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27555,tc_HOL_Obool)),X27554),X27553)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27555,X27556),X27552),X27554) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27555,X27556),X27552),X27553)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27555,tc_HOL_Obool)),X27553),X27554))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27555),X27554))
| ~ class_Groups_Ocomm__monoid__add(X27556) )
& ( hAPP(X27552,esk256_5(X27552,X27553,X27554,X27555,X27556)) != c_Groups_Ozero__class_Ozero(X27556)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27555,X27556),X27552),X27554) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27555,X27556),X27552),X27553)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27555,tc_HOL_Obool)),X27553),X27554))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27555),X27554))
| ~ class_Groups_Ocomm__monoid__add(X27556) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__mono__zero__right])])])]) ).
fof(i_0_6534,plain,
! [X26358,X26359,X26360,X26361,X26362] :
( ( hBOOL(hAPP(hAPP(c_member(X26361),esk190_5(X26358,X26359,X26360,X26361,X26362)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26361,tc_HOL_Obool)),X26360),X26359)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26361,X26362),X26358),X26359) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26361,X26362),X26358),X26360)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26361,tc_HOL_Obool)),X26359),X26360))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26361),X26360))
| ~ class_Groups_Ocomm__monoid__mult(X26362) )
& ( hAPP(X26358,esk190_5(X26358,X26359,X26360,X26361,X26362)) != c_Groups_Oone__class_Oone(X26362)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26361,X26362),X26358),X26359) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26361,X26362),X26358),X26360)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26361,tc_HOL_Obool)),X26359),X26360))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26361),X26360))
| ~ class_Groups_Ocomm__monoid__mult(X26362) ) ),
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_6535,plain,
! [X26352,X26353,X26354,X26355,X26356] :
( ( hBOOL(hAPP(hAPP(c_member(X26355),esk189_5(X26352,X26353,X26354,X26355,X26356)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26355,tc_HOL_Obool)),X26354),X26353)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26355,X26356),X26352),X26354) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26355,X26356),X26352),X26353)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26355,tc_HOL_Obool)),X26353),X26354))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26355),X26354))
| ~ class_Groups_Ocomm__monoid__mult(X26356) )
& ( hAPP(X26352,esk189_5(X26352,X26353,X26354,X26355,X26356)) != c_Groups_Oone__class_Oone(X26356)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26355,X26356),X26352),X26354) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26355,X26356),X26352),X26353)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26355,tc_HOL_Obool)),X26353),X26354))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26355),X26354))
| ~ class_Groups_Ocomm__monoid__mult(X26356) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__mono__one__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,
! [X25817,X25818,X25819,X25820,X25821,X25823,X25824,X25825,X25826,X25827,X25828] :
( ( hBOOL(hAPP(hAPP(c_member(X25821),esk159_5(X25817,X25818,X25819,X25820,X25821)),X25819))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25821,tc_fun(X25820,tc_HOL_Obool)),X25819),X25818),X25817)) )
& ( hBOOL(hAPP(hAPP(X25818,esk159_5(X25817,X25818,X25819,X25820,X25821)),X25817))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25821,tc_fun(X25820,tc_HOL_Obool)),X25819),X25818),X25817)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X25827),X25828),X25825))
| ~ hBOOL(hAPP(hAPP(X25824,X25828),X25823))
| hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25827,tc_fun(X25826,tc_HOL_Obool)),X25825),X25824),X25823)) ) ),
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,
! [X30436,X30437,X30438] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30438,X30438)),X30437),c_Transitive__Closure_Ortrancl(X30438,X30436)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30438,X30438)),X30437),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X30438,X30438),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(X30438,X30438),tc_HOL_Obool),tc_fun(tc_prod(X30438,X30438),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X30438,X30438),tc_HOL_Obool)),X30436)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__imp__UN__rel__pow])]) ).
fof(i_0_6540,plain,
! [X31379,X31380,X31381,X31382,X31383] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31383,tc_fun(X31382,tc_HOL_Obool)),X31381),hAPP(hAPP(c_COMBS(X31383,tc_fun(X31382,tc_HOL_Obool),tc_fun(X31382,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31382,tc_HOL_Obool),tc_fun(tc_fun(X31382,tc_HOL_Obool),tc_fun(X31382,tc_HOL_Obool)),X31383),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31382,tc_HOL_Obool))),X31380)),X31379)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31382,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31382,tc_HOL_Obool),hAPP(c_Set_Oimage(X31383,tc_fun(X31382,tc_HOL_Obool),X31380),X31381))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31382,tc_HOL_Obool),hAPP(c_Set_Oimage(X31383,tc_fun(X31382,tc_HOL_Obool),X31379),X31381))),
inference(variable_rename,[status(thm)],[fact_Int__Inter__image]) ).
fof(i_0_6541,plain,
! [X31395,X31396,X31397,X31398,X31399] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X31399,tc_fun(X31398,tc_HOL_Obool)),X31397),hAPP(hAPP(c_COMBS(X31399,tc_fun(X31398,tc_HOL_Obool),tc_fun(X31398,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31398,tc_HOL_Obool),tc_fun(tc_fun(X31398,tc_HOL_Obool),tc_fun(X31398,tc_HOL_Obool)),X31399),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31398,tc_HOL_Obool))),X31396)),X31395)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31398,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31398,tc_HOL_Obool),hAPP(c_Set_Oimage(X31399,tc_fun(X31398,tc_HOL_Obool),X31396),X31397))),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31398,tc_HOL_Obool),hAPP(c_Set_Oimage(X31399,tc_fun(X31398,tc_HOL_Obool),X31395),X31397))),
inference(variable_rename,[status(thm)],[fact_Un__Union__image]) ).
fof(i_0_6542,plain,
! [X33179,X33180,X33181,X33182,X33183,X33184,X33185] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33185,X33185)),hAPP(hAPP(c_Product__Type_OPair(X33185,X33185),X33184),X33183)),X33182))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33185),tc_List_Olist(X33185))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33185),tc_List_Olist(X33185)),hAPP(hAPP(c_List_Oappend(X33185),X33181),hAPP(hAPP(c_List_Olist_OCons(X33185),X33184),X33180))),hAPP(hAPP(c_List_Oappend(X33185),X33181),hAPP(hAPP(c_List_Olist_OCons(X33185),X33183),X33179)))),c_List_Olexord(X33185,X33182))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__left__rightI])]) ).
fof(i_0_6543,plain,
! [X24189,X24190,X24191,X24192] :
( ( ~ 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),X24192),X24191)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X24190),X24189))),c_Int_Ointrel))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24192),X24189) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24190),X24191) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24192),X24189) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24190),X24191)
| 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),X24192),X24191)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X24190),X24189))),c_Int_Ointrel)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_intrel__iff])]) ).
fof(i_0_6544,plain,
! [X23881,X23882,X23883,X23884,X23885,X23886,X23887] :
( ~ hBOOL(hAPP(X23887,X23886))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23885,X23885)),hAPP(hAPP(c_Product__Type_OPair(X23885,X23885),X23884),X23883)),hAPP(X23882,X23886)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X23881,X23885),tc_prod(X23881,X23885))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X23881,X23885),tc_prod(X23881,X23885)),hAPP(hAPP(c_Product__Type_OPair(X23881,X23885),X23886),X23884)),hAPP(hAPP(c_Product__Type_OPair(X23881,X23885),X23886),X23883))),c_Recdef_Osame__fst(X23881,X23885,X23887,X23882))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__fstI])]) ).
fof(i_0_6545,plain,
! [X25944,X25945,X25946,X25947,X25948,X25950] :
( ( hBOOL(hAPP(hAPP(c_member(X25946),esk164_5(X25944,X25945,X25946,X25947,X25948)),X25945))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25948),X25947),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25946,X25948),X25945),X25944)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X25948)
| ~ class_Orderings_Olinorder(X25948) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25948),X25947),hAPP(X25944,esk164_5(X25944,X25945,X25946,X25947,X25948))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25948),X25947),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25946,X25948),X25945),X25944)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X25948)
| ~ class_Orderings_Olinorder(X25948) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X25946),X25950),X25945))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25948),X25947),hAPP(X25944,X25950)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25948),X25947),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25946,X25948),X25945),X25944)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X25948)
| ~ class_Orderings_Olinorder(X25948) ) ),
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,
! [X22150,X22151,X22152,X22153,X22154,X22155,X22156,X22157] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22157,X22156,X22155),X22154),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22153,X22152,tc_prod(X22157,X22156)),X22151),X22150)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22153,X22152,X22155),hAPP(hAPP(c_COMBB(tc_fun(X22152,tc_prod(X22157,X22156)),tc_fun(X22152,X22155),X22153),hAPP(c_COMBB(tc_prod(X22157,X22156),X22155,X22152),hAPP(c_Product__Type_Oprod_Oprod__case(X22157,X22156,X22155),X22154))),X22151)),X22150),
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,
! [X27588,X27589,X27590,X27591] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X27591),esk259_4(X27588,X27589,X27590,X27591)))
| hBOOL(hAPP(X27588,X27590))
| ~ hBOOL(hAPP(X27588,c_Orderings_Obot__class_Obot(tc_fun(X27591,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27591,tc_HOL_Obool)),X27590),X27589))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27591),X27590)) )
& ( hBOOL(hAPP(hAPP(c_member(X27591),esk258_4(X27588,X27589,X27590,X27591)),X27589))
| hBOOL(hAPP(X27588,X27590))
| ~ hBOOL(hAPP(X27588,c_Orderings_Obot__class_Obot(tc_fun(X27591,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27591,tc_HOL_Obool)),X27590),X27589))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27591),X27590)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X27591),esk258_4(X27588,X27589,X27590,X27591)),esk259_4(X27588,X27589,X27590,X27591)))
| hBOOL(hAPP(X27588,X27590))
| ~ hBOOL(hAPP(X27588,c_Orderings_Obot__class_Obot(tc_fun(X27591,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27591,tc_HOL_Obool)),X27590),X27589))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27591),X27590)) )
& ( hBOOL(hAPP(X27588,esk259_4(X27588,X27589,X27590,X27591)))
| hBOOL(hAPP(X27588,X27590))
| ~ hBOOL(hAPP(X27588,c_Orderings_Obot__class_Obot(tc_fun(X27591,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27591,tc_HOL_Obool)),X27590),X27589))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27591),X27590)) )
& ( ~ hBOOL(hAPP(X27588,hAPP(hAPP(c_Set_Oinsert(X27591),esk258_4(X27588,X27589,X27590,X27591)),esk259_4(X27588,X27589,X27590,X27591))))
| hBOOL(hAPP(X27588,X27590))
| ~ hBOOL(hAPP(X27588,c_Orderings_Obot__class_Obot(tc_fun(X27591,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27591,tc_HOL_Obool)),X27590),X27589))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27591),X27590)) ) ),
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,
! [X33782,X33783,X33784,X33785] :
( ( hBOOL(hAPP(hAPP(c_member(X33785),esk480_4(X33782,X33783,X33784,X33785)),hAPP(c_List_Oset(X33785),X33784)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X33785,X33783,X33784)),c_List_Olist_Olist__size(X33785,X33782,X33784))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X33783,esk480_4(X33782,X33783,X33784,X33785))),hAPP(X33782,esk480_4(X33782,X33783,X33784,X33785))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X33785,X33783,X33784)),c_List_Olist_Olist__size(X33785,X33782,X33784))) ) ),
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,
! [X29309,X29310] : c_Fun_Oinj__on(tc_fun(X29310,X29309),tc_fun(tc_prod(X29310,X29309),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X29310,X29309),tc_HOL_Obool),tc_fun(tc_prod(X29310,X29309),tc_HOL_Obool),tc_fun(X29310,X29309)),c_Set_OCollect(tc_prod(X29310,X29309))),hAPP(hAPP(c_COMBB(tc_fun(X29310,tc_fun(X29309,tc_HOL_Obool)),tc_fun(tc_prod(X29310,X29309),tc_HOL_Obool),tc_fun(X29310,X29309)),c_Product__Type_Oprod_Oprod__case(X29310,X29309,tc_HOL_Obool)),hAPP(c_COMBB(X29309,tc_fun(X29309,tc_HOL_Obool),X29310),hAPP(c_COMBC(X29309,X29309,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X29310,X29309),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,
! [X28553,X28554,X28555,X28556,X28557,X28559,X28560,X28561,X28562,X28564] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X28556),X28554))
| ~ c_Wellfounded_Omax__extp(X28556,X28555,X28554,X28553) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X28556),X28553))
| ~ c_Wellfounded_Omax__extp(X28556,X28555,X28554,X28553) )
& ( X28553 != c_Orderings_Obot__class_Obot(tc_fun(X28556,tc_HOL_Obool))
| ~ c_Wellfounded_Omax__extp(X28556,X28555,X28554,X28553) )
& ( hBOOL(hAPP(hAPP(c_member(X28556),esk275_5(X28553,X28554,X28555,X28556,X28557)),X28553))
| ~ hBOOL(hAPP(hAPP(c_member(X28556),X28557),X28554))
| ~ c_Wellfounded_Omax__extp(X28556,X28555,X28554,X28553) )
& ( hBOOL(hAPP(hAPP(X28555,X28557),esk275_5(X28553,X28554,X28555,X28556,X28557)))
| ~ hBOOL(hAPP(hAPP(c_member(X28556),X28557),X28554))
| ~ c_Wellfounded_Omax__extp(X28556,X28555,X28554,X28553) )
& ( hBOOL(hAPP(hAPP(c_member(X28562),esk276_4(X28559,X28560,X28561,X28562)),X28560))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28562),X28560))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28562),X28559))
| X28559 = c_Orderings_Obot__class_Obot(tc_fun(X28562,tc_HOL_Obool))
| c_Wellfounded_Omax__extp(X28562,X28561,X28560,X28559) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X28562),X28564),X28559))
| ~ hBOOL(hAPP(hAPP(X28561,esk276_4(X28559,X28560,X28561,X28562)),X28564))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28562),X28560))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28562),X28559))
| X28559 = c_Orderings_Obot__class_Obot(tc_fun(X28562,tc_HOL_Obool))
| c_Wellfounded_Omax__extp(X28562,X28561,X28560,X28559) ) ),
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,
! [X29195,X29196,X29197] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29197,tc_HOL_Obool)),X29196),X29195) = hAPP(c_Set_OCollect(X29197),hAPP(hAPP(c_COMBS(X29197,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29197),c_fconj),hAPP(hAPP(c_COMBC(X29197,tc_fun(X29197,tc_HOL_Obool),tc_HOL_Obool),c_member(X29197)),X29196))),hAPP(hAPP(c_COMBC(X29197,tc_fun(X29197,tc_HOL_Obool),tc_HOL_Obool),c_member(X29197)),X29195))),
inference(variable_rename,[status(thm)],[fact_Int__def]) ).
fof(i_0_6560,plain,
! [X29188,X29189,X29190] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29190,tc_HOL_Obool)),X29189),X29188) = hAPP(c_Set_OCollect(X29190),hAPP(hAPP(c_COMBS(X29190,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29190),c_fdisj),hAPP(hAPP(c_COMBC(X29190,tc_fun(X29190,tc_HOL_Obool),tc_HOL_Obool),c_member(X29190)),X29189))),hAPP(hAPP(c_COMBC(X29190,tc_fun(X29190,tc_HOL_Obool),tc_HOL_Obool),c_member(X29190)),X29188))),
inference(variable_rename,[status(thm)],[fact_Un__def]) ).
fof(i_0_6561,plain,
! [X25090,X25091,X25092,X25093,X25094,X25095,X25096,X25097] :
( ~ c_Finite__Set_Ofolding__image__simple(X25097,X25096,X25095,X25094,X25093,X25092)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25096),X25091))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25096),X25090))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25096,tc_HOL_Obool)),X25091),X25090) != c_Orderings_Obot__class_Obot(tc_fun(X25096,tc_HOL_Obool))
| hAPP(X25092,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25096,tc_HOL_Obool)),X25091),X25090)) = hAPP(hAPP(X25095,hAPP(X25092,X25091)),hAPP(X25092,X25090)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Ounion__disjoint])]) ).
fof(i_0_6562,plain,
! [X27426,X27427,X27428,X27429,X27430,X27431] :
( ~ hBOOL(hAPP(hAPP(c_member(X27431),X27430),X27429))
| hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27431,tc_Option_Ooption(X27428)),c_Map_Orestrict__map(X27431,X27428,X27427,X27429)),X27430),X27426) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27431,tc_Option_Ooption(X27428)),c_Map_Orestrict__map(X27431,X27428,X27427,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27431,tc_HOL_Obool)),X27429),hAPP(hAPP(c_Set_Oinsert(X27431),X27430),c_Orderings_Obot__class_Obot(tc_fun(X27431,tc_HOL_Obool)))))),X27430),X27426) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__restrict__conv])]) ).
fof(i_0_6563,plain,
! [X20505,X20506,X20507,X20508,X20509,X20510] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20510),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20510),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20510),X20509),X20508)),X20507)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20510),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20510),X20506),X20508)),X20505)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20510),X20507),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20510),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20510),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20510),X20506),X20509)),X20508)),X20505)))
| ~ class_Rings_Oordered__ring(X20510) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20510),X20507),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20510),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20510),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20510),X20506),X20509)),X20508)),X20505)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20510),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20510),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20510),X20509),X20508)),X20507)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20510),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20510),X20506),X20508)),X20505)))
| ~ class_Rings_Oordered__ring(X20510) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__iff2])])]) ).
fof(i_0_6564,plain,
! [X20517,X20518,X20519,X20520,X20521,X20522] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20522),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20522),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20522),X20521),X20520)),X20519)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20522),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20522),X20518),X20520)),X20517)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20522),X20519),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20522),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20522),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20522),X20518),X20521)),X20520)),X20517)))
| ~ class_Rings_Oordered__ring(X20522) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20522),X20519),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20522),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20522),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20522),X20518),X20521)),X20520)),X20517)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20522),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20522),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20522),X20521),X20520)),X20519)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20522),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20522),X20518),X20520)),X20517)))
| ~ class_Rings_Oordered__ring(X20522) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__iff2])])]) ).
fof(i_0_6565,plain,
! [X31059,X31060,X31061,X31062,X31063,X31064] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31064,tc_HOL_Obool)),hAPP(c_Relation_OImage(X31063,X31064,X31062),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31061,tc_fun(X31063,tc_HOL_Obool)),X31060),X31059))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31061,tc_fun(X31064,tc_HOL_Obool)),X31060),hAPP(hAPP(c_COMBB(tc_fun(X31063,tc_HOL_Obool),tc_fun(X31064,tc_HOL_Obool),X31061),c_Relation_OImage(X31063,X31064,X31062)),X31059)))),
inference(variable_rename,[status(thm)],[fact_Image__INT__subset]) ).
fof(i_0_6566,plain,
! [X31546,X31547,X31548,X31549,X31550,X31551,X31552,X31553] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X31553,X31552,X31551,X31550,X31549,X31548)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31552),X31547))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31552,tc_HOL_Obool)),X31546),X31547))
| hAPP(hAPP(X31551,hAPP(X31548,X31546)),hAPP(X31548,X31547)) = hAPP(X31548,X31547) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Osubset__idem])]) ).
fof(i_0_6567,plain,
! [X19128,X19129,X19130,X19131,X19132] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19130,X19131)),X19129),X19128))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19131),hAPP(X19129,X19132)),hAPP(X19128,X19132)))
| ~ class_Orderings_Oord(X19131) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19131),hAPP(X19129,esk48_4(X19128,X19129,X19130,X19131))),hAPP(X19128,esk48_4(X19128,X19129,X19130,X19131))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19130,X19131)),X19129),X19128))
| ~ class_Orderings_Oord(X19131) ) ),
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,
! [X27389,X27390,X27391,X27392,X27393,X27394] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27394,tc_Option_Ooption(X27393)),c_Map_Orestrict__map(X27394,X27393,X27392,X27391)),X27390),X27389) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27394,tc_Option_Ooption(X27393)),c_Map_Orestrict__map(X27394,X27393,X27392,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27394,tc_HOL_Obool)),X27391),hAPP(hAPP(c_Set_Oinsert(X27394),X27390),c_Orderings_Obot__class_Obot(tc_fun(X27394,tc_HOL_Obool)))))),X27390),X27389),
inference(variable_rename,[status(thm)],[fact_fun__upd__restrict]) ).
fof(i_0_6569,plain,
! [X26252,X26253,X26254,X26255,X26256,X26257,X26258] :
( ~ c_Finite__Set_Ofolding__image__simple(X26258,X26257,X26256,X26255,X26254,X26253)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26257),X26252))
| hAPP(X26253,X26252) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X26258,X26257,X26256),X26254),X26255),X26252) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oeq__fold__g])]) ).
fof(i_0_6570,plain,
! [X31828,X31829,X31830,X31831,X31832,X31833,X31834,X31835,X31836,X31837,X31838] :
( ( hAPP(hAPP(c_List_Omap(X31832,X31831),X31830),X31829) != hAPP(hAPP(c_List_Omap(X31832,X31831),X31828),X31829)
| ~ hBOOL(hAPP(hAPP(c_member(X31832),X31833),hAPP(c_List_Oset(X31832),X31829)))
| hAPP(X31830,X31833) = hAPP(X31828,X31833) )
& ( hBOOL(hAPP(hAPP(c_member(X31838),esk437_5(X31834,X31835,X31836,X31837,X31838)),hAPP(c_List_Oset(X31838),X31835)))
| hAPP(hAPP(c_List_Omap(X31838,X31837),X31836),X31835) = hAPP(hAPP(c_List_Omap(X31838,X31837),X31834),X31835) )
& ( hAPP(X31836,esk437_5(X31834,X31835,X31836,X31837,X31838)) != hAPP(X31834,esk437_5(X31834,X31835,X31836,X31837,X31838))
| hAPP(hAPP(c_List_Omap(X31838,X31837),X31836),X31835) = hAPP(hAPP(c_List_Omap(X31838,X31837),X31834),X31835) ) ),
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,
! [X31512,X31513,X31514,X31515,X31516,X31517,X31518,X31519] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X31519,X31518,X31517,X31516,X31515,X31514)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31518),X31513))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31518),X31512))
| hAPP(X31514,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31518,tc_HOL_Obool)),X31513),X31512)) = hAPP(hAPP(X31517,hAPP(X31514,X31513)),hAPP(X31514,X31512)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Ounion__idem])]) ).
fof(i_0_6572,plain,
! [X26179,X26180,X26181,X26182,X26183,X26184,X26185,X26186] :
( ~ c_Equiv__Relations_Oequiv(X26186,X26185,X26184)
| ~ c_Equiv__Relations_Ocongruent2(X26186,X26183,X26182,X26184,X26181,X26180)
| ~ hBOOL(hAPP(hAPP(c_member(X26186),X26179),X26185))
| c_Equiv__Relations_Ocongruent(X26183,X26182,X26181,hAPP(X26180,X26179)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruent2__implies__congruent])]) ).
fof(i_0_6573,plain,
! [X33101,X33102,X33103,X33104,X33105,X33108,X33109,X33110,X33111,X33112,X33113,X33114] :
( ( hAPP(hAPP(c_List_Oappend(X33105),X33104),esk462_5(X33101,X33102,X33103,X33104,X33105)) = X33102
| X33104 = hAPP(hAPP(c_List_Oappend(X33105),X33102),esk461_5(X33101,X33102,X33103,X33104,X33105))
| hAPP(hAPP(c_List_Oappend(X33105),X33104),X33103) != hAPP(hAPP(c_List_Oappend(X33105),X33102),X33101) )
& ( X33103 = hAPP(hAPP(c_List_Oappend(X33105),esk462_5(X33101,X33102,X33103,X33104,X33105)),X33101)
| X33104 = hAPP(hAPP(c_List_Oappend(X33105),X33102),esk461_5(X33101,X33102,X33103,X33104,X33105))
| hAPP(hAPP(c_List_Oappend(X33105),X33104),X33103) != hAPP(hAPP(c_List_Oappend(X33105),X33102),X33101) )
& ( hAPP(hAPP(c_List_Oappend(X33105),X33104),esk462_5(X33101,X33102,X33103,X33104,X33105)) = X33102
| hAPP(hAPP(c_List_Oappend(X33105),esk461_5(X33101,X33102,X33103,X33104,X33105)),X33103) = X33101
| hAPP(hAPP(c_List_Oappend(X33105),X33104),X33103) != hAPP(hAPP(c_List_Oappend(X33105),X33102),X33101) )
& ( X33103 = hAPP(hAPP(c_List_Oappend(X33105),esk462_5(X33101,X33102,X33103,X33104,X33105)),X33101)
| hAPP(hAPP(c_List_Oappend(X33105),esk461_5(X33101,X33102,X33103,X33104,X33105)),X33103) = X33101
| hAPP(hAPP(c_List_Oappend(X33105),X33104),X33103) != hAPP(hAPP(c_List_Oappend(X33105),X33102),X33101) )
& ( X33111 != hAPP(hAPP(c_List_Oappend(X33112),X33109),X33113)
| hAPP(hAPP(c_List_Oappend(X33112),X33113),X33110) != X33108
| hAPP(hAPP(c_List_Oappend(X33112),X33111),X33110) = hAPP(hAPP(c_List_Oappend(X33112),X33109),X33108) )
& ( hAPP(hAPP(c_List_Oappend(X33112),X33111),X33114) != X33109
| X33110 != hAPP(hAPP(c_List_Oappend(X33112),X33114),X33108)
| hAPP(hAPP(c_List_Oappend(X33112),X33111),X33110) = hAPP(hAPP(c_List_Oappend(X33112),X33109),X33108) ) ),
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,
! [X24638,X24639,X24640,X24641,X24642,X24643,X24644,X24645] :
( ~ c_Finite__Set_Ofolding__image__simple(X24645,X24644,X24643,X24642,X24641,X24640)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24644),X24639))
| hBOOL(hAPP(hAPP(c_member(X24644),X24638),X24639))
| hAPP(X24640,hAPP(hAPP(c_Set_Oinsert(X24644),X24638),X24639)) = hAPP(hAPP(X24643,hAPP(X24641,X24638)),hAPP(X24640,X24639)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5386])]) ).
fof(i_0_6575,plain,
! [X26539,X26540,X26541,X26542,X26543] :
( ( ~ c_Fun_Oinj__on(X26542,X26540,X26543,X26541)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26540,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26542,X26540,X26543),X26541)),X26539))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X26542),X26541)),hAPP(c_Finite__Set_Ocard(X26540),X26539)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26540),X26539))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26542),X26541)) )
& ( c_Fun_Oinj__on(X26542,X26540,esk193_4(X26539,X26540,X26541,X26542),X26541)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X26542),X26541)),hAPP(c_Finite__Set_Ocard(X26540),X26539)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26540),X26539))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26542),X26541)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26540,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26542,X26540,esk193_4(X26539,X26540,X26541,X26542)),X26541)),X26539))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X26542),X26541)),hAPP(c_Finite__Set_Ocard(X26540),X26539)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26540),X26539))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26542),X26541)) ) ),
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,
! [X31530,X31531,X31532,X31533,X31534,X31535,X31536,X31537] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X31537,X31536,X31535,X31534,X31533,X31532)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31536),X31531))
| ~ hBOOL(hAPP(hAPP(c_member(X31536),X31530),X31531))
| hAPP(hAPP(X31535,hAPP(X31533,X31530)),hAPP(X31532,X31531)) = hAPP(X31532,X31531) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oin__idem])]) ).
fof(i_0_6577,plain,
! [X31538,X31539,X31540,X31541,X31542,X31543,X31544,X31545] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X31545,X31544,X31543,X31542,X31541,X31540)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31544),X31539))
| hAPP(X31540,hAPP(hAPP(c_Set_Oinsert(X31544),X31538),X31539)) = hAPP(hAPP(X31543,hAPP(X31541,X31538)),hAPP(X31540,X31539)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oinsert__idem])]) ).
fof(i_0_6578,plain,
! [X30937,X30938,X30939,X30940,X30941] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30941,tc_fun(X30940,tc_HOL_Obool)),X30939),hAPP(hAPP(c_COMBS(X30941,tc_fun(X30940,tc_HOL_Obool),tc_fun(X30940,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30940,tc_HOL_Obool),tc_fun(tc_fun(X30940,tc_HOL_Obool),tc_fun(X30940,tc_HOL_Obool)),X30941),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30940,tc_HOL_Obool))),X30938)),X30937)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30940,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30941,tc_fun(X30940,tc_HOL_Obool)),X30939),X30938)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30941,tc_fun(X30940,tc_HOL_Obool)),X30939),X30937)),
inference(variable_rename,[status(thm)],[fact_INT__Int__distrib]) ).
fof(i_0_6579,plain,
! [X26024,X26025,X26026,X26027,X26028] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26028,tc_fun(X26027,tc_HOL_Obool)),X26026),hAPP(hAPP(c_COMBS(X26028,tc_fun(X26027,tc_HOL_Obool),tc_fun(X26027,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26027,tc_HOL_Obool),tc_fun(tc_fun(X26027,tc_HOL_Obool),tc_fun(X26027,tc_HOL_Obool)),X26028),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26027,tc_HOL_Obool))),X26025)),X26024)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26027,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26028,tc_fun(X26027,tc_HOL_Obool)),X26026),X26025)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26028,tc_fun(X26027,tc_HOL_Obool)),X26026),X26024)),
inference(variable_rename,[status(thm)],[fact_UN__Un__distrib]) ).
fof(i_0_6580,plain,
! [X24607,X24608,X24609,X24610,X24611,X24612] :
( ~ c_Finite__Set_Ofolding__image__simple(X24612,X24611,X24610,X24609,X24608,X24607)
| hAPP(X24607,c_Orderings_Obot__class_Obot(tc_fun(X24611,tc_HOL_Obool))) = X24609 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oempty])]) ).
fof(i_0_6581,plain,
! [X31523,X31524,X31525,X31526,X31527,X31528,X31529] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X31529,X31528,X31527,X31526,X31525,X31524)
| hAPP(hAPP(X31527,X31523),X31523) = X31523 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oidem])]) ).
fof(i_0_6582,plain,
! [X24486] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X24486))
| X24486 = 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))),X24486)),c_FunDef_Omax__strict)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smax__emptyI])]) ).
fof(i_0_6583,plain,
! [X33914,X33915,X33916] : hAPP(c_List_Oset(X33916),hAPP(c_List_Ofilter(X33916,X33915),X33914)) = hAPP(c_Set_OCollect(X33916),hAPP(hAPP(c_COMBS(X33916,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X33916),c_fconj),hAPP(hAPP(c_COMBC(X33916,tc_fun(X33916,tc_HOL_Obool),tc_HOL_Obool),c_member(X33916)),hAPP(c_List_Oset(X33916),X33914)))),X33915)),
inference(variable_rename,[status(thm)],[fact_set__filter]) ).
fof(i_0_6584,plain,
! [X27548,X27549,X27550] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X27550,esk255_3(X27548,X27549,X27550))),hAPP(X27549,esk255_3(X27548,X27549,X27550))))
| 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),X27549),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X27548))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X27550),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X27548))) = 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)),X27549)),X27550)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X27548)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__diff__distrib])])]) ).
fof(i_0_6585,plain,
! [X26662,X26663,X26664,X26665,X26666,X26668] :
( ( ~ c_Fun_Oinj__on(X26664,X26663,X26666,X26665)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26663,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26664,X26663,X26666),X26665)),X26662))
| hAPP(c_Set_Oimage(X26663,X26664,esk196_4(X26662,X26663,X26664,X26665)),X26662) = X26665
| X26665 = c_Orderings_Obot__class_Obot(tc_fun(X26664,tc_HOL_Obool)) )
& ( c_Fun_Oinj__on(X26664,X26663,esk197_4(X26662,X26663,X26664,X26665),X26665)
| hAPP(c_Set_Oimage(X26663,X26664,X26668),X26662) != X26665
| X26665 = c_Orderings_Obot__class_Obot(tc_fun(X26664,tc_HOL_Obool)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26663,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26664,X26663,esk197_4(X26662,X26663,X26664,X26665)),X26665)),X26662))
| hAPP(c_Set_Oimage(X26663,X26664,X26668),X26662) != X26665
| X26665 = c_Orderings_Obot__class_Obot(tc_fun(X26664,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,
! [X29732,X29733,X29734,X29735] :
( ~ hBOOL(hAPP(hAPP(c_member(X29735),X29734),hAPP(c_Relation_ORange(X29733,X29735),X29732)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X29733,X29735)),hAPP(hAPP(c_Product__Type_OPair(X29733,X29735),esk323_4(X29732,X29733,X29734,X29735)),X29734)),X29732)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5387])])]) ).
fof(i_0_6587,plain,
! [X29705,X29706,X29707,X29708,X29710,X29711,X29712,X29713,X29714] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X29708),X29707),hAPP(c_Relation_ORange(X29706,X29708),X29705)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X29706,X29708)),hAPP(hAPP(c_Product__Type_OPair(X29706,X29708),esk322_4(X29705,X29706,X29707,X29708)),X29707)),X29705)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29711,X29713)),hAPP(hAPP(c_Product__Type_OPair(X29711,X29713),X29714),X29712)),X29710))
| hBOOL(hAPP(hAPP(c_member(X29713),X29712),hAPP(c_Relation_ORange(X29711,X29713),X29710))) ) ),
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,
! [X24485] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X24485))
| 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))),X24485)),c_FunDef_Omax__weak)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wmax__emptyI])]) ).
fof(i_0_6589,plain,
! [X31147,X31148,X31149,X31150,X31151] :
( ( X31151 != c_Orderings_Obot__class_Obot(tc_fun(X31150,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31150,tc_fun(X31149,tc_HOL_Obool)),X31151),hAPP(hAPP(c_COMBC(X31150,tc_fun(X31149,tc_HOL_Obool),tc_fun(X31149,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31149,tc_HOL_Obool),tc_fun(tc_fun(X31149,tc_HOL_Obool),tc_fun(X31149,tc_HOL_Obool)),X31150),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31149,tc_HOL_Obool))),X31148)),X31147)) = c_Orderings_Otop__class_Otop(tc_fun(X31149,tc_HOL_Obool)) )
& ( X31151 = c_Orderings_Obot__class_Obot(tc_fun(X31150,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31150,tc_fun(X31149,tc_HOL_Obool)),X31151),hAPP(hAPP(c_COMBC(X31150,tc_fun(X31149,tc_HOL_Obool),tc_fun(X31149,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31149,tc_HOL_Obool),tc_fun(tc_fun(X31149,tc_HOL_Obool),tc_fun(X31149,tc_HOL_Obool)),X31150),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31149,tc_HOL_Obool))),X31148)),X31147)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31149,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31150,tc_fun(X31149,tc_HOL_Obool)),X31151),X31148)),X31147) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__simps_I1_J])]) ).
fof(i_0_6590,plain,
! [X31152,X31153,X31154,X31155,X31156] :
( ( X31156 != c_Orderings_Obot__class_Obot(tc_fun(X31155,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31155,tc_fun(X31154,tc_HOL_Obool)),X31156),hAPP(hAPP(c_COMBC(X31155,tc_fun(X31154,tc_HOL_Obool),tc_fun(X31154,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31154,tc_HOL_Obool),tc_fun(tc_fun(X31154,tc_HOL_Obool),tc_fun(X31154,tc_HOL_Obool)),X31155),c_Groups_Ominus__class_Ominus(tc_fun(X31154,tc_HOL_Obool))),X31153)),X31152)) = c_Orderings_Otop__class_Otop(tc_fun(X31154,tc_HOL_Obool)) )
& ( X31156 = c_Orderings_Obot__class_Obot(tc_fun(X31155,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31155,tc_fun(X31154,tc_HOL_Obool)),X31156),hAPP(hAPP(c_COMBC(X31155,tc_fun(X31154,tc_HOL_Obool),tc_fun(X31154,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31154,tc_HOL_Obool),tc_fun(tc_fun(X31154,tc_HOL_Obool),tc_fun(X31154,tc_HOL_Obool)),X31155),c_Groups_Ominus__class_Ominus(tc_fun(X31154,tc_HOL_Obool))),X31153)),X31152)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X31154,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31155,tc_fun(X31154,tc_HOL_Obool)),X31156),X31153)),X31152) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__simps_I3_J])]) ).
fof(i_0_6591,plain,
! [X26130,X26131,X26132,X26133,X26134] :
( ( X26134 != c_Orderings_Obot__class_Obot(tc_fun(X26133,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26133,tc_fun(X26132,tc_HOL_Obool)),X26134),hAPP(hAPP(c_COMBC(X26133,tc_fun(X26132,tc_HOL_Obool),tc_fun(X26132,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26132,tc_HOL_Obool),tc_fun(tc_fun(X26132,tc_HOL_Obool),tc_fun(X26132,tc_HOL_Obool)),X26133),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26132,tc_HOL_Obool))),X26131)),X26130)) = c_Orderings_Obot__class_Obot(tc_fun(X26132,tc_HOL_Obool)) )
& ( X26134 = c_Orderings_Obot__class_Obot(tc_fun(X26133,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26133,tc_fun(X26132,tc_HOL_Obool)),X26134),hAPP(hAPP(c_COMBC(X26133,tc_fun(X26132,tc_HOL_Obool),tc_fun(X26132,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26132,tc_HOL_Obool),tc_fun(tc_fun(X26132,tc_HOL_Obool),tc_fun(X26132,tc_HOL_Obool)),X26133),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26132,tc_HOL_Obool))),X26131)),X26130)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26132,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26133,tc_fun(X26132,tc_HOL_Obool)),X26134),X26131)),X26130) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__simps_I2_J])]) ).
fof(i_0_6592,plain,
! [X31072,X31073,X31074,X31075,X31076] :
( ( X31076 != c_Orderings_Obot__class_Obot(tc_fun(X31075,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31074,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31075,tc_fun(X31074,tc_HOL_Obool)),X31076),X31073)),X31072) = X31072 )
& ( X31076 = c_Orderings_Obot__class_Obot(tc_fun(X31075,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31074,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31075,tc_fun(X31074,tc_HOL_Obool)),X31076),X31073)),X31072) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31075,tc_fun(X31074,tc_HOL_Obool)),X31076),hAPP(hAPP(c_COMBC(X31075,tc_fun(X31074,tc_HOL_Obool),tc_fun(X31074,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31074,tc_HOL_Obool),tc_fun(tc_fun(X31074,tc_HOL_Obool),tc_fun(X31074,tc_HOL_Obool)),X31075),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31074,tc_HOL_Obool))),X31073)),X31072)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I1_J])]) ).
fof(i_0_6593,plain,
! [X26120,X26121,X26122,X26123,X26124] :
( ( X26124 != c_Orderings_Obot__class_Obot(tc_fun(X26123,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26122,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26123,tc_fun(X26122,tc_HOL_Obool)),X26124),X26121)),X26120) = X26120 )
& ( X26124 = c_Orderings_Obot__class_Obot(tc_fun(X26123,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26122,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26123,tc_fun(X26122,tc_HOL_Obool)),X26124),X26121)),X26120) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26123,tc_fun(X26122,tc_HOL_Obool)),X26124),hAPP(hAPP(c_COMBC(X26123,tc_fun(X26122,tc_HOL_Obool),tc_fun(X26122,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26122,tc_HOL_Obool),tc_fun(tc_fun(X26122,tc_HOL_Obool),tc_fun(X26122,tc_HOL_Obool)),X26123),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26122,tc_HOL_Obool))),X26121)),X26120)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I2_J])]) ).
fof(i_0_6594,plain,
! [X31157,X31158,X31159,X31160,X31161] :
( ( X31161 != c_Orderings_Obot__class_Obot(tc_fun(X31160,tc_HOL_Obool))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X31159,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31160,tc_fun(X31159,tc_HOL_Obool)),X31161),X31158)),X31157) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X31159,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X31159,tc_HOL_Obool))),X31157) )
& ( X31161 = c_Orderings_Obot__class_Obot(tc_fun(X31160,tc_HOL_Obool))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X31159,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31160,tc_fun(X31159,tc_HOL_Obool)),X31161),X31158)),X31157) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31160,tc_fun(X31159,tc_HOL_Obool)),X31161),hAPP(hAPP(c_COMBC(X31160,tc_fun(X31159,tc_HOL_Obool),tc_fun(X31159,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31159,tc_HOL_Obool),tc_fun(tc_fun(X31159,tc_HOL_Obool),tc_fun(X31159,tc_HOL_Obool)),X31160),c_Groups_Ominus__class_Ominus(tc_fun(X31159,tc_HOL_Obool))),X31158)),X31157)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I3_J])]) ).
fof(i_0_6595,plain,
! [X31096,X31097,X31098,X31099,X31100] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31100,tc_fun(X31099,tc_HOL_Obool)),X31098),hAPP(hAPP(c_COMBC(X31100,tc_fun(X31099,tc_HOL_Obool),tc_fun(X31099,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31099,tc_HOL_Obool),tc_fun(tc_fun(X31099,tc_HOL_Obool),tc_fun(X31099,tc_HOL_Obool)),X31100),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31099,tc_HOL_Obool))),X31097)),X31096)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31099,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31100,tc_fun(X31099,tc_HOL_Obool)),X31098),X31097)),X31096),
inference(variable_rename,[status(thm)],[fact_INT__simps_I6_J]) ).
fof(i_0_6596,plain,
! [X26039,X26040,X26041,X26042,X26043] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26043,tc_fun(X26042,tc_HOL_Obool)),X26041),hAPP(hAPP(c_COMBC(X26043,tc_fun(X26042,tc_HOL_Obool),tc_fun(X26042,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26042,tc_HOL_Obool),tc_fun(tc_fun(X26042,tc_HOL_Obool),tc_fun(X26042,tc_HOL_Obool)),X26043),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26042,tc_HOL_Obool))),X26040)),X26039)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26042,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26043,tc_fun(X26042,tc_HOL_Obool)),X26041),X26040)),X26039),
inference(variable_rename,[status(thm)],[fact_UN__simps_I4_J]) ).
fof(i_0_6597,plain,
! [X26072,X26073,X26074,X26075,X26076] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26076,tc_fun(X26075,tc_HOL_Obool)),X26074),hAPP(hAPP(c_COMBC(X26076,tc_fun(X26075,tc_HOL_Obool),tc_fun(X26075,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26075,tc_HOL_Obool),tc_fun(tc_fun(X26075,tc_HOL_Obool),tc_fun(X26075,tc_HOL_Obool)),X26076),c_Groups_Ominus__class_Ominus(tc_fun(X26075,tc_HOL_Obool))),X26073)),X26072)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26075,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26076,tc_fun(X26075,tc_HOL_Obool)),X26074),X26073)),X26072),
inference(variable_rename,[status(thm)],[fact_UN__simps_I6_J]) ).
fof(i_0_6598,plain,
! [X26054,X26055,X26056,X26057,X26058] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26058,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26057,tc_fun(X26058,tc_HOL_Obool)),X26056),X26055)),X26054) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26057,tc_fun(X26058,tc_HOL_Obool)),X26056),hAPP(hAPP(c_COMBC(X26057,tc_fun(X26058,tc_HOL_Obool),tc_fun(X26058,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26058,tc_HOL_Obool),tc_fun(tc_fun(X26058,tc_HOL_Obool),tc_fun(X26058,tc_HOL_Obool)),X26057),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26058,tc_HOL_Obool))),X26055)),X26054)),
inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I4_J]) ).
fof(i_0_6599,plain,
! [X31111,X31112,X31113,X31114,X31115] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31115,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31114,tc_fun(X31115,tc_HOL_Obool)),X31113),X31112)),X31111) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31114,tc_fun(X31115,tc_HOL_Obool)),X31113),hAPP(hAPP(c_COMBC(X31114,tc_fun(X31115,tc_HOL_Obool),tc_fun(X31115,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31115,tc_HOL_Obool),tc_fun(tc_fun(X31115,tc_HOL_Obool),tc_fun(X31115,tc_HOL_Obool)),X31114),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31115,tc_HOL_Obool))),X31112)),X31111)),
inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I6_J]) ).
fof(i_0_6600,plain,
! [X26077,X26078,X26079,X26080,X26081] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26081,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26080,tc_fun(X26081,tc_HOL_Obool)),X26079),X26078)),X26077) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26080,tc_fun(X26081,tc_HOL_Obool)),X26079),hAPP(hAPP(c_COMBC(X26080,tc_fun(X26081,tc_HOL_Obool),tc_fun(X26081,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26081,tc_HOL_Obool),tc_fun(tc_fun(X26081,tc_HOL_Obool),tc_fun(X26081,tc_HOL_Obool)),X26080),c_Groups_Ominus__class_Ominus(tc_fun(X26081,tc_HOL_Obool))),X26078)),X26077)),
inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I6_J]) ).
fof(i_0_6601,plain,
! [X29526,X29527,X29528,X29529,X29530,X29531,X29532,X29533] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29533,X29532),tc_HOL_Obool)),X29531),hAPP(hAPP(c_Product__Type_OSigma(X29533,X29532),X29530),hAPP(c_COMBK(tc_fun(X29532,tc_HOL_Obool),X29533),X29529))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29532,X29528),tc_HOL_Obool)),X29527),hAPP(hAPP(c_Product__Type_OSigma(X29532,X29528),X29529),hAPP(c_COMBK(tc_fun(X29528,tc_HOL_Obool),X29532),X29526))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29533,X29528),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X29533,X29532,X29528),X29531),X29527)),hAPP(hAPP(c_Product__Type_OSigma(X29533,X29528),X29530),hAPP(c_COMBK(tc_fun(X29528,tc_HOL_Obool),X29533),X29526)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__comp__subset__Sigma])]) ).
fof(i_0_6602,plain,
! [X33263,X33264,X33265,X33266,X33267,X33268] :
( ( X33267 = X33265
| hBOOL(hAPP(hAPP(c_member(tc_prod(X33268,X33268)),hAPP(hAPP(c_Product__Type_OPair(X33268,X33268),X33267),X33265)),X33263))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33268),tc_List_Olist(X33268))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33268),tc_List_Olist(X33268)),hAPP(hAPP(c_List_Olist_OCons(X33268),X33267),X33266)),hAPP(hAPP(c_List_Olist_OCons(X33268),X33265),X33264))),c_List_Olistrel1(X33268,X33263))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33268),tc_List_Olist(X33268))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33268),tc_List_Olist(X33268)),X33266),X33264)),c_List_Olistrel1(X33268,X33263)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X33268,X33268)),hAPP(hAPP(c_Product__Type_OPair(X33268,X33268),X33267),X33265)),X33263))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33268),tc_List_Olist(X33268))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33268),tc_List_Olist(X33268)),hAPP(hAPP(c_List_Olist_OCons(X33268),X33267),X33266)),hAPP(hAPP(c_List_Olist_OCons(X33268),X33265),X33264))),c_List_Olistrel1(X33268,X33263))) )
& ( X33267 = X33265
| X33266 = X33264
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33268),tc_List_Olist(X33268))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33268),tc_List_Olist(X33268)),hAPP(hAPP(c_List_Olist_OCons(X33268),X33267),X33266)),hAPP(hAPP(c_List_Olist_OCons(X33268),X33265),X33264))),c_List_Olistrel1(X33268,X33263))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33268),tc_List_Olist(X33268))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33268),tc_List_Olist(X33268)),X33266),X33264)),c_List_Olistrel1(X33268,X33263)))
| X33266 = X33264
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33268),tc_List_Olist(X33268))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33268),tc_List_Olist(X33268)),hAPP(hAPP(c_List_Olist_OCons(X33268),X33267),X33266)),hAPP(hAPP(c_List_Olist_OCons(X33268),X33265),X33264))),c_List_Olistrel1(X33268,X33263))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33268,X33268)),hAPP(hAPP(c_Product__Type_OPair(X33268,X33268),X33267),X33265)),X33263))
| X33266 != X33264
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33268),tc_List_Olist(X33268))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33268),tc_List_Olist(X33268)),hAPP(hAPP(c_List_Olist_OCons(X33268),X33267),X33266)),hAPP(hAPP(c_List_Olist_OCons(X33268),X33265),X33264))),c_List_Olistrel1(X33268,X33263))) )
& ( X33267 != X33265
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33268),tc_List_Olist(X33268))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33268),tc_List_Olist(X33268)),X33266),X33264)),c_List_Olistrel1(X33268,X33263)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33268),tc_List_Olist(X33268))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33268),tc_List_Olist(X33268)),hAPP(hAPP(c_List_Olist_OCons(X33268),X33267),X33266)),hAPP(hAPP(c_List_Olist_OCons(X33268),X33265),X33264))),c_List_Olistrel1(X33268,X33263))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__listrel1__Cons])])]) ).
fof(i_0_6603,plain,
! [X32501,X32502,X32503,X32504,X32505,X32506] :
( ( X32505 = X32503
| hBOOL(hAPP(hAPP(c_member(tc_prod(X32506,X32506)),hAPP(hAPP(c_Product__Type_OPair(X32506,X32506),X32505),X32503)),X32501))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32506),tc_List_Olist(X32506))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32506),tc_List_Olist(X32506)),hAPP(hAPP(c_List_Olist_OCons(X32506),X32505),X32504)),hAPP(hAPP(c_List_Olist_OCons(X32506),X32503),X32502))),c_List_Olexord(X32506,X32501))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32506),tc_List_Olist(X32506))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32506),tc_List_Olist(X32506)),X32504),X32502)),c_List_Olexord(X32506,X32501)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X32506,X32506)),hAPP(hAPP(c_Product__Type_OPair(X32506,X32506),X32505),X32503)),X32501))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32506),tc_List_Olist(X32506))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32506),tc_List_Olist(X32506)),hAPP(hAPP(c_List_Olist_OCons(X32506),X32505),X32504)),hAPP(hAPP(c_List_Olist_OCons(X32506),X32503),X32502))),c_List_Olexord(X32506,X32501))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32506,X32506)),hAPP(hAPP(c_Product__Type_OPair(X32506,X32506),X32505),X32503)),X32501))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32506),tc_List_Olist(X32506))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32506),tc_List_Olist(X32506)),hAPP(hAPP(c_List_Olist_OCons(X32506),X32505),X32504)),hAPP(hAPP(c_List_Olist_OCons(X32506),X32503),X32502))),c_List_Olexord(X32506,X32501))) )
& ( X32505 != X32503
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32506),tc_List_Olist(X32506))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32506),tc_List_Olist(X32506)),X32504),X32502)),c_List_Olexord(X32506,X32501)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32506),tc_List_Olist(X32506))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32506),tc_List_Olist(X32506)),hAPP(hAPP(c_List_Olist_OCons(X32506),X32505),X32504)),hAPP(hAPP(c_List_Olist_OCons(X32506),X32503),X32502))),c_List_Olexord(X32506,X32501))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__cons__cons])])]) ).
fof(i_0_6604,plain,
! [X32355,X32356,X32357,X32358,X32359,X32360] :
( ( X32359 = X32357
| hBOOL(hAPP(hAPP(c_member(tc_prod(X32360,X32360)),hAPP(hAPP(c_Product__Type_OPair(X32360,X32360),X32359),X32357)),X32355))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32360),tc_List_Olist(X32360))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32360),tc_List_Olist(X32360)),hAPP(hAPP(c_List_Olist_OCons(X32360),X32359),X32358)),hAPP(hAPP(c_List_Olist_OCons(X32360),X32357),X32356))),c_List_Olex(X32360,X32355))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32360),tc_List_Olist(X32360))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32360),tc_List_Olist(X32360)),X32358),X32356)),c_List_Olex(X32360,X32355)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X32360,X32360)),hAPP(hAPP(c_Product__Type_OPair(X32360,X32360),X32359),X32357)),X32355))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32360),tc_List_Olist(X32360))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32360),tc_List_Olist(X32360)),hAPP(hAPP(c_List_Olist_OCons(X32360),X32359),X32358)),hAPP(hAPP(c_List_Olist_OCons(X32360),X32357),X32356))),c_List_Olex(X32360,X32355))) )
& ( X32359 = X32357
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32360)),X32358) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32360)),X32356)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32360),tc_List_Olist(X32360))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32360),tc_List_Olist(X32360)),hAPP(hAPP(c_List_Olist_OCons(X32360),X32359),X32358)),hAPP(hAPP(c_List_Olist_OCons(X32360),X32357),X32356))),c_List_Olex(X32360,X32355))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32360),tc_List_Olist(X32360))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32360),tc_List_Olist(X32360)),X32358),X32356)),c_List_Olex(X32360,X32355)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32360)),X32358) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32360)),X32356)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32360),tc_List_Olist(X32360))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32360),tc_List_Olist(X32360)),hAPP(hAPP(c_List_Olist_OCons(X32360),X32359),X32358)),hAPP(hAPP(c_List_Olist_OCons(X32360),X32357),X32356))),c_List_Olex(X32360,X32355))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32360,X32360)),hAPP(hAPP(c_Product__Type_OPair(X32360,X32360),X32359),X32357)),X32355))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32360)),X32358) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32360)),X32356)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32360),tc_List_Olist(X32360))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32360),tc_List_Olist(X32360)),hAPP(hAPP(c_List_Olist_OCons(X32360),X32359),X32358)),hAPP(hAPP(c_List_Olist_OCons(X32360),X32357),X32356))),c_List_Olex(X32360,X32355))) )
& ( X32359 != X32357
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32360),tc_List_Olist(X32360))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32360),tc_List_Olist(X32360)),X32358),X32356)),c_List_Olex(X32360,X32355)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32360),tc_List_Olist(X32360))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32360),tc_List_Olist(X32360)),hAPP(hAPP(c_List_Olist_OCons(X32360),X32359),X32358)),hAPP(hAPP(c_List_Olist_OCons(X32360),X32357),X32356))),c_List_Olex(X32360,X32355))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__in__lex])])]) ).
fof(i_0_6605,plain,
! [X28703,X28704,X28705,X28706,X28707] : hAPP(hAPP(c_Product__Type_OSigma(X28707,X28706),X28705),hAPP(hAPP(c_COMBS(X28707,tc_fun(X28706,tc_HOL_Obool),tc_fun(X28706,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28706,tc_HOL_Obool),tc_fun(tc_fun(X28706,tc_HOL_Obool),tc_fun(X28706,tc_HOL_Obool)),X28707),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28706,tc_HOL_Obool))),X28704)),X28703)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X28707,X28706),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28707,X28706),X28705),X28704)),hAPP(hAPP(c_Product__Type_OSigma(X28707,X28706),X28705),X28703)),
inference(variable_rename,[status(thm)],[fact_Sigma__Int__distrib2]) ).
fof(i_0_6606,plain,
! [X28670,X28671,X28672,X28673,X28674] : hAPP(hAPP(c_Product__Type_OSigma(X28674,X28673),X28672),hAPP(hAPP(c_COMBS(X28674,tc_fun(X28673,tc_HOL_Obool),tc_fun(X28673,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28673,tc_HOL_Obool),tc_fun(tc_fun(X28673,tc_HOL_Obool),tc_fun(X28673,tc_HOL_Obool)),X28674),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28673,tc_HOL_Obool))),X28671)),X28670)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28674,X28673),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28674,X28673),X28672),X28671)),hAPP(hAPP(c_Product__Type_OSigma(X28674,X28673),X28672),X28670)),
inference(variable_rename,[status(thm)],[fact_Sigma__Un__distrib2]) ).
fof(i_0_6607,plain,
! [X28616,X28617,X28618,X28619,X28620] : hAPP(hAPP(c_Product__Type_OSigma(X28620,X28619),X28618),hAPP(hAPP(c_COMBS(X28620,tc_fun(X28619,tc_HOL_Obool),tc_fun(X28619,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28619,tc_HOL_Obool),tc_fun(tc_fun(X28619,tc_HOL_Obool),tc_fun(X28619,tc_HOL_Obool)),X28620),c_Groups_Ominus__class_Ominus(tc_fun(X28619,tc_HOL_Obool))),X28617)),X28616)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X28620,X28619),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28620,X28619),X28618),X28617)),hAPP(hAPP(c_Product__Type_OSigma(X28620,X28619),X28618),X28616)),
inference(variable_rename,[status(thm)],[fact_Sigma__Diff__distrib2]) ).
fof(i_0_6608,plain,
! [X20831,X20832,X20833,X20834,X20835] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20835)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20835),hAPP(c_Groups_Oabs__class_Oabs(X20835),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20835),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20835),X20834),X20833)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20835),X20832),X20831)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20835),hAPP(c_Groups_Oabs__class_Oabs(X20835),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20835),X20834),X20832))),hAPP(c_Groups_Oabs__class_Oabs(X20835),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20835),X20833),X20831))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__diff__triangle__ineq])]) ).
fof(i_0_6609,plain,
! [X20566,X20567,X20568,X20569,X20570] :
( ( ~ 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),X20570),X20568)),X20567)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20569),X20568)),X20566)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20567),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),X20569),X20570)),X20568)),X20566)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20570),X20569)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20567),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),X20569),X20570)),X20568)),X20566)))
| 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),X20570),X20568)),X20567)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20569),X20568)),X20566)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20570),X20569)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff2])])]) ).
fof(i_0_6610,plain,
! [X20598,X20599,X20600,X20601,X20602] :
( ( ~ 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),X20602),X20600)),X20599)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20601),X20600)),X20598)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20599),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),X20601),X20602)),X20600)),X20598)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20602),X20601)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20599),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),X20601),X20602)),X20600)),X20598)))
| 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),X20602),X20600)),X20599)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20601),X20600)),X20598)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20602),X20601)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff2])])]) ).
fof(i_0_6611,plain,
! [X27922,X27923,X27924,X27925,X27926,X27927,X27928,X27929] :
( ~ c_Finite__Set_Ofolding__image(X27929,X27928,X27927,X27926,X27925)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27928),X27924))
| hAPP(hAPP(X27925,hAPP(hAPP(c_COMBS(X27928,X27929,X27929),hAPP(hAPP(c_COMBB(X27929,tc_fun(X27929,X27929),X27928),X27927),X27923)),X27922)),X27924) = hAPP(hAPP(X27927,hAPP(hAPP(X27925,X27923),X27924)),hAPP(hAPP(X27925,X27922),X27924)) ),
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,
! [X26290,X26291,X26292,X26293,X26294] :
( ~ class_Groups_Ocomm__monoid__mult(X26294)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26293),X26292))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26293),X26291))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26294),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X26294,X26293,c_Groups_Otimes__class_Otimes(X26294)),X26290),c_Groups_Oone__class_Oone(X26294)),X26292)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X26294,X26293,c_Groups_Otimes__class_Otimes(X26294)),X26290),c_Groups_Oone__class_Oone(X26294)),X26291)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26294),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X26294,X26293,c_Groups_Otimes__class_Otimes(X26294)),X26290),c_Groups_Oone__class_Oone(X26294)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26293,tc_HOL_Obool)),X26292),X26291))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X26294,X26293,c_Groups_Otimes__class_Otimes(X26294)),X26290),c_Groups_Oone__class_Oone(X26294)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26293,tc_HOL_Obool)),X26292),X26291))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__image__Un__Int])]) ).
fof(i_0_6614,plain,
! [X27516,X27517,X27518] : 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),X27518)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),X27517))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X27516))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27516),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27518),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27518),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X27516),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X27517)))),
inference(variable_rename,[status(thm)],[fact_arith__series__nat]) ).
fof(i_0_6615,plain,
! [X24862,X24863,X24864,X24865] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24865,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24865,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24865,tc_HOL_Obool)),X24864),X24863)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24865,tc_HOL_Obool)),X24863),X24862))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24865,tc_HOL_Obool)),X24862),X24864)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24865,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24865,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24865,tc_HOL_Obool)),X24864),X24863)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24865,tc_HOL_Obool)),X24863),X24862))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24865,tc_HOL_Obool)),X24862),X24864)),
inference(variable_rename,[status(thm)],[fact_Un__Int__crazy]) ).
fof(i_0_6616,plain,
! [X17946,X17947,X17948,X17949,X17950] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X17950)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17949),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X17948,X17949))),X17947))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(X17946,X17950,X17948)),X17949),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17947),hAPP(c_Natural_Ogetlocs,X17949))),X17946),hAPP(hAPP(c_Natural_Ogetlocs,X17947),c_Com_ORes)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc_OCall])]) ).
fof(i_0_6617,plain,
! [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)),c_Transitive__Closure_Ortrancl(X33285,X33282)))
| ~ 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),X33280)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X33285),c_List_Olistrel1(X33285,X33282))))
| 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)),hAPP(hAPP(c_List_Olist_OCons(X33285),X33284),X33281)),hAPP(hAPP(c_List_Olist_OCons(X33285),X33283),X33280))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X33285),c_List_Olistrel1(X33285,X33282)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__ConsI2])]) ).
fof(i_0_6618,plain,
! [X24349,X24350,X24351,X24352,X24353] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24353,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24353,tc_HOL_Obool)),hAPP(c_Set_Oimage(X24352,X24353,X24351),X24350)),hAPP(c_Set_Oimage(X24352,X24353,X24351),X24349))),hAPP(c_Set_Oimage(X24352,X24353,X24351),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24352,tc_HOL_Obool)),X24350),X24349)))),
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,
! [X27432,X27433,X27434,X27435,X27436,X27437] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X27437),X27436),X27435))
| c_Map_Orestrict__map(X27437,X27434,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27437,tc_Option_Ooption(X27434)),X27433),X27436),X27432),X27435) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27437,tc_Option_Ooption(X27434)),c_Map_Orestrict__map(X27437,X27434,X27433,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27437,tc_HOL_Obool)),X27435),hAPP(hAPP(c_Set_Oinsert(X27437),X27436),c_Orderings_Obot__class_Obot(tc_fun(X27437,tc_HOL_Obool)))))),X27436),X27432) )
& ( hBOOL(hAPP(hAPP(c_member(X27437),X27436),X27435))
| c_Map_Orestrict__map(X27437,X27434,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27437,tc_Option_Ooption(X27434)),X27433),X27436),X27432),X27435) = c_Map_Orestrict__map(X27437,X27434,X27433,X27435) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5391])]) ).
fof(i_0_6622,plain,
! [X29324] : hAPP(c_Set_OCollect(tc_Nat_Onat),X29324) = 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),X29324),c_Int_Onat)))),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J]) ).
fof(i_0_6623,plain,
! [X32200,X32201] : c_List_Olenlex(X32201,X32200) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(X32201)),tc_List_Olist(X32201)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(X32201),c_Wellfounded_Oless__than,c_List_Olex(X32201,X32200))),hAPP(hAPP(c_COMBS(tc_List_Olist(X32201),tc_List_Olist(X32201),tc_prod(tc_Nat_Onat,tc_List_Olist(X32201))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(X32201),tc_prod(tc_Nat_Onat,tc_List_Olist(X32201))),tc_List_Olist(X32201)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(X32201))),c_Nat_Osize__class_Osize(tc_List_Olist(X32201)))),c_COMBI(tc_List_Olist(X32201)))),
inference(variable_rename,[status(thm)],[fact_lenlex__def]) ).
fof(i_0_6624,plain,
! [X29069,X29070,X29071] :
( ( hBOOL(hAPP(hAPP(c_member(X29071),esk302_3(X29069,X29070,X29071)),X29069))
| c_Relation_Orefl__on(X29071,X29069,X29070)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29071,X29071),tc_HOL_Obool)),X29070),hAPP(hAPP(c_Product__Type_OSigma(X29071,X29071),X29069),hAPP(c_COMBK(tc_fun(X29071,tc_HOL_Obool),X29071),X29069)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29071,X29071)),hAPP(hAPP(c_Product__Type_OPair(X29071,X29071),esk302_3(X29069,X29070,X29071)),esk302_3(X29069,X29070,X29071))),X29070))
| c_Relation_Orefl__on(X29071,X29069,X29070)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29071,X29071),tc_HOL_Obool)),X29070),hAPP(hAPP(c_Product__Type_OSigma(X29071,X29071),X29069),hAPP(c_COMBK(tc_fun(X29071,tc_HOL_Obool),X29071),X29069)))) ) ),
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,
! [X29034,X29035,X29036,X29037,X29038,X29039,X29040] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29036,X29036),tc_HOL_Obool)),X29034),hAPP(hAPP(c_Product__Type_OSigma(X29036,X29036),X29035),hAPP(c_COMBK(tc_fun(X29036,tc_HOL_Obool),X29036),X29035))))
| ~ c_Relation_Orefl__on(X29036,X29035,X29034) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X29036),X29037),X29035))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X29036,X29036)),hAPP(hAPP(c_Product__Type_OPair(X29036,X29036),X29037),X29037)),X29034))
| ~ c_Relation_Orefl__on(X29036,X29035,X29034) )
& ( hBOOL(hAPP(hAPP(c_member(X29040),esk301_3(X29038,X29039,X29040)),X29039))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29040,X29040),tc_HOL_Obool)),X29038),hAPP(hAPP(c_Product__Type_OSigma(X29040,X29040),X29039),hAPP(c_COMBK(tc_fun(X29040,tc_HOL_Obool),X29040),X29039))))
| c_Relation_Orefl__on(X29040,X29039,X29038) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29040,X29040)),hAPP(hAPP(c_Product__Type_OPair(X29040,X29040),esk301_3(X29038,X29039,X29040)),esk301_3(X29038,X29039,X29040))),X29038))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29040,X29040),tc_HOL_Obool)),X29038),hAPP(hAPP(c_Product__Type_OSigma(X29040,X29040),X29039),hAPP(c_COMBK(tc_fun(X29040,tc_HOL_Obool),X29040),X29039))))
| c_Relation_Orefl__on(X29040,X29039,X29038) ) ),
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,
! [X31818,X31819,X31820,X31821] :
( hAPP(c_List_Oset(X31821),X31820) != c_Map_Odom(X31821,X31819,X31818)
| c_Map_Omap__of(X31821,X31819,hAPP(hAPP(c_List_Omap(X31821,tc_prod(X31821,X31819)),hAPP(hAPP(c_COMBS(X31821,X31819,tc_prod(X31821,X31819)),c_Product__Type_OPair(X31821,X31819)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X31819),X31819,X31821),c_Option_Othe(X31819)),X31818))),X31820)) = X31818 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__map__keys])]) ).
fof(i_0_6627,plain,
! [X29185,X29186,X29187] : hAPP(hAPP(c_Set_Oinsert(X29187),X29186),X29185) = hAPP(c_Set_OCollect(X29187),hAPP(hAPP(c_COMBS(X29187,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29187),c_fdisj),hAPP(hAPP(c_COMBC(X29187,X29187,tc_HOL_Obool),c_fequal),X29186))),hAPP(hAPP(c_COMBC(X29187,tc_fun(X29187,tc_HOL_Obool),tc_HOL_Obool),c_member(X29187)),X29185))),
inference(variable_rename,[status(thm)],[fact_insert__compr__raw]) ).
fof(i_0_6628,plain,
! [X29182,X29183,X29184] : hAPP(hAPP(c_Set_Oinsert(X29184),X29183),X29182) = hAPP(c_Set_OCollect(X29184),hAPP(hAPP(c_COMBS(X29184,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29184),c_fdisj),hAPP(hAPP(c_COMBC(X29184,X29184,tc_HOL_Obool),c_fequal),X29183))),hAPP(hAPP(c_COMBC(X29184,tc_fun(X29184,tc_HOL_Obool),tc_HOL_Obool),c_member(X29184)),X29182))),
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),esk388_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,
! [X32345,X32346,X32347,X32348,X32349,X32350] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32350,X32350)),hAPP(hAPP(c_Product__Type_OPair(X32350,X32350),X32349),X32348)),X32347))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32350),tc_List_Olist(X32350))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32350),tc_List_Olist(X32350)),X32346),X32345)),c_List_Olistrel(X32350,X32347)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32350),tc_List_Olist(X32350))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32350),tc_List_Olist(X32350)),hAPP(hAPP(c_List_Olist_OCons(X32350),X32349),X32346)),hAPP(hAPP(c_List_Olist_OCons(X32350),X32348),X32345))),c_List_Olistrel(X32350,X32347))) ),
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,
! [X28115,X28116,X28117,X28118,X28119] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28119,X28119,X28118,X28117,X28116),X28115))
| hBOOL(hAPP(hAPP(c_member(X28119),X28117),X28116))
| hBOOL(hAPP(c_Finite__Set_Ofold1Set(X28119,X28118,hAPP(hAPP(c_Set_Oinsert(X28119),X28117),X28116)),X28115)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5392])]) ).
fof(i_0_6633,plain,
! [X29225,X29226,X29227] : c_Map_Odom(X29227,X29226,X29225) = hAPP(c_Set_OCollect(X29227),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29227),c_fNot),hAPP(hAPP(c_COMBC(X29227,tc_Option_Ooption(X29226),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X29226),tc_fun(tc_Option_Ooption(X29226),tc_HOL_Obool),X29227),c_fequal),X29225)),c_Option_Ooption_ONone(X29226)))),
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,
! [X23900] :
( X23900 = 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)),X23900),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,
! [X24416,X24417] : 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),X24417),X24416)),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),X24416),X24417)),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,
! [X23913] : 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)),X23913),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,
! [X30811,X30812,X30813,X30814,X30815,X30816] :
( ~ c_Finite__Set_Ofun__left__comm(X30816,X30815,X30814)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X30816,X30815,X30814,X30813,X30812),X30811))
| hAPP(hAPP(c_Finite__Set_Ofold(X30816,X30815,X30814),X30813),X30812) = X30811 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__equality])]) ).
fof(i_0_6640,plain,
! [X28083,X28084,X28085,X28086,X28087] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28087,X28086,X28085,X28084,c_Orderings_Obot__class_Obot(tc_fun(X28087,tc_HOL_Obool))),X28083))
| X28083 = X28084 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_empty__fold__graphE])]) ).
fof(i_0_6641,plain,
! [X24477,X24478,X24479,X24480,X24481] :
( ~ c_Equiv__Relations_Oequiv(X24481,X24480,X24479)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24481,tc_HOL_Obool)),hAPP(c_Relation_OImage(X24481,X24481,X24479),hAPP(hAPP(c_Set_Oinsert(X24481),X24478),c_Orderings_Obot__class_Obot(tc_fun(X24481,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X24481,X24481,X24479),hAPP(hAPP(c_Set_Oinsert(X24481),X24477),c_Orderings_Obot__class_Obot(tc_fun(X24481,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(X24481),X24478),X24480))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X24481,X24481)),hAPP(hAPP(c_Product__Type_OPair(X24481,X24481),X24477),X24478)),X24479)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__equiv__class])]) ).
fof(i_0_6642,plain,
! [X25199,X25200,X25201,X25202,X25203,X25204] :
( ( hBOOL(hAPP(hAPP(X25202,X25200),X25203))
| ~ hBOOL(hAPP(hAPP(c_member(X25204),X25203),c_SetInterval_Oord_OatLeastLessThan(X25204,X25202,X25201,X25200,X25199))) )
& ( hBOOL(hAPP(hAPP(X25201,X25203),X25199))
| ~ hBOOL(hAPP(hAPP(c_member(X25204),X25203),c_SetInterval_Oord_OatLeastLessThan(X25204,X25202,X25201,X25200,X25199))) )
& ( ~ hBOOL(hAPP(hAPP(X25202,X25200),X25203))
| ~ hBOOL(hAPP(hAPP(X25201,X25203),X25199))
| hBOOL(hAPP(hAPP(c_member(X25204),X25203),c_SetInterval_Oord_OatLeastLessThan(X25204,X25202,X25201,X25200,X25199))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeastLessThan__iff])])]) ).
fof(i_0_6643,plain,
! [X25193,X25194,X25195,X25196,X25197,X25198] :
( ( hBOOL(hAPP(hAPP(X25195,X25194),X25197))
| ~ hBOOL(hAPP(hAPP(c_member(X25198),X25197),c_SetInterval_Oord_OgreaterThanAtMost(X25198,X25196,X25195,X25194,X25193))) )
& ( hBOOL(hAPP(hAPP(X25196,X25197),X25193))
| ~ hBOOL(hAPP(hAPP(c_member(X25198),X25197),c_SetInterval_Oord_OgreaterThanAtMost(X25198,X25196,X25195,X25194,X25193))) )
& ( ~ hBOOL(hAPP(hAPP(X25195,X25194),X25197))
| ~ hBOOL(hAPP(hAPP(X25196,X25197),X25193))
| hBOOL(hAPP(hAPP(c_member(X25198),X25197),c_SetInterval_Oord_OgreaterThanAtMost(X25198,X25196,X25195,X25194,X25193))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanAtMost__iff])])]) ).
fof(i_0_6644,plain,
! [X28123,X28124,X28125,X28126,X28127] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk267_5(X28123,X28124,X28125,X28126,X28127)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X28127),X28124),X28126) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X28127),X28123),X28125)
| ~ c_Nat__Transfer_Onat__set(X28125)
| X28126 != X28125
| ~ class_Groups_Ocomm__monoid__add(X28127)
| ~ class_Groups_Ocomm__monoid__mult(X28127) )
& ( hAPP(X28124,esk267_5(X28123,X28124,X28125,X28126,X28127)) != hAPP(X28123,esk267_5(X28123,X28124,X28125,X28126,X28127))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X28127),X28124),X28126) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X28127),X28123),X28125)
| ~ c_Nat__Transfer_Onat__set(X28125)
| X28126 != X28125
| ~ class_Groups_Ocomm__monoid__add(X28127)
| ~ class_Groups_Ocomm__monoid__mult(X28127) ) ),
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_6645,plain,
! [X27679,X27680,X27681,X27682,X27683] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk261_5(X27679,X27680,X27681,X27682,X27683)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X27683),X27680),X27682) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X27683),X27679),X27681)
| ~ c_Nat__Transfer_Onat__set(X27681)
| X27682 != X27681
| ~ class_Groups_Ocomm__monoid__add(X27683)
| ~ class_Groups_Ocomm__monoid__mult(X27683) )
& ( hAPP(X27680,esk261_5(X27679,X27680,X27681,X27682,X27683)) != hAPP(X27679,esk261_5(X27679,X27680,X27681,X27682,X27683))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X27683),X27680),X27682) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X27683),X27679),X27681)
| ~ c_Nat__Transfer_Onat__set(X27681)
| X27682 != X27681
| ~ class_Groups_Ocomm__monoid__add(X27683)
| ~ class_Groups_Ocomm__monoid__mult(X27683) ) ),
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_6646,plain,
! [X33991,X33992] : c_Random_Oselect__weight(X33992,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X33992),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X33992,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X33992,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X33992)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X33991)) = c_Random_Oselect__weight(X33992,X33991),
inference(variable_rename,[status(thm)],[fact_select__weigth__drop__zero]) ).
fof(i_0_6647,plain,
! [X33993,X33994] : c_Random_Opick(X33994,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X33994),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X33994,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X33994,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X33994)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X33993)) = c_Random_Opick(X33994,X33993),
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,
! [X31648,X31649,X31650,X31651] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X31651)),hAPP(c_Set_Oimage(X31650,tc_Option_Ooption(X31651),X31649),c_Orderings_Otop__class_Otop(tc_fun(X31650,tc_HOL_Obool)))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X31651)),hAPP(c_Set_Oimage(X31650,tc_Option_Ooption(X31651),c_Map_Omap__add(X31650,X31651,X31649,c_Map_Omap__of(X31650,X31651,X31648))),c_Orderings_Otop__class_Otop(tc_fun(X31650,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,
! [X29811,X29812,X29813,X29814] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29814,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X29814,X29813),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X29814,X29813),tc_HOL_Obool)),X29812),X29811))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(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__Int__subset]) ).
fof(i_0_6652,plain,
! [X29720,X29721,X29722,X29723] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29723,tc_HOL_Obool)),hAPP(c_Relation_ORange(X29722,X29723),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X29722,X29723),tc_HOL_Obool)),X29721),X29720))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29723,tc_HOL_Obool)),hAPP(c_Relation_ORange(X29722,X29723),X29721)),hAPP(c_Relation_ORange(X29722,X29723),X29720)))),
inference(variable_rename,[status(thm)],[fact_Range__Int__subset]) ).
fof(i_0_6653,plain,
! [X27236,X27237,X27238,X27239,X27240] :
( ~ class_Groups_Ocomm__monoid__add(X27240)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27239),X27238))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27239,X27240),hAPP(hAPP(c_COMBS(X27239,X27240,X27240),hAPP(hAPP(c_COMBB(X27240,tc_fun(X27240,X27240),X27239),c_Groups_Oplus__class_Oplus(X27240)),X27237)),X27236)),X27238) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27240),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27239,X27240),X27237),X27238)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27239,X27240),X27236),X27238)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Odistrib])]) ).
fof(i_0_6654,plain,
! [X25665,X25666,X25667,X25668,X25669] :
( ~ class_Fields_Ofield__inverse__zero(X25669)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25668),X25667))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25668,X25669),hAPP(hAPP(c_COMBS(X25668,X25669,X25669),hAPP(hAPP(c_COMBB(X25669,tc_fun(X25669,X25669),X25668),c_Rings_Oinverse__class_Odivide(X25669)),X25666)),X25665)),X25667) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25669),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25668,X25669),X25666),X25667)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25668,X25669),X25665),X25667)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__dividef])]) ).
fof(i_0_6655,plain,
! [X25660,X25661,X25662,X25663,X25664] :
( ~ class_Groups_Ocomm__monoid__mult(X25664)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25663),X25662))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25663,X25664),hAPP(hAPP(c_COMBS(X25663,X25664,X25664),hAPP(hAPP(c_COMBB(X25664,tc_fun(X25664,X25664),X25663),c_Groups_Otimes__class_Otimes(X25664)),X25661)),X25660)),X25662) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25664),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25663,X25664),X25661),X25662)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25663,X25664),X25660),X25662)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Odistrib])]) ).
fof(i_0_6656,plain,
! [X32111,X32112,X32113,X32114,X32115,X32116,X32117,X32118] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32118)),X32117) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32116)),X32115)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32118)),X32114) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32116)),X32115)
| hBOOL(hAPP(hAPP(c_member(X32116),X32113),hAPP(c_List_Oset(X32116),X32115)))
| hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X32116,tc_Option_Ooption(X32118)),c_Map_Omap__of(X32116,X32118,hAPP(hAPP(c_List_Ozip(X32116,X32118),X32115),X32117))),X32113),hAPP(c_Option_Ooption_OSome(X32118),X32112)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X32116,tc_Option_Ooption(X32118)),c_Map_Omap__of(X32116,X32118,hAPP(hAPP(c_List_Ozip(X32116,X32118),X32115),X32114))),X32113),hAPP(c_Option_Ooption_OSome(X32118),X32111))
| c_Map_Omap__of(X32116,X32118,hAPP(hAPP(c_List_Ozip(X32116,X32118),X32115),X32117)) = c_Map_Omap__of(X32116,X32118,hAPP(hAPP(c_List_Ozip(X32116,X32118),X32115),X32114)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5395])]) ).
fof(i_0_6657,plain,
! [X28077,X28078,X28079,X28080,X28081,X28082] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28082,X28081,X28080,X28079,X28078),X28077))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X28082),X28078)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__graph__imp__finite])]) ).
fof(i_0_6658,plain,
! [X33306,X33307] : hAPP(c_List_Orotate1(X33307),X33306) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(X33307),X33307,c_List_Olist_ONil(X33307),hAPP(hAPP(c_COMBB(tc_List_Olist(X33307),tc_fun(tc_List_Olist(X33307),tc_List_Olist(X33307)),X33307),hAPP(c_COMBC(tc_List_Olist(X33307),tc_List_Olist(X33307),tc_List_Olist(X33307)),c_List_Oappend(X33307))),hAPP(hAPP(c_COMBC(X33307,tc_List_Olist(X33307),tc_List_Olist(X33307)),c_List_Olist_OCons(X33307)),c_List_Olist_ONil(X33307)))),X33306),
inference(variable_rename,[status(thm)],[fact_rotate1__def]) ).
fof(i_0_6659,plain,
! [X27227,X27228,X27229,X27230,X27231] :
( ~ class_Groups_Oab__group__add(X27231)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27230,X27231),hAPP(hAPP(c_COMBS(X27230,X27231,X27231),hAPP(hAPP(c_COMBB(X27231,tc_fun(X27231,X27231),X27230),c_Groups_Ominus__class_Ominus(X27231)),X27229)),X27228)),X27227) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27231),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27230,X27231),X27229),X27227)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27230,X27231),X27228),X27227)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__subtractf])]) ).
fof(i_0_6660,plain,
! [X27222,X27223,X27224,X27225,X27226] :
( ~ class_Groups_Ocomm__monoid__add(X27226)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27225,X27226),hAPP(hAPP(c_COMBS(X27225,X27226,X27226),hAPP(hAPP(c_COMBB(X27226,tc_fun(X27226,X27226),X27225),c_Groups_Oplus__class_Oplus(X27226)),X27224)),X27223)),X27222) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27226),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27225,X27226),X27224),X27222)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27225,X27226),X27223),X27222)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__addf])]) ).
fof(i_0_6661,plain,
! [X25578,X25579,X25580,X25581,X25582] :
( ~ class_Groups_Ocomm__monoid__mult(X25582)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25581,X25582),hAPP(hAPP(c_COMBS(X25581,X25582,X25582),hAPP(hAPP(c_COMBB(X25582,tc_fun(X25582,X25582),X25581),c_Groups_Otimes__class_Otimes(X25582)),X25580)),X25579)),X25578) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25582),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25581,X25582),X25580),X25578)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25581,X25582),X25579),X25578)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__timesf])]) ).
fof(i_0_6662,plain,
! [X21988,X21989,X21990,X21991,X21992] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X21992,X21991),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X21990),X21989)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21991))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21988))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X21992,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21991),X21988)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X21990),X21988)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21991),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21990,X21988))),X21989)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__mult2__eq])]) ).
fof(i_0_6663,plain,
! [X32443,X32444] : c_Random_Oselect__weight(X32444,X32443) = 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(X32444,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,X32444),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X32444)),X32443)))),hAPP(hAPP(c_COMBB(X32444,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X32444,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X32444,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(X32444,X32443))),
inference(variable_rename,[status(thm)],[fact_select__weight__def]) ).
fof(i_0_6664,plain,
! [X28787,X28788,X28789,X28790,X28791,X28792] : hAPP(hAPP(c_Product__Type_OSigma(X28792,X28791),hAPP(hAPP(c_Set_Oinsert(X28792),X28790),X28789)),hAPP(c_COMBK(tc_fun(X28791,tc_HOL_Obool),X28792),hAPP(hAPP(c_Set_Oinsert(X28791),X28788),X28787))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(X28792,X28791)),hAPP(hAPP(c_Product__Type_OPair(X28792,X28791),X28790),X28788)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28792,X28791),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28792,X28791),X28789),hAPP(c_COMBK(tc_fun(X28791,tc_HOL_Obool),X28792),hAPP(hAPP(c_Set_Oinsert(X28791),X28788),X28787)))),hAPP(hAPP(c_Product__Type_OSigma(X28792,X28791),hAPP(hAPP(c_Set_Oinsert(X28792),X28790),X28789)),hAPP(c_COMBK(tc_fun(X28791,tc_HOL_Obool),X28792),X28787)))),
inference(variable_rename,[status(thm)],[fact_insert__times__insert]) ).
fof(i_0_6665,plain,
! [X27175,X27176,X27177,X27178,X27179] :
( ~ class_Fields_Ofield(X27179)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27179),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27178,X27179),X27177),X27176)),X27175) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27178,X27179),hAPP(hAPP(c_COMBC(X27178,X27179,X27179),hAPP(hAPP(c_COMBB(X27179,tc_fun(X27179,X27179),X27178),c_Rings_Oinverse__class_Odivide(X27179)),X27177)),X27175)),X27176) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__divide__distrib])]) ).
fof(i_0_6666,plain,
! [X27210,X27211,X27212,X27213,X27214] :
( ~ class_Rings_Osemiring__0(X27214)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27214),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27213,X27214),X27212),X27211)),X27210) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27213,X27214),hAPP(hAPP(c_COMBC(X27213,X27214,X27214),hAPP(hAPP(c_COMBB(X27214,tc_fun(X27214,X27214),X27213),c_Groups_Otimes__class_Otimes(X27214)),X27212)),X27210)),X27211) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__left__distrib])]) ).
fof(i_0_6667,plain,
! [X22167,X22168,X22169,X22170,X22171] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22171,X22170),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22169),X22168)))
| X22170 = 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)),X22167))
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22171,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22170),X22167)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22169),X22167)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22170),c_Divides_Odiv__class_Omod(tc_Int_Oint,X22169,X22167))),X22168)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma])]) ).
fof(i_0_6668,plain,
! [X32254,X32255,X32256,X32257,X32258] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32258),tc_List_Olist(X32258))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32258),tc_List_Olist(X32258)),X32257),X32256)),c_List_Olistrel(X32258,c_Transitive__Closure_Ortrancl(X32258,X32255))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32258),tc_List_Olist(X32258))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32258),tc_List_Olist(X32258)),X32256),X32254)),c_List_Olistrel(X32258,c_Transitive__Closure_Ortrancl(X32258,X32255))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32258),tc_List_Olist(X32258))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32258),tc_List_Olist(X32258)),X32257),X32254)),c_List_Olistrel(X32258,c_Transitive__Closure_Ortrancl(X32258,X32255)))) ),
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,
! [X23715,X23716,X23717] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23717,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X23717,tc_fun(X23717,tc_HOL_Obool),tc_HOL_Obool),c_member(X23717)),X23716)),hAPP(hAPP(c_COMBC(X23717,tc_fun(X23717,tc_HOL_Obool),tc_HOL_Obool),c_member(X23717)),X23715)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23717,tc_HOL_Obool)),X23716),X23715)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23717,tc_HOL_Obool)),X23716),X23715))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23717,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X23717,tc_fun(X23717,tc_HOL_Obool),tc_HOL_Obool),c_member(X23717)),X23716)),hAPP(hAPP(c_COMBC(X23717,tc_fun(X23717,tc_HOL_Obool),tc_HOL_Obool),c_member(X23717)),X23715))) ) ),
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,
! [X29651,X29652,X29653,X29654] :
( ~ c_FunDef_Oreduction__pair(X29654,X29653)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29654,X29654),tc_HOL_Obool)),X29652),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X29654,X29654),tc_HOL_Obool),tc_fun(tc_prod(X29654,X29654),tc_HOL_Obool)),X29653)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29654,X29654),tc_HOL_Obool)),X29651),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X29654,X29654),tc_HOL_Obool),tc_fun(tc_prod(X29654,X29654),tc_HOL_Obool)),X29653)))
| ~ c_Wellfounded_Owf(X29654,X29651)
| c_Wellfounded_Owf(X29654,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29654,X29654),tc_HOL_Obool)),X29652),X29651)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reduction__pair__lemma])]) ).
fof(i_0_6675,plain,
! [X31400,X31401,X31402] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31402,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31402,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X31402,tc_HOL_Obool),tc_HOL_Obool)),X31401),X31400))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31402,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31402,tc_HOL_Obool),X31401)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31402,tc_HOL_Obool),X31400)))),
inference(variable_rename,[status(thm)],[fact_Union__Int__subset]) ).
fof(i_0_6676,plain,
! [X30417,X30418,X30419,X30420,X30421] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30421,tc_HOL_Obool)),hAPP(c_Relation_OImage(X30420,X30421,X30419),X30418)),X30417))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30420,tc_HOL_Obool)),X30418),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X30420,tc_HOL_Obool)),hAPP(c_Relation_OImage(X30421,X30420,hAPP(c_Relation_Oconverse(X30420,X30421),X30419)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X30421,tc_HOL_Obool)),X30417))))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30420,tc_HOL_Obool)),X30418),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X30420,tc_HOL_Obool)),hAPP(c_Relation_OImage(X30421,X30420,hAPP(c_Relation_Oconverse(X30420,X30421),X30419)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X30421,tc_HOL_Obool)),X30417)))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30421,tc_HOL_Obool)),hAPP(c_Relation_OImage(X30420,X30421,X30419),X30418)),X30417)) ) ),
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,
! [X25873,X25874,X25875,X25876] : hAPP(c_Set_Oimage(X25876,X25875,X25874),X25873) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25876,tc_fun(X25875,tc_HOL_Obool)),X25873),hAPP(hAPP(c_COMBC(X25876,tc_fun(X25875,tc_HOL_Obool),tc_fun(X25875,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X25875,tc_fun(tc_fun(X25875,tc_HOL_Obool),tc_fun(X25875,tc_HOL_Obool)),X25876),c_Set_Oinsert(X25875)),X25874)),c_Orderings_Obot__class_Obot(tc_fun(X25875,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_image__eq__UN]) ).
fof(i_0_6680,plain,
! [X29198,X29199,X29200] :
( ( ~ hBOOL(hAPP(X29200,X29199))
| hAPP(c_Set_OCollect(X29198),hAPP(hAPP(c_COMBS(X29198,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29198),c_fconj),hAPP(hAPP(c_COMBC(X29198,X29198,tc_HOL_Obool),c_fequal),X29199))),X29200)) = hAPP(hAPP(c_Set_Oinsert(X29198),X29199),c_Orderings_Obot__class_Obot(tc_fun(X29198,tc_HOL_Obool))) )
& ( hBOOL(hAPP(X29200,X29199))
| hAPP(c_Set_OCollect(X29198),hAPP(hAPP(c_COMBS(X29198,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29198),c_fconj),hAPP(hAPP(c_COMBC(X29198,X29198,tc_HOL_Obool),c_fequal),X29199))),X29200)) = c_Orderings_Obot__class_Obot(tc_fun(X29198,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5402])]) ).
fof(i_0_6681,plain,
! [X31857,X31858,X31859,X31860,X31861,X31862,X31863] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(X31863),tc_Option_Ooption(X31862),tc_sum(X31861,X31860),hAPP(c_Option_Omap(X31863,X31862),X31859)),c_Sum__Type_Osum_Osum__case(X31861,tc_Option_Ooption(X31863),X31860,X31858,X31857)) = c_Sum__Type_Osum_Osum__case(X31861,tc_Option_Ooption(X31862),X31860,hAPP(c_Fun_Ocomp(tc_Option_Ooption(X31863),tc_Option_Ooption(X31862),X31861,hAPP(c_Option_Omap(X31863,X31862),X31859)),X31858),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X31863),tc_Option_Ooption(X31862),X31860,hAPP(c_Option_Omap(X31863,X31862),X31859)),X31857)),
inference(variable_rename,[status(thm)],[fact_option__map__o__sum__case]) ).
fof(i_0_6682,plain,
! [X33221,X33222,X33223,X33224,X33225] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33225),tc_List_Olist(X33225))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33225),tc_List_Olist(X33225)),X33224),X33223)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X33225),c_List_Olistrel1(X33225,X33222))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33225),tc_List_Olist(X33225))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33225),tc_List_Olist(X33225)),hAPP(hAPP(c_List_Olist_OCons(X33225),X33221),X33224)),hAPP(hAPP(c_List_Olist_OCons(X33225),X33221),X33223))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X33225),c_List_Olistrel1(X33225,X33222)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__ConsI1])]) ).
fof(i_0_6683,plain,
! [X31900,X31901,X31902,X31903,X31904,X31905,X31906] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(X31906),tc_Option_Ooption(X31905),X31904,hAPP(c_Option_Omap(X31906,X31905),X31903)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X31904,tc_Option_Ooption(X31906)),X31902),X31901),hAPP(c_Option_Ooption_OSome(X31906),X31900))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X31904,tc_Option_Ooption(X31905)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X31906),tc_Option_Ooption(X31905),X31904,hAPP(c_Option_Omap(X31906,X31905),X31903)),X31902)),X31901),hAPP(c_Option_Ooption_OSome(X31905),hAPP(X31903,X31900))),
inference(variable_rename,[status(thm)],[fact_option__map__o__map__upd]) ).
fof(i_0_6684,plain,
! [X23888,X23889,X23890,X23891] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23891),X23890))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23889),X23888))
| 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),X23891),X23889)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X23890),X23888))),c_FunDef_Opair__leq)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__leqI2])]) ).
fof(i_0_6685,plain,
! [X23847,X23848,X23849,X23850] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23850),X23849))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23848),X23847))
| 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),X23850),X23848)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X23849),X23847))),c_FunDef_Opair__less)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__lessI2])]) ).
fof(i_0_6686,plain,
! [X30230,X30231,X30232] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30232,X30232),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30232,X30232),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X30232,X30231)),c_Transitive__Closure_Ortrancl(X30232,X30230))),c_Transitive__Closure_Ortrancl(X30232,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30232,X30232),tc_HOL_Obool)),X30231),X30230)))),
inference(variable_rename,[status(thm)],[fact_rtrancl__Un__subset]) ).
fof(i_0_6687,plain,
! [X25050,X25051,X25052,X25053,X25054] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25054,tc_HOL_Obool)),hAPP(c_Relation_OImage(X25053,X25054,X25052),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25053,tc_HOL_Obool)),X25051),X25050))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25054,tc_HOL_Obool)),hAPP(c_Relation_OImage(X25053,X25054,X25052),X25051)),hAPP(c_Relation_OImage(X25053,X25054,X25052),X25050)))),
inference(variable_rename,[status(thm)],[fact_Image__Int__subset]) ).
fof(i_0_6688,plain,
! [X25018,X25019,X25020,X25021,X25022] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25022,tc_HOL_Obool)),hAPP(c_Set_Oimage(X25021,X25022,X25020),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25021,tc_HOL_Obool)),X25019),X25018))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25022,tc_HOL_Obool)),hAPP(c_Set_Oimage(X25021,X25022,X25020),X25019)),hAPP(c_Set_Oimage(X25021,X25022,X25020),X25018)))),
inference(variable_rename,[status(thm)],[fact_image__Int__subset]) ).
fof(i_0_6689,plain,
! [X31520,X31521] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk424_2(X31520,X31521)))
| 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)))),X31521)) = 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)))),X31520)) )
& ( ~ hBOOL(hAPP(X31521,esk424_2(X31520,X31521)))
| ~ hBOOL(hAPP(X31520,esk424_2(X31520,X31521)))
| 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)))),X31521)) = 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)))),X31520)) )
& ( hBOOL(hAPP(X31521,esk424_2(X31520,X31521)))
| hBOOL(hAPP(X31520,esk424_2(X31520,X31521)))
| 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)))),X31521)) = 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)))),X31520)) ) ),
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,
! [X23901,X23902,X23903,X23904] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23904),X23903))
| 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),X23904),X23902)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X23903),X23901))),c_FunDef_Opair__leq)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__leqI1])]) ).
fof(i_0_6692,plain,
! [X23875,X23876,X23877,X23878] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23878),X23877))
| 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),X23878),X23876)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X23877),X23875))),c_FunDef_Opair__less)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__lessI1])]) ).
fof(i_0_6693,plain,
! [X33698,X33699] : c_List_Olists(X33699,X33698) = hAPP(c_Set_OCollect(tc_List_Olist(X33699)),hAPP(hAPP(c_COMBC(tc_List_Olist(X33699),tc_fun(X33699,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X33699,tc_HOL_Obool),tc_fun(tc_fun(X33699,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X33699)),c_Orderings_Oord__class_Oless__eq(tc_fun(X33699,tc_HOL_Obool))),c_List_Oset(X33699))),X33698)),
inference(variable_rename,[status(thm)],[fact_lists__eq__set]) ).
fof(i_0_6694,plain,
! [X33240,X33241,X33242,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),X33243)),c_List_Olistrel1(X33245,X33242)))
| X33241 != X33240
| 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)),hAPP(hAPP(c_List_Oappend(X33245),X33244),X33241)),hAPP(hAPP(c_List_Oappend(X33245),X33243),X33240))),c_List_Olistrel1(X33245,X33242))) )
& ( X33244 != X33243
| ~ 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)),X33241),X33240)),c_List_Olistrel1(X33245,X33242)))
| 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)),hAPP(hAPP(c_List_Oappend(X33245),X33244),X33241)),hAPP(hAPP(c_List_Oappend(X33245),X33243),X33240))),c_List_Olistrel1(X33245,X33242))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__listrel1I])])]) ).
fof(i_0_6695,plain,
! [X33158,X33159,X33160,X33161,X33162] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33162),tc_List_Olist(X33162))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33162),tc_List_Olist(X33162)),X33161),X33160)),c_List_Olexord(X33162,X33159)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33162),tc_List_Olist(X33162))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33162),tc_List_Olist(X33162)),hAPP(hAPP(c_List_Oappend(X33162),X33158),X33161)),hAPP(hAPP(c_List_Oappend(X33162),X33158),X33160))),c_List_Olexord(X33162,X33159))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__leftI])]) ).
fof(i_0_6696,plain,
! [X33216,X33217,X33218,X33219,X33220] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33220),tc_List_Olist(X33220))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33220),tc_List_Olist(X33220)),X33219),X33218)),c_List_Olistrel1(X33220,X33217)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33220),tc_List_Olist(X33220))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33220),tc_List_Olist(X33220)),hAPP(hAPP(c_List_Olist_OCons(X33220),X33216),X33219)),hAPP(hAPP(c_List_Olist_OCons(X33220),X33216),X33218))),c_List_Olistrel1(X33220,X33217))) ),
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,
! [X29311] : 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)))),X29311))),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J]) ).
fof(i_0_6699,plain,
! [X28303,X28304,X28305,X28306,X28307] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X28307)),hAPP(c_Set_Oimage(X28306,tc_Option_Ooption(X28307),X28305),c_Orderings_Otop__class_Otop(tc_fun(X28306,tc_HOL_Obool)))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X28307)),hAPP(c_Set_Oimage(X28306,tc_Option_Ooption(X28307),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X28306,tc_Option_Ooption(X28307)),X28305),X28304),hAPP(c_Option_Ooption_OSome(X28307),X28303))),c_Orderings_Otop__class_Otop(tc_fun(X28306,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__range__updI])]) ).
fof(i_0_6700,plain,
! [X32096,X32097,X32098,X32099,X32100,X32101] : hAPP(hAPP(c_List_Ozip(X32101,X32100),hAPP(hAPP(c_List_Omap(X32099,X32101),X32098),X32097)),X32096) = hAPP(hAPP(c_List_Omap(tc_prod(X32099,X32100),tc_prod(X32101,X32100)),hAPP(c_Product__Type_Oprod_Oprod__case(X32099,X32100,tc_prod(X32101,X32100)),hAPP(hAPP(c_COMBB(X32101,tc_fun(X32100,tc_prod(X32101,X32100)),X32099),c_Product__Type_OPair(X32101,X32100)),X32098))),hAPP(hAPP(c_List_Ozip(X32099,X32100),X32097),X32096)),
inference(variable_rename,[status(thm)],[fact_zip__map1]) ).
fof(i_0_6701,plain,
! [X24186,X24187,X24188] : c_Wellfounded_Omlex__prod(X24188,X24187,X24186) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X24188),X24188),c_Wellfounded_Olex__prod(tc_Nat_Onat,X24188,c_Wellfounded_Oless__than,X24186)),hAPP(hAPP(c_COMBS(X24188,X24188,tc_prod(tc_Nat_Onat,X24188)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X24188,tc_prod(tc_Nat_Onat,X24188)),X24188),c_Product__Type_OPair(tc_Nat_Onat,X24188)),X24187)),c_COMBI(X24188))),
inference(variable_rename,[status(thm)],[fact_mlex__prod__def]) ).
fof(i_0_6702,plain,
! [X26366,X26367,X26368] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X26368),esk192_3(X26366,X26367,X26368)))
| hBOOL(hAPP(X26366,c_Orderings_Obot__class_Obot(tc_fun(X26368,tc_HOL_Obool))))
| ~ hBOOL(hAPP(X26366,X26367))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26368),X26367)) )
& ( hBOOL(hAPP(hAPP(c_member(X26368),esk191_3(X26366,X26367,X26368)),esk192_3(X26366,X26367,X26368)))
| hBOOL(hAPP(X26366,c_Orderings_Obot__class_Obot(tc_fun(X26368,tc_HOL_Obool))))
| ~ hBOOL(hAPP(X26366,X26367))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26368),X26367)) )
& ( hBOOL(hAPP(X26366,esk192_3(X26366,X26367,X26368)))
| hBOOL(hAPP(X26366,c_Orderings_Obot__class_Obot(tc_fun(X26368,tc_HOL_Obool))))
| ~ hBOOL(hAPP(X26366,X26367))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26368),X26367)) )
& ( ~ hBOOL(hAPP(X26366,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26368,tc_HOL_Obool)),esk192_3(X26366,X26367,X26368)),hAPP(hAPP(c_Set_Oinsert(X26368),esk191_3(X26366,X26367,X26368)),c_Orderings_Obot__class_Obot(tc_fun(X26368,tc_HOL_Obool))))))
| hBOOL(hAPP(X26366,c_Orderings_Obot__class_Obot(tc_fun(X26368,tc_HOL_Obool))))
| ~ hBOOL(hAPP(X26366,X26367))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26368),X26367)) ) ),
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,
! [X28744,X28745,X28746,X28747,X28748,X28749] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28746,X28749),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28746,X28749),X28745),hAPP(c_COMBK(tc_fun(X28749,tc_HOL_Obool),X28746),X28747))),hAPP(hAPP(c_Product__Type_OSigma(X28746,X28749),X28744),hAPP(c_COMBK(tc_fun(X28749,tc_HOL_Obool),X28746),X28747))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28746,tc_HOL_Obool)),X28745),X28744))
| ~ hBOOL(hAPP(hAPP(c_member(X28749),X28748),X28747)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28746,tc_HOL_Obool)),X28745),X28744))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28746,X28749),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28746,X28749),X28745),hAPP(c_COMBK(tc_fun(X28749,tc_HOL_Obool),X28746),X28747))),hAPP(hAPP(c_Product__Type_OSigma(X28746,X28749),X28744),hAPP(c_COMBK(tc_fun(X28749,tc_HOL_Obool),X28746),X28747))))
| ~ hBOOL(hAPP(hAPP(c_member(X28749),X28748),X28747)) ) ),
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,
! [X30492,X30493,X30494,X30495,X30496,X30497] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30497,X30497)),hAPP(hAPP(c_Product__Type_OPair(X30497,X30497),X30496),X30495)),X30494))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30497,X30497)),hAPP(hAPP(c_Product__Type_OPair(X30497,X30497),X30495),X30493)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30497,X30497),tc_HOL_Obool),X30492),X30494)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30497,X30497)),hAPP(hAPP(c_Product__Type_OPair(X30497,X30497),X30496),X30493)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30497,X30497),tc_HOL_Obool),hAPP(c_Nat_OSuc,X30492)),X30494))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__I2])]) ).
fof(i_0_6706,plain,
! [X30498,X30499,X30500,X30501,X30502,X30503] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30503,X30503)),hAPP(hAPP(c_Product__Type_OPair(X30503,X30503),X30502),X30501)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30503,X30503),tc_HOL_Obool),X30500),X30499)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30503,X30503)),hAPP(hAPP(c_Product__Type_OPair(X30503,X30503),X30501),X30498)),X30499))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30503,X30503)),hAPP(hAPP(c_Product__Type_OPair(X30503,X30503),X30502),X30498)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30503,X30503),tc_HOL_Obool),hAPP(c_Nat_OSuc,X30500)),X30499))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__I])]) ).
fof(i_0_6707,plain,
! [X26399,X26400,X26401,X26402,X26403] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26403,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26402,X26403,X26401),X26400)),X26399))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X26403,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(X26402,tc_HOL_Obool),tc_fun(X26403,tc_HOL_Obool),c_Set_Oimage(X26402,X26403,X26401)),hAPP(c_Set_OPow(X26402),X26400))),hAPP(c_Set_OPow(X26403),X26399))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__Pow__mono])]) ).
fof(i_0_6708,plain,
! [X22076,X22077] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22076),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Nitpick_Onorm__frac(X22077,X22076) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22077),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22076))
| ~ 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),X22077),X22076))) )
& ( X22077 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Nitpick_Onorm__frac(X22077,X22076) = 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),X22076),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),X22077),X22076))) )
& ( X22076 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Nitpick_Onorm__frac(X22077,X22076) = 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),X22076),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),X22077),X22076))) )
& ( X22077 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X22076 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Nitpick_Onorm__frac(X22077,X22076) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X22077),X22076)),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),X22077))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22076)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22076),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),X22077),X22076))) ) ),
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,
! [X32466,X32467,X32468] :
( ~ 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,X32468),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X32468)),X32467))))
| hBOOL(hAPP(hAPP(c_member(X32468),hAPP(c_Product__Type_Ofst(X32468,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(X32468,X32467),X32466))),hAPP(c_List_Oset(X32468),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X32468),X32468),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X32468)),X32467)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_select__weight__member])]) ).
fof(i_0_6711,plain,
! [X27143,X27144,X27145,X27146] :
( ~ class_Groups_Oordered__ab__group__add__abs(X27146)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27146),hAPP(c_Groups_Oabs__class_Oabs(X27146),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27145,X27146),X27144),X27143))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27145,X27146),hAPP(hAPP(c_COMBB(X27146,X27146,X27145),c_Groups_Oabs__class_Oabs(X27146)),X27144)),X27143))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__abs])]) ).
fof(i_0_6712,plain,
! [X33932,X33933,X33934] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X33934,tc_HOL_Obool)),hAPP(c_List_Oset(X33934),X33933)),hAPP(hAPP(c_Set_Oinsert(X33934),X33932),c_Orderings_Obot__class_Obot(tc_fun(X33934,tc_HOL_Obool)))) = hAPP(c_List_Oset(X33934),hAPP(c_List_Ofilter(X33934,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X33934),c_fNot),hAPP(hAPP(c_COMBC(X33934,X33934,tc_HOL_Obool),c_fequal),X33932))),X33933)),
inference(variable_rename,[status(thm)],[fact_set__minus__filter__out]) ).
fof(i_0_6713,plain,
! [X33896,X33897,X33898,X33899] : hAPP(c_List_Ofilter(X33899,X33898),hAPP(c_List_Ofilter(X33899,X33897),X33896)) = hAPP(c_List_Ofilter(X33899,hAPP(hAPP(c_COMBS(X33899,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X33899),c_fconj),X33897)),X33898)),X33896),
inference(variable_rename,[status(thm)],[fact_filter__filter]) ).
fof(i_0_6714,plain,
! [X29815,X29816,X29817,X29818] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29818,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29818,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X29818,X29817),X29816)),hAPP(c_Relation_ODomain(X29818,X29817),X29815))),hAPP(c_Relation_ODomain(X29818,X29817),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X29818,X29817),tc_HOL_Obool)),X29816),X29815)))),
inference(variable_rename,[status(thm)],[fact_Domain__Diff__subset]) ).
fof(i_0_6715,plain,
! [X29724,X29725,X29726,X29727] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29727,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29727,tc_HOL_Obool)),hAPP(c_Relation_ORange(X29726,X29727),X29725)),hAPP(c_Relation_ORange(X29726,X29727),X29724))),hAPP(c_Relation_ORange(X29726,X29727),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X29726,X29727),tc_HOL_Obool)),X29725),X29724)))),
inference(variable_rename,[status(thm)],[fact_Range__Diff__subset]) ).
fof(i_0_6716,plain,
! [X23560,X23561,X23562,X23563] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X23563),X23561),X23560))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23563,tc_HOL_Obool)),X23562),X23560))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23563,tc_HOL_Obool)),X23562),hAPP(hAPP(c_Set_Oinsert(X23563),X23561),X23560))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X23563),X23561),X23562))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23563,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23563,tc_HOL_Obool)),X23562),hAPP(hAPP(c_Set_Oinsert(X23563),X23561),c_Orderings_Obot__class_Obot(tc_fun(X23563,tc_HOL_Obool))))),X23560))
| hBOOL(hAPP(hAPP(c_member(X23563),X23561),X23560))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23563,tc_HOL_Obool)),X23562),hAPP(hAPP(c_Set_Oinsert(X23563),X23561),X23560))) )
& ( hBOOL(hAPP(hAPP(c_member(X23563),X23561),X23562))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23563,tc_HOL_Obool)),X23562),X23560))
| hBOOL(hAPP(hAPP(c_member(X23563),X23561),X23560))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23563,tc_HOL_Obool)),X23562),hAPP(hAPP(c_Set_Oinsert(X23563),X23561),X23560))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X23563),X23561),X23560))
| hBOOL(hAPP(hAPP(c_member(X23563),X23561),X23560))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23563,tc_HOL_Obool)),X23562),hAPP(hAPP(c_Set_Oinsert(X23563),X23561),X23560))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X23563),X23561),X23562))
| hBOOL(hAPP(hAPP(c_member(X23563),X23561),X23562))
| hBOOL(hAPP(hAPP(c_member(X23563),X23561),X23560))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23563,tc_HOL_Obool)),X23562),hAPP(hAPP(c_Set_Oinsert(X23563),X23561),X23560))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23563,tc_HOL_Obool)),X23562),X23560))
| hBOOL(hAPP(hAPP(c_member(X23563),X23561),X23562))
| hBOOL(hAPP(hAPP(c_member(X23563),X23561),X23560))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23563,tc_HOL_Obool)),X23562),hAPP(hAPP(c_Set_Oinsert(X23563),X23561),X23560))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X23563),X23561),X23562))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23563,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23563,tc_HOL_Obool)),X23562),hAPP(hAPP(c_Set_Oinsert(X23563),X23561),c_Orderings_Obot__class_Obot(tc_fun(X23563,tc_HOL_Obool))))),X23560))
| hBOOL(hAPP(hAPP(c_member(X23563),X23561),X23560))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23563,tc_HOL_Obool)),X23562),hAPP(hAPP(c_Set_Oinsert(X23563),X23561),X23560))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23563,tc_HOL_Obool)),X23562),X23560))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23563,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23563,tc_HOL_Obool)),X23562),hAPP(hAPP(c_Set_Oinsert(X23563),X23561),c_Orderings_Obot__class_Obot(tc_fun(X23563,tc_HOL_Obool))))),X23560))
| hBOOL(hAPP(hAPP(c_member(X23563),X23561),X23560))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23563,tc_HOL_Obool)),X23562),hAPP(hAPP(c_Set_Oinsert(X23563),X23561),X23560))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X23563),X23561),X23560))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23563,tc_HOL_Obool)),X23562),X23560))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23563,tc_HOL_Obool)),X23562),hAPP(hAPP(c_Set_Oinsert(X23563),X23561),X23560))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X23563),X23561),X23562))
| hBOOL(hAPP(hAPP(c_member(X23563),X23561),X23562))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23563,tc_HOL_Obool)),X23562),X23560))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23563,tc_HOL_Obool)),X23562),hAPP(hAPP(c_Set_Oinsert(X23563),X23561),X23560))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23563,tc_HOL_Obool)),X23562),X23560))
| hBOOL(hAPP(hAPP(c_member(X23563),X23561),X23562))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23563,tc_HOL_Obool)),X23562),X23560))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23563,tc_HOL_Obool)),X23562),hAPP(hAPP(c_Set_Oinsert(X23563),X23561),X23560))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X23563),X23561),X23562))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23563,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23563,tc_HOL_Obool)),X23562),hAPP(hAPP(c_Set_Oinsert(X23563),X23561),c_Orderings_Obot__class_Obot(tc_fun(X23563,tc_HOL_Obool))))),X23560))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23563,tc_HOL_Obool)),X23562),X23560))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23563,tc_HOL_Obool)),X23562),hAPP(hAPP(c_Set_Oinsert(X23563),X23561),X23560))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23563,tc_HOL_Obool)),X23562),X23560))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23563,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23563,tc_HOL_Obool)),X23562),hAPP(hAPP(c_Set_Oinsert(X23563),X23561),c_Orderings_Obot__class_Obot(tc_fun(X23563,tc_HOL_Obool))))),X23560))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23563,tc_HOL_Obool)),X23562),X23560))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23563,tc_HOL_Obool)),X23562),hAPP(hAPP(c_Set_Oinsert(X23563),X23561),X23560))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5408])])]) ).
fof(i_0_6717,plain,
! [X33768,X33769,X33770] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X33770,X33770)),hAPP(hAPP(c_Product__Type_OPair(X33770,X33770),esk477_3(X33768,X33769,X33770)),esk477_3(X33768,X33769,X33770))),X33769))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33770),tc_List_Olist(X33770))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33770),tc_List_Olist(X33770)),X33768),X33768)),c_List_Olexord(X33770,X33769))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5409])])]) ).
fof(i_0_6718,plain,
! [X29089] : c_Finite__Set_Ofun__left__comm__idem(X29089,tc_fun(X29089,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X29089,tc_HOL_Obool),tc_fun(tc_fun(X29089,tc_HOL_Obool),tc_fun(X29089,tc_HOL_Obool)),X29089),hAPP(c_COMBC(tc_fun(X29089,tc_HOL_Obool),tc_fun(X29089,tc_HOL_Obool),tc_fun(X29089,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X29089,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X29089,tc_fun(X29089,tc_HOL_Obool),tc_fun(X29089,tc_HOL_Obool)),c_Set_Oinsert(X29089)),c_Orderings_Obot__class_Obot(tc_fun(X29089,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,
! [X25518,X25519,X25520] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25520),X25519))
| ~ hBOOL(hAPP(hAPP(c_member(X25520),X25518),X25519))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25520),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25520,tc_HOL_Obool)),X25519),hAPP(hAPP(c_Set_Oinsert(X25520),X25518),c_Orderings_Obot__class_Obot(tc_fun(X25520,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X25520),X25519))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff1__less])]) ).
fof(i_0_6721,plain,
! [X22332,X22333,X22334,X22335,X22336,X22337] : hAPP(hAPP(c_COMBS(tc_prod(X22337,X22336),X22336,X22335),hAPP(hAPP(c_COMBB(X22334,tc_fun(X22336,X22335),tc_prod(X22337,X22336)),X22333),hAPP(hAPP(c_COMBB(X22337,X22334,tc_prod(X22337,X22336)),X22332),c_Product__Type_Ofst(X22337,X22336)))),c_Product__Type_Osnd(X22337,X22336)) = hAPP(c_Product__Type_Oprod_Oprod__case(X22337,X22336,X22335),hAPP(hAPP(c_COMBB(X22334,tc_fun(X22336,X22335),X22337),X22333),X22332)),
inference(variable_rename,[status(thm)],[fact_split__comp__eq]) ).
fof(i_0_6722,plain,
! [X34005,X34006,X34007,X34008,X34009] :
( ~ class_Orderings_Olinorder(X34009)
| ~ hBOOL(hAPP(hAPP(c_member(X34008),X34007),hAPP(c_List_Oset(X34008),X34006)))
| ~ c_List_Olinorder__class_Osorted(X34009,hAPP(hAPP(c_List_Omap(X34008,X34009),X34005),X34006))
| hAPP(c_List_Ohd(X34008),hAPP(c_List_Ofilter(X34008,hAPP(hAPP(c_COMBB(X34009,tc_HOL_Obool,X34008),hAPP(c_fequal,hAPP(X34005,X34007))),X34005)),X34006)) != X34007
| hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X34008,X34009,X34005),X34007),c_List_Oremove1(X34008,X34007,X34006)) = X34006 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__key__remove1])]) ).
fof(i_0_6723,plain,
! [X18467,X18468,X18469,X18470,X18471,X18472] : c_Sum__Type_Osum_Osum__rec(X18472,X18471,X18470,X18469,X18468,hAPP(c_Sum__Type_OInl(X18472,X18470),X18467)) = hAPP(X18469,X18467),
inference(variable_rename,[status(thm)],[fact_sum_Orecs_I1_J]) ).
fof(i_0_6724,plain,
! [X18473,X18474,X18475,X18476,X18477,X18478] : c_Sum__Type_Osum_Osum__rec(X18478,X18477,X18476,X18475,X18474,hAPP(c_Sum__Type_OInr(X18476,X18478),X18473)) = hAPP(X18474,X18473),
inference(variable_rename,[status(thm)],[fact_sum_Orecs_I2_J]) ).
fof(i_0_6725,plain,
! [X24226,X24227] :
( ( 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)),X24227),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)),X24226),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)),X24227),X24226)),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)),X24227),X24226)),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)),X24227),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)),X24226),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,
! [X23789,X23790,X23791,X23792] : c_Nitpick_Ofold__graph_H(X23792,X23791,X23790,X23789,c_Orderings_Obot__class_Obot(tc_fun(X23792,tc_HOL_Obool)),X23789),
inference(variable_rename,[status(thm)],[fact_fold__graph_H_Ointros_I1_J]) ).
fof(i_0_6727,plain,
! [X23785,X23786,X23787,X23788] : c_Nitpick_Ofold__graph_H(X23788,X23787,X23786,X23785,c_Orderings_Obot__class_Obot(tc_fun(X23788,tc_HOL_Obool)),X23785),
inference(variable_rename,[status(thm)],[fact_fold__graph_H_Oequations_I1_J]) ).
fof(i_0_6728,plain,
! [X26564,X26565,X26566,X26567,X26568] :
( ( c_Fun_Oinj__on(X26568,X26567,X26566,X26564)
| ~ c_Fun_Oinj__on(X26568,X26567,X26566,hAPP(hAPP(c_Set_Oinsert(X26568),X26565),X26564)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X26567),hAPP(X26566,X26565)),hAPP(c_Set_Oimage(X26568,X26567,X26566),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26568,tc_HOL_Obool)),X26564),hAPP(hAPP(c_Set_Oinsert(X26568),X26565),c_Orderings_Obot__class_Obot(tc_fun(X26568,tc_HOL_Obool)))))))
| ~ c_Fun_Oinj__on(X26568,X26567,X26566,hAPP(hAPP(c_Set_Oinsert(X26568),X26565),X26564)) )
& ( ~ c_Fun_Oinj__on(X26568,X26567,X26566,X26564)
| hBOOL(hAPP(hAPP(c_member(X26567),hAPP(X26566,X26565)),hAPP(c_Set_Oimage(X26568,X26567,X26566),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26568,tc_HOL_Obool)),X26564),hAPP(hAPP(c_Set_Oinsert(X26568),X26565),c_Orderings_Obot__class_Obot(tc_fun(X26568,tc_HOL_Obool)))))))
| c_Fun_Oinj__on(X26568,X26567,X26566,hAPP(hAPP(c_Set_Oinsert(X26568),X26565),X26564)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5411])])]) ).
fof(i_0_6729,plain,
! [X29420,X29421] : c_Product__Type_Omap__pair(X29421,X29421,X29420,X29420,c_Fun_Oid(X29421),c_Fun_Oid(X29420)) = c_Fun_Oid(tc_prod(X29421,X29420)),
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,
! [X29422,X29423] : c_Product__Type_Omap__pair(X29423,X29423,X29422,X29422,c_COMBI(X29423),c_COMBI(X29422)) = c_Fun_Oid(tc_prod(X29423,X29422)),
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,
! [X30817,X30818,X30819,X30820,X30821] :
( ~ c_Finite__Set_Ofun__left__comm(X30821,X30820,X30819)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30821),X30818))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X30821,X30820,X30819,X30817,X30818),hAPP(hAPP(c_Finite__Set_Ofold(X30821,X30820,X30819),X30817),X30818))) ),
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,
! [X25509,X25510,X25511] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25511),X25510))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25511),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25511,tc_HOL_Obool)),X25510),hAPP(hAPP(c_Set_Oinsert(X25511),X25509),c_Orderings_Obot__class_Obot(tc_fun(X25511,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X25511),X25510))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff1__le])]) ).
fof(i_0_6736,plain,
! [X29484,X29485,X29486,X29487,X29488,X29489,X29490] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29490,X29489),tc_HOL_Obool)),X29488),X29487))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29489,X29486),tc_HOL_Obool)),X29485),X29484))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29490,X29486),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X29490,X29489,X29486),X29488),X29485)),hAPP(hAPP(c_Relation_Orel__comp(X29490,X29489,X29486),X29487),X29484))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__comp__mono])]) ).
fof(i_0_6737,plain,
! [X24528,X24529,X24530,X24531,X24532] :
( ~ c_Equiv__Relations_Oequiv(X24532,X24531,X24530)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24532,X24532)),hAPP(hAPP(c_Product__Type_OPair(X24532,X24532),X24529),X24528)),X24530))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24532,tc_HOL_Obool)),hAPP(c_Relation_OImage(X24532,X24532,X24530),hAPP(hAPP(c_Set_Oinsert(X24532),X24529),c_Orderings_Obot__class_Obot(tc_fun(X24532,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X24532,X24532,X24530),hAPP(hAPP(c_Set_Oinsert(X24532),X24528),c_Orderings_Obot__class_Obot(tc_fun(X24532,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__subset])]) ).
fof(i_0_6738,plain,
! [X26930,X26931,X26932,X26933,X26934,X26935] :
( ~ c_Fun_Oinj__on(X26935,X26934,X26933,X26932)
| ~ hBOOL(hAPP(hAPP(c_member(X26934),X26931),hAPP(c_Set_Oimage(X26935,X26934,X26933),X26932)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26935,tc_HOL_Obool)),X26932),X26930))
| hBOOL(hAPP(hAPP(c_member(X26935),hAPP(c_Fun_Othe__inv__into(X26935,X26934,X26932,X26933),X26931)),X26930)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__into])]) ).
fof(i_0_6739,plain,
! [X28236,X28237,X28238,X28239,X28240] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28240),hAPP(c_Set_Oimage(X28239,X28240,X28238),c_Orderings_Otop__class_Otop(tc_fun(X28239,tc_HOL_Obool)))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X28237),hAPP(c_Set_Oimage(X28239,X28237,hAPP(hAPP(c_COMBB(X28240,X28237,X28239),X28236),X28238)),c_Orderings_Otop__class_Otop(tc_fun(X28239,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__range__imageI])]) ).
fof(i_0_6740,plain,
! [X31406,X31407,X31408] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31408,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31408,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31408,tc_HOL_Obool),X31407)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31408,tc_HOL_Obool),X31406))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31408,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X31408,tc_HOL_Obool),tc_HOL_Obool)),X31407),X31406)))),
inference(variable_rename,[status(thm)],[fact_Inter__Un__subset]) ).
fof(i_0_6741,plain,
! [X33664,X33665,X33666] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X33666,X33666),tc_HOL_Obool)),X33665),hAPP(hAPP(c_Product__Type_OSigma(X33666,X33666),X33664),hAPP(c_COMBK(tc_fun(X33666,tc_HOL_Obool),X33666),X33664))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X33666),tc_List_Olist(X33666)),tc_HOL_Obool)),c_List_Olistrel(X33666,X33665)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(X33666),tc_List_Olist(X33666)),c_List_Olists(X33666,X33664)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X33666),tc_HOL_Obool),tc_List_Olist(X33666)),c_List_Olists(X33666,X33664))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__subset])]) ).
fof(i_0_6742,plain,
! [X27859,X27860,X27861,X27862,X27863,X27864,X27865] :
( ~ class_Groups_Oab__semigroup__mult(X27865)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27864),X27863))
| ~ c_Fun_Oinj__on(X27864,X27862,X27861,X27863)
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X27865,X27862,c_Groups_Otimes__class_Otimes(X27865)),X27860),X27859),hAPP(c_Set_Oimage(X27864,X27862,X27861),X27863)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X27865,X27864,c_Groups_Otimes__class_Otimes(X27865)),hAPP(c_Fun_Ocomp(X27862,X27865,X27864,X27860),X27861)),X27859),X27863) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__image__reindex])]) ).
fof(i_0_6743,plain,
! [X19786,X19787,X19788,X19789] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19789))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19788))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19788),X19787))
| 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),X19787),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19786,X19789))),X19788)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19787),X19789))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux4])]) ).
fof(i_0_6744,plain,
! [X32973,X32974,X32975,X32976,X32977,X32978] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32978)),X32977) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32976)),X32975)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32978,tc_HOL_Obool)),hAPP(c_List_Oset(X32978),X32977)),X32974))
| c_Map_Orestrict__map(X32978,X32976,c_Map_Omap__upds(X32978,X32976,X32973,X32977,X32975),X32974) = c_Map_Omap__upds(X32978,X32976,c_Map_Orestrict__map(X32978,X32976,X32973,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X32978,tc_HOL_Obool)),X32974),hAPP(c_List_Oset(X32978),X32977))),X32977,X32975) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_restrict__map__upds])]) ).
fof(i_0_6745,plain,
! [X31495,X31496,X31497,X31498] :
( ( hBOOL(hAPP(hAPP(c_member(X31498),esk419_4(X31495,X31496,X31497,X31498)),X31497))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31498),hAPP(hAPP(c_Finite__Set_Ofold(X31498,X31498,c_Lattices_Osemilattice__sup__class_Osup(X31498)),X31495),X31497)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X31498),X31496),X31495)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31498),X31497))
| ~ class_Lattices_Osemilattice__sup(X31498) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31498),esk419_4(X31495,X31496,X31497,X31498)),X31496))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31498),hAPP(hAPP(c_Finite__Set_Ofold(X31498,X31498,c_Lattices_Osemilattice__sup__class_Osup(X31498)),X31495),X31497)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X31498),X31496),X31495)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31498),X31497))
| ~ class_Lattices_Osemilattice__sup(X31498) ) ),
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,
! [X31476,X31477,X31478,X31479] :
( ( hBOOL(hAPP(hAPP(c_member(X31479),esk415_4(X31476,X31477,X31478,X31479)),X31478))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31479),hAPP(hAPP(c_Finite__Set_Ofold(X31479,X31479,c_Orderings_Oord__class_Omax(X31479)),X31476),X31478)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X31479),X31477),X31476)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31479),X31478))
| ~ class_Orderings_Olinorder(X31479) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31479),esk415_4(X31476,X31477,X31478,X31479)),X31477))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31479),hAPP(hAPP(c_Finite__Set_Ofold(X31479,X31479,c_Orderings_Oord__class_Omax(X31479)),X31476),X31478)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X31479),X31477),X31476)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31479),X31478))
| ~ class_Orderings_Olinorder(X31479) ) ),
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,
! [X23753,X23754,X23755,X23756] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X23756),X23754),X23755))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23756,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23756,tc_HOL_Obool)),X23755),hAPP(hAPP(c_Set_Oinsert(X23756),X23754),c_Orderings_Obot__class_Obot(tc_fun(X23756,tc_HOL_Obool))))),X23753))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23756,tc_HOL_Obool)),X23755),hAPP(hAPP(c_Set_Oinsert(X23756),X23754),X23753))) )
& ( hBOOL(hAPP(hAPP(c_member(X23756),X23754),X23755))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23756,tc_HOL_Obool)),X23755),X23753))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23756,tc_HOL_Obool)),X23755),hAPP(hAPP(c_Set_Oinsert(X23756),X23754),X23753))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X23756),X23754),X23755))
| hBOOL(hAPP(hAPP(c_member(X23756),X23754),X23755))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23756,tc_HOL_Obool)),X23755),hAPP(hAPP(c_Set_Oinsert(X23756),X23754),X23753))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23756,tc_HOL_Obool)),X23755),X23753))
| hBOOL(hAPP(hAPP(c_member(X23756),X23754),X23755))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23756,tc_HOL_Obool)),X23755),hAPP(hAPP(c_Set_Oinsert(X23756),X23754),X23753))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X23756),X23754),X23755))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23756,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23756,tc_HOL_Obool)),X23755),hAPP(hAPP(c_Set_Oinsert(X23756),X23754),c_Orderings_Obot__class_Obot(tc_fun(X23756,tc_HOL_Obool))))),X23753))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23756,tc_HOL_Obool)),X23755),hAPP(hAPP(c_Set_Oinsert(X23756),X23754),X23753))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23756,tc_HOL_Obool)),X23755),X23753))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23756,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23756,tc_HOL_Obool)),X23755),hAPP(hAPP(c_Set_Oinsert(X23756),X23754),c_Orderings_Obot__class_Obot(tc_fun(X23756,tc_HOL_Obool))))),X23753))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23756,tc_HOL_Obool)),X23755),hAPP(hAPP(c_Set_Oinsert(X23756),X23754),X23753))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5415])])]) ).
fof(i_0_6749,plain,
! [X33258,X33259,X33260,X33261,X33262] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33262,X33262)),hAPP(hAPP(c_Product__Type_OPair(X33262,X33262),X33261),X33260)),X33259))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33262),tc_List_Olist(X33262))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33262),tc_List_Olist(X33262)),hAPP(hAPP(c_List_Olist_OCons(X33262),X33261),X33258)),hAPP(hAPP(c_List_Olist_OCons(X33262),X33260),X33258))),c_List_Olistrel1(X33262,X33259))) ),
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,
! [X34203,X34204,X34205] :
( ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X34205),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X34205))),X34204)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34203),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34205))),X34204)))
| hAPP(hAPP(c_List_Omap(tc_List_Olist(X34205),X34205),hAPP(hAPP(c_COMBC(tc_List_Olist(X34205),tc_Nat_Onat,X34205),c_List_Onth(X34205)),X34203)),hAPP(c_List_Ofilter(tc_List_Olist(X34205),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X34205)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34203)),c_Nat_Osize__class_Osize(tc_List_Olist(X34205)))),c_List_Otranspose(X34205,X34204))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(X34205)),X34204),X34203) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose__column])]) ).
fof(i_0_6753,plain,
! [X30010,X30011,X30012] : c_Hilbert__Choice_OEps(tc_prod(X30012,X30011),X30010) = c_Hilbert__Choice_OEps(tc_prod(X30012,X30011),hAPP(c_Product__Type_Oprod_Oprod__case(X30012,X30011,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X30011,tc_prod(X30012,X30011)),tc_fun(X30011,tc_HOL_Obool),X30012),hAPP(c_COMBB(tc_prod(X30012,X30011),tc_HOL_Obool,X30011),X30010)),c_Product__Type_OPair(X30012,X30011)))),
inference(variable_rename,[status(thm)],[fact_split__paired__Eps]) ).
fof(i_0_6754,plain,
! [X23000,X23001,X23002] : c_HOL_OThe(tc_prod(X23002,X23001),X23000) = c_HOL_OThe(tc_prod(X23002,X23001),hAPP(c_Product__Type_Oprod_Oprod__case(X23002,X23001,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X23001,tc_prod(X23002,X23001)),tc_fun(X23001,tc_HOL_Obool),X23002),hAPP(c_COMBB(tc_prod(X23002,X23001),tc_HOL_Obool,X23001),X23000)),c_Product__Type_OPair(X23002,X23001)))),
inference(variable_rename,[status(thm)],[fact_split__paired__The]) ).
fof(i_0_6755,plain,
! [X23120,X23121,X23122,X23123,X23124,X23125,X23126] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X23126,X23125,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X23126)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X23126),X23124),X23123),X23122)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X23126),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X23126,X23125,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X23126)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X23126),X23122),X23121),X23120)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X23126),tc_HOL_Obool))))
| c_Hoare__Mirabelle_Ohoare__derivs(X23126,X23125,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X23126)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X23126),X23124),c_Com_Ocom_OSemi(X23123,X23121)),X23120)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X23126),tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Comp])]) ).
fof(i_0_6756,plain,
! [X30521,X30522,X30523,X30524,X30525,X30526,X30527,X30528] :
( ( ~ c_Relation_Ototal__on(X30523,X30522,X30521)
| ~ hBOOL(hAPP(hAPP(c_member(X30523),X30524),X30522))
| ~ hBOOL(hAPP(hAPP(c_member(X30523),X30525),X30522))
| X30524 = X30525
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30523,X30523)),hAPP(hAPP(c_Product__Type_OPair(X30523,X30523),X30524),X30525)),X30521))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30523,X30523)),hAPP(hAPP(c_Product__Type_OPair(X30523,X30523),X30525),X30524)),X30521)) )
& ( hBOOL(hAPP(hAPP(c_member(X30528),esk370_3(X30526,X30527,X30528)),X30527))
| c_Relation_Ototal__on(X30528,X30527,X30526) )
& ( hBOOL(hAPP(hAPP(c_member(X30528),esk371_3(X30526,X30527,X30528)),X30527))
| c_Relation_Ototal__on(X30528,X30527,X30526) )
& ( esk370_3(X30526,X30527,X30528) != esk371_3(X30526,X30527,X30528)
| c_Relation_Ototal__on(X30528,X30527,X30526) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30528,X30528)),hAPP(hAPP(c_Product__Type_OPair(X30528,X30528),esk370_3(X30526,X30527,X30528)),esk371_3(X30526,X30527,X30528))),X30526))
| c_Relation_Ototal__on(X30528,X30527,X30526) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30528,X30528)),hAPP(hAPP(c_Product__Type_OPair(X30528,X30528),esk371_3(X30526,X30527,X30528)),esk370_3(X30526,X30527,X30528))),X30526))
| c_Relation_Ototal__on(X30528,X30527,X30526) ) ),
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,
! [X20218,X20219,X20220,X20221] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20221))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20220),X20219))
| 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),X20219),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20218,X20221))),X20220)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20219),X20221))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__lemma])]) ).
fof(i_0_6758,plain,
! [X31679,X31680,X31681] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X31680),X31679))
| c_Smallcheck_Osmall_H(X31681,X31680,X31679) = 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)),X31681),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X31680),X31679)))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X31680),X31679))
| c_Smallcheck_Osmall_H(X31681,X31680,X31679) = 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(X31681,X31680,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X31679),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(X31681,X31679))
| ~ 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)),X31681),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X31680),X31679)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5418])])]) ).
fof(i_0_6759,plain,
! [X30596,X30597,X30598,X30599,X30600] :
( ~ c_Relation_Osingle__valued(X30600,X30600,X30599)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30600,X30600)),hAPP(hAPP(c_Product__Type_OPair(X30600,X30600),X30598),X30597)),c_Transitive__Closure_Ortrancl(X30600,X30599)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30600,X30600)),hAPP(hAPP(c_Product__Type_OPair(X30600,X30600),X30598),X30596)),c_Transitive__Closure_Ortrancl(X30600,X30599)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30600,X30600)),hAPP(hAPP(c_Product__Type_OPair(X30600,X30600),X30597),X30596)),c_Transitive__Closure_Ortrancl(X30600,X30599)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30600,X30600)),hAPP(hAPP(c_Product__Type_OPair(X30600,X30600),X30596),X30597)),c_Transitive__Closure_Ortrancl(X30600,X30599))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__confluent])]) ).
fof(i_0_6760,plain,
! [X29547,X29548,X29549] :
( ~ c_Wellfounded_Owf(X29549,X29548)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29549,X29549),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X29549,X29549,X29549),X29548),X29547)),X29548))
| c_FunDef_Oreduction__pair(X29549,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(X29549,X29549),tc_HOL_Obool),tc_fun(tc_prod(X29549,X29549),tc_HOL_Obool)),X29548),X29547)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reduction__pairI])]) ).
fof(i_0_6761,plain,
! [X19954,X19955,X19956,X19957] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19957))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19956),X19955))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19955),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),X19956),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19954,X19957))),X19955)),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,
! [X32607,X32608] : c_Random_Oselect(X32608,X32607) = 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(X32608,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(X32608)),X32607)))),hAPP(hAPP(c_COMBB(X32608,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X32608,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X32608,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X32608,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(X32608),X32607)),c_Code__Numeral_Onat__of))),
inference(variable_rename,[status(thm)],[fact_select__def]) ).
fof(i_0_6763,plain,
! [X21947,X21948] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21948),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Nitpick_Onorm__frac(X21947,X21948) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21947),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21948)) )
& ( X21947 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Nitpick_Onorm__frac(X21947,X21948) = 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),X21948),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( X21948 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Nitpick_Onorm__frac(X21947,X21948) = 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),X21948),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( X21947 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X21948 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Nitpick_Onorm__frac(X21947,X21948) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X21947),X21948)),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),X21947))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21948)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21948),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,
! [X24387,X24388,X24389] :
( ~ class_Rings_Oring__1(X24389)
| hAPP(c_Int_Oring__1__class_Oof__int(X24389),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),X24388),X24387)),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(X24389),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X24389),X24388)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X24389),X24387)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int])]) ).
fof(i_0_6765,plain,
! [X31866,X31867,X31868,X31869,X31870] : c_Map_Odom(X31870,X31869,hAPP(hAPP(c_COMBS(X31870,tc_Option_Ooption(X31868),tc_Option_Ooption(X31869)),hAPP(hAPP(c_COMBB(tc_fun(X31868,X31869),tc_fun(tc_Option_Ooption(X31868),tc_Option_Ooption(X31869)),X31870),c_Option_Omap(X31868,X31869)),X31867)),X31866)) = c_Map_Odom(X31870,X31868,X31866),
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,
! [X23572,X23573,X23574,X23575] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23575,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23575,tc_HOL_Obool)),X23574),hAPP(hAPP(c_Set_Oinsert(X23575),X23573),c_Orderings_Obot__class_Obot(tc_fun(X23575,tc_HOL_Obool))))),X23572))
| ~ hBOOL(hAPP(hAPP(c_member(X23575),X23573),X23574))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23575,tc_HOL_Obool)),X23574),hAPP(hAPP(c_Set_Oinsert(X23575),X23573),X23572))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__single__insert])]) ).
fof(i_0_6769,plain,
! [X24423,X24424] : 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),X24424),X24423)),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),X24424),X24423),
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,
! [X26559,X26560,X26561,X26562,X26563] :
( ( c_Fun_Oinj__on(X26563,X26562,X26561,X26560)
| ~ c_Fun_Oinj__on(X26563,X26562,X26561,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26563,tc_HOL_Obool)),X26560),X26559)) )
& ( c_Fun_Oinj__on(X26563,X26562,X26561,X26559)
| ~ c_Fun_Oinj__on(X26563,X26562,X26561,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26563,tc_HOL_Obool)),X26560),X26559)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26562,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26563,X26562,X26561),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26563,tc_HOL_Obool)),X26560),X26559))),hAPP(c_Set_Oimage(X26563,X26562,X26561),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26563,tc_HOL_Obool)),X26559),X26560))) = c_Orderings_Obot__class_Obot(tc_fun(X26562,tc_HOL_Obool))
| ~ c_Fun_Oinj__on(X26563,X26562,X26561,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26563,tc_HOL_Obool)),X26560),X26559)) )
& ( ~ c_Fun_Oinj__on(X26563,X26562,X26561,X26560)
| ~ c_Fun_Oinj__on(X26563,X26562,X26561,X26559)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26562,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26563,X26562,X26561),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26563,tc_HOL_Obool)),X26560),X26559))),hAPP(c_Set_Oimage(X26563,X26562,X26561),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26563,tc_HOL_Obool)),X26559),X26560))) != c_Orderings_Obot__class_Obot(tc_fun(X26562,tc_HOL_Obool))
| c_Fun_Oinj__on(X26563,X26562,X26561,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26563,tc_HOL_Obool)),X26560),X26559)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__Un])])]) ).
fof(i_0_6774,plain,
! [X24578,X24579,X24580] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X24580,tc_HOL_Obool)),X24579),X24578))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X24580,tc_HOL_Obool),tc_fun(X24580,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X24580,tc_HOL_Obool),tc_fun(X24580,tc_HOL_Obool)),X24579),X24578)),c_Wellfounded_Ofinite__psubset(X24580))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X24580),X24578))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X24580,tc_HOL_Obool),tc_fun(X24580,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X24580,tc_HOL_Obool),tc_fun(X24580,tc_HOL_Obool)),X24579),X24578)),c_Wellfounded_Ofinite__psubset(X24580))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X24580,tc_HOL_Obool)),X24579),X24578))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24580),X24578))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X24580,tc_HOL_Obool),tc_fun(X24580,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X24580,tc_HOL_Obool),tc_fun(X24580,tc_HOL_Obool)),X24579),X24578)),c_Wellfounded_Ofinite__psubset(X24580))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__finite__psubset])])]) ).
fof(i_0_6775,plain,
! [X29832,X29833,X29834,X29835] :
( ~ hBOOL(hAPP(hAPP(c_member(X29835),X29834),hAPP(c_Relation_ODomain(X29835,X29833),X29832)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X29835,X29833)),hAPP(hAPP(c_Product__Type_OPair(X29835,X29833),X29834),esk327_4(X29832,X29833,X29834,X29835))),X29832)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5425])])]) ).
fof(i_0_6776,plain,
! [X29796,X29797,X29798,X29799,X29801,X29802,X29803,X29804,X29805] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X29799),X29798),hAPP(c_Relation_ODomain(X29799,X29797),X29796)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X29799,X29797)),hAPP(hAPP(c_Product__Type_OPair(X29799,X29797),X29798),esk326_4(X29796,X29797,X29798,X29799))),X29796)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29804,X29802)),hAPP(hAPP(c_Product__Type_OPair(X29804,X29802),X29803),X29805)),X29801))
| hBOOL(hAPP(hAPP(c_member(X29804),X29803),hAPP(c_Relation_ODomain(X29804,X29802),X29801))) ) ),
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,
! [X26383,X26384,X26385] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X26385,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X26385,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X26385),X26384)),hAPP(c_Set_OPow(X26385),X26383))),hAPP(c_Set_OPow(X26385),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26385,tc_HOL_Obool)),X26384),X26383)))),
inference(variable_rename,[status(thm)],[fact_Un__Pow__subset]) ).
fof(i_0_6778,plain,
! [X20576,X20577,X20578,X20579,X20580] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20580),X20579))
| 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),X20579),X20578)),X20577)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20580),X20578)),X20576)) = 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),X20579),X20580)),X20578)),X20577)),X20576) ),
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,
! [X32406,X32407,X32408] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X32408),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X32407),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X32407)),X32406))))
| hBOOL(hAPP(hAPP(c_member(X32407),hAPP(c_Random_Opick(X32407,X32406),X32408)),hAPP(c_List_Oset(X32407),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X32407),X32407),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X32407)),X32406)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pick__member])]) ).
fof(i_0_6781,plain,
! [X25224,X25225,X25226,X25227] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25225),X25227))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25227),X25226))
| ~ 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),X25227,X25226)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25225,X25224))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25226),X25224))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25227),X25226))
| ~ 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),X25227,X25226)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25225,X25224))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25227),X25226))
| 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),X25227,X25226)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25225,X25224))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25225),X25227))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25226),X25224))
| 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),X25227,X25226)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25225,X25224))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5427])])]) ).
fof(i_0_6782,plain,
! [X29462,X29463,X29464,X29465,X29466,X29467,X29468,X29469] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29469,X29468)),hAPP(hAPP(c_Product__Type_OPair(X29469,X29468),X29467),X29466)),X29465))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29468,X29464)),hAPP(hAPP(c_Product__Type_OPair(X29468,X29464),X29466),X29463)),X29462))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X29469,X29464)),hAPP(hAPP(c_Product__Type_OPair(X29469,X29464),X29467),X29463)),hAPP(hAPP(c_Relation_Orel__comp(X29469,X29468,X29464),X29465),X29462))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__compI])]) ).
fof(i_0_6783,plain,
! [X34126,X34127,X34128,X34129,X34130] :
( ~ class_Orderings_Olinorder(X34130)
| ~ c_List_Olinorder__class_Osorted(X34130,hAPP(hAPP(c_List_Omap(X34129,X34130),X34128),X34127))
| c_List_Olinorder__class_Osorted(X34130,hAPP(hAPP(c_List_Omap(X34129,X34130),X34128),c_List_Olinorder__class_Oinsort__insert__key(X34129,X34130,X34128,X34126,X34127))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__insort__insert__key])]) ).
fof(i_0_6784,plain,
! [X24042,X24043,X24044,X24045,X24046,X24049,X24050,X24051,X24052,X24053,X24054] :
( ( hBOOL(hAPP(hAPP(c_member(X24045),esk115_4(X24042,X24043,X24044,X24045)),X24043))
| hBOOL(hAPP(hAPP(c_member(X24045),esk114_4(X24042,X24043,X24044,X24045)),X24044))
| ~ hBOOL(hAPP(hAPP(c_member(X24045),X24046),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24045,tc_HOL_Obool)),X24044),X24043)))
| ~ hBOOL(hAPP(X24042,X24046)) )
& ( hBOOL(hAPP(X24042,esk115_4(X24042,X24043,X24044,X24045)))
| hBOOL(hAPP(hAPP(c_member(X24045),esk114_4(X24042,X24043,X24044,X24045)),X24044))
| ~ hBOOL(hAPP(hAPP(c_member(X24045),X24046),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24045,tc_HOL_Obool)),X24044),X24043)))
| ~ hBOOL(hAPP(X24042,X24046)) )
& ( hBOOL(hAPP(hAPP(c_member(X24045),esk115_4(X24042,X24043,X24044,X24045)),X24043))
| hBOOL(hAPP(X24042,esk114_4(X24042,X24043,X24044,X24045)))
| ~ hBOOL(hAPP(hAPP(c_member(X24045),X24046),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24045,tc_HOL_Obool)),X24044),X24043)))
| ~ hBOOL(hAPP(X24042,X24046)) )
& ( hBOOL(hAPP(X24042,esk115_4(X24042,X24043,X24044,X24045)))
| hBOOL(hAPP(X24042,esk114_4(X24042,X24043,X24044,X24045)))
| ~ hBOOL(hAPP(hAPP(c_member(X24045),X24046),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24045,tc_HOL_Obool)),X24044),X24043)))
| ~ hBOOL(hAPP(X24042,X24046)) )
& ( hBOOL(hAPP(hAPP(c_member(X24052),esk116_4(X24049,X24050,X24051,X24052)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24052,tc_HOL_Obool)),X24051),X24050)))
| ~ hBOOL(hAPP(hAPP(c_member(X24052),X24053),X24051))
| ~ hBOOL(hAPP(X24049,X24053)) )
& ( hBOOL(hAPP(X24049,esk116_4(X24049,X24050,X24051,X24052)))
| ~ hBOOL(hAPP(hAPP(c_member(X24052),X24053),X24051))
| ~ hBOOL(hAPP(X24049,X24053)) )
& ( hBOOL(hAPP(hAPP(c_member(X24052),esk116_4(X24049,X24050,X24051,X24052)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24052,tc_HOL_Obool)),X24051),X24050)))
| ~ hBOOL(hAPP(hAPP(c_member(X24052),X24054),X24050))
| ~ hBOOL(hAPP(X24049,X24054)) )
& ( hBOOL(hAPP(X24049,esk116_4(X24049,X24050,X24051,X24052)))
| ~ hBOOL(hAPP(hAPP(c_member(X24052),X24054),X24050))
| ~ hBOOL(hAPP(X24049,X24054)) ) ),
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,
! [X24028,X24029,X24030,X24031,X24033,X24034,X24035,X24036,X24037,X24038,X24041] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X24031),X24033),X24030))
| hBOOL(hAPP(X24028,X24033))
| hBOOL(hAPP(hAPP(c_member(X24031),esk111_4(X24028,X24029,X24030,X24031)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24031,tc_HOL_Obool)),X24030),X24029))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X24031),X24034),X24029))
| hBOOL(hAPP(X24028,X24034))
| hBOOL(hAPP(hAPP(c_member(X24031),esk111_4(X24028,X24029,X24030,X24031)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24031,tc_HOL_Obool)),X24030),X24029))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X24031),X24033),X24030))
| hBOOL(hAPP(X24028,X24033))
| ~ hBOOL(hAPP(X24028,esk111_4(X24028,X24029,X24030,X24031))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X24031),X24034),X24029))
| hBOOL(hAPP(X24028,X24034))
| ~ hBOOL(hAPP(X24028,esk111_4(X24028,X24029,X24030,X24031))) )
& ( hBOOL(hAPP(hAPP(c_member(X24038),esk113_4(X24035,X24036,X24037,X24038)),X24036))
| hBOOL(hAPP(hAPP(c_member(X24038),esk112_4(X24035,X24036,X24037,X24038)),X24037))
| ~ hBOOL(hAPP(hAPP(c_member(X24038),X24041),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24038,tc_HOL_Obool)),X24037),X24036)))
| hBOOL(hAPP(X24035,X24041)) )
& ( ~ hBOOL(hAPP(X24035,esk113_4(X24035,X24036,X24037,X24038)))
| hBOOL(hAPP(hAPP(c_member(X24038),esk112_4(X24035,X24036,X24037,X24038)),X24037))
| ~ hBOOL(hAPP(hAPP(c_member(X24038),X24041),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24038,tc_HOL_Obool)),X24037),X24036)))
| hBOOL(hAPP(X24035,X24041)) )
& ( hBOOL(hAPP(hAPP(c_member(X24038),esk113_4(X24035,X24036,X24037,X24038)),X24036))
| ~ hBOOL(hAPP(X24035,esk112_4(X24035,X24036,X24037,X24038)))
| ~ hBOOL(hAPP(hAPP(c_member(X24038),X24041),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24038,tc_HOL_Obool)),X24037),X24036)))
| hBOOL(hAPP(X24035,X24041)) )
& ( ~ hBOOL(hAPP(X24035,esk113_4(X24035,X24036,X24037,X24038)))
| ~ hBOOL(hAPP(X24035,esk112_4(X24035,X24036,X24037,X24038)))
| ~ hBOOL(hAPP(hAPP(c_member(X24038),X24041),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24038,tc_HOL_Obool)),X24037),X24036)))
| hBOOL(hAPP(X24035,X24041)) ) ),
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,
! [X30854,X30855,X30856,X30857,X30858,X30859,X30860,X30861] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30861,tc_fun(X30860,tc_fun(X30859,tc_HOL_Obool))),X30858),X30857),X30856),X30855))
| ~ hBOOL(hAPP(hAPP(c_member(X30861),X30854),X30858))
| hBOOL(hAPP(hAPP(hAPP(X30857,X30854),X30856),X30855)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF2__D])]) ).
fof(i_0_6791,plain,
! [X30846,X30847,X30848,X30849,X30850,X30851,X30852,X30853] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30853,tc_fun(X30852,tc_fun(X30851,tc_HOL_Obool))),X30850),X30849),X30848),X30847))
| hBOOL(hAPP(hAPP(hAPP(X30849,X30846),X30848),X30847))
| ~ hBOOL(hAPP(hAPP(c_member(X30853),X30846),X30850)) ),
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,
! [X27763,X27764,X27765,X27766,X27767,X27768,X27769] : hAPP(c_Fun_Ocomp(X27769,X27768,X27767,X27766),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27767,X27769),X27765),X27764),X27763)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27767,X27768),hAPP(c_Fun_Ocomp(X27769,X27768,X27767,X27766),X27765)),X27764),hAPP(X27766,X27763)),
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,
! [X29218,X29219,X29220,X29221] : hAPP(c_Set_Ovimage(X29221,X29220,X29219),X29218) = hAPP(c_Set_OCollect(X29221),hAPP(hAPP(c_COMBC(X29221,tc_fun(X29220,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(X29220,tc_fun(tc_fun(X29220,tc_HOL_Obool),tc_HOL_Obool),X29221),c_member(X29220)),X29219)),X29218)),
inference(variable_rename,[status(thm)],[fact_vimage__def]) ).
fof(i_0_6802,plain,
! [X33431,X33432,X33433,X33434,X33435] : hAPP(hAPP(c_List_Ozip(X33435,X33434),X33433),hAPP(hAPP(c_List_Oappend(X33434),X33432),X33431)) = hAPP(hAPP(c_List_Oappend(tc_prod(X33435,X33434)),hAPP(hAPP(c_List_Ozip(X33435,X33434),hAPP(hAPP(c_List_Otake(X33435),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33434)),X33432)),X33433)),X33432)),hAPP(hAPP(c_List_Ozip(X33435,X33434),hAPP(hAPP(c_List_Odrop(X33435),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33434)),X33432)),X33433)),X33431)),
inference(variable_rename,[status(thm)],[fact_zip__append2]) ).
fof(i_0_6803,plain,
! [X33246,X33247,X33248,X33249] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33249),tc_List_Olist(X33249))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33249),tc_List_Olist(X33249)),X33248),X33247)),c_List_Olistrel1(X33249,hAPP(c_Relation_Oconverse(X33249,X33249),X33246))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33249),tc_List_Olist(X33249))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33249),tc_List_Olist(X33249)),X33248),X33247)),hAPP(c_Relation_Oconverse(tc_List_Olist(X33249),tc_List_Olist(X33249)),c_List_Olistrel1(X33249,X33246)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33249),tc_List_Olist(X33249))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33249),tc_List_Olist(X33249)),X33248),X33247)),hAPP(c_Relation_Oconverse(tc_List_Olist(X33249),tc_List_Olist(X33249)),c_List_Olistrel1(X33249,X33246))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33249),tc_List_Olist(X33249))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33249),tc_List_Olist(X33249)),X33248),X33247)),c_List_Olistrel1(X33249,hAPP(c_Relation_Oconverse(X33249,X33249),X33246)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__listrel1__converse])]) ).
fof(i_0_6804,plain,
! [X33970,X33971,X33972,X33973,X33974] : c_List_Omap__filter(X33974,X33973,X33972,hAPP(hAPP(c_List_Olist_OCons(X33974),X33971),X33970)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(X33973),X33973,c_List_Omap__filter(X33974,X33973,X33972,X33970),hAPP(hAPP(c_COMBC(X33973,tc_List_Olist(X33973),tc_List_Olist(X33973)),c_List_Olist_OCons(X33973)),c_List_Omap__filter(X33974,X33973,X33972,X33970))),hAPP(X33972,X33971)),
inference(variable_rename,[status(thm)],[fact_map__filter__simps_I1_J]) ).
fof(i_0_6805,plain,
! [X33006,X33007,X33008,X33009,X33010,X33012,X33013,X33014,X33015,X33016,X33017] :
( ( hAPP(hAPP(c_List_Olist_OCons(X33010),X33009),esk460_5(X33006,X33007,X33008,X33009,X33010)) = X33007
| X33007 = c_List_Olist_ONil(X33010)
| hAPP(hAPP(c_List_Olist_OCons(X33010),X33009),X33008) != hAPP(hAPP(c_List_Oappend(X33010),X33007),X33006) )
& ( X33008 = hAPP(hAPP(c_List_Oappend(X33010),esk460_5(X33006,X33007,X33008,X33009,X33010)),X33006)
| X33007 = c_List_Olist_ONil(X33010)
| hAPP(hAPP(c_List_Olist_OCons(X33010),X33009),X33008) != hAPP(hAPP(c_List_Oappend(X33010),X33007),X33006) )
& ( hAPP(hAPP(c_List_Olist_OCons(X33010),X33009),esk460_5(X33006,X33007,X33008,X33009,X33010)) = X33007
| hAPP(hAPP(c_List_Olist_OCons(X33010),X33009),X33008) = X33006
| hAPP(hAPP(c_List_Olist_OCons(X33010),X33009),X33008) != hAPP(hAPP(c_List_Oappend(X33010),X33007),X33006) )
& ( X33008 = hAPP(hAPP(c_List_Oappend(X33010),esk460_5(X33006,X33007,X33008,X33009,X33010)),X33006)
| hAPP(hAPP(c_List_Olist_OCons(X33010),X33009),X33008) = X33006
| hAPP(hAPP(c_List_Olist_OCons(X33010),X33009),X33008) != hAPP(hAPP(c_List_Oappend(X33010),X33007),X33006) )
& ( X33013 != c_List_Olist_ONil(X33016)
| hAPP(hAPP(c_List_Olist_OCons(X33016),X33015),X33014) != X33012
| hAPP(hAPP(c_List_Olist_OCons(X33016),X33015),X33014) = hAPP(hAPP(c_List_Oappend(X33016),X33013),X33012) )
& ( hAPP(hAPP(c_List_Olist_OCons(X33016),X33015),X33017) != X33013
| X33014 != hAPP(hAPP(c_List_Oappend(X33016),X33017),X33012)
| hAPP(hAPP(c_List_Olist_OCons(X33016),X33015),X33014) = hAPP(hAPP(c_List_Oappend(X33016),X33013),X33012) ) ),
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,
! [X32994,X32995,X32996,X32997,X32998,X33000,X33001,X33002,X33003,X33004,X33005] :
( ( X32997 = hAPP(hAPP(c_List_Olist_OCons(X32998),X32995),esk459_5(X32994,X32995,X32996,X32997,X32998))
| X32997 = c_List_Olist_ONil(X32998)
| hAPP(hAPP(c_List_Oappend(X32998),X32997),X32996) != hAPP(hAPP(c_List_Olist_OCons(X32998),X32995),X32994) )
& ( hAPP(hAPP(c_List_Oappend(X32998),esk459_5(X32994,X32995,X32996,X32997,X32998)),X32996) = X32994
| X32997 = c_List_Olist_ONil(X32998)
| hAPP(hAPP(c_List_Oappend(X32998),X32997),X32996) != hAPP(hAPP(c_List_Olist_OCons(X32998),X32995),X32994) )
& ( X32997 = hAPP(hAPP(c_List_Olist_OCons(X32998),X32995),esk459_5(X32994,X32995,X32996,X32997,X32998))
| X32996 = hAPP(hAPP(c_List_Olist_OCons(X32998),X32995),X32994)
| hAPP(hAPP(c_List_Oappend(X32998),X32997),X32996) != hAPP(hAPP(c_List_Olist_OCons(X32998),X32995),X32994) )
& ( hAPP(hAPP(c_List_Oappend(X32998),esk459_5(X32994,X32995,X32996,X32997,X32998)),X32996) = X32994
| X32996 = hAPP(hAPP(c_List_Olist_OCons(X32998),X32995),X32994)
| hAPP(hAPP(c_List_Oappend(X32998),X32997),X32996) != hAPP(hAPP(c_List_Olist_OCons(X32998),X32995),X32994) )
& ( X33003 != c_List_Olist_ONil(X33004)
| X33002 != hAPP(hAPP(c_List_Olist_OCons(X33004),X33001),X33000)
| hAPP(hAPP(c_List_Oappend(X33004),X33003),X33002) = hAPP(hAPP(c_List_Olist_OCons(X33004),X33001),X33000) )
& ( X33003 != hAPP(hAPP(c_List_Olist_OCons(X33004),X33001),X33005)
| hAPP(hAPP(c_List_Oappend(X33004),X33005),X33002) != X33000
| hAPP(hAPP(c_List_Oappend(X33004),X33003),X33002) = hAPP(hAPP(c_List_Olist_OCons(X33004),X33001),X33000) ) ),
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,
! [X25442,X25443] :
( ~ class_Orderings_Olinorder(X25443)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25443),X25442))
| X25442 = c_Orderings_Obot__class_Obot(tc_fun(X25443,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X25443),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25443),esk145_2(X25442,X25443)),esk146_2(X25442,X25443))),hAPP(hAPP(c_Set_Oinsert(X25443),esk145_2(X25442,X25443)),hAPP(hAPP(c_Set_Oinsert(X25443),esk146_2(X25442,X25443)),c_Orderings_Obot__class_Obot(tc_fun(X25443,tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_member(X25443),c_Big__Operators_Olattice_OInf__fin(X25443,c_Orderings_Oord__class_Omin(X25443),X25442)),X25442)) ),
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,
! [X25386,X25387] :
( ~ class_Orderings_Olinorder(X25387)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25387),X25386))
| X25386 = c_Orderings_Obot__class_Obot(tc_fun(X25387,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X25387),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25387),esk135_2(X25386,X25387)),esk136_2(X25386,X25387))),hAPP(hAPP(c_Set_Oinsert(X25387),esk135_2(X25386,X25387)),hAPP(hAPP(c_Set_Oinsert(X25387),esk136_2(X25386,X25387)),c_Orderings_Obot__class_Obot(tc_fun(X25387,tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_member(X25387),c_Big__Operators_Olattice_OSup__fin(X25387,c_Orderings_Oord__class_Omax(X25387),X25386)),X25386)) ),
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,
! [X17135,X17136,X17137,X17138,X17139,X17140,X17141,X17142,X17143,X17144,X17145,X17146,X17150] :
( ( ~ c_Hoare__Mirabelle_Otriple__valid(X17139,X17138,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17139),X17137),X17136),X17135))
| ~ hBOOL(hAPP(hAPP(X17137,X17140),X17141))
| ~ c_Natural_Oevaln(X17136,X17141,X17138,X17142)
| hBOOL(hAPP(hAPP(X17135,X17140),X17142)) )
& ( hBOOL(hAPP(hAPP(X17145,esk2_4(X17143,X17144,X17145,X17146)),esk3_4(X17143,X17144,X17145,X17146)))
| c_Hoare__Mirabelle_Otriple__valid(X17150,X17146,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17150),X17145),X17144),X17143)) )
& ( c_Natural_Oevaln(X17144,esk3_4(X17143,X17144,X17145,X17146),X17146,esk4_4(X17143,X17144,X17145,X17146))
| c_Hoare__Mirabelle_Otriple__valid(X17150,X17146,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17150),X17145),X17144),X17143)) )
& ( ~ hBOOL(hAPP(hAPP(X17143,esk2_4(X17143,X17144,X17145,X17146)),esk4_4(X17143,X17144,X17145,X17146)))
| c_Hoare__Mirabelle_Otriple__valid(X17150,X17146,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17150),X17145),X17144),X17143)) ) ),
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,
! [X31953,X31954,X31955,X31956] : c_Map_Omap__of(X31956,X31955,hAPP(hAPP(c_List_Omap(X31956,tc_prod(X31956,X31955)),hAPP(hAPP(c_COMBS(X31956,X31955,tc_prod(X31956,X31955)),c_Product__Type_OPair(X31956,X31955)),X31954)),X31953)) = c_Map_Orestrict__map(X31956,X31955,hAPP(c_Fun_Ocomp(X31955,tc_Option_Ooption(X31955),X31956,c_Option_Ooption_OSome(X31955)),X31954),hAPP(c_List_Oset(X31956),X31953)),
inference(variable_rename,[status(thm)],[fact_map__of__map__restrict]) ).
fof(i_0_6811,plain,
! [X28891,X28892,X28893,X28894] :
( ( hBOOL(hAPP(hAPP(c_member(X28894),esk291_4(X28891,X28892,X28893,X28894)),X28893))
| hAPP(c_Finite__Set_Ocard(tc_prod(X28894,X28892)),hAPP(hAPP(c_Product__Type_OSigma(X28894,X28892),X28893),X28891)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28894,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X28892,tc_HOL_Obool),tc_Nat_Onat,X28894),c_Finite__Set_Ocard(X28892)),X28891)),X28893)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28894),X28893)) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28892),hAPP(X28891,esk291_4(X28891,X28892,X28893,X28894))))
| hAPP(c_Finite__Set_Ocard(tc_prod(X28894,X28892)),hAPP(hAPP(c_Product__Type_OSigma(X28894,X28892),X28893),X28891)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28894,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X28892,tc_HOL_Obool),tc_Nat_Onat,X28894),c_Finite__Set_Ocard(X28892)),X28891)),X28893)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28894),X28893)) ) ),
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,
! [X28092,X28093,X28094,X28095] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28095,X28094,X28093,X28092,c_Orderings_Obot__class_Obot(tc_fun(X28095,tc_HOL_Obool))),X28092)),
inference(variable_rename,[status(thm)],[fact_fold__graph_Oequations_I1_J]) ).
fof(i_0_6813,plain,
! [X28088,X28089,X28090,X28091] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X28091,X28090,X28089,X28088,c_Orderings_Obot__class_Obot(tc_fun(X28091,tc_HOL_Obool))),X28088)),
inference(variable_rename,[status(thm)],[fact_fold__graph_OemptyI]) ).
fof(i_0_6814,plain,
! [X29645,X29646,X29647] :
( ~ c_Wellfounded_Owf(X29647,X29646)
| ~ c_Wellfounded_Owf(X29647,X29645)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29647,X29647),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X29647,X29647,X29647),X29646),X29645)),X29646))
| c_Wellfounded_Owf(X29647,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29647,X29647),tc_HOL_Obool)),X29646),X29645)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__union__compatible])]) ).
fof(i_0_6815,plain,
! [X28896,X28897] :
( ~ class_Groups_Oab__semigroup__mult(X28897)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28897),X28896))
| X28896 = c_Orderings_Obot__class_Obot(tc_fun(X28897,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X28897),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X28897),esk292_2(X28896,X28897)),esk293_2(X28896,X28897))),hAPP(hAPP(c_Set_Oinsert(X28897),esk292_2(X28896,X28897)),hAPP(hAPP(c_Set_Oinsert(X28897),esk293_2(X28896,X28897)),c_Orderings_Obot__class_Obot(tc_fun(X28897,tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_member(X28897),hAPP(c_Finite__Set_Ofold1(X28897,c_Groups_Otimes__class_Otimes(X28897)),X28896)),X28896)) ),
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,
! [X19728,X19729,X19730,X19731,X19732] :
( ~ 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),X19732),X19731)),X19730)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19732),X19729)),X19728)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19730))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19730),X19732))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19728),X19732))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19731),X19729)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma])]) ).
fof(i_0_6818,plain,
! [X19717,X19718,X19719,X19720,X19721] :
( ~ 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),X19721),X19720)),X19719)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19721),X19718)),X19717)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19717),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19721),X19717))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19721),X19719))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19718),X19720)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma__neg])]) ).
fof(i_0_6819,plain,
! [X32482,X32483,X32484,X32485,X32486] :
( ~ class_Orderings_Olinorder(X32486)
| ~ hBOOL(hAPP(c_List_Odistinct(X32485),X32484))
| hBOOL(hAPP(c_List_Odistinct(X32485),c_List_Olinorder__class_Oinsort__insert__key(X32485,X32486,X32483,X32482,X32484))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__insort__insert])]) ).
fof(i_0_6820,plain,
! [X33995,X33996,X33997] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33997),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X33996))),c_List_Otranspose(X33996,X33995))))
| hAPP(hAPP(c_List_Onth(tc_List_Olist(X33996)),c_List_Otranspose(X33996,X33995)),X33997) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X33996),X33996),hAPP(hAPP(c_COMBC(tc_List_Olist(X33996),tc_Nat_Onat,X33996),c_List_Onth(X33996)),X33997)),hAPP(c_List_Ofilter(tc_List_Olist(X33996),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X33996)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33997)),c_Nat_Osize__class_Osize(tc_List_Olist(X33996)))),X33995)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__transpose])]) ).
fof(i_0_6821,plain,
! [X26415,X26416,X26417] :
( ( ~ hBOOL(hAPP(c_Predicate_OPowp(X26417,hAPP(hAPP(c_COMBC(X26417,tc_fun(X26417,tc_HOL_Obool),tc_HOL_Obool),c_member(X26417)),X26416)),X26415))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X26417,tc_HOL_Obool)),X26415),hAPP(c_Set_OPow(X26417),X26416))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26417,tc_HOL_Obool)),X26415),hAPP(c_Set_OPow(X26417),X26416)))
| hBOOL(hAPP(c_Predicate_OPowp(X26417,hAPP(hAPP(c_COMBC(X26417,tc_fun(X26417,tc_HOL_Obool),tc_HOL_Obool),c_member(X26417)),X26416)),X26415)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Powp__Pow__eq])]) ).
fof(i_0_6822,plain,
! [X26505,X26506,X26507,X26508,X26509,X26510] :
( ~ c_Fun_Oinj__on(X26510,X26509,X26508,X26507)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26509,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26510,X26509,X26508),X26507)),X26506))
| ~ c_Fun_Oinj__on(X26509,X26510,X26505,X26506)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26510,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26509,X26510,X26505),X26506)),X26507))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26510),X26507))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26509),X26506))
| hAPP(c_Finite__Set_Ocard(X26510),X26507) = hAPP(c_Finite__Set_Ocard(X26509),X26506) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__bij__eq])]) ).
fof(i_0_6823,plain,
! [X29981,X29982,X29983] : c_Hilbert__Choice_OEps(tc_prod(X29983,X29982),hAPP(c_Product__Type_Oprod_Oprod__case(X29983,X29982,tc_HOL_Obool),X29981)) = c_Hilbert__Choice_OEps(tc_prod(X29983,X29982),hAPP(hAPP(c_COMBS(tc_prod(X29983,X29982),X29982,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X29983,tc_fun(X29982,tc_HOL_Obool),tc_prod(X29983,X29982)),X29981),c_Product__Type_Ofst(X29983,X29982))),c_Product__Type_Osnd(X29983,X29982))),
inference(variable_rename,[status(thm)],[fact_Eps__split]) ).
fof(i_0_6824,plain,
! [X22989,X22990,X22991] : c_HOL_OThe(tc_prod(X22991,X22990),hAPP(c_Product__Type_Oprod_Oprod__case(X22991,X22990,tc_HOL_Obool),X22989)) = c_HOL_OThe(tc_prod(X22991,X22990),hAPP(hAPP(c_COMBS(tc_prod(X22991,X22990),X22990,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X22991,tc_fun(X22990,tc_HOL_Obool),tc_prod(X22991,X22990)),X22989),c_Product__Type_Ofst(X22991,X22990))),c_Product__Type_Osnd(X22991,X22990))),
inference(variable_rename,[status(thm)],[fact_The__split]) ).
fof(i_0_6825,plain,
! [X23439,X23440,X23441,X23442,X23443,X23444] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23442),X23441),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23442),X23443),X23439)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23442),X23441),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23442),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23442),X23443),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23442),X23444),X23440))),X23439)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23442),X23441),X23440))
| ~ class_Rings_Ocomm__ring(X23442)
| ~ class_Rings_Odvd(X23442) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23442),X23441),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23442),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23442),X23443),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23442),X23444),X23440))),X23439)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23442),X23441),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23442),X23443),X23439)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23442),X23441),X23440))
| ~ class_Rings_Ocomm__ring(X23442)
| ~ class_Rings_Odvd(X23442) ) ),
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,
! [X23433,X23434,X23435,X23436,X23437,X23438] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23436),X23435),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23436),X23437),X23433)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23436),X23435),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23436),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23436),X23437),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23436),X23438),X23434))),X23433)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23436),X23435),X23434))
| ~ class_Rings_Ocomm__ring(X23436)
| ~ class_Rings_Odvd(X23436) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23436),X23435),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23436),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23436),X23437),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23436),X23438),X23434))),X23433)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23436),X23435),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23436),X23437),X23433)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23436),X23435),X23434))
| ~ class_Rings_Ocomm__ring(X23436)
| ~ class_Rings_Odvd(X23436) ) ),
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,
! [X20194,X20195,X20196,X20197] :
( ~ class_Divides_Osemiring__div(X20197)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20197),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20197),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20197),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20197),X20196),X20195)),X20195)),c_Divides_Odiv__class_Omod(X20197,X20196,X20195))),X20194) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20197),X20196),X20194) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mod__equality])]) ).
fof(i_0_6828,plain,
! [X26235,X26236,X26237,X26238,X26239] :
( ~ class_Groups_Ocomm__monoid__mult(X26239)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26238),X26237))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26238),X26236))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26238,tc_HOL_Obool)),X26237),X26236) != c_Orderings_Obot__class_Obot(tc_fun(X26238,tc_HOL_Obool))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X26239,X26238,c_Groups_Otimes__class_Otimes(X26239)),X26235),c_Groups_Oone__class_Oone(X26239)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26238,tc_HOL_Obool)),X26237),X26236)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26239),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X26239,X26238,c_Groups_Otimes__class_Otimes(X26239)),X26235),c_Groups_Oone__class_Oone(X26239)),X26237)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X26239,X26238,c_Groups_Otimes__class_Otimes(X26239)),X26235),c_Groups_Oone__class_Oone(X26239)),X26236)) ),
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,
! [X32437,X32438,X32439,X32440] :
( ~ class_Groups_Oab__group__add(X32440)
| hAPP(c_Groups_Ouminus__class_Ouminus(X32440),hAPP(c_List_Omonoid__add__class_Olistsum(X32440),hAPP(hAPP(c_List_Omap(X32439,X32440),X32438),X32437))) = hAPP(c_List_Omonoid__add__class_Olistsum(X32440),hAPP(hAPP(c_List_Omap(X32439,X32440),hAPP(c_Fun_Ocomp(X32440,X32440,X32439,c_Groups_Ouminus__class_Ouminus(X32440)),X32438)),X32437)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_uminus__listsum__map])]) ).
fof(i_0_6831,plain,
! [X29854,X29855,X29856,X29857] : c_New__Random__Sequence_Oneg__map(X29857,X29856,X29855,X29854) = c_New__Random__Sequence_Oneg__bind(X29857,X29856,X29854,hAPP(c_Fun_Ocomp(X29856,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(X29856)))))),X29857,c_New__Random__Sequence_Oneg__single(X29856)),X29855)),
inference(variable_rename,[status(thm)],[fact_neg__map__def]) ).
fof(i_0_6832,plain,
! [X27147,X27148,X27149,X27150] :
( ~ class_Groups_Oordered__ab__group__add__abs(X27150)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27150),c_Groups_Ozero__class_Ozero(X27150)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27149,X27150),hAPP(hAPP(c_COMBB(X27150,X27150,X27149),c_Groups_Oabs__class_Oabs(X27150)),X27148)),X27147))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__abs__ge__zero])]) ).
fof(i_0_6833,plain,
! [X29289,X29290] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29290),X29289))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X29290,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(X29290,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X29290,tc_HOL_Obool),tc_fun(X29290,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X29290,tc_HOL_Obool))),X29289)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Collect__subsets])]) ).
fof(i_0_6834,plain,
! [X19645,X19646,X19647] :
( ( X19646 = c_Groups_Ozero__class_Ozero(X19647)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19647),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19647),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19647),X19646),X19646)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19647),X19645),X19645))),c_Groups_Ozero__class_Ozero(X19647)))
| ~ class_Rings_Olinordered__ring__strict(X19647) )
& ( X19645 = c_Groups_Ozero__class_Ozero(X19647)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19647),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19647),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19647),X19646),X19646)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19647),X19645),X19645))),c_Groups_Ozero__class_Ozero(X19647)))
| ~ class_Rings_Olinordered__ring__strict(X19647) )
& ( X19646 != c_Groups_Ozero__class_Ozero(X19647)
| X19645 != c_Groups_Ozero__class_Ozero(X19647)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19647),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19647),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19647),X19646),X19646)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19647),X19645),X19645))),c_Groups_Ozero__class_Ozero(X19647)))
| ~ class_Rings_Olinordered__ring__strict(X19647) ) ),
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,
! [X25394,X25395] :
( ~ class_Orderings_Olinorder(X25395)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25395),X25394))
| X25394 = c_Orderings_Obot__class_Obot(tc_fun(X25395,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X25395),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25395),esk139_2(X25394,X25395)),esk140_2(X25394,X25395))),hAPP(hAPP(c_Set_Oinsert(X25395),esk139_2(X25394,X25395)),hAPP(hAPP(c_Set_Oinsert(X25395),esk140_2(X25394,X25395)),c_Orderings_Obot__class_Obot(tc_fun(X25395,tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_member(X25395),c_Big__Operators_Olinorder__class_OMin(X25395,X25394)),X25394)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oclosed])])]) ).
fof(i_0_6836,plain,
! [X25390,X25391] :
( ~ class_Orderings_Olinorder(X25391)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25391),X25390))
| X25390 = c_Orderings_Obot__class_Obot(tc_fun(X25391,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X25391),hAPP(hAPP(c_Orderings_Oord__class_Omax(X25391),esk137_2(X25390,X25391)),esk138_2(X25390,X25391))),hAPP(hAPP(c_Set_Oinsert(X25391),esk137_2(X25390,X25391)),hAPP(hAPP(c_Set_Oinsert(X25391),esk138_2(X25390,X25391)),c_Orderings_Obot__class_Obot(tc_fun(X25391,tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_member(X25391),c_Big__Operators_Olinorder__class_OMax(X25391,X25390)),X25390)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oclosed])])]) ).
fof(i_0_6837,plain,
! [X25398,X25399] :
( ~ class_Lattices_Olattice(X25399)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25399),X25398))
| X25398 = c_Orderings_Obot__class_Obot(tc_fun(X25399,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X25399),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25399),esk141_2(X25398,X25399)),esk142_2(X25398,X25399))),hAPP(hAPP(c_Set_Oinsert(X25399),esk141_2(X25398,X25399)),hAPP(hAPP(c_Set_Oinsert(X25399),esk142_2(X25398,X25399)),c_Orderings_Obot__class_Obot(tc_fun(X25399,tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_member(X25399),c_Big__Operators_Olattice__class_OInf__fin(X25399,X25398)),X25398)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oclosed])])]) ).
fof(i_0_6838,plain,
! [X25161,X25162] :
( ~ class_Lattices_Olattice(X25162)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25162),X25161))
| X25161 = c_Orderings_Obot__class_Obot(tc_fun(X25162,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X25162),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25162),esk133_2(X25161,X25162)),esk134_2(X25161,X25162))),hAPP(hAPP(c_Set_Oinsert(X25162),esk133_2(X25161,X25162)),hAPP(hAPP(c_Set_Oinsert(X25162),esk134_2(X25161,X25162)),c_Orderings_Obot__class_Obot(tc_fun(X25162,tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_member(X25162),c_Big__Operators_Olattice__class_OSup__fin(X25162,X25161)),X25161)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oclosed])])]) ).
fof(i_0_6839,plain,
! [X19002,X19003,X19004] :
( ~ class_Rings_Olinordered__ring(X19004)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19004),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19004),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19004),X19003),X19003)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19004),X19002),X19002))),c_Groups_Ozero__class_Ozero(X19004))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5438])]) ).
fof(i_0_6840,plain,
! [X27877,X27878,X27879,X27880,X27881,X27882,X27883,X27884] :
( ~ c_Finite__Set_Ofolding__image(X27884,X27883,X27882,X27881,X27880)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27883),X27879))
| ~ c_Fun_Oinj__on(X27883,X27883,X27878,X27879)
| hAPP(hAPP(X27880,X27877),hAPP(c_Set_Oimage(X27883,X27883,X27878),X27879)) = hAPP(hAPP(X27880,hAPP(c_Fun_Ocomp(X27883,X27884,X27883,X27877),X27878)),X27879) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image_Oreindex])]) ).
fof(i_0_6841,plain,
! [X34358,X34359,X34360] :
( ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X34360),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X34360))),X34359)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34358),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34360))),X34359)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34360))),hAPP(c_List_Ofilter(tc_List_Olist(X34360),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X34360)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34358)),c_Nat_Osize__class_Osize(tc_List_Olist(X34360)))),c_List_Otranspose(X34360,X34359))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34360)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X34360)),X34359),X34358)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose__column__length])]) ).
fof(i_0_6842,plain,
! [X24398,X24399,X24400,X24401,X24402,X24403,X24404] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24404,X24403)),hAPP(hAPP(c_Product__Type_OPair(X24404,X24403),X24402),X24401)),X24400))
| hBOOL(hAPP(hAPP(c_member(X24399),hAPP(hAPP(X24398,X24402),X24401)),hAPP(c_Set_Oimage(tc_prod(X24404,X24403),X24399,hAPP(c_Product__Type_Oprod_Oprod__case(X24404,X24403,X24399),X24398)),X24400))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__imageI])]) ).
fof(i_0_6843,plain,
! [X31988,X31989,X31990,X31991,X31992] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31992,X31991)),hAPP(hAPP(c_Product__Type_OPair(X31992,X31991),X31990),X31989)),hAPP(c_List_Oset(tc_prod(X31992,X31991)),X31988)))
| hAPP(c_Map_Omap__of(X31992,X31991,X31988),X31990) = hAPP(c_Option_Ooption_OSome(X31991),esk440_5(X31988,X31989,X31990,X31991,X31992)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_weak__map__of__SomeI])])]) ).
fof(i_0_6844,plain,
! [X33850,X33851,X33852,X33853,X33854] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33854)),hAPP(c_List_Ofilter(X33854,X33853),hAPP(hAPP(c_List_Omap(X33852,X33854),X33851),X33850))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33852)),hAPP(c_List_Ofilter(X33852,hAPP(c_Fun_Ocomp(X33854,tc_HOL_Obool,X33852,X33853),X33851)),X33850)),
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,
! [X30316,X30317,X30318,X30319,X30320] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30320,X30320)),hAPP(hAPP(c_Product__Type_OPair(X30320,X30320),X30319),X30318)),c_Transitive__Closure_Ortrancl(X30320,X30317)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30320,X30320),tc_HOL_Obool)),X30317),hAPP(hAPP(c_Product__Type_OSigma(X30320,X30320),X30316),hAPP(c_COMBK(tc_fun(X30320,tc_HOL_Obool),X30320),X30316))))
| X30319 = X30318
| hBOOL(hAPP(hAPP(c_member(X30320),X30319),X30316)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__subset__Sigma__aux])]) ).
fof(i_0_6847,plain,
! [X24234,X24235,X24236,X24237,X24238,X24239] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24239,tc_fun(X24238,tc_HOL_Obool))),X24237),X24236),X24235),X24234))
| hBOOL(hAPP(hAPP(X24237,X24235),X24234))
| hBOOL(hAPP(hAPP(X24236,X24235),X24234)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5440])]) ).
fof(i_0_6848,plain,
! [X33903,X33904,X33905] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33905)),hAPP(c_List_Ofilter(X33905,X33904),X33903))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33905)),hAPP(c_List_Ofilter(X33905,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X33905),c_fNot),X33904)),X33903))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33905)),X33903),
inference(variable_rename,[status(thm)],[fact_sum__length__filter__compl]) ).
fof(i_0_6849,plain,
! [X30200,X30201,X30202,X30203,X30204] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30204,X30204)),hAPP(hAPP(c_Product__Type_OPair(X30204,X30204),X30203),X30202)),c_Transitive__Closure_Ortrancl(X30204,X30201)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30204,X30204)),hAPP(hAPP(c_Product__Type_OPair(X30204,X30204),X30202),X30200)),c_Transitive__Closure_Ortrancl(X30204,X30201)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30204,X30204)),hAPP(hAPP(c_Product__Type_OPair(X30204,X30204),X30203),X30200)),c_Transitive__Closure_Ortrancl(X30204,X30201))) ),
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,
! [X20074,X20075,X20076] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20076),X20075)),X20074) = 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),X20076),X20074)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20075),X20074))),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,X20076,X20074)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20075,X20074))),X20074)),
inference(variable_rename,[status(thm)],[fact_zdiv__zadd1__eq]) ).
fof(i_0_6853,plain,
! [X19994,X19995,X19996] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19996),X19995)),X19994) = 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),X19996),X19994)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19995),X19994))),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,X19996,X19994)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19995,X19994))),X19994)),
inference(variable_rename,[status(thm)],[fact_div__add1__eq]) ).
fof(i_0_6854,plain,
! [X25175,X25176,X25177,X25178,X25179,X25180] :
( ( hBOOL(hAPP(hAPP(X25178,X25176),X25175))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25180,tc_fun(X25179,tc_HOL_Obool))),X25178),X25177),X25176),X25175)) )
& ( hBOOL(hAPP(hAPP(X25177,X25176),X25175))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25180,tc_fun(X25179,tc_HOL_Obool))),X25178),X25177),X25176),X25175)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5443])])]) ).
fof(i_0_6855,plain,
! [X25181,X25182,X25183,X25184,X25185,X25186] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25186,tc_fun(X25185,tc_HOL_Obool))),X25184),X25183),X25182),X25181))
| hBOOL(hAPP(hAPP(X25184,X25182),X25181)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2D1])]) ).
fof(i_0_6856,plain,
! [X25187,X25188,X25189,X25190,X25191,X25192] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25192,tc_fun(X25191,tc_HOL_Obool))),X25190),X25189),X25188),X25187))
| hBOOL(hAPP(hAPP(X25189,X25188),X25187)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2D2])]) ).
cnf(i_0_6857,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk495_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_5240]) ).
cnf(i_0_6858,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk494_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_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,
! [X30190,X30191,X30192,X30193,X30194] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30194,X30194)),hAPP(hAPP(c_Product__Type_OPair(X30194,X30194),X30193),X30192)),X30191))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30194,X30194)),hAPP(hAPP(c_Product__Type_OPair(X30194,X30194),X30192),X30190)),c_Transitive__Closure_Ortrancl(X30194,X30191)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30194,X30194)),hAPP(hAPP(c_Product__Type_OPair(X30194,X30194),X30193),X30190)),c_Transitive__Closure_Ortrancl(X30194,X30191))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converse__rtrancl__into__rtrancl])]) ).
fof(i_0_6864,plain,
! [X30195,X30196,X30197,X30198,X30199] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30199,X30199)),hAPP(hAPP(c_Product__Type_OPair(X30199,X30199),X30198),X30197)),c_Transitive__Closure_Ortrancl(X30199,X30196)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30199,X30199)),hAPP(hAPP(c_Product__Type_OPair(X30199,X30199),X30197),X30195)),X30196))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30199,X30199)),hAPP(hAPP(c_Product__Type_OPair(X30199,X30199),X30198),X30195)),c_Transitive__Closure_Ortrancl(X30199,X30196))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl_Ortrancl__into__rtrancl])]) ).
fof(i_0_6865,plain,
! [X33250,X33251,X33252,X33253] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33253),tc_List_Olist(X33253))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33253),tc_List_Olist(X33253)),X33252),X33251)),c_List_Olistrel(X33253,X33250)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33253),tc_List_Olist(X33253))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33253),tc_List_Olist(X33253)),X33252),X33251)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X33253),c_List_Olistrel1(X33253,X33250)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__if__listrel])]) ).
fof(i_0_6866,plain,
! [X27891,X27892,X27893,X27894,X27895,X27896,X27897,X27898,X27899,X27900,X27901] :
( ~ c_Finite__Set_Ofolding(X27901,X27900,X27899,X27898)
| hAPP(c_Fun_Ocomp(X27897,X27896,X27895,X27894),hAPP(c_Fun_Ocomp(X27893,X27897,X27895,X27892),X27891)) = hAPP(c_Fun_Ocomp(X27893,X27896,X27895,hAPP(c_Fun_Ocomp(X27897,X27896,X27893,X27894),X27892)),X27891) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comps_I1_J])]) ).
fof(i_0_6867,plain,
! [X19711,X19712,X19713,X19714,X19715,X19716] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19716),X19715)),X19714) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19713),X19712)),X19711)
| ~ 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),X19713),X19712)),X19711)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19714),X19716))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19711))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19713))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19713),X19716))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19712),X19715)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg__lemma])]) ).
fof(i_0_6868,plain,
! [X29323] : 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)))),X29323)) = 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),X29323),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,
! [X33254,X33255,X33256,X33257] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33257),tc_List_Olist(X33257))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33257),tc_List_Olist(X33257)),X33256),X33255)),c_List_Olistrel1(X33257,X33254)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33257),tc_List_Olist(X33257))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33257),tc_List_Olist(X33257)),X33256),X33255)),c_List_Olistrel(X33257,c_Transitive__Closure_Ortrancl(X33257,X33254)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__reflcl__if__listrel1])]) ).
fof(i_0_6870,plain,
! [X32590,X32591,X32592,X32593] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32593),tc_List_Olist(X32593))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32593),tc_List_Olist(X32593)),X32592),X32591)),c_List_Olexord(X32593,X32590)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32593),tc_List_Olist(X32593))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32593),tc_List_Olist(X32593)),X32592),X32591)),c_List_Olex(X32593,X32590))) )
& ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32593)),X32592) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32593)),X32591)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32593),tc_List_Olist(X32593))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32593),tc_List_Olist(X32593)),X32592),X32591)),c_List_Olex(X32593,X32590))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32593),tc_List_Olist(X32593))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32593),tc_List_Olist(X32593)),X32592),X32591)),c_List_Olexord(X32593,X32590)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32593)),X32592) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32593)),X32591)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32593),tc_List_Olist(X32593))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32593),tc_List_Olist(X32593)),X32592),X32591)),c_List_Olex(X32593,X32590))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__lex])])]) ).
fof(i_0_6871,plain,
! [X33920,X33921,X33922,X33923,X33924] : hAPP(c_List_Ofilter(X33924,X33923),hAPP(hAPP(c_List_Omap(X33922,X33924),X33921),X33920)) = hAPP(hAPP(c_List_Omap(X33922,X33924),X33921),hAPP(c_List_Ofilter(X33922,hAPP(c_Fun_Ocomp(X33924,tc_HOL_Obool,X33922,X33923),X33921)),X33920)),
inference(variable_rename,[status(thm)],[fact_filter__map]) ).
fof(i_0_6872,plain,
! [X29950,X29951,X29952] :
( ( hAPP(X29951,esk342_3(X29950,X29951,X29952)) != hAPP(X29951,esk343_3(X29950,X29951,X29952))
| c_Wellfounded_OwfP(X29952,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29950,tc_fun(X29952,tc_fun(X29952,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X29950,tc_HOL_Obool))),X29951))
| ~ c_Wellfounded_OwfP(X29952,hAPP(X29951,esk341_3(X29950,X29951,X29952))) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29952,tc_HOL_Obool)),c_Predicate_ODomainP(X29952,X29952,hAPP(X29951,esk342_3(X29950,X29951,X29952)))),c_Predicate_ORangeP(X29952,X29952,hAPP(X29951,esk343_3(X29950,X29951,X29952)))) != c_Orderings_Obot__class_Obot(tc_fun(X29952,tc_HOL_Obool))
| c_Wellfounded_OwfP(X29952,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29950,tc_fun(X29952,tc_fun(X29952,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X29950,tc_HOL_Obool))),X29951))
| ~ c_Wellfounded_OwfP(X29952,hAPP(X29951,esk341_3(X29950,X29951,X29952))) ) ),
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,
! [X33917,X33918,X33919] : c_List_Opartition(X33919,X33918,X33917) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33919),tc_List_Olist(X33919)),hAPP(c_List_Ofilter(X33919,X33918),X33917)),hAPP(c_List_Ofilter(X33919,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X33919,c_fNot),X33918)),X33917)),
inference(variable_rename,[status(thm)],[fact_partition__filter__conv]) ).
fof(i_0_6874,plain,
! [X32920,X32921,X32922] :
( ( 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),esk457_3(X32920,X32921,X32922)),esk458_3(X32920,X32921,X32922))))
| hBOOL(hAPP(hAPP(X32920,X32922),X32921))
| ~ 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),X32922),X32921))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk457_3(X32920,X32921,X32922)),esk458_3(X32920,X32921,X32922)))
| hBOOL(hAPP(hAPP(X32920,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk457_3(X32920,X32921,X32922)),c_Groups_Oone__class_Oone(tc_Int_Oint))),esk458_3(X32920,X32921,X32922)))
| hBOOL(hAPP(hAPP(X32920,X32922),X32921))
| ~ 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),X32922),X32921))) )
& ( ~ hBOOL(hAPP(hAPP(X32920,esk457_3(X32920,X32921,X32922)),esk458_3(X32920,X32921,X32922)))
| hBOOL(hAPP(hAPP(X32920,X32922),X32921))
| ~ 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),X32922),X32921))) ) ),
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,
! [X32946,X32947,X32948,X32949,X32950,X32951] : c_Map_Omap__add(X32951,X32950,X32949,c_Map_Omap__upds(X32951,X32950,X32948,X32947,X32946)) = c_Map_Omap__upds(X32951,X32950,c_Map_Omap__add(X32951,X32950,X32949,X32948),X32947,X32946),
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,
! [X23819,X23820] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23820),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23820),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23820),c_Groups_Oone__class_Oone(X23820)),X23819)),X23819)),c_Groups_Ozero__class_Ozero(X23820)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23820),X23819),c_Groups_Ozero__class_Ozero(X23820)))
| ~ hBOOL(hAPP(hAPP(c_member(X23820),X23819),c_Int_Oring__1__class_OInts(X23820)))
| ~ class_Rings_Olinordered__idom(X23820) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23820),X23819),c_Groups_Ozero__class_Ozero(X23820)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23820),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23820),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23820),c_Groups_Oone__class_Oone(X23820)),X23819)),X23819)),c_Groups_Ozero__class_Ozero(X23820)))
| ~ hBOOL(hAPP(hAPP(c_member(X23820),X23819),c_Int_Oring__1__class_OInts(X23820)))
| ~ class_Rings_Olinordered__idom(X23820) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__odd__less__0])])]) ).
fof(i_0_6878,plain,
! [X20164,X20165,X20166] : 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),X20166),X20165)),X20165)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20166,X20165))),X20164) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20166),X20164),
inference(variable_rename,[status(thm)],[fact_zdiv__zmod__equality2]) ).
fof(i_0_6879,plain,
! [X23522,X23523,X23524,X23525,X23526] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23526),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23524),X23523)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23526),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23524),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23522),X23525))),X23523)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23526),X23525)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23526),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23524),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23522),X23525))),X23523)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23526),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23524),X23523)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23526),X23525)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__period])])]) ).
fof(i_0_6880,plain,
! [X32979,X32980,X32981,X32982,X32983] : c_Map_Odom(X32983,X32982,c_Map_Omap__upds(X32983,X32982,X32981,X32980,X32979)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X32983,tc_HOL_Obool)),hAPP(c_List_Oset(X32983),hAPP(hAPP(c_List_Otake(X32983),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32982)),X32979)),X32980))),c_Map_Odom(X32983,X32982,X32981)),
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),esk369_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,
! [X33640,X33641,X33642,X33643] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X33643)
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33642,X33643),hAPP(c_List_Oset(X33642),X33641)),X33640) = hAPP(c_List_Ofoldl(X33643,X33642,hAPP(c_COMBC(X33642,X33643,X33643),hAPP(hAPP(c_COMBB(X33643,tc_fun(X33643,X33643),X33642),c_Lattices_Osemilattice__inf__class_Oinf(X33643)),X33640)),c_Orderings_Otop__class_Otop(X33643)),X33641) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INFI__set__fold])]) ).
fof(i_0_6884,plain,
! [X33636,X33637,X33638,X33639] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X33639)
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33638,X33639),hAPP(c_List_Oset(X33638),X33637)),X33636) = hAPP(c_List_Ofoldl(X33639,X33638,hAPP(c_COMBC(X33638,X33639,X33639),hAPP(hAPP(c_COMBB(X33639,tc_fun(X33639,X33639),X33638),c_Lattices_Osemilattice__sup__class_Osup(X33639)),X33636)),c_Orderings_Obot__class_Obot(X33639)),X33637) ),
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,
! [X29942,X29943,X29944,X29945] :
( ( hBOOL(hAPP(hAPP(c_member(X29945),esk339_4(X29942,X29943,X29944,X29945)),X29944))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29943),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29945,tc_fun(X29943,tc_HOL_Obool)),X29944),X29942)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29945),X29944)) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29943),hAPP(X29942,esk339_4(X29942,X29943,X29944,X29945))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29943),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29945,tc_fun(X29943,tc_HOL_Obool)),X29944),X29942)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29945),X29944)) ) ),
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,
! [X25805,X25806,X25807,X25808,X25809] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25806),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25808,tc_fun(X25806,tc_HOL_Obool)),X25807),X25805)))
| ~ hBOOL(hAPP(hAPP(c_member(X25808),X25809),X25807))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X25806),hAPP(X25805,X25809)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25808),X25807)) )
& ( hBOOL(hAPP(hAPP(c_member(X25808),esk158_4(X25805,X25806,X25807,X25808)),X25807))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X25806),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25808,tc_fun(X25806,tc_HOL_Obool)),X25807),X25805)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25808),X25807)) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25806),hAPP(X25805,esk158_4(X25805,X25806,X25807,X25808))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X25806),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25808,tc_fun(X25806,tc_HOL_Obool)),X25807),X25805)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25808),X25807)) ) ),
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,
! [X29477,X29478,X29479,X29480,X29481,X29482,X29483] : hAPP(hAPP(c_Relation_Orel__comp(X29483,X29482,X29481),X29480),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29479,tc_fun(tc_prod(X29482,X29481),tc_HOL_Obool)),X29478),X29477)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29479,tc_fun(tc_prod(X29483,X29481),tc_HOL_Obool)),X29478),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X29482,X29481),tc_HOL_Obool),tc_fun(tc_prod(X29483,X29481),tc_HOL_Obool),X29479),hAPP(c_Relation_Orel__comp(X29483,X29482,X29481),X29480)),X29477)),
inference(variable_rename,[status(thm)],[fact_rel__comp__UNION__distrib]) ).
fof(i_0_6889,plain,
! [X27695,X27696,X27697,X27698,X27699,X27700,X27701] : hAPP(c_Fun_Ocomp(X27701,X27700,X27699,X27698),hAPP(c_Fun_Ocomp(X27697,X27701,X27699,X27696),X27695)) = hAPP(c_Fun_Ocomp(X27697,X27700,X27699,hAPP(c_Fun_Ocomp(X27701,X27700,X27697,X27698),X27696)),X27695),
inference(variable_rename,[status(thm)],[fact_o__assoc]) ).
fof(i_0_6890,plain,
! [X28294,X28295,X28296,X28297] :
( hAPP(c_Set_Oimage(X28297,X28296,X28295),c_Orderings_Otop__class_Otop(tc_fun(X28297,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X28296,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28296,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28296,tc_HOL_Obool)),hAPP(c_Set_Oimage(X28297,X28296,X28295),X28294))),hAPP(c_Set_Oimage(X28297,X28296,X28295),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28297,tc_HOL_Obool)),X28294)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__Compl__image__subset])]) ).
fof(i_0_6891,plain,
! [X24215,X24216,X24217,X24218,X24219,X24220] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24220,X24220)),hAPP(hAPP(c_Product__Type_OPair(X24220,X24220),X24219),X24218)),hAPP(hAPP(c_Relation_Oinv__image(X24217,X24220),X24216),X24215)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X24217,X24217)),hAPP(hAPP(c_Product__Type_OPair(X24217,X24217),hAPP(X24215,X24219)),hAPP(X24215,X24218))),X24216)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24217,X24217)),hAPP(hAPP(c_Product__Type_OPair(X24217,X24217),hAPP(X24215,X24219)),hAPP(X24215,X24218))),X24216))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X24220,X24220)),hAPP(hAPP(c_Product__Type_OPair(X24220,X24220),X24219),X24218)),hAPP(hAPP(c_Relation_Oinv__image(X24217,X24220),X24216),X24215))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__inv__image])]) ).
fof(i_0_6892,plain,
! [X27871,X27872,X27873,X27874,X27875,X27876] :
( ~ c_Finite__Set_Ofolding(X27876,X27875,X27874,X27873)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27876),X27872))
| ~ hBOOL(hAPP(hAPP(c_member(X27876),X27871),X27872))
| hAPP(X27873,X27872) = hAPP(c_Fun_Ocomp(X27875,X27875,X27875,hAPP(X27873,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27876,tc_HOL_Obool)),X27872),hAPP(hAPP(c_Set_Oinsert(X27876),X27871),c_Orderings_Obot__class_Obot(tc_fun(X27876,tc_HOL_Obool)))))),hAPP(X27874,X27871)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Oremove])]) ).
fof(i_0_6893,plain,
! [X28750,X28751,X28752,X28753,X28754,X28755] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28755,X28754),tc_HOL_Obool)),X28753),hAPP(hAPP(c_Product__Type_OSigma(X28755,X28754),X28752),hAPP(c_COMBK(tc_fun(X28754,tc_HOL_Obool),X28755),X28751))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28754,tc_HOL_Obool)),hAPP(c_Relation_OImage(X28755,X28754,X28753),X28750)),X28751)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__subset])]) ).
fof(i_0_6894,plain,
! [X33524,X33525,X33526] : hAPP(c_List_Otl(X33526),hAPP(hAPP(c_List_Oappend(X33526),X33525),X33524)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(X33526),X33526,hAPP(c_List_Otl(X33526),X33524),hAPP(c_COMBK(tc_fun(tc_List_Olist(X33526),tc_List_Olist(X33526)),X33526),hAPP(hAPP(c_COMBC(tc_List_Olist(X33526),tc_List_Olist(X33526),tc_List_Olist(X33526)),c_List_Oappend(X33526)),X33524))),X33525),
inference(variable_rename,[status(thm)],[fact_tl__append]) ).
fof(i_0_6895,plain,
! [X29872,X29873,X29874,X29875] : c_New__Random__Sequence_Opos__map(X29875,X29874,X29873,X29872) = c_New__Random__Sequence_Opos__bind(X29875,X29874,X29872,hAPP(c_Fun_Ocomp(X29874,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(X29874))))),X29875,c_New__Random__Sequence_Opos__single(X29874)),X29873)),
inference(variable_rename,[status(thm)],[fact_pos__map__def]) ).
fof(i_0_6896,plain,
! [X28312,X28313,X28314,X28315] :
( ~ c_Fun_Oinj__on(X28315,X28314,X28313,c_Orderings_Otop__class_Otop(tc_fun(X28315,tc_HOL_Obool)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28314,tc_HOL_Obool)),hAPP(c_Set_Oimage(X28315,X28314,X28313),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28315,tc_HOL_Obool)),X28312))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28314,tc_HOL_Obool)),hAPP(c_Set_Oimage(X28315,X28314,X28313),X28312)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__image__Compl__subset])]) ).
fof(i_0_6897,plain,
! [X27984,X27985,X27986,X27987,X27988,X27989] :
( ~ c_Finite__Set_Ofolding(X27989,X27988,X27987,X27986)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27989),X27985))
| hAPP(X27986,hAPP(hAPP(c_Set_Oinsert(X27989),X27984),X27985)) = hAPP(c_Fun_Ocomp(X27988,X27988,X27988,hAPP(X27986,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27989,tc_HOL_Obool)),X27985),hAPP(hAPP(c_Set_Oinsert(X27989),X27984),c_Orderings_Obot__class_Obot(tc_fun(X27989,tc_HOL_Obool)))))),hAPP(X27987,X27984)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Oinsert__remove])]) ).
fof(i_0_6898,plain,
! [X32885,X32886,X32887,X32888] :
( ~ hBOOL(hAPP(c_List_Odistinct(X32888),X32887))
| hBOOL(hAPP(hAPP(c_member(X32888),X32886),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X32888,tc_HOL_Obool)),hAPP(c_List_Oset(X32888),X32887)),hAPP(hAPP(c_Set_Oinsert(X32888),hAPP(hAPP(c_List_Onth(X32888),X32887),X32885)),c_Orderings_Obot__class_Obot(tc_fun(X32888,tc_HOL_Obool))))))
| hBOOL(hAPP(c_List_Odistinct(X32888),hAPP(hAPP(c_List_Olist__update(X32888,X32887),X32885),X32886))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5452])]) ).
fof(i_0_6899,plain,
! [X26490,X26491,X26492,X26493] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X26493),hAPP(c_Set_Oimage(X26492,X26493,X26491),X26490))),hAPP(c_Finite__Set_Ocard(X26492),X26490)))
| ~ c_Fun_Oinj__on(X26492,X26493,X26491,X26490) ),
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_5454]) ).
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_5441]) ).
fof(i_0_6902,plain,
! [X27937,X27938,X27939,X27940,X27941,X27942,X27943,X27944] :
( ~ c_Finite__Set_Ofolding(X27944,X27943,X27942,X27941)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27944),X27940))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27944),X27939))
| hAPP(c_Fun_Ocomp(X27943,X27943,X27938,hAPP(X27941,X27939)),hAPP(c_Fun_Ocomp(X27943,X27943,X27938,hAPP(X27941,X27940)),X27937)) = hAPP(c_Fun_Ocomp(X27943,X27943,X27938,hAPP(X27941,X27940)),hAPP(c_Fun_Ocomp(X27943,X27943,X27938,hAPP(X27941,X27939)),X27937)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp_H_H])]) ).
fof(i_0_6903,plain,
! [X31981,X31982,X31983,X31984,X31985] :
( ~ hBOOL(hAPP(c_List_Odistinct(X31985),hAPP(hAPP(c_List_Omap(tc_prod(X31985,X31984),X31985),c_Product__Type_Ofst(X31985,X31984)),X31983)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31985,X31984)),hAPP(hAPP(c_Product__Type_OPair(X31985,X31984),X31982),X31981)),hAPP(c_List_Oset(tc_prod(X31985,X31984)),X31983)))
| hAPP(c_Map_Omap__of(X31985,X31984,X31983),X31982) = hAPP(c_Option_Ooption_OSome(X31984),X31981) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__is__SomeI])]) ).
fof(i_0_6904,plain,
! [X31976,X31977,X31978,X31979,X31980] :
( ( hAPP(c_Map_Omap__of(X31980,X31979,X31978),X31977) != hAPP(c_Option_Ooption_OSome(X31979),X31976)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X31980,X31979)),hAPP(hAPP(c_Product__Type_OPair(X31980,X31979),X31977),X31976)),hAPP(c_List_Oset(tc_prod(X31980,X31979)),X31978)))
| ~ hBOOL(hAPP(c_List_Odistinct(X31980),hAPP(hAPP(c_List_Omap(tc_prod(X31980,X31979),X31980),c_Product__Type_Ofst(X31980,X31979)),X31978))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31980,X31979)),hAPP(hAPP(c_Product__Type_OPair(X31980,X31979),X31977),X31976)),hAPP(c_List_Oset(tc_prod(X31980,X31979)),X31978)))
| hAPP(c_Map_Omap__of(X31980,X31979,X31978),X31977) = hAPP(c_Option_Ooption_OSome(X31979),X31976)
| ~ hBOOL(hAPP(c_List_Odistinct(X31980),hAPP(hAPP(c_List_Omap(tc_prod(X31980,X31979),X31980),c_Product__Type_Ofst(X31980,X31979)),X31978))) ) ),
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,
! [X31971,X31972,X31973,X31974,X31975] :
( ( hAPP(c_Option_Ooption_OSome(X31974),X31972) != hAPP(c_Map_Omap__of(X31975,X31974,X31973),X31971)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X31975,X31974)),hAPP(hAPP(c_Product__Type_OPair(X31975,X31974),X31971),X31972)),hAPP(c_List_Oset(tc_prod(X31975,X31974)),X31973)))
| ~ hBOOL(hAPP(c_List_Odistinct(X31975),hAPP(hAPP(c_List_Omap(tc_prod(X31975,X31974),X31975),c_Product__Type_Ofst(X31975,X31974)),X31973))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31975,X31974)),hAPP(hAPP(c_Product__Type_OPair(X31975,X31974),X31971),X31972)),hAPP(c_List_Oset(tc_prod(X31975,X31974)),X31973)))
| hAPP(c_Option_Ooption_OSome(X31974),X31972) = hAPP(c_Map_Omap__of(X31975,X31974,X31973),X31971)
| ~ hBOOL(hAPP(c_List_Odistinct(X31975),hAPP(hAPP(c_List_Omap(tc_prod(X31975,X31974),X31975),c_Product__Type_Ofst(X31975,X31974)),X31973))) ) ),
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,
! [X28900,X28901,X28902,X28903] :
( ( hBOOL(hAPP(hAPP(c_member(X28903),esk294_4(X28900,X28901,X28902,X28903)),X28902))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28903,X28901)),hAPP(hAPP(c_Product__Type_OSigma(X28903,X28901),X28902),X28900)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28903),X28902)) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28901),hAPP(X28900,esk294_4(X28900,X28901,X28902,X28903))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28903,X28901)),hAPP(hAPP(c_Product__Type_OSigma(X28903,X28901),X28902),X28900)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28903),X28902)) ) ),
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,
! [X19681,X19682,X19683,X19684,X19685,X19686] :
( ~ class_Rings_Olinordered__semiring__1(X19686)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19686),X19685),X19684))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19686),X19683),X19684))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19686),c_Groups_Ozero__class_Ozero(X19686)),X19682))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19686),c_Groups_Ozero__class_Ozero(X19686)),X19681))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19686),X19682),X19681) != c_Groups_Oone__class_Oone(X19686)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19686),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19686),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19686),X19682),X19685)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19686),X19681),X19683))),X19684)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__le])]) ).
fof(i_0_6908,plain,
! [X19022,X19023,X19024,X19025,X19026,X19027] :
( ~ class_Rings_Olinordered__semiring__1__strict(X19027)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19027),X19026),X19025))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19027),X19024),X19025))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19027),c_Groups_Ozero__class_Ozero(X19027)),X19023))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19027),c_Groups_Ozero__class_Ozero(X19027)),X19022))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19027),X19023),X19022) != c_Groups_Oone__class_Oone(X19027)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19027),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19027),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19027),X19023),X19026)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19027),X19022),X19024))),X19025)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__lt])]) ).
fof(i_0_6909,plain,
! [X26686,X26687,X26688,X26689] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk202_4(X26686,X26687,X26688,X26689)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26688)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26689),X26687))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26689),X26688)),X26687))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26687),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26686))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26688)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk203_4(X26686,X26687,X26688,X26689)),X26686))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26689),X26687))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26689),X26688)),X26687))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26687),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26686))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26688)) )
& ( X26689 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk203_4(X26686,X26687,X26688,X26689)),esk202_4(X26686,X26687,X26688,X26689))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26689),X26687))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26689),X26688)),X26687))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26687),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26686))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26688)) ) ),
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,
! [X27951,X27952,X27953,X27954,X27955,X27956,X27957,X27958] :
( ~ c_Finite__Set_Ofolding(X27958,X27957,X27956,X27955)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27958),X27954))
| hAPP(c_Fun_Ocomp(X27957,X27957,X27953,hAPP(X27956,X27952)),hAPP(c_Fun_Ocomp(X27957,X27957,X27953,hAPP(X27955,X27954)),X27951)) = hAPP(c_Fun_Ocomp(X27957,X27957,X27953,hAPP(X27955,X27954)),hAPP(c_Fun_Ocomp(X27957,X27957,X27953,hAPP(X27956,X27952)),X27951)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp_H])]) ).
fof(i_0_6911,plain,
! [X33272,X33273,X33274,X33275,X33276,X33277,X33278,X33279] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33279,X33279)),hAPP(hAPP(c_Product__Type_OPair(X33279,X33279),X33278),X33277)),X33276))
| X33275 != hAPP(hAPP(c_List_Oappend(X33279),X33274),hAPP(hAPP(c_List_Olist_OCons(X33279),X33278),X33273))
| X33272 != hAPP(hAPP(c_List_Oappend(X33279),X33274),hAPP(hAPP(c_List_Olist_OCons(X33279),X33277),X33273))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33279),tc_List_Olist(X33279))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33279),tc_List_Olist(X33279)),X33275),X33272)),c_List_Olistrel1(X33279,X33276))) ),
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,
! [X22846,X22847,X22848,X22849,X22850,X22851,X22852] :
( ( X22849 = X22847
| c_Sum__Type_Osum_Osum__case(X22852,X22851,X22850,X22849,X22848) != c_Sum__Type_Osum_Osum__case(X22852,X22851,X22850,X22847,X22846) )
& ( X22848 = X22846
| c_Sum__Type_Osum_Osum__case(X22852,X22851,X22850,X22849,X22848) != c_Sum__Type_Osum_Osum__case(X22852,X22851,X22850,X22847,X22846) ) ),
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,
! [X31490,X31491,X31492,X31493] :
( ( hBOOL(hAPP(hAPP(c_member(X31493),esk418_4(X31490,X31491,X31492,X31493)),X31492))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31493),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X31493),X31491),X31490)),hAPP(hAPP(c_Finite__Set_Ofold(X31493,X31493,c_Lattices_Osemilattice__inf__class_Oinf(X31493)),X31490),X31492)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31493),X31492))
| ~ class_Lattices_Osemilattice__inf(X31493) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31493),X31491),esk418_4(X31490,X31491,X31492,X31493)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31493),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X31493),X31491),X31490)),hAPP(hAPP(c_Finite__Set_Ofold(X31493,X31493,c_Lattices_Osemilattice__inf__class_Oinf(X31493)),X31490),X31492)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31493),X31492))
| ~ class_Lattices_Osemilattice__inf(X31493) ) ),
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,
! [X31481,X31482,X31483,X31484] :
( ( hBOOL(hAPP(hAPP(c_member(X31484),esk416_4(X31481,X31482,X31483,X31484)),X31483))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31484),hAPP(hAPP(c_Orderings_Oord__class_Omin(X31484),X31482),X31481)),hAPP(hAPP(c_Finite__Set_Ofold(X31484,X31484,c_Orderings_Oord__class_Omin(X31484)),X31481),X31483)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31484),X31483))
| ~ class_Orderings_Olinorder(X31484) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31484),X31482),esk416_4(X31481,X31482,X31483,X31484)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31484),hAPP(hAPP(c_Orderings_Oord__class_Omin(X31484),X31482),X31481)),hAPP(hAPP(c_Finite__Set_Ofold(X31484,X31484,c_Orderings_Oord__class_Omin(X31484)),X31481),X31483)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31484),X31483))
| ~ class_Orderings_Olinorder(X31484) ) ),
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,
! [X27245,X27246,X27247,X27248,X27249] :
( ~ class_Groups_Ocomm__monoid__add(X27249)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27249),X27248),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27247),X27246)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27245),X27246))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27249),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X27249,tc_Nat_Onat),X27248),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X27246))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X27247),X27245)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__nat__ivl])]) ).
fof(i_0_6919,plain,
! [X30207,X30208,X30209,X30210] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30210,X30210)),X30209),c_Transitive__Closure_Ortrancl(X30210,X30208)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30210,X30210)),X30209),c_Transitive__Closure_Ortrancl(X30210,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30210,X30210),tc_HOL_Obool)),X30208),X30207)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30210,X30210)),X30209),c_Transitive__Closure_Ortrancl(X30210,X30207)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30210,X30210)),X30209),c_Transitive__Closure_Ortrancl(X30210,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30210,X30210),tc_HOL_Obool)),X30208),X30207)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rtrancl__UnI])])]) ).
fof(i_0_6920,plain,
! [X27908,X27909,X27910,X27911,X27912,X27913,X27914,X27915] :
( ~ c_Finite__Set_Ofolding(X27915,X27914,X27913,X27912)
| hAPP(c_Fun_Ocomp(X27914,X27914,X27911,hAPP(X27913,X27910)),hAPP(c_Fun_Ocomp(X27914,X27914,X27911,hAPP(X27913,X27909)),X27908)) = hAPP(c_Fun_Ocomp(X27914,X27914,X27911,hAPP(X27913,X27909)),hAPP(c_Fun_Ocomp(X27914,X27914,X27911,hAPP(X27913,X27910)),X27908)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp])]) ).
fof(i_0_6921,plain,
! [X28267,X28268,X28269,X28270,X28272,X28273] :
( ( X28267 = hAPP(X28268,esk268_4(X28267,X28268,X28269,X28270))
| ~ hBOOL(hAPP(hAPP(c_member(X28269),X28267),hAPP(c_Set_Oimage(X28270,X28269,X28268),c_Orderings_Otop__class_Otop(tc_fun(X28270,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X28270,X28269,X28268,c_Orderings_Otop__class_Otop(tc_fun(X28270,tc_HOL_Obool))) )
& ( X28267 != hAPP(X28268,X28272)
| X28272 = esk268_4(X28267,X28268,X28269,X28270)
| ~ hBOOL(hAPP(hAPP(c_member(X28269),X28267),hAPP(c_Set_Oimage(X28270,X28269,X28268),c_Orderings_Otop__class_Otop(tc_fun(X28270,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X28270,X28269,X28268,c_Orderings_Otop__class_Otop(tc_fun(X28270,tc_HOL_Obool))) )
& ( X28267 = hAPP(X28268,esk269_5(X28267,X28268,X28269,X28270,X28273))
| X28267 != hAPP(X28268,X28273)
| hBOOL(hAPP(hAPP(c_member(X28269),X28267),hAPP(c_Set_Oimage(X28270,X28269,X28268),c_Orderings_Otop__class_Otop(tc_fun(X28270,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X28270,X28269,X28268,c_Orderings_Otop__class_Otop(tc_fun(X28270,tc_HOL_Obool))) )
& ( esk269_5(X28267,X28268,X28269,X28270,X28273) != X28273
| X28267 != hAPP(X28268,X28273)
| hBOOL(hAPP(hAPP(c_member(X28269),X28267),hAPP(c_Set_Oimage(X28270,X28269,X28268),c_Orderings_Otop__class_Otop(tc_fun(X28270,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X28270,X28269,X28268,c_Orderings_Otop__class_Otop(tc_fun(X28270,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,
! [X27367,X27368,X27369,X27370,X27371] :
( ~ class_Groups_Oab__group__add(X27371)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27370),X27369))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27370),X27368))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27370,X27371),X27367),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27370,tc_HOL_Obool)),X27369),X27368)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27371),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27371),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27370,X27371),X27367),X27369)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27370,X27371),X27367),X27368))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27370,X27371),X27367),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27370,tc_HOL_Obool)),X27369),X27368))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Un])]) ).
fof(i_0_6923,plain,
! [X34337,X34338,X34339,X34340] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34340),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34339)),X34338)))
| hAPP(c_List_Orev(X34339),hAPP(hAPP(c_List_Olist__update(X34339,X34338),X34340),X34337)) = hAPP(hAPP(c_List_Olist__update(X34339,hAPP(c_List_Orev(X34339),X34338)),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(X34339)),X34338)),X34340)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X34337) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__update])]) ).
fof(i_0_6924,plain,
! [X25549,X25550,X25551,X25552] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X25552,tc_HOL_Obool)),esk150_4(X25549,X25550,X25551,X25552)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25552),X25551),X25550)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25549),hAPP(c_Finite__Set_Ocard(X25552),X25551)))
| ~ c_Equiv__Relations_Oequiv(X25552,X25551,X25550)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25552),X25551)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25549),hAPP(c_Finite__Set_Ocard(X25552),esk150_4(X25549,X25550,X25551,X25552))))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25549),hAPP(c_Finite__Set_Ocard(X25552),X25551)))
| ~ c_Equiv__Relations_Oequiv(X25552,X25551,X25550)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25552),X25551)) ) ),
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,
! [X29222,X29223,X29224] : hAPP(c_Set_OCollect(X29224),hAPP(hAPP(c_COMBS(X29224,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29224),c_fimplies),X29223)),X29222)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29224,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X29224,tc_HOL_Obool)),hAPP(c_Set_OCollect(X29224),X29223))),hAPP(c_Set_OCollect(X29224),X29222)),
inference(variable_rename,[status(thm)],[fact_Collect__imp__eq]) ).
fof(i_0_6928,plain,
! [X21820,X21821,X21822,X21823] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21823),c_Groups_Ozero__class_Ozero(X21823)),X21821))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21823),X21822),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21823),hAPP(c_Int_Onumber__class_Onumber__of(X21823),X21820)),X21821)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21823),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21823),X21822),X21821)),hAPP(c_Int_Onumber__class_Onumber__of(X21823),X21820)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21823)
| ~ class_Int_Onumber(X21823) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21823),X21821),c_Groups_Ozero__class_Ozero(X21823)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21823),hAPP(c_Int_Onumber__class_Onumber__of(X21823),X21820)),X21821)),X21822))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21823),c_Groups_Ozero__class_Ozero(X21823)),X21821))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21823),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21823),X21822),X21821)),hAPP(c_Int_Onumber__class_Onumber__of(X21823),X21820)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21823)
| ~ class_Int_Onumber(X21823) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21823),X21821),c_Groups_Ozero__class_Ozero(X21823)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21823),c_Groups_Ozero__class_Ozero(X21823)),hAPP(c_Int_Onumber__class_Onumber__of(X21823),X21820)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21823),c_Groups_Ozero__class_Ozero(X21823)),X21821))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21823),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21823),X21822),X21821)),hAPP(c_Int_Onumber__class_Onumber__of(X21823),X21820)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21823)
| ~ class_Int_Onumber(X21823) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21823),c_Groups_Ozero__class_Ozero(X21823)),X21821))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21823),c_Groups_Ozero__class_Ozero(X21823)),X21821))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21823),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21823),X21822),X21821)),hAPP(c_Int_Onumber__class_Onumber__of(X21823),X21820)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21823)
| ~ class_Int_Onumber(X21823) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21823),X21821),c_Groups_Ozero__class_Ozero(X21823)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21823),X21821),c_Groups_Ozero__class_Ozero(X21823)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21823),c_Groups_Ozero__class_Ozero(X21823)),X21821))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21823),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21823),X21822),X21821)),hAPP(c_Int_Onumber__class_Onumber__of(X21823),X21820)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21823)
| ~ class_Int_Onumber(X21823) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21823),c_Groups_Ozero__class_Ozero(X21823)),hAPP(c_Int_Onumber__class_Onumber__of(X21823),X21820)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21823),X21821),c_Groups_Ozero__class_Ozero(X21823)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21823),c_Groups_Ozero__class_Ozero(X21823)),X21821))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21823),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21823),X21822),X21821)),hAPP(c_Int_Onumber__class_Onumber__of(X21823),X21820)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21823)
| ~ class_Int_Onumber(X21823) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21823),X21821),c_Groups_Ozero__class_Ozero(X21823)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21823),hAPP(c_Int_Onumber__class_Onumber__of(X21823),X21820)),X21821)),X21822))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21823),c_Groups_Ozero__class_Ozero(X21823)),X21821))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21823),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21823),X21822),X21821)),hAPP(c_Int_Onumber__class_Onumber__of(X21823),X21820)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21823)
| ~ class_Int_Onumber(X21823) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21823),c_Groups_Ozero__class_Ozero(X21823)),hAPP(c_Int_Onumber__class_Onumber__of(X21823),X21820)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21823),hAPP(c_Int_Onumber__class_Onumber__of(X21823),X21820)),X21821)),X21822))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21823),c_Groups_Ozero__class_Ozero(X21823)),X21821))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21823),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21823),X21822),X21821)),hAPP(c_Int_Onumber__class_Onumber__of(X21823),X21820)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21823)
| ~ class_Int_Onumber(X21823) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21823),c_Groups_Ozero__class_Ozero(X21823)),X21821))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21823),X21822),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21823),hAPP(c_Int_Onumber__class_Onumber__of(X21823),X21820)),X21821)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21823),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21823),X21822),X21821)),hAPP(c_Int_Onumber__class_Onumber__of(X21823),X21820)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21823)
| ~ class_Int_Onumber(X21823) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21823),X21821),c_Groups_Ozero__class_Ozero(X21823)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21823),X21821),c_Groups_Ozero__class_Ozero(X21823)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21823),X21822),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21823),hAPP(c_Int_Onumber__class_Onumber__of(X21823),X21820)),X21821)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21823),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21823),X21822),X21821)),hAPP(c_Int_Onumber__class_Onumber__of(X21823),X21820)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21823)
| ~ class_Int_Onumber(X21823) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21823),c_Groups_Ozero__class_Ozero(X21823)),hAPP(c_Int_Onumber__class_Onumber__of(X21823),X21820)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21823),X21821),c_Groups_Ozero__class_Ozero(X21823)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21823),X21822),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21823),hAPP(c_Int_Onumber__class_Onumber__of(X21823),X21820)),X21821)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21823),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21823),X21822),X21821)),hAPP(c_Int_Onumber__class_Onumber__of(X21823),X21820)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21823)
| ~ class_Int_Onumber(X21823) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21823),X21821),c_Groups_Ozero__class_Ozero(X21823)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21823),hAPP(c_Int_Onumber__class_Onumber__of(X21823),X21820)),X21821)),X21822))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21823),X21822),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21823),hAPP(c_Int_Onumber__class_Onumber__of(X21823),X21820)),X21821)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21823),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21823),X21822),X21821)),hAPP(c_Int_Onumber__class_Onumber__of(X21823),X21820)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21823)
| ~ class_Int_Onumber(X21823) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21823),c_Groups_Ozero__class_Ozero(X21823)),hAPP(c_Int_Onumber__class_Onumber__of(X21823),X21820)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21823),hAPP(c_Int_Onumber__class_Onumber__of(X21823),X21820)),X21821)),X21822))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21823),X21822),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21823),hAPP(c_Int_Onumber__class_Onumber__of(X21823),X21820)),X21821)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21823),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21823),X21822),X21821)),hAPP(c_Int_Onumber__class_Onumber__of(X21823),X21820)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21823)
| ~ class_Int_Onumber(X21823) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5457])])]) ).
fof(i_0_6929,plain,
! [X21802,X21803,X21804,X21805] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),c_Groups_Ozero__class_Ozero(X21805)),X21803))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),X21804),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21805),hAPP(c_Int_Onumber__class_Onumber__of(X21805),X21802)),X21803)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21805),X21804),X21803)),hAPP(c_Int_Onumber__class_Onumber__of(X21805),X21802)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21805)
| ~ class_Int_Onumber(X21805) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),X21803),c_Groups_Ozero__class_Ozero(X21805)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21805),hAPP(c_Int_Onumber__class_Onumber__of(X21805),X21802)),X21803)),X21804))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),c_Groups_Ozero__class_Ozero(X21805)),X21803))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21805),X21804),X21803)),hAPP(c_Int_Onumber__class_Onumber__of(X21805),X21802)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21805)
| ~ class_Int_Onumber(X21805) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),X21803),c_Groups_Ozero__class_Ozero(X21805)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),c_Groups_Ozero__class_Ozero(X21805)),hAPP(c_Int_Onumber__class_Onumber__of(X21805),X21802)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),c_Groups_Ozero__class_Ozero(X21805)),X21803))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21805),X21804),X21803)),hAPP(c_Int_Onumber__class_Onumber__of(X21805),X21802)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21805)
| ~ class_Int_Onumber(X21805) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),c_Groups_Ozero__class_Ozero(X21805)),X21803))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),c_Groups_Ozero__class_Ozero(X21805)),X21803))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21805),X21804),X21803)),hAPP(c_Int_Onumber__class_Onumber__of(X21805),X21802)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21805)
| ~ class_Int_Onumber(X21805) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),X21803),c_Groups_Ozero__class_Ozero(X21805)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),X21803),c_Groups_Ozero__class_Ozero(X21805)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),c_Groups_Ozero__class_Ozero(X21805)),X21803))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21805),X21804),X21803)),hAPP(c_Int_Onumber__class_Onumber__of(X21805),X21802)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21805)
| ~ class_Int_Onumber(X21805) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),c_Groups_Ozero__class_Ozero(X21805)),hAPP(c_Int_Onumber__class_Onumber__of(X21805),X21802)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),X21803),c_Groups_Ozero__class_Ozero(X21805)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),c_Groups_Ozero__class_Ozero(X21805)),X21803))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21805),X21804),X21803)),hAPP(c_Int_Onumber__class_Onumber__of(X21805),X21802)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21805)
| ~ class_Int_Onumber(X21805) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),X21803),c_Groups_Ozero__class_Ozero(X21805)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21805),hAPP(c_Int_Onumber__class_Onumber__of(X21805),X21802)),X21803)),X21804))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),c_Groups_Ozero__class_Ozero(X21805)),X21803))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21805),X21804),X21803)),hAPP(c_Int_Onumber__class_Onumber__of(X21805),X21802)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21805)
| ~ class_Int_Onumber(X21805) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),c_Groups_Ozero__class_Ozero(X21805)),hAPP(c_Int_Onumber__class_Onumber__of(X21805),X21802)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21805),hAPP(c_Int_Onumber__class_Onumber__of(X21805),X21802)),X21803)),X21804))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),c_Groups_Ozero__class_Ozero(X21805)),X21803))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21805),X21804),X21803)),hAPP(c_Int_Onumber__class_Onumber__of(X21805),X21802)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21805)
| ~ class_Int_Onumber(X21805) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),c_Groups_Ozero__class_Ozero(X21805)),X21803))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),X21804),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21805),hAPP(c_Int_Onumber__class_Onumber__of(X21805),X21802)),X21803)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21805),X21804),X21803)),hAPP(c_Int_Onumber__class_Onumber__of(X21805),X21802)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21805)
| ~ class_Int_Onumber(X21805) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),X21803),c_Groups_Ozero__class_Ozero(X21805)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),X21803),c_Groups_Ozero__class_Ozero(X21805)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),X21804),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21805),hAPP(c_Int_Onumber__class_Onumber__of(X21805),X21802)),X21803)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21805),X21804),X21803)),hAPP(c_Int_Onumber__class_Onumber__of(X21805),X21802)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21805)
| ~ class_Int_Onumber(X21805) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),c_Groups_Ozero__class_Ozero(X21805)),hAPP(c_Int_Onumber__class_Onumber__of(X21805),X21802)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),X21803),c_Groups_Ozero__class_Ozero(X21805)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),X21804),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21805),hAPP(c_Int_Onumber__class_Onumber__of(X21805),X21802)),X21803)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21805),X21804),X21803)),hAPP(c_Int_Onumber__class_Onumber__of(X21805),X21802)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21805)
| ~ class_Int_Onumber(X21805) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),X21803),c_Groups_Ozero__class_Ozero(X21805)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21805),hAPP(c_Int_Onumber__class_Onumber__of(X21805),X21802)),X21803)),X21804))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),X21804),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21805),hAPP(c_Int_Onumber__class_Onumber__of(X21805),X21802)),X21803)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21805),X21804),X21803)),hAPP(c_Int_Onumber__class_Onumber__of(X21805),X21802)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21805)
| ~ class_Int_Onumber(X21805) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),c_Groups_Ozero__class_Ozero(X21805)),hAPP(c_Int_Onumber__class_Onumber__of(X21805),X21802)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21805),hAPP(c_Int_Onumber__class_Onumber__of(X21805),X21802)),X21803)),X21804))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),X21804),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21805),hAPP(c_Int_Onumber__class_Onumber__of(X21805),X21802)),X21803)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21805),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21805),X21804),X21803)),hAPP(c_Int_Onumber__class_Onumber__of(X21805),X21802)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21805)
| ~ class_Int_Onumber(X21805) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5458])])]) ).
fof(i_0_6930,plain,
! [X30578,X30579,X30580,X30581,X30582,X30583,X30584,X30585,X30586] :
( ( ~ c_Relation_Osingle__valued(X30580,X30579,X30578)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30580,X30579)),hAPP(hAPP(c_Product__Type_OPair(X30580,X30579),X30581),X30582)),X30578))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30580,X30579)),hAPP(hAPP(c_Product__Type_OPair(X30580,X30579),X30581),X30583)),X30578))
| X30582 = X30583 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30586,X30585)),hAPP(hAPP(c_Product__Type_OPair(X30586,X30585),esk379_3(X30584,X30585,X30586)),esk380_3(X30584,X30585,X30586))),X30584))
| c_Relation_Osingle__valued(X30586,X30585,X30584) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30586,X30585)),hAPP(hAPP(c_Product__Type_OPair(X30586,X30585),esk379_3(X30584,X30585,X30586)),esk381_3(X30584,X30585,X30586))),X30584))
| c_Relation_Osingle__valued(X30586,X30585,X30584) )
& ( esk380_3(X30584,X30585,X30586) != esk381_3(X30584,X30585,X30586)
| c_Relation_Osingle__valued(X30586,X30585,X30584) ) ),
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,
! [X21824,X21825,X21826,X21827] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21827),c_Groups_Ozero__class_Ozero(X21827)),X21824))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21827),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21827),hAPP(c_Int_Onumber__class_Onumber__of(X21827),X21826)),X21824)),X21825))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21827),hAPP(c_Int_Onumber__class_Onumber__of(X21827),X21826)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21827),X21825),X21824)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21827)
| ~ class_Int_Onumber(X21827) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21827),X21824),c_Groups_Ozero__class_Ozero(X21827)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21827),X21825),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21827),hAPP(c_Int_Onumber__class_Onumber__of(X21827),X21826)),X21824)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21827),c_Groups_Ozero__class_Ozero(X21827)),X21824))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21827),hAPP(c_Int_Onumber__class_Onumber__of(X21827),X21826)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21827),X21825),X21824)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21827)
| ~ class_Int_Onumber(X21827) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21827),X21824),c_Groups_Ozero__class_Ozero(X21827)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21827),hAPP(c_Int_Onumber__class_Onumber__of(X21827),X21826)),c_Groups_Ozero__class_Ozero(X21827)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21827),c_Groups_Ozero__class_Ozero(X21827)),X21824))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21827),hAPP(c_Int_Onumber__class_Onumber__of(X21827),X21826)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21827),X21825),X21824)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21827)
| ~ class_Int_Onumber(X21827) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21827),c_Groups_Ozero__class_Ozero(X21827)),X21824))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21827),c_Groups_Ozero__class_Ozero(X21827)),X21824))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21827),hAPP(c_Int_Onumber__class_Onumber__of(X21827),X21826)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21827),X21825),X21824)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21827)
| ~ class_Int_Onumber(X21827) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21827),X21824),c_Groups_Ozero__class_Ozero(X21827)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21827),X21824),c_Groups_Ozero__class_Ozero(X21827)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21827),c_Groups_Ozero__class_Ozero(X21827)),X21824))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21827),hAPP(c_Int_Onumber__class_Onumber__of(X21827),X21826)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21827),X21825),X21824)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21827)
| ~ class_Int_Onumber(X21827) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21827),hAPP(c_Int_Onumber__class_Onumber__of(X21827),X21826)),c_Groups_Ozero__class_Ozero(X21827)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21827),X21824),c_Groups_Ozero__class_Ozero(X21827)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21827),c_Groups_Ozero__class_Ozero(X21827)),X21824))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21827),hAPP(c_Int_Onumber__class_Onumber__of(X21827),X21826)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21827),X21825),X21824)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21827)
| ~ class_Int_Onumber(X21827) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21827),X21824),c_Groups_Ozero__class_Ozero(X21827)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21827),X21825),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21827),hAPP(c_Int_Onumber__class_Onumber__of(X21827),X21826)),X21824)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21827),c_Groups_Ozero__class_Ozero(X21827)),X21824))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21827),hAPP(c_Int_Onumber__class_Onumber__of(X21827),X21826)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21827),X21825),X21824)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21827)
| ~ class_Int_Onumber(X21827) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21827),hAPP(c_Int_Onumber__class_Onumber__of(X21827),X21826)),c_Groups_Ozero__class_Ozero(X21827)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21827),X21825),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21827),hAPP(c_Int_Onumber__class_Onumber__of(X21827),X21826)),X21824)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21827),c_Groups_Ozero__class_Ozero(X21827)),X21824))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21827),hAPP(c_Int_Onumber__class_Onumber__of(X21827),X21826)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21827),X21825),X21824)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21827)
| ~ class_Int_Onumber(X21827) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21827),c_Groups_Ozero__class_Ozero(X21827)),X21824))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21827),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21827),hAPP(c_Int_Onumber__class_Onumber__of(X21827),X21826)),X21824)),X21825))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21827),hAPP(c_Int_Onumber__class_Onumber__of(X21827),X21826)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21827),X21825),X21824)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21827)
| ~ class_Int_Onumber(X21827) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21827),X21824),c_Groups_Ozero__class_Ozero(X21827)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21827),X21824),c_Groups_Ozero__class_Ozero(X21827)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21827),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21827),hAPP(c_Int_Onumber__class_Onumber__of(X21827),X21826)),X21824)),X21825))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21827),hAPP(c_Int_Onumber__class_Onumber__of(X21827),X21826)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21827),X21825),X21824)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21827)
| ~ class_Int_Onumber(X21827) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21827),hAPP(c_Int_Onumber__class_Onumber__of(X21827),X21826)),c_Groups_Ozero__class_Ozero(X21827)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21827),X21824),c_Groups_Ozero__class_Ozero(X21827)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21827),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21827),hAPP(c_Int_Onumber__class_Onumber__of(X21827),X21826)),X21824)),X21825))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21827),hAPP(c_Int_Onumber__class_Onumber__of(X21827),X21826)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21827),X21825),X21824)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21827)
| ~ class_Int_Onumber(X21827) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21827),X21824),c_Groups_Ozero__class_Ozero(X21827)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21827),X21825),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21827),hAPP(c_Int_Onumber__class_Onumber__of(X21827),X21826)),X21824)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21827),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21827),hAPP(c_Int_Onumber__class_Onumber__of(X21827),X21826)),X21824)),X21825))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21827),hAPP(c_Int_Onumber__class_Onumber__of(X21827),X21826)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21827),X21825),X21824)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21827)
| ~ class_Int_Onumber(X21827) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21827),hAPP(c_Int_Onumber__class_Onumber__of(X21827),X21826)),c_Groups_Ozero__class_Ozero(X21827)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21827),X21825),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21827),hAPP(c_Int_Onumber__class_Onumber__of(X21827),X21826)),X21824)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21827),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21827),hAPP(c_Int_Onumber__class_Onumber__of(X21827),X21826)),X21824)),X21825))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21827),hAPP(c_Int_Onumber__class_Onumber__of(X21827),X21826)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21827),X21825),X21824)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21827)
| ~ class_Int_Onumber(X21827) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5459])])]) ).
fof(i_0_6932,plain,
! [X21798,X21799,X21800,X21801] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),c_Groups_Ozero__class_Ozero(X21801)),X21798))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21801),hAPP(c_Int_Onumber__class_Onumber__of(X21801),X21800)),X21798)),X21799))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),hAPP(c_Int_Onumber__class_Onumber__of(X21801),X21800)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21801),X21799),X21798)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21801)
| ~ class_Int_Onumber(X21801) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),X21798),c_Groups_Ozero__class_Ozero(X21801)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),X21799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21801),hAPP(c_Int_Onumber__class_Onumber__of(X21801),X21800)),X21798)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),c_Groups_Ozero__class_Ozero(X21801)),X21798))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),hAPP(c_Int_Onumber__class_Onumber__of(X21801),X21800)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21801),X21799),X21798)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21801)
| ~ class_Int_Onumber(X21801) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),X21798),c_Groups_Ozero__class_Ozero(X21801)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),hAPP(c_Int_Onumber__class_Onumber__of(X21801),X21800)),c_Groups_Ozero__class_Ozero(X21801)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),c_Groups_Ozero__class_Ozero(X21801)),X21798))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),hAPP(c_Int_Onumber__class_Onumber__of(X21801),X21800)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21801),X21799),X21798)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21801)
| ~ class_Int_Onumber(X21801) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),c_Groups_Ozero__class_Ozero(X21801)),X21798))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),c_Groups_Ozero__class_Ozero(X21801)),X21798))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),hAPP(c_Int_Onumber__class_Onumber__of(X21801),X21800)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21801),X21799),X21798)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21801)
| ~ class_Int_Onumber(X21801) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),X21798),c_Groups_Ozero__class_Ozero(X21801)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),X21798),c_Groups_Ozero__class_Ozero(X21801)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),c_Groups_Ozero__class_Ozero(X21801)),X21798))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),hAPP(c_Int_Onumber__class_Onumber__of(X21801),X21800)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21801),X21799),X21798)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21801)
| ~ class_Int_Onumber(X21801) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),hAPP(c_Int_Onumber__class_Onumber__of(X21801),X21800)),c_Groups_Ozero__class_Ozero(X21801)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),X21798),c_Groups_Ozero__class_Ozero(X21801)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),c_Groups_Ozero__class_Ozero(X21801)),X21798))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),hAPP(c_Int_Onumber__class_Onumber__of(X21801),X21800)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21801),X21799),X21798)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21801)
| ~ class_Int_Onumber(X21801) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),X21798),c_Groups_Ozero__class_Ozero(X21801)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),X21799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21801),hAPP(c_Int_Onumber__class_Onumber__of(X21801),X21800)),X21798)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),c_Groups_Ozero__class_Ozero(X21801)),X21798))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),hAPP(c_Int_Onumber__class_Onumber__of(X21801),X21800)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21801),X21799),X21798)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21801)
| ~ class_Int_Onumber(X21801) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),hAPP(c_Int_Onumber__class_Onumber__of(X21801),X21800)),c_Groups_Ozero__class_Ozero(X21801)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),X21799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21801),hAPP(c_Int_Onumber__class_Onumber__of(X21801),X21800)),X21798)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),c_Groups_Ozero__class_Ozero(X21801)),X21798))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),hAPP(c_Int_Onumber__class_Onumber__of(X21801),X21800)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21801),X21799),X21798)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21801)
| ~ class_Int_Onumber(X21801) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),c_Groups_Ozero__class_Ozero(X21801)),X21798))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21801),hAPP(c_Int_Onumber__class_Onumber__of(X21801),X21800)),X21798)),X21799))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),hAPP(c_Int_Onumber__class_Onumber__of(X21801),X21800)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21801),X21799),X21798)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21801)
| ~ class_Int_Onumber(X21801) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),X21798),c_Groups_Ozero__class_Ozero(X21801)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),X21798),c_Groups_Ozero__class_Ozero(X21801)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21801),hAPP(c_Int_Onumber__class_Onumber__of(X21801),X21800)),X21798)),X21799))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),hAPP(c_Int_Onumber__class_Onumber__of(X21801),X21800)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21801),X21799),X21798)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21801)
| ~ class_Int_Onumber(X21801) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),hAPP(c_Int_Onumber__class_Onumber__of(X21801),X21800)),c_Groups_Ozero__class_Ozero(X21801)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),X21798),c_Groups_Ozero__class_Ozero(X21801)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21801),hAPP(c_Int_Onumber__class_Onumber__of(X21801),X21800)),X21798)),X21799))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),hAPP(c_Int_Onumber__class_Onumber__of(X21801),X21800)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21801),X21799),X21798)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21801)
| ~ class_Int_Onumber(X21801) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),X21798),c_Groups_Ozero__class_Ozero(X21801)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),X21799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21801),hAPP(c_Int_Onumber__class_Onumber__of(X21801),X21800)),X21798)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21801),hAPP(c_Int_Onumber__class_Onumber__of(X21801),X21800)),X21798)),X21799))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),hAPP(c_Int_Onumber__class_Onumber__of(X21801),X21800)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21801),X21799),X21798)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21801)
| ~ class_Int_Onumber(X21801) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),hAPP(c_Int_Onumber__class_Onumber__of(X21801),X21800)),c_Groups_Ozero__class_Ozero(X21801)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),X21799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21801),hAPP(c_Int_Onumber__class_Onumber__of(X21801),X21800)),X21798)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21801),hAPP(c_Int_Onumber__class_Onumber__of(X21801),X21800)),X21798)),X21799))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21801),hAPP(c_Int_Onumber__class_Onumber__of(X21801),X21800)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21801),X21799),X21798)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21801)
| ~ class_Int_Onumber(X21801) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5460])])]) ).
fof(i_0_6933,plain,
! [X22408,X22409,X22410,X22411,X22412] : c_Product__Type_Oprod_Oprod__size(X22412,X22411,X22410,X22409,X22408) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X22410,hAPP(c_Product__Type_Ofst(X22412,X22411),X22408))),hAPP(X22409,hAPP(c_Product__Type_Osnd(X22412,X22411),X22408)))),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,
! [X27254,X27255,X27256,X27257,X27258] :
( ~ class_Groups_Ocomm__monoid__add(X27258)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27258),X27257),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27256),X27255),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27254),X27255))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27258),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X27258,tc_Nat_Onat),X27257),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X27255))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X27256,X27254)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__cl__nat__ivl])]) ).
fof(i_0_6935,plain,
! [X26692,X26693,X26694,X26695] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk204_4(X26692,X26693,X26694,X26695)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26694)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26693),X26695))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26693),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26695),X26694)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26693),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26692))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26694)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk205_4(X26692,X26693,X26694,X26695)),X26692))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26693),X26695))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26693),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26695),X26694)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26693),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26692))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26694)) )
& ( X26695 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk205_4(X26692,X26693,X26694,X26695)),esk204_4(X26692,X26693,X26694,X26695))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26693),X26695))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26693),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26695),X26694)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26693),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26692))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26694)) ) ),
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,
! [X28793,X28794,X28795,X28796] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28796),X28795))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28796,X28796),tc_HOL_Obool)),X28794),hAPP(hAPP(c_Product__Type_OSigma(X28796,X28796),X28795),hAPP(c_COMBK(tc_fun(X28796,tc_HOL_Obool),X28796),X28795))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X28796,tc_HOL_Obool)),X28793),hAPP(hAPP(c_Equiv__Relations_Oquotient(X28796),X28795),X28794)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X28796),X28793)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__equiv__class])]) ).
fof(i_0_6937,plain,
! [X24631,X24632,X24633,X24634,X24635,X24636,X24637] :
( ~ c_Equiv__Relations_Oequiv(X24637,X24636,X24635)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24637,tc_HOL_Obool)),X24634),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24637),X24636),X24635)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24637,tc_HOL_Obool)),X24633),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24637),X24636),X24635)))
| ~ hBOOL(hAPP(hAPP(c_member(X24637),X24632),X24634))
| ~ hBOOL(hAPP(hAPP(c_member(X24637),X24631),X24633))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24637,X24637)),hAPP(hAPP(c_Product__Type_OPair(X24637,X24637),X24632),X24631)),X24635))
| X24634 = X24633 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__eqI])]) ).
fof(i_0_6938,plain,
! [X24624,X24625,X24626,X24627,X24628,X24629,X24630] :
( ( X24627 != X24626
| hBOOL(hAPP(hAPP(c_member(tc_prod(X24630,X24630)),hAPP(hAPP(c_Product__Type_OPair(X24630,X24630),X24625),X24624)),X24628))
| ~ hBOOL(hAPP(hAPP(c_member(X24630),X24624),X24626))
| ~ hBOOL(hAPP(hAPP(c_member(X24630),X24625),X24627))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24630,tc_HOL_Obool)),X24626),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24630),X24629),X24628)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24630,tc_HOL_Obool)),X24627),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24630),X24629),X24628)))
| ~ c_Equiv__Relations_Oequiv(X24630,X24629,X24628) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24630,X24630)),hAPP(hAPP(c_Product__Type_OPair(X24630,X24630),X24625),X24624)),X24628))
| X24627 = X24626
| ~ hBOOL(hAPP(hAPP(c_member(X24630),X24624),X24626))
| ~ hBOOL(hAPP(hAPP(c_member(X24630),X24625),X24627))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24630,tc_HOL_Obool)),X24626),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24630),X24629),X24628)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24630,tc_HOL_Obool)),X24627),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24630),X24629),X24628)))
| ~ c_Equiv__Relations_Oequiv(X24630,X24629,X24628) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__eq__iff])])]) ).
fof(i_0_6939,plain,
! [X20249,X20250,X20251] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20251),c_Groups_Ozero__class_Ozero(X20251)),esk72_3(X20249,X20250,X20251)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20251),X20250),X20249))
| ~ class_Fields_Olinordered__field__inverse__zero(X20251) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20251),esk72_3(X20249,X20250,X20251)),c_Groups_Oone__class_Oone(X20251)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20251),X20250),X20249))
| ~ class_Fields_Olinordered__field__inverse__zero(X20251) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20251),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20251),esk72_3(X20249,X20250,X20251)),X20250)),X20249))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20251),X20250),X20249))
| ~ class_Fields_Olinordered__field__inverse__zero(X20251) ) ),
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,
! [X23413,X23414,X23415,X23416,X23417] :
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X23417,X23416,tc_HOL_Obool,X23415),X23414),X23413))
| hBOOL(hAPP(X23415,hAPP(hAPP(c_Product__Type_OPair(X23417,X23416),X23414),X23413))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_curryD])]) ).
fof(i_0_6941,plain,
! [X23408,X23409,X23410,X23411,X23412] :
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X23412,X23411,tc_HOL_Obool,X23410),X23409),X23408))
| hBOOL(hAPP(X23410,hAPP(hAPP(c_Product__Type_OPair(X23412,X23411),X23409),X23408))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_curryE])]) ).
fof(i_0_6942,plain,
! [X28496,X28497,X28498,X28499] : hAPP(c_Set_Ovimage(X28499,X28498,X28497),X28496) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28498,tc_fun(X28499,tc_HOL_Obool)),X28496),hAPP(hAPP(c_COMBB(tc_fun(X28498,tc_HOL_Obool),tc_fun(X28499,tc_HOL_Obool),X28498),c_Set_Ovimage(X28499,X28498,X28497)),hAPP(hAPP(c_COMBC(X28498,tc_fun(X28498,tc_HOL_Obool),tc_fun(X28498,tc_HOL_Obool)),c_Set_Oinsert(X28498)),c_Orderings_Obot__class_Obot(tc_fun(X28498,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_vimage__eq__UN]) ).
fof(i_0_6943,plain,
! [X25848,X25849,X25850,X25851] : hAPP(c_Relation_OImage(X25851,X25850,X25849),X25848) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25851,tc_fun(X25850,tc_HOL_Obool)),X25848),hAPP(hAPP(c_COMBB(tc_fun(X25851,tc_HOL_Obool),tc_fun(X25850,tc_HOL_Obool),X25851),c_Relation_OImage(X25851,X25850,X25849)),hAPP(hAPP(c_COMBC(X25851,tc_fun(X25851,tc_HOL_Obool),tc_fun(X25851,tc_HOL_Obool)),c_Set_Oinsert(X25851)),c_Orderings_Obot__class_Obot(tc_fun(X25851,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_Image__eq__UN]) ).
fof(i_0_6944,plain,
! [X24971,X24972,X24973,X24974] :
( ~ class_Lattices_Olattice(X24974)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24974),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24974),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24974),X24973),X24972)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24974),X24973),X24971))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24974),X24973),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24974),X24972),X24971)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distrib__inf__le])]) ).
fof(i_0_6945,plain,
! [X22709,X22710,X22711,X22712] :
( ~ class_Orderings_Olinorder(X22712)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22712),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22712),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22712),X22711),X22710)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22712),X22711),X22709))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22712),X22711),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22712),X22710),X22709)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Odistrib__inf__le])]) ).
fof(i_0_6946,plain,
! [X31967,X31968,X31969,X31970] :
( ( c_Map_Omap__of(X31970,X31969,X31968) != c_Map_Omap__of(X31970,X31969,X31967)
| hAPP(c_List_Oset(tc_prod(X31970,X31969)),X31968) = hAPP(c_List_Oset(tc_prod(X31970,X31969)),X31967)
| ~ hBOOL(hAPP(c_List_Odistinct(X31970),hAPP(hAPP(c_List_Omap(tc_prod(X31970,X31969),X31970),c_Product__Type_Ofst(X31970,X31969)),X31967)))
| ~ hBOOL(hAPP(c_List_Odistinct(X31970),hAPP(hAPP(c_List_Omap(tc_prod(X31970,X31969),X31970),c_Product__Type_Ofst(X31970,X31969)),X31968))) )
& ( hAPP(c_List_Oset(tc_prod(X31970,X31969)),X31968) != hAPP(c_List_Oset(tc_prod(X31970,X31969)),X31967)
| c_Map_Omap__of(X31970,X31969,X31968) = c_Map_Omap__of(X31970,X31969,X31967)
| ~ hBOOL(hAPP(c_List_Odistinct(X31970),hAPP(hAPP(c_List_Omap(tc_prod(X31970,X31969),X31970),c_Product__Type_Ofst(X31970,X31969)),X31967)))
| ~ hBOOL(hAPP(c_List_Odistinct(X31970),hAPP(hAPP(c_List_Omap(tc_prod(X31970,X31969),X31970),c_Product__Type_Ofst(X31970,X31969)),X31968))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__inject__set])])]) ).
fof(i_0_6947,plain,
! [X26161,X26162,X26163,X26164,X26165,X26166,X26167,X26168] :
( ~ hBOOL(hAPP(hAPP(c_member(X26168),X26167),X26166))
| ~ hBOOL(hAPP(hAPP(hAPP(X26165,X26167),X26164),X26163))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26168,tc_fun(X26162,tc_fun(X26161,tc_HOL_Obool))),X26166),X26165),X26164),X26163)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP2__I])]) ).
fof(i_0_6948,plain,
! [X22173,X22174,X22175,X22176,X22177,X22178,X22179] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22179,X22178,tc_fun(X22177,tc_HOL_Obool)),X22176),hAPP(hAPP(c_Product__Type_OPair(X22179,X22178),X22175),X22174)),X22173))
| hBOOL(hAPP(hAPP(hAPP(X22176,X22175),X22174),X22173)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_splitD_H])]) ).
fof(i_0_6949,plain,
! [X29497,X29498,X29499,X29500,X29501,X29502] : hAPP(hAPP(c_Relation_Orel__comp(X29502,X29501,X29500),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29502,X29501),tc_HOL_Obool)),X29499),X29498)),X29497) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29502,X29500),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X29502,X29501,X29500),X29499),X29497)),hAPP(hAPP(c_Relation_Orel__comp(X29502,X29501,X29500),X29498),X29497)),
inference(variable_rename,[status(thm)],[fact_rel__comp__distrib2]) ).
fof(i_0_6950,plain,
! [X31183,X31184,X31185,X31186,X31187] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31187)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31186),X31185))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X31187),X31184),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31186,X31187),X31185),X31183)) = hAPP(hAPP(c_Finite__Set_Ofold(X31186,X31187,hAPP(hAPP(c_COMBB(X31187,tc_fun(X31187,X31187),X31186),c_Lattices_Osemilattice__inf__class_Oinf(X31187)),X31183)),X31184),X31185) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__INFI__fold__inf])]) ).
fof(i_0_6951,plain,
! [X30692,X30693,X30694,X30695,X30696] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X30696)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30695),X30694))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X30696),X30693),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30695,X30696),X30694),X30692)) = hAPP(hAPP(c_Finite__Set_Ofold(X30695,X30696,hAPP(hAPP(c_COMBB(X30696,tc_fun(X30696,X30696),X30695),c_Lattices_Osemilattice__sup__class_Osup(X30696)),X30692)),X30693),X30694) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__SUPR__fold__sup])]) ).
fof(i_0_6952,plain,
! [X26961,X26962,X26963,X26964,X26965,X26966,X26967] :
( X26967 = X26966
| hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26965,X26964),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26965,X26964),X26963),X26967),X26962)),X26966),X26961) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26965,X26964),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26965,X26964),X26963),X26966),X26961)),X26967),X26962) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__twist])]) ).
fof(i_0_6953,plain,
! [X27509,X27510,X27511,X27512] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27512),X27511))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27512),X27510))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27512,tc_Nat_Onat),X27509),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27512,tc_HOL_Obool)),X27511),X27510)) = 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(X27512,tc_Nat_Onat),X27509),X27511)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27512,tc_Nat_Onat),X27509),X27510))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27512,tc_Nat_Onat),X27509),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27512,tc_HOL_Obool)),X27511),X27510))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Un__nat])]) ).
fof(i_0_6954,plain,
! [X29211,X29212] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29212),hAPP(c_Set_OCollect(X29212),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29212),c_fNot),X29211))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29212),c_Orderings_Otop__class_Otop(tc_fun(X29212,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29212),hAPP(c_Set_OCollect(X29212),X29211))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29212),c_Orderings_Otop__class_Otop(tc_fun(X29212,tc_HOL_Obool))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29212),hAPP(c_Set_OCollect(X29212),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29212),c_fNot),X29211))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29212),hAPP(c_Set_OCollect(X29212),X29211))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Collect__not])])]) ).
fof(i_0_6955,plain,
! [X19790,X19791,X19792,X19793] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19793))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19792),X19791))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19791),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),X19792),X19793)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19792),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19790,X19793))),X19791))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux1])]) ).
fof(i_0_6956,plain,
! [X20561,X20562,X20563,X20564,X20565] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20565),X20564))
| 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),X20565),X20563)),X20562)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20564),X20563)),X20561)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20562),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),X20564),X20565)),X20563)),X20561)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq2])]) ).
fof(i_0_6957,plain,
! [X27180,X27181,X27182,X27183] :
( ~ class_Groups_Oordered__ab__group__add__abs(X27183)
| hAPP(c_Groups_Oabs__class_Oabs(X27183),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27182,X27183),hAPP(hAPP(c_COMBB(X27183,X27183,X27182),c_Groups_Oabs__class_Oabs(X27183)),X27181)),X27180)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27182,X27183),hAPP(hAPP(c_COMBB(X27183,X27183,X27182),c_Groups_Oabs__class_Oabs(X27183)),X27181)),X27180) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__setsum__abs])]) ).
fof(i_0_6958,plain,
! [X32959,X32960,X32961,X32962,X32963,X32964,X32965] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32965)),X32964)),X32963))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32963),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32962)),X32961)))
| c_Map_Omap__upds(X32965,X32962,X32960,X32964,hAPP(hAPP(c_List_Olist__update(X32962,X32961),X32963),X32959)) = c_Map_Omap__upds(X32965,X32962,X32960,X32964,X32961) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__upds__list__update2__drop])]) ).
fof(i_0_6959,plain,
! [X28279,X28280,X28281,X28282,X28283] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28282,tc_HOL_Obool)),hAPP(c_Set_Oimage(X28283,X28282,X28281),X28280)),hAPP(c_Set_Oimage(X28283,X28282,X28281),X28279)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28283,tc_HOL_Obool)),X28280),X28279))
| ~ c_Fun_Oinj__on(X28283,X28282,X28281,c_Orderings_Otop__class_Otop(tc_fun(X28283,tc_HOL_Obool))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28283,tc_HOL_Obool)),X28280),X28279))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28282,tc_HOL_Obool)),hAPP(c_Set_Oimage(X28283,X28282,X28281),X28280)),hAPP(c_Set_Oimage(X28283,X28282,X28281),X28279)))
| ~ c_Fun_Oinj__on(X28283,X28282,X28281,c_Orderings_Otop__class_Otop(tc_fun(X28283,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,
! [X21740,X21741,X21742] :
( ~ class_Fields_Olinordered__field(X21742)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21742),X21741),X21740))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21742),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21742),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21742),X21741),X21740)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21742),c_Groups_Oone__class_Oone(X21742)),c_Groups_Oone__class_Oone(X21742)))),X21740)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gt__half__sum])]) ).
fof(i_0_6961,plain,
! [X19733,X19734,X19735] :
( ~ 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),X19735),X19734)),X19733)),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)),X19733))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19735))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19734),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,
! [X29201,X29202,X29203] :
( ( ~ hBOOL(hAPP(X29203,X29202))
| hAPP(c_Set_OCollect(X29201),hAPP(hAPP(c_COMBS(X29201,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29201),c_fconj),hAPP(c_fequal,X29202))),X29203)) = hAPP(hAPP(c_Set_Oinsert(X29201),X29202),c_Orderings_Obot__class_Obot(tc_fun(X29201,tc_HOL_Obool))) )
& ( hBOOL(hAPP(X29203,X29202))
| hAPP(c_Set_OCollect(X29201),hAPP(hAPP(c_COMBS(X29201,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29201),c_fconj),hAPP(c_fequal,X29202))),X29203)) = c_Orderings_Obot__class_Obot(tc_fun(X29201,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,
! [X32066,X32067,X32068,X32069] :
( ( hBOOL(hAPP(hAPP(c_member(X32069),X32068),hAPP(c_List_Oset(X32069),X32066)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32069,X32069)),hAPP(hAPP(c_Product__Type_OPair(X32069,X32069),X32068),X32067)),hAPP(c_List_Oset(tc_prod(X32069,X32069)),hAPP(hAPP(c_List_Ozip(X32069,X32069),X32066),X32066)))) )
& ( X32068 = X32067
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32069,X32069)),hAPP(hAPP(c_Product__Type_OPair(X32069,X32069),X32068),X32067)),hAPP(c_List_Oset(tc_prod(X32069,X32069)),hAPP(hAPP(c_List_Ozip(X32069,X32069),X32066),X32066)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X32069),X32068),hAPP(c_List_Oset(X32069),X32066)))
| X32068 != X32067
| hBOOL(hAPP(hAPP(c_member(tc_prod(X32069,X32069)),hAPP(hAPP(c_Product__Type_OPair(X32069,X32069),X32068),X32067)),hAPP(c_List_Oset(tc_prod(X32069,X32069)),hAPP(hAPP(c_List_Ozip(X32069,X32069),X32066),X32066)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__same])])]) ).
fof(i_0_6966,plain,
! [X32082,X32083,X32084,X32085,X32086,X32087] :
( ( hBOOL(hAPP(hAPP(c_member(X32087),X32085),hAPP(c_List_Oset(X32087),X32083)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32087,X32086)),hAPP(hAPP(c_Product__Type_OPair(X32087,X32086),X32085),X32084)),hAPP(c_List_Oset(tc_prod(X32087,X32086)),hAPP(hAPP(c_List_Ozip(X32087,X32086),X32083),X32082)))) )
& ( hBOOL(hAPP(hAPP(c_member(X32086),X32084),hAPP(c_List_Oset(X32086),X32082)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32087,X32086)),hAPP(hAPP(c_Product__Type_OPair(X32087,X32086),X32085),X32084)),hAPP(c_List_Oset(tc_prod(X32087,X32086)),hAPP(hAPP(c_List_Ozip(X32087,X32086),X32083),X32082)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5464])])]) ).
fof(i_0_6967,plain,
! [X32070,X32071,X32072,X32073,X32074,X32075] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32075,X32074)),hAPP(hAPP(c_Product__Type_OPair(X32075,X32074),X32073),X32072)),hAPP(c_List_Oset(tc_prod(X32075,X32074)),hAPP(hAPP(c_List_Ozip(X32075,X32074),X32071),X32070))))
| hBOOL(hAPP(hAPP(c_member(X32075),X32073),hAPP(c_List_Oset(X32075),X32071))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__zip__leftD])]) ).
fof(i_0_6968,plain,
! [X32076,X32077,X32078,X32079,X32080,X32081] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32081,X32080)),hAPP(hAPP(c_Product__Type_OPair(X32081,X32080),X32079),X32078)),hAPP(c_List_Oset(tc_prod(X32081,X32080)),hAPP(hAPP(c_List_Ozip(X32081,X32080),X32077),X32076))))
| hBOOL(hAPP(hAPP(c_member(X32080),X32078),hAPP(c_List_Oset(X32080),X32076))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__zip__rightD])]) ).
fof(i_0_6969,plain,
! [X27978,X27979,X27980,X27981,X27982,X27983] :
( ~ c_Finite__Set_Ofolding(X27983,X27982,X27981,X27980)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27983),X27979))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27983),X27978))
| hAPP(c_Fun_Ocomp(X27982,X27982,X27982,hAPP(X27980,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27983,tc_HOL_Obool)),X27979),X27978))),hAPP(X27980,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27983,tc_HOL_Obool)),X27979),X27978))) = hAPP(c_Fun_Ocomp(X27982,X27982,X27982,hAPP(X27980,X27979)),hAPP(X27980,X27978)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ounion__inter])]) ).
fof(i_0_6970,plain,
! [X20724,X20725,X20726] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20726)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20726),hAPP(c_Groups_Oabs__class_Oabs(X20726),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20726),hAPP(c_Groups_Oabs__class_Oabs(X20726),X20725)),hAPP(c_Groups_Oabs__class_Oabs(X20726),X20724)))),hAPP(c_Groups_Oabs__class_Oabs(X20726),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20726),X20725),X20724)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq3])]) ).
fof(i_0_6971,plain,
! [X18664] :
( ( ~ 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)),X18664)),X18664)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18664),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18664),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)),X18664)),X18664)),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,
! [X31564,X31565,X31566,X31567,X31568,X31569] :
( hBOOL(hAPP(hAPP(c_member(X31569),X31568),c_Map_Odom(X31569,X31567,X31566)))
| c_Map_Omap__add(X31569,X31567,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X31569,tc_Option_Ooption(X31567)),X31565),X31568),hAPP(c_Option_Ooption_OSome(X31567),X31564)),X31566) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X31569,tc_Option_Ooption(X31567)),c_Map_Omap__add(X31569,X31567,X31565,X31566)),X31568),hAPP(c_Option_Ooption_OSome(X31567),X31564)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5465])]) ).
fof(i_0_6973,plain,
! [X30842,X30843,X30844,X30845] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X30845)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30844),X30843))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30844,X30845),X30843),X30842) = hAPP(hAPP(c_Finite__Set_Ofold(X30844,X30845,hAPP(hAPP(c_COMBB(X30845,tc_fun(X30845,X30845),X30844),c_Lattices_Osemilattice__inf__class_Oinf(X30845)),X30842)),c_Orderings_Otop__class_Otop(X30845)),X30843) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INFI__fold__inf])]) ).
fof(i_0_6974,plain,
! [X30747,X30748,X30749,X30750] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X30750)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30749),X30748))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30749,X30750),X30748),X30747) = hAPP(hAPP(c_Finite__Set_Ofold(X30749,X30750,hAPP(hAPP(c_COMBB(X30750,tc_fun(X30750,X30750),X30749),c_Lattices_Osemilattice__sup__class_Osup(X30750)),X30747)),c_Orderings_Obot__class_Obot(X30750)),X30748) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUPR__fold__sup])]) ).
fof(i_0_6975,plain,
! [X30305,X30306,X30307,X30308] :
( ( c_Wellfounded_Oacyclic(X30308,X30305)
| ~ c_Wellfounded_Oacyclic(X30308,hAPP(hAPP(c_Set_Oinsert(tc_prod(X30308,X30308)),hAPP(hAPP(c_Product__Type_OPair(X30308,X30308),X30307),X30306)),X30305)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30308,X30308)),hAPP(hAPP(c_Product__Type_OPair(X30308,X30308),X30306),X30307)),c_Transitive__Closure_Ortrancl(X30308,X30305)))
| ~ c_Wellfounded_Oacyclic(X30308,hAPP(hAPP(c_Set_Oinsert(tc_prod(X30308,X30308)),hAPP(hAPP(c_Product__Type_OPair(X30308,X30308),X30307),X30306)),X30305)) )
& ( ~ c_Wellfounded_Oacyclic(X30308,X30305)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30308,X30308)),hAPP(hAPP(c_Product__Type_OPair(X30308,X30308),X30306),X30307)),c_Transitive__Closure_Ortrancl(X30308,X30305)))
| c_Wellfounded_Oacyclic(X30308,hAPP(hAPP(c_Set_Oinsert(tc_prod(X30308,X30308)),hAPP(hAPP(c_Product__Type_OPair(X30308,X30308),X30307),X30306)),X30305)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5466])])]) ).
fof(i_0_6976,plain,
! [X30301,X30302,X30303,X30304] :
( ( c_Wellfounded_Owf(X30304,X30301)
| ~ c_Wellfounded_Owf(X30304,hAPP(hAPP(c_Set_Oinsert(tc_prod(X30304,X30304)),hAPP(hAPP(c_Product__Type_OPair(X30304,X30304),X30303),X30302)),X30301)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30304,X30304)),hAPP(hAPP(c_Product__Type_OPair(X30304,X30304),X30302),X30303)),c_Transitive__Closure_Ortrancl(X30304,X30301)))
| ~ c_Wellfounded_Owf(X30304,hAPP(hAPP(c_Set_Oinsert(tc_prod(X30304,X30304)),hAPP(hAPP(c_Product__Type_OPair(X30304,X30304),X30303),X30302)),X30301)) )
& ( ~ c_Wellfounded_Owf(X30304,X30301)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30304,X30304)),hAPP(hAPP(c_Product__Type_OPair(X30304,X30304),X30302),X30303)),c_Transitive__Closure_Ortrancl(X30304,X30301)))
| c_Wellfounded_Owf(X30304,hAPP(hAPP(c_Set_Oinsert(tc_prod(X30304,X30304)),hAPP(hAPP(c_Product__Type_OPair(X30304,X30304),X30303),X30302)),X30301)) ) ),
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,
! [X30590,X30591,X30592,X30593,X30594,X30595] :
( ~ c_Relation_Osingle__valued(X30595,X30594,X30593)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30595,X30594)),hAPP(hAPP(c_Product__Type_OPair(X30595,X30594),X30592),X30591)),X30593))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30595,X30594)),hAPP(hAPP(c_Product__Type_OPair(X30595,X30594),X30592),X30590)),X30593))
| X30591 = X30590 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valuedD])]) ).
fof(i_0_6979,plain,
! [X17716,X17717,X17718,X17719,X17720] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17720),hAPP(hAPP(hAPP(c_Natural_Oupdate,X17719),c_Com_Ovname_OLoc(X17718)),hAPP(X17717,X17719))),X17716))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(X17718,X17717,X17720)),X17719),hAPP(hAPP(hAPP(c_Natural_Oupdate,X17716),c_Com_Ovname_OLoc(X17718)),hAPP(hAPP(c_Natural_Ogetlocs,X17719),X17718)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc_OLocal])]) ).
fof(i_0_6980,plain,
! [X29164,X29165,X29166] : 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),X29165)),X29164)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29166,tc_HOL_Obool)),hAPP(c_Set_OCollect(X29166),X29165)),hAPP(c_Set_OCollect(X29166),X29164)),
inference(variable_rename,[status(thm)],[fact_Collect__disj__eq]) ).
fof(i_0_6981,plain,
! [X29161,X29162,X29163] : hAPP(c_Set_OCollect(X29163),hAPP(hAPP(c_COMBS(X29163,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29163),c_fconj),X29162)),X29161)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29163,tc_HOL_Obool)),hAPP(c_Set_OCollect(X29163),X29162)),hAPP(c_Set_OCollect(X29163),X29161)),
inference(variable_rename,[status(thm)],[fact_Collect__conj__eq]) ).
fof(i_0_6982,plain,
! [X31500,X31501,X31502,X31503,X31505,X31506,X31507,X31510] :
( ( hBOOL(hAPP(hAPP(c_member(X31501),esk420_3(X31500,X31501,X31502)),X31502))
| ~ hBOOL(hAPP(hAPP(c_member(X31501),X31503),X31502))
| ~ c_Wellfounded_Owf(X31501,X31500) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31501,X31501)),hAPP(hAPP(c_Product__Type_OPair(X31501,X31501),X31505),esk420_3(X31500,X31501,X31502))),X31500))
| ~ hBOOL(hAPP(hAPP(c_member(X31501),X31505),X31502))
| ~ hBOOL(hAPP(hAPP(c_member(X31501),X31503),X31502))
| ~ c_Wellfounded_Owf(X31501,X31500) )
& ( hBOOL(hAPP(hAPP(c_member(X31507),esk422_2(X31506,X31507)),esk421_2(X31506,X31507)))
| c_Wellfounded_Owf(X31507,X31506) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X31507,X31507)),hAPP(hAPP(c_Product__Type_OPair(X31507,X31507),esk423_3(X31506,X31507,X31510)),X31510)),X31506))
| ~ hBOOL(hAPP(hAPP(c_member(X31507),X31510),esk421_2(X31506,X31507)))
| c_Wellfounded_Owf(X31507,X31506) )
& ( hBOOL(hAPP(hAPP(c_member(X31507),esk423_3(X31506,X31507,X31510)),esk421_2(X31506,X31507)))
| ~ hBOOL(hAPP(hAPP(c_member(X31507),X31510),esk421_2(X31506,X31507)))
| c_Wellfounded_Owf(X31507,X31506) ) ),
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,
! [X27138,X27139,X27140,X27141,X27142] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X27142),X27141),X27140))
| hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27142,tc_Option_Ooption(X27139)),c_Map_Orestrict__map(X27142,X27139,X27138,X27140)),X27141),c_Option_Ooption_ONone(X27139)) = c_Map_Orestrict__map(X27142,X27139,X27138,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27142,tc_HOL_Obool)),X27140),hAPP(hAPP(c_Set_Oinsert(X27142),X27141),c_Orderings_Obot__class_Obot(tc_fun(X27142,tc_HOL_Obool))))) )
& ( hBOOL(hAPP(hAPP(c_member(X27142),X27141),X27140))
| hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27142,tc_Option_Ooption(X27139)),c_Map_Orestrict__map(X27142,X27139,X27138,X27140)),X27141),c_Option_Ooption_ONone(X27139)) = c_Map_Orestrict__map(X27142,X27139,X27138,X27140) ) ),
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,
! [X32218,X32219,X32220,X32221,X32222,X32224] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X32222),X32218),hAPP(c_List_Oset(X32222),X32221)))
| hAPP(c_Map_Omap__of(X32222,X32220,hAPP(hAPP(c_List_Ozip(X32222,X32220),X32221),X32219)),X32218) = hAPP(c_Option_Ooption_OSome(X32220),esk442_5(X32218,X32219,X32220,X32221,X32222))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32222)),X32221) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32220)),X32219) )
& ( hAPP(c_Map_Omap__of(X32222,X32220,hAPP(hAPP(c_List_Ozip(X32222,X32220),X32221),X32219)),X32218) != hAPP(c_Option_Ooption_OSome(X32220),X32224)
| hBOOL(hAPP(hAPP(c_member(X32222),X32218),hAPP(c_List_Oset(X32222),X32221)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32222)),X32221) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32220)),X32219) ) ),
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,
! [X30401,X30402,X30403,X30404] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30404,X30404)),hAPP(hAPP(c_Product__Type_OPair(X30404,X30404),X30403),X30402)),c_Transitive__Closure_Ortrancl(X30404,hAPP(c_Relation_Oconverse(X30404,X30404),X30401))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30404,X30404)),hAPP(hAPP(c_Product__Type_OPair(X30404,X30404),X30402),X30403)),c_Transitive__Closure_Ortrancl(X30404,X30401))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__converseD])]) ).
fof(i_0_6993,plain,
! [X29626,X29627,X29628,X29629] :
( ~ c_Wellfounded_Owf(X29629,X29628)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29629,X29629)),hAPP(hAPP(c_Product__Type_OPair(X29629,X29629),X29627),X29626)),X29628))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29629,X29629)),hAPP(hAPP(c_Product__Type_OPair(X29629,X29629),X29626),X29627)),X29628)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5478])]) ).
fof(i_0_6994,plain,
! [X29622,X29623,X29624,X29625] :
( ~ c_Wellfounded_Owf(X29625,X29624)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29625,X29625)),hAPP(hAPP(c_Product__Type_OPair(X29625,X29625),X29623),X29622)),X29624))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29625,X29625)),hAPP(hAPP(c_Product__Type_OPair(X29625,X29625),X29622),X29623)),X29624)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5479])]) ).
fof(i_0_6995,plain,
! [X32417,X32418,X32419,X32420,X32421] :
( ~ class_Rings_Osemiring__0(X32421)
| hAPP(c_List_Omonoid__add__class_Olistsum(X32421),hAPP(hAPP(c_List_Omap(X32420,X32421),hAPP(hAPP(c_COMBB(X32421,X32421,X32420),hAPP(c_Groups_Otimes__class_Otimes(X32421),X32419)),X32418)),X32417)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X32421),X32419),hAPP(c_List_Omonoid__add__class_Olistsum(X32421),hAPP(hAPP(c_List_Omap(X32420,X32421),X32418),X32417))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__const__mult])]) ).
fof(i_0_6996,plain,
! [X24333,X24334,X24335,X24336,X24337,X24338] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X24338,X24337),tc_HOL_Obool)),X24336),X24335))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24338,tc_HOL_Obool)),X24334),X24333))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24337,tc_HOL_Obool)),hAPP(c_Relation_OImage(X24338,X24337,X24336),X24334)),hAPP(c_Relation_OImage(X24338,X24337,X24335),X24333))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__mono])]) ).
fof(i_0_6997,plain,
! [X22558,X22559,X22560] :
( ( X22560 = 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),X22558)),X22559)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22558))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22560,X22559),X22558)) )
& ( X22559 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22558) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22560,X22559),X22558)) )
& ( 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),X22558)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22559))
| X22559 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22560,X22559),X22558)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22558)),X22559))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22559))
| X22559 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22560,X22559),X22558)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22559),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22558)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22559))
| X22559 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22560,X22559),X22558)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22558)),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)),X22559))
| X22559 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22560,X22559),X22558)) )
& ( X22559 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X22559 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X22560 != 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),X22558)),X22559)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22558))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22560,X22559),X22558)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22559))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22559))
| X22559 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X22560 != 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),X22558)),X22559)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22558))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22560,X22559),X22558)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22559),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22558)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22558)),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)),X22559))
| X22559 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X22560 != 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),X22558)),X22559)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22558))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22560,X22559),X22558)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22559))
| ~ 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),X22558)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22558)),X22559))
| X22559 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X22560 != 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),X22558)),X22559)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22558))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22560,X22559),X22558)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22559),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22558)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22558)),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),X22558)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22558)),X22559))
| X22559 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X22560 != 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),X22558)),X22559)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22558))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22560,X22559),X22558)) )
& ( X22559 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22558) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X22560 != 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),X22558)),X22559)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22558))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22560,X22559),X22558)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22559))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22559))
| hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22558) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X22560 != 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),X22558)),X22559)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22558))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22560,X22559),X22558)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22559),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22558)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22558)),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)),X22559))
| hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22558) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X22560 != 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),X22558)),X22559)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22558))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22560,X22559),X22558)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22559))
| ~ 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),X22558)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22558)),X22559))
| hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22558) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X22560 != 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),X22558)),X22559)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22558))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22560,X22559),X22558)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22559),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22558)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22558)),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),X22558)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22558)),X22559))
| hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22558) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X22560 != 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),X22558)),X22559)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22558))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22560,X22559),X22558)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5480])])]) ).
fof(i_0_6998,plain,
! [X23797,X23798,X23799,X23800,X23801] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X23801,X23800)),hAPP(X23801,X23799)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23798,X23798)),hAPP(hAPP(c_Product__Type_OPair(X23798,X23798),X23800),X23799)),X23797))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X23798,X23798)),hAPP(hAPP(c_Product__Type_OPair(X23798,X23798),X23800),X23799)),c_Wellfounded_Omlex__prod(X23798,X23801,X23797))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__leq])]) ).
fof(i_0_6999,plain,
! [X21816,X21817,X21818,X21819] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21819),c_Groups_Ozero__class_Ozero(X21819)),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21819),X21818),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21819),X21816),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21819),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21819),X21818),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817))),X21816))
| ~ class_Fields_Olinordered__field__inverse__zero(X21819)
| ~ class_Int_Onumber(X21819) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21819),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817)),c_Groups_Ozero__class_Ozero(X21819)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21819),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21819),X21816),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817))),X21818))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21819),c_Groups_Ozero__class_Ozero(X21819)),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21819),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21819),X21818),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817))),X21816))
| ~ class_Fields_Olinordered__field__inverse__zero(X21819)
| ~ class_Int_Onumber(X21819) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21819),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817)),c_Groups_Ozero__class_Ozero(X21819)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21819),c_Groups_Ozero__class_Ozero(X21819)),X21816))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21819),c_Groups_Ozero__class_Ozero(X21819)),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21819),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21819),X21818),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817))),X21816))
| ~ class_Fields_Olinordered__field__inverse__zero(X21819)
| ~ class_Int_Onumber(X21819) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21819),c_Groups_Ozero__class_Ozero(X21819)),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21819),c_Groups_Ozero__class_Ozero(X21819)),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21819),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21819),X21818),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817))),X21816))
| ~ class_Fields_Olinordered__field__inverse__zero(X21819)
| ~ class_Int_Onumber(X21819) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21819),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817)),c_Groups_Ozero__class_Ozero(X21819)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21819),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817)),c_Groups_Ozero__class_Ozero(X21819)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21819),c_Groups_Ozero__class_Ozero(X21819)),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21819),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21819),X21818),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817))),X21816))
| ~ class_Fields_Olinordered__field__inverse__zero(X21819)
| ~ class_Int_Onumber(X21819) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21819),c_Groups_Ozero__class_Ozero(X21819)),X21816))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21819),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817)),c_Groups_Ozero__class_Ozero(X21819)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21819),c_Groups_Ozero__class_Ozero(X21819)),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21819),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21819),X21818),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817))),X21816))
| ~ class_Fields_Olinordered__field__inverse__zero(X21819)
| ~ class_Int_Onumber(X21819) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21819),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817)),c_Groups_Ozero__class_Ozero(X21819)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21819),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21819),X21816),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817))),X21818))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21819),c_Groups_Ozero__class_Ozero(X21819)),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21819),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21819),X21818),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817))),X21816))
| ~ class_Fields_Olinordered__field__inverse__zero(X21819)
| ~ class_Int_Onumber(X21819) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21819),c_Groups_Ozero__class_Ozero(X21819)),X21816))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21819),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21819),X21816),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817))),X21818))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21819),c_Groups_Ozero__class_Ozero(X21819)),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21819),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21819),X21818),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817))),X21816))
| ~ class_Fields_Olinordered__field__inverse__zero(X21819)
| ~ class_Int_Onumber(X21819) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21819),c_Groups_Ozero__class_Ozero(X21819)),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21819),X21818),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21819),X21816),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21819),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21819),X21818),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817))),X21816))
| ~ class_Fields_Olinordered__field__inverse__zero(X21819)
| ~ class_Int_Onumber(X21819) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21819),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817)),c_Groups_Ozero__class_Ozero(X21819)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21819),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817)),c_Groups_Ozero__class_Ozero(X21819)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21819),X21818),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21819),X21816),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21819),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21819),X21818),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817))),X21816))
| ~ class_Fields_Olinordered__field__inverse__zero(X21819)
| ~ class_Int_Onumber(X21819) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21819),c_Groups_Ozero__class_Ozero(X21819)),X21816))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21819),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817)),c_Groups_Ozero__class_Ozero(X21819)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21819),X21818),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21819),X21816),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21819),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21819),X21818),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817))),X21816))
| ~ class_Fields_Olinordered__field__inverse__zero(X21819)
| ~ class_Int_Onumber(X21819) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21819),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817)),c_Groups_Ozero__class_Ozero(X21819)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21819),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21819),X21816),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817))),X21818))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21819),X21818),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21819),X21816),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21819),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21819),X21818),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817))),X21816))
| ~ class_Fields_Olinordered__field__inverse__zero(X21819)
| ~ class_Int_Onumber(X21819) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21819),c_Groups_Ozero__class_Ozero(X21819)),X21816))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21819),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21819),X21816),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817))),X21818))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21819),X21818),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21819),X21816),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21819),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21819),X21818),hAPP(c_Int_Onumber__class_Onumber__of(X21819),X21817))),X21816))
| ~ class_Fields_Olinordered__field__inverse__zero(X21819)
| ~ class_Int_Onumber(X21819) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5481])])]) ).
fof(i_0_7000,plain,
! [X21806,X21807,X21808,X21809] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),c_Groups_Ozero__class_Ozero(X21809)),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),X21808),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21809),X21806),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21809),X21808),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807))),X21806))
| ~ class_Fields_Olinordered__field__inverse__zero(X21809)
| ~ class_Int_Onumber(X21809) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807)),c_Groups_Ozero__class_Ozero(X21809)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21809),X21806),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807))),X21808))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),c_Groups_Ozero__class_Ozero(X21809)),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21809),X21808),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807))),X21806))
| ~ class_Fields_Olinordered__field__inverse__zero(X21809)
| ~ class_Int_Onumber(X21809) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807)),c_Groups_Ozero__class_Ozero(X21809)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),c_Groups_Ozero__class_Ozero(X21809)),X21806))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),c_Groups_Ozero__class_Ozero(X21809)),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21809),X21808),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807))),X21806))
| ~ class_Fields_Olinordered__field__inverse__zero(X21809)
| ~ class_Int_Onumber(X21809) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),c_Groups_Ozero__class_Ozero(X21809)),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),c_Groups_Ozero__class_Ozero(X21809)),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21809),X21808),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807))),X21806))
| ~ class_Fields_Olinordered__field__inverse__zero(X21809)
| ~ class_Int_Onumber(X21809) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807)),c_Groups_Ozero__class_Ozero(X21809)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807)),c_Groups_Ozero__class_Ozero(X21809)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),c_Groups_Ozero__class_Ozero(X21809)),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21809),X21808),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807))),X21806))
| ~ class_Fields_Olinordered__field__inverse__zero(X21809)
| ~ class_Int_Onumber(X21809) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),c_Groups_Ozero__class_Ozero(X21809)),X21806))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807)),c_Groups_Ozero__class_Ozero(X21809)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),c_Groups_Ozero__class_Ozero(X21809)),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21809),X21808),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807))),X21806))
| ~ class_Fields_Olinordered__field__inverse__zero(X21809)
| ~ class_Int_Onumber(X21809) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807)),c_Groups_Ozero__class_Ozero(X21809)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21809),X21806),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807))),X21808))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),c_Groups_Ozero__class_Ozero(X21809)),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21809),X21808),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807))),X21806))
| ~ class_Fields_Olinordered__field__inverse__zero(X21809)
| ~ class_Int_Onumber(X21809) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),c_Groups_Ozero__class_Ozero(X21809)),X21806))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21809),X21806),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807))),X21808))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),c_Groups_Ozero__class_Ozero(X21809)),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21809),X21808),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807))),X21806))
| ~ class_Fields_Olinordered__field__inverse__zero(X21809)
| ~ class_Int_Onumber(X21809) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),c_Groups_Ozero__class_Ozero(X21809)),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),X21808),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21809),X21806),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21809),X21808),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807))),X21806))
| ~ class_Fields_Olinordered__field__inverse__zero(X21809)
| ~ class_Int_Onumber(X21809) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807)),c_Groups_Ozero__class_Ozero(X21809)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807)),c_Groups_Ozero__class_Ozero(X21809)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),X21808),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21809),X21806),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21809),X21808),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807))),X21806))
| ~ class_Fields_Olinordered__field__inverse__zero(X21809)
| ~ class_Int_Onumber(X21809) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),c_Groups_Ozero__class_Ozero(X21809)),X21806))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807)),c_Groups_Ozero__class_Ozero(X21809)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),X21808),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21809),X21806),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21809),X21808),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807))),X21806))
| ~ class_Fields_Olinordered__field__inverse__zero(X21809)
| ~ class_Int_Onumber(X21809) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807)),c_Groups_Ozero__class_Ozero(X21809)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21809),X21806),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807))),X21808))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),X21808),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21809),X21806),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21809),X21808),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807))),X21806))
| ~ class_Fields_Olinordered__field__inverse__zero(X21809)
| ~ class_Int_Onumber(X21809) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),c_Groups_Ozero__class_Ozero(X21809)),X21806))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21809),X21806),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807))),X21808))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),X21808),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21809),X21806),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21809),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21809),X21808),hAPP(c_Int_Onumber__class_Onumber__of(X21809),X21807))),X21806))
| ~ class_Fields_Olinordered__field__inverse__zero(X21809)
| ~ class_Int_Onumber(X21809) ) ),
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,
! [X28675,X28676,X28677,X28678] : hAPP(c_Set_Oimage(tc_prod(X28678,X28677),tc_prod(X28677,X28678),hAPP(c_Product__Type_Oprod_Oprod__case(X28678,X28677,tc_prod(X28677,X28678)),hAPP(c_COMBC(X28677,X28678,tc_prod(X28677,X28678)),c_Product__Type_OPair(X28677,X28678)))),hAPP(hAPP(c_Product__Type_OSigma(X28678,X28677),X28676),hAPP(c_COMBK(tc_fun(X28677,tc_HOL_Obool),X28678),X28675))) = hAPP(hAPP(c_Product__Type_OSigma(X28677,X28678),X28675),hAPP(c_COMBK(tc_fun(X28678,tc_HOL_Obool),X28677),X28676)),
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,
! [X24620,X24621,X24622,X24623] :
( ~ hBOOL(hAPP(hAPP(c_member(X24623),X24622),X24621))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X24623,tc_HOL_Obool)),hAPP(c_Relation_OImage(X24623,X24623,X24620),hAPP(hAPP(c_Set_Oinsert(X24623),X24622),c_Orderings_Obot__class_Obot(tc_fun(X24623,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24623),X24621),X24620))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotientI])]) ).
fof(i_0_7005,plain,
! [X17951,X17952,X17953,X17954,X17955,X17956] :
( ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X17956),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17955),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(X17954,X17955)),X17953,X17952)
| c_Natural_Oevaln(c_Com_Ocom_OCall(X17951,X17956,X17954),X17955,X17953,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,X17952),hAPP(c_Natural_Ogetlocs,X17955))),X17951),hAPP(hAPP(c_Natural_Ogetlocs,X17952),c_Com_ORes))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln_OCall])]) ).
fof(i_0_7006,plain,
! [X24381,X24382,X24383,X24384,X24385] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X24385),X24384),hAPP(c_Relation_OImage(X24383,X24385,X24382),hAPP(hAPP(c_Set_Oinsert(X24383),X24381),c_Orderings_Obot__class_Obot(tc_fun(X24383,tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X24383,X24385)),hAPP(hAPP(c_Product__Type_OPair(X24383,X24385),X24381),X24384)),X24382)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24383,X24385)),hAPP(hAPP(c_Product__Type_OPair(X24383,X24385),X24381),X24384)),X24382))
| hBOOL(hAPP(hAPP(c_member(X24385),X24384),hAPP(c_Relation_OImage(X24383,X24385,X24382),hAPP(hAPP(c_Set_Oinsert(X24383),X24381),c_Orderings_Obot__class_Obot(tc_fun(X24383,tc_HOL_Obool)))))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__singleton__iff])]) ).
fof(i_0_7007,plain,
! [X22276,X22277,X22278] :
( ( 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),esk94_3(X22276,X22277,X22278)),esk95_3(X22276,X22277,X22278))))
| hBOOL(hAPP(hAPP(X22276,X22278),X22277))
| ~ 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),X22278),X22277))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk95_3(X22276,X22277,X22278)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(X22276,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk94_3(X22276,X22277,X22278))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk95_3(X22276,X22277,X22278))))
| hBOOL(hAPP(hAPP(X22276,X22278),X22277))
| ~ 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),X22278),X22277))) )
& ( ~ hBOOL(hAPP(hAPP(X22276,esk94_3(X22276,X22277,X22278)),esk95_3(X22276,X22277,X22278)))
| hBOOL(hAPP(hAPP(X22276,X22278),X22277))
| ~ 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),X22278),X22277))) ) ),
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,
! [X26726,X26727,X26728,X26729] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk216_4(X26726,X26727,X26728,X26729)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26728)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26729),X26727))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26729),X26728)),X26727))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X26727),X26726))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26728)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk217_4(X26726,X26727,X26728,X26729)),X26726))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26729),X26727))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26729),X26728)),X26727))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X26727),X26726))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26728)) )
& ( X26729 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk217_4(X26726,X26727,X26728,X26729)),esk216_4(X26726,X26727,X26728,X26729))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26729),X26727))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26729),X26728)),X26727))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X26727),X26726))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26728)) ) ),
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,
! [X20190,X20191,X20192,X20193] :
( ~ class_Divides_Osemiring__div(X20193)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20193),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20193),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20193),X20192),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20193),X20191),X20192))),c_Divides_Odiv__class_Omod(X20193,X20191,X20192))),X20190) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20193),X20191),X20190) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mod__equality2])]) ).
fof(i_0_7010,plain,
! [X32952,X32953,X32954,X32955,X32956,X32957,X32958] : c_Map_Omap__upds(X32958,X32957,X32956,hAPP(hAPP(c_List_Olist_OCons(X32958),X32955),X32954),hAPP(hAPP(c_List_Olist_OCons(X32957),X32953),X32952)) = c_Map_Omap__upds(X32958,X32957,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X32958,tc_Option_Ooption(X32957)),X32956),X32955),hAPP(c_Option_Ooption_OSome(X32957),X32953)),X32954,X32952),
inference(variable_rename,[status(thm)],[fact_map__upds__Cons]) ).
fof(i_0_7011,plain,
! [X33710,X33711,X33712,X33715,X33716,X33717,X33718,X33719] :
( ( ~ 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)),c_List_Olist_ONil(X33712)),X33711)),c_List_Olexord(X33712,X33710)))
| X33711 = hAPP(hAPP(c_List_Olist_OCons(X33712),esk472_3(X33710,X33711,X33712)),esk473_3(X33710,X33711,X33712)) )
& ( X33716 != hAPP(hAPP(c_List_Olist_OCons(X33717),X33718),X33719)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33717),tc_List_Olist(X33717))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33717),tc_List_Olist(X33717)),c_List_Olist_ONil(X33717)),X33716)),c_List_Olexord(X33717,X33715))) ) ),
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,
! [X28389,X28390,X28391,X28392] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28392,tc_HOL_Obool)),hAPP(c_Set_Oimage(X28391,X28392,X28390),hAPP(c_Set_Ovimage(X28391,X28392,X28390),X28389))),X28389)),
inference(variable_rename,[status(thm)],[fact_image__vimage__subset]) ).
fof(i_0_7013,plain,
! [X34187,X34188,X34189,X34190,X34191] :
( ~ class_Orderings_Olinorder(X34191)
| ~ c_Fun_Oinj__on(X34190,X34191,X34189,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X34190,tc_HOL_Obool)),hAPP(c_List_Oset(X34190),X34188)),hAPP(c_List_Oset(X34190),X34187)))
| ~ c_List_Olinorder__class_Osorted(X34191,hAPP(hAPP(c_List_Omap(X34190,X34191),X34189),X34188))
| ~ hBOOL(hAPP(c_List_Odistinct(X34191),hAPP(hAPP(c_List_Omap(X34190,X34191),X34189),X34188)))
| ~ c_List_Olinorder__class_Osorted(X34191,hAPP(hAPP(c_List_Omap(X34190,X34191),X34189),X34187))
| ~ hBOOL(hAPP(c_List_Odistinct(X34191),hAPP(hAPP(c_List_Omap(X34190,X34191),X34189),X34187)))
| hAPP(c_List_Oset(X34190),X34188) != hAPP(c_List_Oset(X34190),X34187)
| X34188 = X34187 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__sorted__distinct__set__unique])]) ).
fof(i_0_7014,plain,
! [X18220,X18221,X18222,X18223,X18224] :
( ( hBOOL(hAPP(X18224,X18222))
| X18220 = X18222
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X18224,X18223),X18222,X18221,X18220) )
& ( c_Natural_Oevaln(X18223,X18222,X18221,esk32_5(X18220,X18221,X18222,X18223,X18224))
| X18220 = X18222
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X18224,X18223),X18222,X18221,X18220) )
& ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X18224,X18223),esk32_5(X18220,X18221,X18222,X18223,X18224),X18221,X18220)
| X18220 = X18222
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X18224,X18223),X18222,X18221,X18220) )
& ( hBOOL(hAPP(X18224,X18222))
| ~ hBOOL(hAPP(X18224,X18222))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X18224,X18223),X18222,X18221,X18220) )
& ( c_Natural_Oevaln(X18223,X18222,X18221,esk32_5(X18220,X18221,X18222,X18223,X18224))
| ~ hBOOL(hAPP(X18224,X18222))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X18224,X18223),X18222,X18221,X18220) )
& ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X18224,X18223),esk32_5(X18220,X18221,X18222,X18223,X18224),X18221,X18220)
| ~ hBOOL(hAPP(X18224,X18222))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X18224,X18223),X18222,X18221,X18220) ) ),
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,
! [X17806,X17807,X17808,X17809,X17810,X17812,X17813,X17814,X17815,X17816,X17817] :
( ( hBOOL(hAPP(X17810,X17808))
| X17806 = X17808
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17810,X17809),X17808,X17807,X17806) )
& ( c_Natural_Oevaln(X17809,X17808,X17807,esk17_5(X17806,X17807,X17808,X17809,X17810))
| X17806 = X17808
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17810,X17809),X17808,X17807,X17806) )
& ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X17810,X17809),esk17_5(X17806,X17807,X17808,X17809,X17810),X17807,X17806)
| X17806 = X17808
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17810,X17809),X17808,X17807,X17806) )
& ( hBOOL(hAPP(X17810,X17808))
| ~ hBOOL(hAPP(X17810,X17808))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17810,X17809),X17808,X17807,X17806) )
& ( c_Natural_Oevaln(X17809,X17808,X17807,esk17_5(X17806,X17807,X17808,X17809,X17810))
| ~ hBOOL(hAPP(X17810,X17808))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17810,X17809),X17808,X17807,X17806) )
& ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X17810,X17809),esk17_5(X17806,X17807,X17808,X17809,X17810),X17807,X17806)
| ~ hBOOL(hAPP(X17810,X17808))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17810,X17809),X17808,X17807,X17806) )
& ( X17812 != X17814
| hBOOL(hAPP(X17816,X17814))
| c_Natural_Oevaln(c_Com_Ocom_OWhile(X17816,X17815),X17814,X17813,X17812) )
& ( ~ hBOOL(hAPP(X17816,X17814))
| ~ c_Natural_Oevaln(X17815,X17814,X17813,X17817)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17816,X17815),X17817,X17813,X17812)
| c_Natural_Oevaln(c_Com_Ocom_OWhile(X17816,X17815),X17814,X17813,X17812) ) ),
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,
! [X19782,X19783,X19784,X19785] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19785))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19784))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19784),X19783))
| 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),X19783),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19782,X19785))),X19784))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux3])]) ).
fof(i_0_7017,plain,
! [X28812,X28813,X28814] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28814),X28813))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28814,X28814),tc_HOL_Obool)),X28812),hAPP(hAPP(c_Product__Type_OSigma(X28814,X28814),X28813),hAPP(c_COMBK(tc_fun(X28814,tc_HOL_Obool),X28814),X28813))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X28814,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X28814),X28813),X28812))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__quotient])]) ).
fof(i_0_7018,plain,
! [X33554,X33555,X33556,X33557,X33558,X33559] : hAPP(c_List_Ofoldl(X33559,X33558,X33557,X33556),hAPP(hAPP(c_List_Oappend(X33558),X33555),X33554)) = hAPP(c_List_Ofoldl(X33559,X33558,X33557,hAPP(c_List_Ofoldl(X33559,X33558,X33557,X33556),X33555)),X33554),
inference(variable_rename,[status(thm)],[fact_foldl__append]) ).
fof(i_0_7019,plain,
! [X30405,X30406,X30407,X30408] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30408,X30408)),hAPP(hAPP(c_Product__Type_OPair(X30408,X30408),X30407),X30406)),c_Transitive__Closure_Ortrancl(X30408,X30405)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30408,X30408)),hAPP(hAPP(c_Product__Type_OPair(X30408,X30408),X30406),X30407)),c_Transitive__Closure_Ortrancl(X30408,hAPP(c_Relation_Oconverse(X30408,X30408),X30405)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__converseI])]) ).
fof(i_0_7020,plain,
! [X33426,X33427,X33428,X33429,X33430] : hAPP(hAPP(c_List_Ozip(X33430,X33429),hAPP(hAPP(c_List_Oappend(X33430),X33428),X33427)),X33426) = hAPP(hAPP(c_List_Oappend(tc_prod(X33430,X33429)),hAPP(hAPP(c_List_Ozip(X33430,X33429),X33428),hAPP(hAPP(c_List_Otake(X33429),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33430)),X33428)),X33426))),hAPP(hAPP(c_List_Ozip(X33430,X33429),X33427),hAPP(hAPP(c_List_Odrop(X33429),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33430)),X33428)),X33426))),
inference(variable_rename,[status(thm)],[fact_zip__append1]) ).
fof(i_0_7021,plain,
! [X24176,X24177,X24178,X24179] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24179,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24179,tc_HOL_Obool)),X24178),X24177)),X24176))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24179,tc_HOL_Obool)),X24178),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24179,tc_HOL_Obool)),X24177),X24176))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24179,tc_HOL_Obool)),X24178),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24179,tc_HOL_Obool)),X24177),X24176)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24179,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24179,tc_HOL_Obool)),X24178),X24177)),X24176)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__subset__conv])]) ).
fof(i_0_7022,plain,
! [X17415,X17416,X17417,X17418,X17419] :
( ( c_Natural_Oevaln(X17419,X17417,X17416,esk9_5(X17415,X17416,X17417,X17418,X17419))
| ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(X17419,X17418),X17417,X17416,X17415) )
& ( c_Natural_Oevaln(X17418,esk9_5(X17415,X17416,X17417,X17418,X17419),X17416,X17415)
| ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(X17419,X17418),X17417,X17416,X17415) ) ),
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,
! [X17357,X17358,X17359,X17360,X17361,X17363,X17364,X17365,X17366,X17367,X17368] :
( ( c_Natural_Oevaln(X17361,X17359,X17358,esk8_5(X17357,X17358,X17359,X17360,X17361))
| ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(X17361,X17360),X17359,X17358,X17357) )
& ( c_Natural_Oevaln(X17360,esk8_5(X17357,X17358,X17359,X17360,X17361),X17358,X17357)
| ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(X17361,X17360),X17359,X17358,X17357) )
& ( ~ c_Natural_Oevaln(X17367,X17365,X17364,X17368)
| ~ c_Natural_Oevaln(X17366,X17368,X17364,X17363)
| c_Natural_Oevaln(c_Com_Ocom_OSemi(X17367,X17366),X17365,X17364,X17363) ) ),
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,
! [X25156,X25157,X25158,X25159] :
( ( X25158 = hAPP(c_Relation_OImage(X25159,X25159,X25156),hAPP(hAPP(c_Set_Oinsert(X25159),esk132_4(X25156,X25157,X25158,X25159)),c_Orderings_Obot__class_Obot(tc_fun(X25159,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25159,tc_HOL_Obool)),X25158),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25159),X25157),X25156))) )
& ( hBOOL(hAPP(hAPP(c_member(X25159),esk132_4(X25156,X25157,X25158,X25159)),X25157))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25159,tc_HOL_Obool)),X25158),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25159),X25157),X25156))) ) ),
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,
! [X31634,X31635,X31636,X31637,X31638,X31639] : c_Map_Omap__add(X31639,X31638,X31637,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X31639,tc_Option_Ooption(X31638)),X31636),X31635),hAPP(c_Option_Ooption_OSome(X31638),X31634))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X31639,tc_Option_Ooption(X31638)),c_Map_Omap__add(X31639,X31638,X31637,X31636)),X31635),hAPP(c_Option_Ooption_OSome(X31638),X31634)),
inference(variable_rename,[status(thm)],[fact_map__add__upd]) ).
fof(i_0_7030,plain,
! [X26732,X26733,X26734,X26735] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk218_4(X26732,X26733,X26734,X26735)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26734)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26735),X26732))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26735),X26734)),X26732))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26734)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk219_4(X26732,X26733,X26734,X26735)),X26733))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26735),X26732))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26735),X26734)),X26732))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26734)) )
& ( X26735 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk219_4(X26732,X26733,X26734,X26735)),esk218_4(X26732,X26733,X26734,X26735))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26735),X26732))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26735),X26734)),X26732))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26734)) ) ),
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,
! [X26752,X26753,X26754,X26755] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk226_4(X26752,X26753,X26754,X26755)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26754)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26755),X26752))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26755),X26754)),X26752))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26754)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk227_4(X26752,X26753,X26754,X26755)),X26753))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26755),X26752))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26755),X26754)),X26752))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26754)) )
& ( X26755 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk227_4(X26752,X26753,X26754,X26755)),esk226_4(X26752,X26753,X26754,X26755))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26755),X26752))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26755),X26754)),X26752))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26754)) ) ),
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,
! [X33404,X33405,X33406,X33407,X33408] :
( ( X33407 = hAPP(hAPP(c_List_Otake(X33408),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33408)),X33407)),X33405)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33408)),X33407)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33408)),X33405)))
| hAPP(hAPP(c_List_Oappend(X33408),X33407),X33406) != hAPP(hAPP(c_List_Oappend(X33408),X33405),X33404) )
& ( X33406 = hAPP(hAPP(c_List_Oappend(X33408),hAPP(hAPP(c_List_Odrop(X33408),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33408)),X33407)),X33405)),X33404)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33408)),X33407)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33408)),X33405)))
| hAPP(hAPP(c_List_Oappend(X33408),X33407),X33406) != hAPP(hAPP(c_List_Oappend(X33408),X33405),X33404) )
& ( hAPP(hAPP(c_List_Otake(X33408),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33408)),X33405)),X33407) = X33405
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33408)),X33407)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33408)),X33405)))
| hAPP(hAPP(c_List_Oappend(X33408),X33407),X33406) != hAPP(hAPP(c_List_Oappend(X33408),X33405),X33404) )
& ( hAPP(hAPP(c_List_Oappend(X33408),hAPP(hAPP(c_List_Odrop(X33408),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33408)),X33405)),X33407)),X33406) = X33404
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33408)),X33407)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33408)),X33405)))
| hAPP(hAPP(c_List_Oappend(X33408),X33407),X33406) != hAPP(hAPP(c_List_Oappend(X33408),X33405),X33404) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33408)),X33407)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33408)),X33405)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33408)),X33407)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33408)),X33405)))
| hAPP(hAPP(c_List_Oappend(X33408),X33407),X33406) = hAPP(hAPP(c_List_Oappend(X33408),X33405),X33404) )
& ( hAPP(hAPP(c_List_Otake(X33408),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33408)),X33405)),X33407) != X33405
| hAPP(hAPP(c_List_Oappend(X33408),hAPP(hAPP(c_List_Odrop(X33408),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33408)),X33405)),X33407)),X33406) != X33404
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33408)),X33407)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33408)),X33405)))
| hAPP(hAPP(c_List_Oappend(X33408),X33407),X33406) = hAPP(hAPP(c_List_Oappend(X33408),X33405),X33404) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33408)),X33407)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33408)),X33405)))
| X33407 != hAPP(hAPP(c_List_Otake(X33408),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33408)),X33407)),X33405)
| X33406 != hAPP(hAPP(c_List_Oappend(X33408),hAPP(hAPP(c_List_Odrop(X33408),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33408)),X33407)),X33405)),X33404)
| hAPP(hAPP(c_List_Oappend(X33408),X33407),X33406) = hAPP(hAPP(c_List_Oappend(X33408),X33405),X33404) )
& ( hAPP(hAPP(c_List_Otake(X33408),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33408)),X33405)),X33407) != X33405
| hAPP(hAPP(c_List_Oappend(X33408),hAPP(hAPP(c_List_Odrop(X33408),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33408)),X33405)),X33407)),X33406) != X33404
| X33407 != hAPP(hAPP(c_List_Otake(X33408),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33408)),X33407)),X33405)
| X33406 != hAPP(hAPP(c_List_Oappend(X33408),hAPP(hAPP(c_List_Odrop(X33408),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33408)),X33407)),X33405)),X33404)
| hAPP(hAPP(c_List_Oappend(X33408),X33407),X33406) = hAPP(hAPP(c_List_Oappend(X33408),X33405),X33404) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5492])])]) ).
fof(i_0_7033,plain,
! [X25720,X25721,X25722,X25723,X25724] :
( ~ class_Groups_Ocomm__monoid__mult(X25724)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25723),X25722))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25723),X25721))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25724),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25723,X25724),X25720),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25723,tc_HOL_Obool)),X25722),X25721))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25723,X25724),X25720),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25723,tc_HOL_Obool)),X25722),X25721))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25724),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25723,X25724),X25720),X25722)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25723,X25724),X25720),X25721)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__Un__Int])]) ).
fof(i_0_7034,plain,
! [X25715,X25716,X25717,X25718,X25719] :
( ~ class_Groups_Ocomm__monoid__mult(X25719)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25718),X25717))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25718),X25716))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25719),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25718,X25719),X25715),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25718,tc_HOL_Obool)),X25717),X25716))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25718,X25719),X25715),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25718,tc_HOL_Obool)),X25717),X25716))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25719),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25718,X25719),X25715),X25717)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25718,X25719),X25715),X25716)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__inter])]) ).
fof(i_0_7035,plain,
! [X27318,X27319,X27320,X27321,X27322] :
( ~ class_Groups_Ocomm__monoid__add(X27322)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27321),X27320))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27321),X27319))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27322),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27321,X27322),X27318),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27321,tc_HOL_Obool)),X27320),X27319))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27321,X27322),X27318),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27321,tc_HOL_Obool)),X27320),X27319))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27322),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27321,X27322),X27318),X27320)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27321,X27322),X27318),X27319)) ),
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,
! [X25169,X25170,X25171,X25172,X25173,X25174] :
( ~ hBOOL(hAPP(hAPP(X25174,X25173),X25172))
| ~ hBOOL(hAPP(hAPP(X25171,X25173),X25172))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25170,tc_fun(X25169,tc_HOL_Obool))),X25174),X25171),X25173),X25172)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2I])]) ).
fof(i_0_7042,plain,
! [X28475,X28476,X28477,X28478,X28479] :
( hAPP(c_Set_Oimage(X28479,X28478,X28477),c_Orderings_Otop__class_Otop(tc_fun(X28479,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X28478,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28479,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X28479,X28478,X28477),X28476)),X28475))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28478,tc_HOL_Obool)),X28476),hAPP(c_Set_Oimage(X28479,X28478,X28477),X28475))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__subsetD])]) ).
fof(i_0_7043,plain,
! [X26715,X26716,X26717,X26718] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk212_4(X26715,X26716,X26717,X26718)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26717)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26716),X26718))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26716),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26718),X26717)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X26716),X26715))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26717)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk213_4(X26715,X26716,X26717,X26718)),X26715))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26716),X26718))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26716),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26718),X26717)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X26716),X26715))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26717)) )
& ( X26718 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk213_4(X26715,X26716,X26717,X26718)),esk212_4(X26715,X26716,X26717,X26718))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26716),X26718))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26716),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26718),X26717)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X26716),X26715))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26717)) ) ),
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,
! [X19722,X19723,X19724,X19725,X19726,X19727] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19727),X19726)),X19725) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19724),X19723)),X19722)
| ~ 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),X19724),X19723)),X19722)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19722),X19724))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19725))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19724))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19724),X19727))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19726),X19723)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__lemma])]) ).
fof(i_0_7045,plain,
! [X31128,X31129,X31130,X31131,X31132] : hAPP(c_Relation_Oconverse(X31132,X31131),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31130,tc_fun(tc_prod(X31132,X31131),tc_HOL_Obool)),X31129),X31128)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31130,tc_fun(tc_prod(X31131,X31132),tc_HOL_Obool)),X31129),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X31132,X31131),tc_HOL_Obool),tc_fun(tc_prod(X31131,X31132),tc_HOL_Obool),X31130),c_Relation_Oconverse(X31132,X31131)),X31128)),
inference(variable_rename,[status(thm)],[fact_converse__INTER]) ).
fof(i_0_7046,plain,
! [X30345,X30346,X30347,X30348,X30349] : hAPP(c_Relation_Oconverse(X30349,X30348),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30347,tc_fun(tc_prod(X30349,X30348),tc_HOL_Obool)),X30346),X30345)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30347,tc_fun(tc_prod(X30348,X30349),tc_HOL_Obool)),X30346),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X30349,X30348),tc_HOL_Obool),tc_fun(tc_prod(X30348,X30349),tc_HOL_Obool),X30347),c_Relation_Oconverse(X30349,X30348)),X30345)),
inference(variable_rename,[status(thm)],[fact_converse__UNION]) ).
fof(i_0_7047,plain,
! [X24435] : X24435 = 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),esk121_1(X24435)),esk122_1(X24435))),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,
! [X24302,X24303,X24304,X24305,X24306,X24308,X24309,X24310,X24311,X24312,X24313] :
( ( hBOOL(hAPP(hAPP(c_member(X24304),esk118_4(X24302,X24303,X24304,X24305)),X24302))
| ~ hBOOL(hAPP(hAPP(c_member(X24306),X24305),hAPP(c_Set_Oimage(X24304,X24306,X24303),X24302))) )
& ( X24305 = hAPP(X24303,esk118_4(X24302,X24303,X24304,X24305))
| ~ hBOOL(hAPP(hAPP(c_member(X24306),X24305),hAPP(c_Set_Oimage(X24304,X24306,X24303),X24302))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X24310),X24312),X24308))
| X24311 != hAPP(X24309,X24312)
| hBOOL(hAPP(hAPP(c_member(X24313),X24311),hAPP(c_Set_Oimage(X24310,X24313,X24309),X24308))) ) ),
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,
! [X24594,X24595,X24596,X24597,X24598] :
( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(X24598),hAPP(hAPP(c_Set_Oinsert(X24598),X24595),c_Orderings_Obot__class_Obot(tc_fun(X24598,tc_HOL_Obool)))),X24596) != hAPP(hAPP(c_Equiv__Relations_Oquotient(X24598),hAPP(hAPP(c_Set_Oinsert(X24598),X24594),c_Orderings_Obot__class_Obot(tc_fun(X24598,tc_HOL_Obool)))),X24596)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X24598,X24598)),hAPP(hAPP(c_Product__Type_OPair(X24598,X24598),X24595),X24594)),X24596))
| ~ hBOOL(hAPP(hAPP(c_member(X24598),X24594),X24597))
| ~ hBOOL(hAPP(hAPP(c_member(X24598),X24595),X24597))
| ~ c_Equiv__Relations_Oequiv(X24598,X24597,X24596) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24598,X24598)),hAPP(hAPP(c_Product__Type_OPair(X24598,X24598),X24595),X24594)),X24596))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(X24598),hAPP(hAPP(c_Set_Oinsert(X24598),X24595),c_Orderings_Obot__class_Obot(tc_fun(X24598,tc_HOL_Obool)))),X24596) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X24598),hAPP(hAPP(c_Set_Oinsert(X24598),X24594),c_Orderings_Obot__class_Obot(tc_fun(X24598,tc_HOL_Obool)))),X24596)
| ~ hBOOL(hAPP(hAPP(c_member(X24598),X24594),X24597))
| ~ hBOOL(hAPP(hAPP(c_member(X24598),X24595),X24597))
| ~ c_Equiv__Relations_Oequiv(X24598,X24597,X24596) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__equiv__class__iff2])])]) ).
fof(i_0_7050,plain,
! [X27930,X27931,X27932,X27933,X27934,X27935,X27936] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X27936,X27935,X27934),hAPP(c_Fun_Ocomp(X27933,tc_fun(X27935,X27934),X27936,X27932),X27931)),X27930) = hAPP(hAPP(X27932,hAPP(X27931,hAPP(c_Product__Type_Ofst(X27936,X27935),X27930))),hAPP(c_Product__Type_Osnd(X27936,X27935),X27930)),
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,
! [X24407,X24408] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X24408),X24407))
| 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)),X24408)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X24407))) )
& ( ~ 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)),X24408)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X24407)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X24408),X24407)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I5_J])]) ).
fof(i_0_7054,plain,
! [X24412,X24413] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X24413),X24412))
| 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)),X24413)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X24412))) )
& ( ~ 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)),X24413)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X24412)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X24413),X24412)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I4_J])]) ).
fof(i_0_7055,plain,
! [X26327,X26328,X26329] :
( ~ class_Orderings_Olinorder(X26329)
| hAPP(X26328,hAPP(hAPP(c_Orderings_Oord__class_Omin(X26329),esk179_3(X26327,X26328,X26329)),esk180_3(X26327,X26328,X26329))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(X26329),hAPP(X26328,esk179_3(X26327,X26328,X26329))),hAPP(X26328,esk180_3(X26327,X26328,X26329)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26329),X26327))
| X26327 = c_Orderings_Obot__class_Obot(tc_fun(X26329,tc_HOL_Obool))
| hAPP(X26328,c_Big__Operators_Olattice_OInf__fin(X26329,c_Orderings_Oord__class_Omin(X26329),X26327)) = c_Big__Operators_Olattice_OInf__fin(X26329,c_Orderings_Oord__class_Omin(X26329),hAPP(c_Set_Oimage(X26329,X26329,X26328),X26327)) ),
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,
! [X26240,X26241,X26242] :
( ~ class_Orderings_Olinorder(X26242)
| hAPP(X26241,hAPP(hAPP(c_Orderings_Oord__class_Omax(X26242),esk175_3(X26240,X26241,X26242)),esk176_3(X26240,X26241,X26242))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(X26242),hAPP(X26241,esk175_3(X26240,X26241,X26242))),hAPP(X26241,esk176_3(X26240,X26241,X26242)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26242),X26240))
| X26240 = c_Orderings_Obot__class_Obot(tc_fun(X26242,tc_HOL_Obool))
| hAPP(X26241,c_Big__Operators_Olattice_OSup__fin(X26242,c_Orderings_Oord__class_Omax(X26242),X26240)) = c_Big__Operators_Olattice_OSup__fin(X26242,c_Orderings_Oord__class_Omax(X26242),hAPP(c_Set_Oimage(X26242,X26242,X26241),X26240)) ),
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,
! [X28500,X28501,X28502,X28503,X28504] :
( ~ c_Fun_Oinj__on(X28504,X28503,X28502,c_Orderings_Otop__class_Otop(tc_fun(X28504,tc_HOL_Obool)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28503,tc_HOL_Obool)),X28501),hAPP(c_Set_Oimage(X28504,X28503,X28502),X28500)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28504,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X28504,X28503,X28502),X28501)),X28500)) ),
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,
! [X21828,X21829,X21830,X21831] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21831),c_Groups_Ozero__class_Ozero(X21831)),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21831),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21831),X21830),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828))),X21829))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21831),X21830),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21831),X21829),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21831)
| ~ class_Int_Onumber(X21831) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21831),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828)),c_Groups_Ozero__class_Ozero(X21831)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21831),X21829),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21831),X21830),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21831),c_Groups_Ozero__class_Ozero(X21831)),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21831),X21830),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21831),X21829),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21831)
| ~ class_Int_Onumber(X21831) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21831),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828)),c_Groups_Ozero__class_Ozero(X21831)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21831),X21830),c_Groups_Ozero__class_Ozero(X21831)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21831),c_Groups_Ozero__class_Ozero(X21831)),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21831),X21830),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21831),X21829),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21831)
| ~ class_Int_Onumber(X21831) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21831),c_Groups_Ozero__class_Ozero(X21831)),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21831),c_Groups_Ozero__class_Ozero(X21831)),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21831),X21830),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21831),X21829),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21831)
| ~ class_Int_Onumber(X21831) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21831),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828)),c_Groups_Ozero__class_Ozero(X21831)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21831),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828)),c_Groups_Ozero__class_Ozero(X21831)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21831),c_Groups_Ozero__class_Ozero(X21831)),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21831),X21830),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21831),X21829),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21831)
| ~ class_Int_Onumber(X21831) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21831),X21830),c_Groups_Ozero__class_Ozero(X21831)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21831),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828)),c_Groups_Ozero__class_Ozero(X21831)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21831),c_Groups_Ozero__class_Ozero(X21831)),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21831),X21830),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21831),X21829),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21831)
| ~ class_Int_Onumber(X21831) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21831),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828)),c_Groups_Ozero__class_Ozero(X21831)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21831),X21829),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21831),X21830),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21831),c_Groups_Ozero__class_Ozero(X21831)),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21831),X21830),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21831),X21829),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21831)
| ~ class_Int_Onumber(X21831) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21831),X21830),c_Groups_Ozero__class_Ozero(X21831)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21831),X21829),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21831),X21830),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21831),c_Groups_Ozero__class_Ozero(X21831)),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21831),X21830),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21831),X21829),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21831)
| ~ class_Int_Onumber(X21831) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21831),c_Groups_Ozero__class_Ozero(X21831)),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21831),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21831),X21830),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828))),X21829))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21831),X21830),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21831),X21829),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21831)
| ~ class_Int_Onumber(X21831) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21831),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828)),c_Groups_Ozero__class_Ozero(X21831)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21831),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828)),c_Groups_Ozero__class_Ozero(X21831)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21831),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21831),X21830),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828))),X21829))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21831),X21830),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21831),X21829),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21831)
| ~ class_Int_Onumber(X21831) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21831),X21830),c_Groups_Ozero__class_Ozero(X21831)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21831),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828)),c_Groups_Ozero__class_Ozero(X21831)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21831),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21831),X21830),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828))),X21829))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21831),X21830),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21831),X21829),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21831)
| ~ class_Int_Onumber(X21831) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21831),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828)),c_Groups_Ozero__class_Ozero(X21831)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21831),X21829),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21831),X21830),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21831),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21831),X21830),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828))),X21829))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21831),X21830),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21831),X21829),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21831)
| ~ class_Int_Onumber(X21831) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21831),X21830),c_Groups_Ozero__class_Ozero(X21831)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21831),X21829),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21831),X21830),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21831),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21831),X21830),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828))),X21829))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21831),X21830),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21831),X21829),hAPP(c_Int_Onumber__class_Onumber__of(X21831),X21828))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21831)
| ~ class_Int_Onumber(X21831) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5500])])]) ).
fof(i_0_7063,plain,
! [X21794,X21795,X21796,X21797] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),c_Groups_Ozero__class_Ozero(X21797)),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21797),X21796),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794))),X21795))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),X21796),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21797),X21795),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21797)
| ~ class_Int_Onumber(X21797) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794)),c_Groups_Ozero__class_Ozero(X21797)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),X21795),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21797),X21796),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),c_Groups_Ozero__class_Ozero(X21797)),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),X21796),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21797),X21795),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21797)
| ~ class_Int_Onumber(X21797) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794)),c_Groups_Ozero__class_Ozero(X21797)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),X21796),c_Groups_Ozero__class_Ozero(X21797)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),c_Groups_Ozero__class_Ozero(X21797)),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),X21796),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21797),X21795),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21797)
| ~ class_Int_Onumber(X21797) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),c_Groups_Ozero__class_Ozero(X21797)),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),c_Groups_Ozero__class_Ozero(X21797)),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),X21796),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21797),X21795),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21797)
| ~ class_Int_Onumber(X21797) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794)),c_Groups_Ozero__class_Ozero(X21797)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794)),c_Groups_Ozero__class_Ozero(X21797)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),c_Groups_Ozero__class_Ozero(X21797)),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),X21796),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21797),X21795),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21797)
| ~ class_Int_Onumber(X21797) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),X21796),c_Groups_Ozero__class_Ozero(X21797)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794)),c_Groups_Ozero__class_Ozero(X21797)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),c_Groups_Ozero__class_Ozero(X21797)),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),X21796),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21797),X21795),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21797)
| ~ class_Int_Onumber(X21797) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794)),c_Groups_Ozero__class_Ozero(X21797)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),X21795),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21797),X21796),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),c_Groups_Ozero__class_Ozero(X21797)),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),X21796),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21797),X21795),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21797)
| ~ class_Int_Onumber(X21797) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),X21796),c_Groups_Ozero__class_Ozero(X21797)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),X21795),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21797),X21796),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),c_Groups_Ozero__class_Ozero(X21797)),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),X21796),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21797),X21795),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21797)
| ~ class_Int_Onumber(X21797) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),c_Groups_Ozero__class_Ozero(X21797)),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21797),X21796),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794))),X21795))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),X21796),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21797),X21795),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21797)
| ~ class_Int_Onumber(X21797) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794)),c_Groups_Ozero__class_Ozero(X21797)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794)),c_Groups_Ozero__class_Ozero(X21797)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21797),X21796),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794))),X21795))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),X21796),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21797),X21795),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21797)
| ~ class_Int_Onumber(X21797) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),X21796),c_Groups_Ozero__class_Ozero(X21797)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794)),c_Groups_Ozero__class_Ozero(X21797)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21797),X21796),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794))),X21795))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),X21796),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21797),X21795),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21797)
| ~ class_Int_Onumber(X21797) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794)),c_Groups_Ozero__class_Ozero(X21797)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),X21795),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21797),X21796),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21797),X21796),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794))),X21795))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),X21796),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21797),X21795),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21797)
| ~ class_Int_Onumber(X21797) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),X21796),c_Groups_Ozero__class_Ozero(X21797)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),X21795),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21797),X21796),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21797),X21796),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794))),X21795))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21797),X21796),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21797),X21795),hAPP(c_Int_Onumber__class_Onumber__of(X21797),X21794))))
| ~ class_Fields_Olinordered__field__inverse__zero(X21797)
| ~ class_Int_Onumber(X21797) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5501])])]) ).
fof(i_0_7064,plain,
! [X30381,X30382,X30383,X30384,X30385] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30385,X30384)),hAPP(hAPP(c_Product__Type_OPair(X30385,X30384),X30383),X30382)),hAPP(c_Relation_Oconverse(X30384,X30385),X30381)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30384,X30385)),hAPP(hAPP(c_Product__Type_OPair(X30384,X30385),X30382),X30383)),X30381)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30384,X30385)),hAPP(hAPP(c_Product__Type_OPair(X30384,X30385),X30382),X30383)),X30381))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30385,X30384)),hAPP(hAPP(c_Product__Type_OPair(X30385,X30384),X30383),X30382)),hAPP(c_Relation_Oconverse(X30384,X30385),X30381))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converse__iff])]) ).
fof(i_0_7065,plain,
! [X30371,X30372,X30373,X30374,X30375] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30375,X30374)),hAPP(hAPP(c_Product__Type_OPair(X30375,X30374),X30373),X30372)),hAPP(c_Relation_Oconverse(X30374,X30375),X30371)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30374,X30375)),hAPP(hAPP(c_Product__Type_OPair(X30374,X30375),X30372),X30373)),X30371)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converseD])]) ).
fof(i_0_7066,plain,
! [X24252,X24253,X24254,X24255,X24256,X24257] :
( ~ hBOOL(hAPP(hAPP(X24257,X24256),X24255))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24254,tc_fun(X24253,tc_HOL_Obool))),X24257),X24252),X24256),X24255)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup2I1])]) ).
fof(i_0_7067,plain,
! [X24228,X24229,X24230,X24231,X24232,X24233] :
( ( ~ hBOOL(hAPP(hAPP(X24233,X24232),X24231))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24229,tc_fun(X24228,tc_HOL_Obool))),X24230),X24233),X24232),X24231)) )
& ( ~ hBOOL(hAPP(hAPP(X24230,X24232),X24231))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24229,tc_fun(X24228,tc_HOL_Obool))),X24230),X24233),X24232),X24231)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5502])])]) ).
fof(i_0_7068,plain,
! [X24246,X24247,X24248,X24249,X24250,X24251] :
( ~ hBOOL(hAPP(hAPP(X24251,X24250),X24249))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24248,tc_fun(X24247,tc_HOL_Obool))),X24246),X24251),X24250),X24249)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup2I2])]) ).
fof(i_0_7069,plain,
! [X24711,X24712,X24713,X24714,X24715] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24715,tc_HOL_Obool)),X24714),X24713))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24715,tc_HOL_Obool)),X24712),X24711))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24715,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24715,tc_HOL_Obool)),X24714),X24712)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24715,tc_HOL_Obool)),X24713),X24711))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__mono])]) ).
fof(i_0_7070,plain,
! [X23996,X23997,X23998,X23999,X24000] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24000,tc_HOL_Obool)),X23999),X23998))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24000,tc_HOL_Obool)),X23997),X23996))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24000,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24000,tc_HOL_Obool)),X23999),X23997)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24000,tc_HOL_Obool)),X23998),X23996))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__mono])]) ).
fof(i_0_7071,plain,
! [X22351,X22352,X22353,X22354,X22355] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22355,tc_HOL_Obool)),X22354),X22353))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22355,tc_HOL_Obool)),X22352),X22351))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22355,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22355,tc_HOL_Obool)),X22354),X22351)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22355,tc_HOL_Obool)),X22353),X22352))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__mono])]) ).
fof(i_0_7072,plain,
! [X28905,X28906,X28907] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X28907)
| hAPP(X28906,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X28907),esk295_3(X28905,X28906,X28907)),esk296_3(X28905,X28906,X28907))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X28907),hAPP(X28906,esk295_3(X28905,X28906,X28907))),hAPP(X28906,esk296_3(X28905,X28906,X28907)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28907),X28905))
| X28905 = c_Orderings_Obot__class_Obot(tc_fun(X28907,tc_HOL_Obool))
| hAPP(X28906,hAPP(c_Finite__Set_Ofold1(X28907,c_Groups_Otimes__class_Otimes(X28907)),X28905)) = hAPP(c_Finite__Set_Ofold1(X28907,c_Groups_Otimes__class_Otimes(X28907)),hAPP(c_Set_Oimage(X28907,X28907,X28906),X28905)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hom__fold1__commute])])]) ).
fof(i_0_7073,plain,
! [X27842,X27843,X27844,X27845,X27846] :
( ~ class_Groups_Ocomm__monoid__add(X27846)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27845),X27844))
| ~ c_Fun_Oinj__on(X27845,X27845,X27843,X27844)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27845,X27846),X27842),hAPP(c_Set_Oimage(X27845,X27845,X27843),X27844)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27845,X27846),hAPP(c_Fun_Ocomp(X27845,X27846,X27845,X27842),X27843)),X27844) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oreindex])]) ).
fof(i_0_7074,plain,
! [X27847,X27848,X27849,X27850,X27851] :
( ~ class_Groups_Ocomm__monoid__mult(X27851)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27850),X27849))
| ~ c_Fun_Oinj__on(X27850,X27850,X27848,X27849)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27850,X27851),X27847),hAPP(c_Set_Oimage(X27850,X27850,X27848),X27849)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27850,X27851),hAPP(c_Fun_Ocomp(X27850,X27851,X27850,X27847),X27848)),X27849) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oreindex])]) ).
fof(i_0_7075,plain,
! [X30028,X30029,X30030] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30030,X30030)),hAPP(hAPP(c_Product__Type_OPair(X30030,X30030),esk354_3(X30028,X30029,X30030)),X30029)),X30028))
| hBOOL(hAPP(hAPP(c_member(X30030),X30029),c_Wellfounded_Oacc(X30030,X30028))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X30030),esk354_3(X30028,X30029,X30030)),c_Wellfounded_Oacc(X30030,X30028)))
| hBOOL(hAPP(hAPP(c_member(X30030),X30029),c_Wellfounded_Oacc(X30030,X30028))) ) ),
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,
! [X30024,X30025,X30026] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30026,X30026)),hAPP(hAPP(c_Product__Type_OPair(X30026,X30026),esk353_3(X30024,X30025,X30026)),X30025)),X30024))
| hBOOL(hAPP(hAPP(c_member(X30026),X30025),c_Wellfounded_Oacc(X30026,X30024))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X30026),esk353_3(X30024,X30025,X30026)),c_Wellfounded_Oacc(X30026,X30024)))
| hBOOL(hAPP(hAPP(c_member(X30026),X30025),c_Wellfounded_Oacc(X30026,X30024))) ) ),
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,
! [X24500,X24501,X24502,X24503,X24504,X24505,X24506] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X24502),X24501),c_Wellfounded_Oacc(X24502,X24500)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24502,X24502)),hAPP(hAPP(c_Product__Type_OPair(X24502,X24502),X24503),X24501)),X24500))
| hBOOL(hAPP(hAPP(c_member(X24502),X24503),c_Wellfounded_Oacc(X24502,X24500))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X24506,X24506)),hAPP(hAPP(c_Product__Type_OPair(X24506,X24506),esk125_3(X24504,X24505,X24506)),X24505)),X24504))
| hBOOL(hAPP(hAPP(c_member(X24506),X24505),c_Wellfounded_Oacc(X24506,X24504))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X24506),esk125_3(X24504,X24505,X24506)),c_Wellfounded_Oacc(X24506,X24504)))
| hBOOL(hAPP(hAPP(c_member(X24506),X24505),c_Wellfounded_Oacc(X24506,X24504))) ) ),
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,
! [X33230,X33231,X33232,X33233] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33233),tc_List_Olist(X33233))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33233),tc_List_Olist(X33233)),X33232),X33231)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X33233),c_List_Olistrel1(X33233,X33230))))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33233)),X33232) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33233)),X33231) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__eq__len])]) ).
fof(i_0_7079,plain,
! [X32758,X32759,X32760,X32761,X32762] : hAPP(hAPP(c_List_Olist__update(X32762,hAPP(hAPP(c_List_Olist_OCons(X32762),X32761),X32760)),X32759),X32758) = c_Nat_Onat_Onat__case(tc_List_Olist(X32762),hAPP(hAPP(c_List_Olist_OCons(X32762),X32758),X32760),hAPP(hAPP(c_COMBB(tc_List_Olist(X32762),tc_List_Olist(X32762),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X32762),X32761)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X32762,tc_List_Olist(X32762)),c_List_Olist__update(X32762,X32760)),X32758)),X32759),
inference(variable_rename,[status(thm)],[fact_list__update_Osimps_I2_J]) ).
fof(i_0_7080,plain,
! [X22146,X22147,X22148,X22149] : hAPP(c_Product__Type_Oprod_Oprod__case(X22149,X22148,X22147),hAPP(hAPP(c_COMBB(tc_fun(X22148,tc_prod(X22149,X22148)),tc_fun(X22148,X22147),X22149),hAPP(c_COMBB(tc_prod(X22149,X22148),X22147,X22148),X22146)),c_Product__Type_OPair(X22149,X22148))) = X22146,
inference(variable_rename,[status(thm)],[fact_split__eta]) ).
fof(i_0_7081,plain,
! [X26738,X26739,X26740,X26741] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk220_4(X26738,X26739,X26740,X26741)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26740)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26738),X26741))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26738),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26741),X26740)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26740)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk221_4(X26738,X26739,X26740,X26741)),X26739))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26738),X26741))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26738),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26741),X26740)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26740)) )
& ( X26741 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk221_4(X26738,X26739,X26740,X26741)),esk220_4(X26738,X26739,X26740,X26741))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26738),X26741))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26738),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26741),X26740)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26740)) ) ),
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,
! [X26758,X26759,X26760,X26761] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk228_4(X26758,X26759,X26760,X26761)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26760)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26758),X26761))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26758),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26761),X26760)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26760)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk229_4(X26758,X26759,X26760,X26761)),X26759))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26758),X26761))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26758),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26761),X26760)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26760)) )
& ( X26761 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk229_4(X26758,X26759,X26760,X26761)),esk228_4(X26758,X26759,X26760,X26761))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26758),X26761))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26758),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26761),X26760)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26760)) ) ),
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,
! [X23775,X23776,X23777] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23777,tc_HOL_Obool)),X23776),hAPP(hAPP(c_Set_Oinsert(X23777),X23775),c_Orderings_Obot__class_Obot(tc_fun(X23777,tc_HOL_Obool)))))
| c_Partial__Function_Oflat__lub(X23777,X23775,X23776) = X23775 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23777,tc_HOL_Obool)),X23776),hAPP(hAPP(c_Set_Oinsert(X23777),X23775),c_Orderings_Obot__class_Obot(tc_fun(X23777,tc_HOL_Obool)))))
| c_Partial__Function_Oflat__lub(X23777,X23775,X23776) = c_HOL_OThe(X23777,hAPP(hAPP(c_COMBC(X23777,tc_fun(X23777,tc_HOL_Obool),tc_HOL_Obool),c_member(X23777)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23777,tc_HOL_Obool)),X23776),hAPP(hAPP(c_Set_Oinsert(X23777),X23775),c_Orderings_Obot__class_Obot(tc_fun(X23777,tc_HOL_Obool)))))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5504])]) ).
fof(i_0_7084,plain,
! [X33790,X33791,X33792,X33793] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk481_4(X33790,X33791,X33792,X33793)),X33793))
| hAPP(hAPP(c_List_Otake(X33792),X33793),X33791) = hAPP(hAPP(c_List_Otake(X33792),X33793),X33790)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33793),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33792)),X33790)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33793),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33792)),X33791))) )
& ( hAPP(hAPP(c_List_Onth(X33792),X33791),esk481_4(X33790,X33791,X33792,X33793)) != hAPP(hAPP(c_List_Onth(X33792),X33790),esk481_4(X33790,X33791,X33792,X33793))
| hAPP(hAPP(c_List_Otake(X33792),X33793),X33791) = hAPP(hAPP(c_List_Otake(X33792),X33793),X33790)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33793),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33792)),X33790)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33793),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33792)),X33791))) ) ),
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,
! [X30488,X30489,X30490,X30491] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30491,X30491)),hAPP(hAPP(c_Product__Type_OPair(X30491,X30491),X30490),X30489)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30491,X30491),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30488)))
| X30490 = X30489 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__pow__0__E])]) ).
fof(i_0_7086,plain,
! [X22413,X22414,X22415,X22416,X22417] :
( ~ hBOOL(hAPP(hAPP(X22417,X22416),X22415))
| hBOOL(hAPP(hAPP(X22417,hAPP(c_Product__Type_Osnd(X22414,X22413),hAPP(hAPP(c_Product__Type_OPair(X22414,X22413),X22415),X22416))),hAPP(c_Product__Type_Ofst(X22414,X22413),hAPP(hAPP(c_Product__Type_OPair(X22414,X22413),X22415),X22416)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exI__realizer])]) ).
fof(i_0_7087,plain,
! [X27788,X27789,X27790,X27791,X27792,X27793] :
( ( ~ c_Fun_Oinj__on(X27792,X27789,X27788,hAPP(c_Set_Oimage(X27793,X27792,X27791),X27790))
| c_Fun_Oinj__on(X27793,X27789,hAPP(c_Fun_Ocomp(X27792,X27789,X27793,X27788),X27791),X27790)
| ~ c_Fun_Oinj__on(X27793,X27792,X27791,X27790) )
& ( ~ c_Fun_Oinj__on(X27793,X27789,hAPP(c_Fun_Ocomp(X27792,X27789,X27793,X27788),X27791),X27790)
| c_Fun_Oinj__on(X27792,X27789,X27788,hAPP(c_Set_Oimage(X27793,X27792,X27791),X27790))
| ~ c_Fun_Oinj__on(X27793,X27792,X27791,X27790) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comp__inj__on__iff])])]) ).
fof(i_0_7088,plain,
! [X28203,X28204,X28205,X28206,X28207] :
( hAPP(c_Set_Oimage(X28207,X28206,X28205),c_Orderings_Otop__class_Otop(tc_fun(X28207,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X28206,tc_HOL_Obool))
| hAPP(c_Set_Oimage(X28206,X28204,X28203),c_Orderings_Otop__class_Otop(tc_fun(X28206,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X28204,tc_HOL_Obool))
| hAPP(c_Set_Oimage(X28207,X28204,hAPP(c_Fun_Ocomp(X28206,X28204,X28207,X28203),X28205)),c_Orderings_Otop__class_Otop(tc_fun(X28207,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X28204,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comp__surj])]) ).
fof(i_0_7089,plain,
! [X20161,X20162,X20163] : 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),X20163),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20162),X20163))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20162,X20163))),X20161) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20162),X20161),
inference(variable_rename,[status(thm)],[fact_zdiv__zmod__equality]) ).
fof(i_0_7090,plain,
! [X27817,X27818,X27819,X27820,X27821,X27822] :
( ~ class_Groups_Ocomm__monoid__add(X27822)
| ~ c_Fun_Oinj__on(X27821,X27820,X27819,X27818)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27820,X27822),X27817),hAPP(c_Set_Oimage(X27821,X27820,X27819),X27818)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27821,X27822),hAPP(c_Fun_Ocomp(X27820,X27822,X27821,X27817),X27819)),X27818) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__reindex])]) ).
fof(i_0_7091,plain,
! [X27831,X27832,X27833,X27834,X27835,X27836] :
( ~ class_Groups_Ocomm__monoid__mult(X27836)
| ~ c_Fun_Oinj__on(X27835,X27834,X27833,X27832)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27834,X27836),X27831),hAPP(c_Set_Oimage(X27835,X27834,X27833),X27832)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27835,X27836),hAPP(c_Fun_Ocomp(X27834,X27836,X27835,X27831),X27833)),X27832) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__reindex])]) ).
fof(i_0_7092,plain,
! [X25344,X25345,X25346] :
( ~ class_Orderings_Olinorder(X25346)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25346),X25345))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25346),X25344))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25346,tc_HOL_Obool)),X25345),X25344) = c_Orderings_Obot__class_Obot(tc_fun(X25346,tc_HOL_Obool))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X25346),c_Big__Operators_Olattice_OSup__fin(X25346,c_Orderings_Oord__class_Omax(X25346),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25346,tc_HOL_Obool)),X25345),X25344))),c_Big__Operators_Olattice_OSup__fin(X25346,c_Orderings_Oord__class_Omax(X25346),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25346,tc_HOL_Obool)),X25345),X25344))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25346),c_Big__Operators_Olattice_OSup__fin(X25346,c_Orderings_Oord__class_Omax(X25346),X25345)),c_Big__Operators_Olattice_OSup__fin(X25346,c_Orderings_Oord__class_Omax(X25346),X25344)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__inter])]) ).
fof(i_0_7093,plain,
! [X25439,X25440,X25441] :
( ~ class_Orderings_Olinorder(X25441)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25441),X25440))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25441),X25439))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25441,tc_HOL_Obool)),X25440),X25439) = c_Orderings_Obot__class_Obot(tc_fun(X25441,tc_HOL_Obool))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X25441),c_Big__Operators_Olattice_OInf__fin(X25441,c_Orderings_Oord__class_Omin(X25441),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25441,tc_HOL_Obool)),X25440),X25439))),c_Big__Operators_Olattice_OInf__fin(X25441,c_Orderings_Oord__class_Omin(X25441),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25441,tc_HOL_Obool)),X25440),X25439))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25441),c_Big__Operators_Olattice_OInf__fin(X25441,c_Orderings_Oord__class_Omin(X25441),X25440)),c_Big__Operators_Olattice_OInf__fin(X25441,c_Orderings_Oord__class_Omin(X25441),X25439)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__inter])]) ).
fof(i_0_7094,plain,
! [X32147,X32148,X32149,X32150,X32151] :
( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32151)),X32150) = X32147
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32151),tc_List_Olist(X32151))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32151),tc_List_Olist(X32151)),X32150),X32149)),hAPP(c_List_Olexn(X32151,X32148),X32147))) )
& ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32151)),X32149) = X32147
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32151),tc_List_Olist(X32151))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32151),tc_List_Olist(X32151)),X32150),X32149)),hAPP(c_List_Olexn(X32151,X32148),X32147))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexn__length])])]) ).
fof(i_0_7095,plain,
! [X30376,X30377,X30378,X30379,X30380] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30380,X30379)),hAPP(hAPP(c_Product__Type_OPair(X30380,X30379),X30378),X30377)),X30376))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30379,X30380)),hAPP(hAPP(c_Product__Type_OPair(X30379,X30380),X30377),X30378)),hAPP(c_Relation_Oconverse(X30380,X30379),X30376))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converseI])]) ).
fof(i_0_7096,plain,
! [X18215,X18216,X18217,X18218] :
( ( hBOOL(hAPP(X18218,X18216))
| X18215 = X18216
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X18218,X18217)),X18216),X18215)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X18217),X18216),esk31_4(X18215,X18216,X18217,X18218)))
| X18215 = X18216
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X18218,X18217)),X18216),X18215)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X18218,X18217)),esk31_4(X18215,X18216,X18217,X18218)),X18215))
| X18215 = X18216
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X18218,X18217)),X18216),X18215)) )
& ( hBOOL(hAPP(X18218,X18216))
| ~ hBOOL(hAPP(X18218,X18216))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X18218,X18217)),X18216),X18215)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X18217),X18216),esk31_4(X18215,X18216,X18217,X18218)))
| ~ hBOOL(hAPP(X18218,X18216))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X18218,X18217)),X18216),X18215)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X18218,X18217)),esk31_4(X18215,X18216,X18217,X18218)),X18215))
| ~ hBOOL(hAPP(X18218,X18216))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X18218,X18217)),X18216),X18215)) ) ),
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,
! [X17818,X17819,X17820,X17821,X17823,X17824,X17825,X17826,X17827] :
( ( hBOOL(hAPP(X17821,X17819))
| X17818 = X17819
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17821,X17820)),X17819),X17818)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17820),X17819),esk18_4(X17818,X17819,X17820,X17821)))
| X17818 = X17819
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17821,X17820)),X17819),X17818)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17821,X17820)),esk18_4(X17818,X17819,X17820,X17821)),X17818))
| X17818 = X17819
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17821,X17820)),X17819),X17818)) )
& ( hBOOL(hAPP(X17821,X17819))
| ~ hBOOL(hAPP(X17821,X17819))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17821,X17820)),X17819),X17818)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17820),X17819),esk18_4(X17818,X17819,X17820,X17821)))
| ~ hBOOL(hAPP(X17821,X17819))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17821,X17820)),X17819),X17818)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17821,X17820)),esk18_4(X17818,X17819,X17820,X17821)),X17818))
| ~ hBOOL(hAPP(X17821,X17819))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17821,X17820)),X17819),X17818)) )
& ( X17823 != X17824
| hBOOL(hAPP(X17826,X17824))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17826,X17825)),X17824),X17823)) )
& ( ~ hBOOL(hAPP(X17826,X17824))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17825),X17824),X17827))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17826,X17825)),X17827),X17823))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17826,X17825)),X17824),X17823)) ) ),
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,
! [X29491,X29492,X29493,X29494,X29495,X29496] : hAPP(hAPP(c_Relation_Orel__comp(X29496,X29495,X29494),X29493),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29495,X29494),tc_HOL_Obool)),X29492),X29491)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29496,X29494),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X29496,X29495,X29494),X29493),X29492)),hAPP(hAPP(c_Relation_Orel__comp(X29496,X29495,X29494),X29493),X29491)),
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,
! [X23711,X23712,X23713,X23714] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X23714,tc_fun(X23713,tc_HOL_Obool))),X23712),X23711))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X23714,X23713)),hAPP(hAPP(c_Product__Type_OPair(X23714,X23713),X23712),X23711)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X23714,X23713),tc_HOL_Obool)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23714,X23713)),hAPP(hAPP(c_Product__Type_OPair(X23714,X23713),X23712),X23711)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X23714,X23713),tc_HOL_Obool))))
| hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X23714,tc_fun(X23713,tc_HOL_Obool))),X23712),X23711)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__empty__eq2])]) ).
fof(i_0_7101,plain,
! [X34367,X34368] :
( ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X34368),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X34368))),X34367)))
| c_List_Otranspose(X34368,c_List_Otranspose(X34368,X34367)) = c_List_OtakeWhile(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)],[inference(fof_nnf,[status(thm)],[fact_transpose__transpose])]) ).
fof(i_0_7102,plain,
! [X26337,X26338,X26339] :
( ~ class_Orderings_Olinorder(X26339)
| hAPP(X26338,hAPP(hAPP(c_Orderings_Oord__class_Omin(X26339),esk183_3(X26337,X26338,X26339)),esk184_3(X26337,X26338,X26339))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(X26339),hAPP(X26338,esk183_3(X26337,X26338,X26339))),hAPP(X26338,esk184_3(X26337,X26338,X26339)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26339),X26337))
| X26337 = c_Orderings_Obot__class_Obot(tc_fun(X26339,tc_HOL_Obool))
| hAPP(X26338,c_Big__Operators_Olinorder__class_OMin(X26339,X26337)) = c_Big__Operators_Olinorder__class_OMin(X26339,hAPP(c_Set_Oimage(X26339,X26339,X26338),X26337)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Ohom__commute])])]) ).
fof(i_0_7103,plain,
! [X26332,X26333,X26334] :
( ~ class_Orderings_Olinorder(X26334)
| hAPP(X26333,hAPP(hAPP(c_Orderings_Oord__class_Omax(X26334),esk181_3(X26332,X26333,X26334)),esk182_3(X26332,X26333,X26334))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(X26334),hAPP(X26333,esk181_3(X26332,X26333,X26334))),hAPP(X26333,esk182_3(X26332,X26333,X26334)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26334),X26332))
| X26332 = c_Orderings_Obot__class_Obot(tc_fun(X26334,tc_HOL_Obool))
| hAPP(X26333,c_Big__Operators_Olinorder__class_OMax(X26334,X26332)) = c_Big__Operators_Olinorder__class_OMax(X26334,hAPP(c_Set_Oimage(X26334,X26334,X26333),X26332)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Ohom__commute])])]) ).
fof(i_0_7104,plain,
! [X26342,X26343,X26344] :
( ~ class_Lattices_Olattice(X26344)
| hAPP(X26343,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X26344),esk185_3(X26342,X26343,X26344)),esk186_3(X26342,X26343,X26344))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X26344),hAPP(X26343,esk185_3(X26342,X26343,X26344))),hAPP(X26343,esk186_3(X26342,X26343,X26344)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26344),X26342))
| X26342 = c_Orderings_Obot__class_Obot(tc_fun(X26344,tc_HOL_Obool))
| hAPP(X26343,c_Big__Operators_Olattice__class_OInf__fin(X26344,X26342)) = c_Big__Operators_Olattice__class_OInf__fin(X26344,hAPP(c_Set_Oimage(X26344,X26344,X26343),X26342)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ohom__commute])])]) ).
fof(i_0_7105,plain,
! [X26347,X26348,X26349] :
( ~ class_Lattices_Olattice(X26349)
| hAPP(X26348,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X26349),esk187_3(X26347,X26348,X26349)),esk188_3(X26347,X26348,X26349))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X26349),hAPP(X26348,esk187_3(X26347,X26348,X26349))),hAPP(X26348,esk188_3(X26347,X26348,X26349)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26349),X26347))
| X26347 = c_Orderings_Obot__class_Obot(tc_fun(X26349,tc_HOL_Obool))
| hAPP(X26348,c_Big__Operators_Olattice__class_OSup__fin(X26349,X26347)) = c_Big__Operators_Olattice__class_OSup__fin(X26349,hAPP(c_Set_Oimage(X26349,X26349,X26348),X26347)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ohom__commute])])]) ).
fof(i_0_7106,plain,
! [X26744,X26745,X26748,X26750] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk224_2(X26744,X26745)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26745)))
| ~ hBOOL(hAPP(X26744,X26748))
| ~ hBOOL(hAPP(X26744,esk222_2(X26744,X26745)))
| ~ hBOOL(hAPP(X26744,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk222_2(X26744,X26745)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk223_2(X26744,X26745)),X26745))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26745)) )
& ( hBOOL(hAPP(X26744,esk224_2(X26744,X26745)))
| ~ hBOOL(hAPP(X26744,X26748))
| ~ hBOOL(hAPP(X26744,esk222_2(X26744,X26745)))
| ~ hBOOL(hAPP(X26744,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk222_2(X26744,X26745)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk223_2(X26744,X26745)),X26745))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26745)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X26750),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26745)))
| ~ hBOOL(hAPP(X26744,X26750))
| hBOOL(hAPP(X26744,esk225_2(X26744,X26745)))
| ~ hBOOL(hAPP(X26744,esk222_2(X26744,X26745)))
| ~ hBOOL(hAPP(X26744,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk222_2(X26744,X26745)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk223_2(X26744,X26745)),X26745))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26745)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk224_2(X26744,X26745)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26745)))
| ~ hBOOL(hAPP(X26744,X26748))
| hBOOL(hAPP(X26744,esk222_2(X26744,X26745)))
| hBOOL(hAPP(X26744,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk222_2(X26744,X26745)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk223_2(X26744,X26745)),X26745))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26745)) )
& ( hBOOL(hAPP(X26744,esk224_2(X26744,X26745)))
| ~ hBOOL(hAPP(X26744,X26748))
| hBOOL(hAPP(X26744,esk222_2(X26744,X26745)))
| hBOOL(hAPP(X26744,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk222_2(X26744,X26745)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk223_2(X26744,X26745)),X26745))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26745)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X26750),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26745)))
| ~ hBOOL(hAPP(X26744,X26750))
| hBOOL(hAPP(X26744,esk225_2(X26744,X26745)))
| hBOOL(hAPP(X26744,esk222_2(X26744,X26745)))
| hBOOL(hAPP(X26744,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk222_2(X26744,X26745)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk223_2(X26744,X26745)),X26745))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26745)) ) ),
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,
! [X32672,X32673,X32674] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32674),tc_List_Olist(X32674))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32674),tc_List_Olist(X32674)),c_List_Olist_ONil(X32674)),X32673)),c_List_Olistrel(X32674,X32672)))
| X32673 = c_List_Olist_ONil(X32674) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__Nil1])]) ).
fof(i_0_7108,plain,
! [X23480,X23481] : c_Set_Othe__elem(X23481,X23480) = c_HOL_OThe(X23481,hAPP(hAPP(c_COMBB(tc_fun(X23481,tc_HOL_Obool),tc_HOL_Obool,X23481),hAPP(c_fequal,X23480)),hAPP(hAPP(c_COMBC(X23481,tc_fun(X23481,tc_HOL_Obool),tc_fun(X23481,tc_HOL_Obool)),c_Set_Oinsert(X23481)),c_Orderings_Obot__class_Obot(tc_fun(X23481,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),esk376_2(X2,X1)),esk376_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),esk366_2(X2,X1)),esk366_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,
! [X33234,X33235,X33236] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33236),tc_List_Olist(X33236))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33236),tc_List_Olist(X33236)),c_List_Olist_ONil(X33236)),X33235)),c_List_Olistrel1(X33236,X33234))),
inference(variable_rename,[status(thm)],[i_0_5509]) ).
fof(i_0_7112,plain,
! [X32853,X32854,X32855] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32855),tc_List_Olist(X32855))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32855),tc_List_Olist(X32855)),c_List_Olist_ONil(X32855)),X32854)),c_List_Olex(X32855,X32853))),
inference(variable_rename,[status(thm)],[i_0_5510]) ).
fof(i_0_7113,plain,
! [X24459,X24460] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X24460),X24459))
| 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),X24460)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X24459)))
| ~ c_Nat__Transfer_Onat__set(X24459)
| ~ c_Nat__Transfer_Onat__set(X24460) )
& ( ~ 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),X24460)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X24459)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X24460),X24459))
| ~ c_Nat__Transfer_Onat__set(X24459)
| ~ c_Nat__Transfer_Onat__set(X24460) ) ),
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,
! [X24457,X24458] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X24458),X24457))
| 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),X24458)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X24457)))
| ~ c_Nat__Transfer_Onat__set(X24457)
| ~ c_Nat__Transfer_Onat__set(X24458) )
& ( ~ 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),X24458)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X24457)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X24458),X24457))
| ~ c_Nat__Transfer_Onat__set(X24457)
| ~ c_Nat__Transfer_Onat__set(X24458) ) ),
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,
! [X29522,X29523,X29524,X29525] :
( hAPP(hAPP(c_Relation_Orel__comp(X29525,X29525,X29525),X29524),X29523) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29525,X29525),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(X29525,X29525,X29525),X29522),X29523) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29525,X29525),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(X29525,X29525,X29525),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29525,X29525),tc_HOL_Obool)),X29524),X29522)),X29523) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29525,X29525),tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_union__comp__emptyL])]) ).
fof(i_0_7116,plain,
! [X24418] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24418) = 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),X24418),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,
! [X24967,X24968,X24969,X24970] :
( ~ class_Lattices_Olattice(X24970)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24970),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24970),X24969),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24970),X24968),X24967))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24970),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24970),X24969),X24968)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24970),X24969),X24967)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distrib__sup__le])]) ).
fof(i_0_7118,plain,
! [X22705,X22706,X22707,X22708] :
( ~ class_Orderings_Olinorder(X22708)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22708),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22708),X22707),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22708),X22706),X22705))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22708),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22708),X22707),X22706)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22708),X22707),X22705)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Odistrib__sup__le])]) ).
fof(i_0_7119,plain,
! [X30706,X30707,X30708,X30709] :
( ~ class_Lattices_Osemilattice__inf(X30709)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30709),X30708))
| ~ hBOOL(hAPP(hAPP(c_member(X30709),X30707),X30708))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30709),hAPP(hAPP(c_Finite__Set_Ofold(X30709,X30709,c_Lattices_Osemilattice__inf__class_Oinf(X30709)),X30706),X30708)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X30709),X30707),X30706))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__inf__le__inf])]) ).
fof(i_0_7120,plain,
! [X30710,X30711,X30712,X30713] :
( ~ class_Orderings_Olinorder(X30713)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30713),X30712))
| ~ hBOOL(hAPP(hAPP(c_member(X30713),X30711),X30712))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30713),hAPP(hAPP(c_Finite__Set_Ofold(X30713,X30713,c_Orderings_Oord__class_Omin(X30713)),X30710),X30712)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X30713),X30711),X30710))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__inf__le__inf])]) ).
fof(i_0_7121,plain,
! [X32823,X32824,X32825,X32826,X32827] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32827,tc_HOL_Obool)),hAPP(c_List_Oset(X32827),X32826)),X32825))
| ~ hBOOL(hAPP(hAPP(c_member(X32827),X32824),X32825))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32827,tc_HOL_Obool)),hAPP(c_List_Oset(X32827),hAPP(hAPP(c_List_Olist__update(X32827,X32826),X32823),X32824))),X32825)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__update__subsetI])]) ).
fof(i_0_7122,plain,
! [X27384,X27385,X27386,X27387,X27388] :
( ~ class_Groups_Ocomm__monoid__add(X27388)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X27387),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27386),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27388),X27385),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X27387,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27386),X27384))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27388),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27388),X27385),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X27387,X27386))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27388),X27385),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27386),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27386),X27384)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__ub__add__nat])]) ).
fof(i_0_7123,plain,
! [X26924,X26925,X26926,X26927,X26928,X26929] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X26929),X26928),X26927))
| hAPP(c_Set_Oimage(X26929,X26926,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26929,X26926),X26925),X26928),X26924)),X26927) = hAPP(hAPP(c_Set_Oinsert(X26926),X26924),hAPP(c_Set_Oimage(X26929,X26926,X26925),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26929,tc_HOL_Obool)),X26927),hAPP(hAPP(c_Set_Oinsert(X26929),X26928),c_Orderings_Obot__class_Obot(tc_fun(X26929,tc_HOL_Obool)))))) )
& ( hBOOL(hAPP(hAPP(c_member(X26929),X26928),X26927))
| hAPP(c_Set_Oimage(X26929,X26926,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26929,X26926),X26925),X26928),X26924)),X26927) = hAPP(c_Set_Oimage(X26929,X26926,X26925),X26927) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5511])]) ).
fof(i_0_7124,plain,
! [X28698,X28699,X28700,X28701,X28702] : hAPP(hAPP(c_Product__Type_OSigma(X28702,X28701),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28702,tc_HOL_Obool)),X28700),X28699)),hAPP(c_COMBK(tc_fun(X28701,tc_HOL_Obool),X28702),X28698)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X28702,X28701),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28702,X28701),X28700),hAPP(c_COMBK(tc_fun(X28701,tc_HOL_Obool),X28702),X28698))),hAPP(hAPP(c_Product__Type_OSigma(X28702,X28701),X28699),hAPP(c_COMBK(tc_fun(X28701,tc_HOL_Obool),X28702),X28698))),
inference(variable_rename,[status(thm)],[fact_Times__Int__distrib1]) ).
fof(i_0_7125,plain,
! [X28665,X28666,X28667,X28668,X28669] : hAPP(hAPP(c_Product__Type_OSigma(X28669,X28668),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28669,tc_HOL_Obool)),X28667),X28666)),hAPP(c_COMBK(tc_fun(X28668,tc_HOL_Obool),X28669),X28665)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28669,X28668),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28669,X28668),X28667),hAPP(c_COMBK(tc_fun(X28668,tc_HOL_Obool),X28669),X28665))),hAPP(hAPP(c_Product__Type_OSigma(X28669,X28668),X28666),hAPP(c_COMBK(tc_fun(X28668,tc_HOL_Obool),X28669),X28665))),
inference(variable_rename,[status(thm)],[fact_Times__Un__distrib1]) ).
fof(i_0_7126,plain,
! [X28621,X28622,X28623,X28624,X28625] : hAPP(hAPP(c_Product__Type_OSigma(X28625,X28624),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28625,tc_HOL_Obool)),X28623),X28622)),hAPP(c_COMBK(tc_fun(X28624,tc_HOL_Obool),X28625),X28621)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X28625,X28624),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28625,X28624),X28623),hAPP(c_COMBK(tc_fun(X28624,tc_HOL_Obool),X28625),X28621))),hAPP(hAPP(c_Product__Type_OSigma(X28625,X28624),X28622),hAPP(c_COMBK(tc_fun(X28624,tc_HOL_Obool),X28625),X28621))),
inference(variable_rename,[status(thm)],[fact_Times__Diff__distrib1]) ).
fof(i_0_7127,plain,
! [X26545,X26546,X26547,X26548,X26549] :
( ~ c_Fun_Oinj__on(X26549,X26548,X26547,X26546)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26548,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26549,X26548,X26547),X26546)),X26545))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26548),X26545))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X26549),X26546)),hAPP(c_Finite__Set_Ocard(X26548),X26545))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__inj__on__le])]) ).
fof(i_0_7128,plain,
! [X30032,X30033,X30034,X30035] :
( ( hBOOL(hAPP(hAPP(c_member(X30034),esk355_4(X30032,X30033,X30034,X30035)),X30033))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X30035,X30034,c_Groups_Otimes__class_Otimes(X30035)),X30032),c_Groups_Oone__class_Oone(X30035)),X30033) = c_Groups_Oone__class_Oone(X30035)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30034),X30033))
| ~ class_Groups_Ocomm__monoid__mult(X30035) )
& ( hAPP(X30032,esk355_4(X30032,X30033,X30034,X30035)) != c_Groups_Oone__class_Oone(X30035)
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X30035,X30034,c_Groups_Otimes__class_Otimes(X30035)),X30032),c_Groups_Oone__class_Oone(X30035)),X30033) = c_Groups_Oone__class_Oone(X30035)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30034),X30033))
| ~ class_Groups_Ocomm__monoid__mult(X30035) ) ),
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,
! [X22809,X22810,X22811,X22812] : c_Sum__Type_Osum_Osum__case(X22812,X22811,X22810,hAPP(hAPP(c_COMBB(tc_sum(X22812,X22810),X22811,X22812),X22809),c_Sum__Type_OInl(X22812,X22810)),hAPP(hAPP(c_COMBB(tc_sum(X22812,X22810),X22811,X22810),X22809),c_Sum__Type_OInr(X22810,X22812))) = X22809,
inference(variable_rename,[status(thm)],[fact_surjective__sum]) ).
fof(i_0_7130,plain,
! [X22834,X22835,X22836,X22837,X22838] : hAPP(c_Sum__Type_Osum_Osum__case(X22838,X22837,X22836,hAPP(c_COMBK(X22837,X22838),X22835),hAPP(c_COMBK(X22837,X22836),X22835)),X22834) = X22835,
inference(variable_rename,[status(thm)],[fact_sum__case__KK]) ).
fof(i_0_7131,plain,
! [X33960,X33961,X33962,X33963,X33964,X33965] :
( hAPP(c_Map_Omap__of(X33965,X33964,X33963),X33962) != hAPP(c_Option_Ooption_OSome(X33964),X33961)
| ~ hBOOL(hAPP(hAPP(X33960,X33962),X33961))
| hAPP(c_Map_Omap__of(X33965,X33964,hAPP(c_List_Ofilter(tc_prod(X33965,X33964),hAPP(c_Product__Type_Oprod_Oprod__case(X33965,X33964,tc_HOL_Obool),X33960)),X33963)),X33962) = hAPP(c_Option_Ooption_OSome(X33964),X33961) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__filter__in])]) ).
fof(i_0_7132,plain,
! [X32669,X32670,X32671] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32671),tc_List_Olist(X32671))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32671),tc_List_Olist(X32671)),X32670),c_List_Olist_ONil(X32671))),c_List_Olistrel(X32671,X32669)))
| X32670 = c_List_Olist_ONil(X32671) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__Nil2])]) ).
fof(i_0_7133,plain,
! [X30925,X30926,X30927,X30928,X30929,X30930] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X30930)
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30929,X30930),X30928),hAPP(hAPP(c_COMBB(tc_fun(X30927,X30930),X30930,X30929),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30927,X30930),X30926)),X30925)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30927,X30930),X30926),hAPP(hAPP(c_COMBB(tc_fun(X30929,X30930),X30930,X30927),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30929,X30930),X30928)),hAPP(c_COMBC(X30929,X30927,X30930),X30925))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__commute])]) ).
fof(i_0_7134,plain,
! [X25903,X25904,X25905,X25906,X25907,X25908] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X25908)
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25907,X25908),X25906),hAPP(hAPP(c_COMBB(tc_fun(X25905,X25908),X25908,X25907),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25905,X25908),X25904)),X25903)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25905,X25908),X25904),hAPP(hAPP(c_COMBB(tc_fun(X25907,X25908),X25908,X25905),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25907,X25908),X25906)),hAPP(c_COMBC(X25907,X25905,X25908),X25903))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__commute])]) ).
fof(i_0_7135,plain,
! [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),c_List_Olist_ONil(X33239))),c_List_Olistrel1(X33239,X33237))),
inference(variable_rename,[status(thm)],[i_0_5512]) ).
fof(i_0_7136,plain,
! [X32850,X32851,X32852] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32852),tc_List_Olist(X32852))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32852),tc_List_Olist(X32852)),X32851),c_List_Olist_ONil(X32852))),c_List_Olexord(X32852,X32850))),
inference(variable_rename,[status(thm)],[i_0_5513]) ).
fof(i_0_7137,plain,
! [X32856,X32857,X32858] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32858),tc_List_Olist(X32858))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32858),tc_List_Olist(X32858)),X32857),c_List_Olist_ONil(X32858))),c_List_Olex(X32858,X32856))),
inference(variable_rename,[status(thm)],[i_0_5514]) ).
fof(i_0_7138,plain,
! [X24518,X24519,X24520,X24521,X24522] :
( ( hAPP(c_Relation_OImage(X24522,X24522,X24520),hAPP(hAPP(c_Set_Oinsert(X24522),X24519),c_Orderings_Obot__class_Obot(tc_fun(X24522,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(X24522,X24522,X24520),hAPP(hAPP(c_Set_Oinsert(X24522),X24518),c_Orderings_Obot__class_Obot(tc_fun(X24522,tc_HOL_Obool))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X24522,X24522)),hAPP(hAPP(c_Product__Type_OPair(X24522,X24522),X24519),X24518)),X24520))
| ~ hBOOL(hAPP(hAPP(c_member(X24522),X24518),X24521))
| ~ hBOOL(hAPP(hAPP(c_member(X24522),X24519),X24521))
| ~ c_Equiv__Relations_Oequiv(X24522,X24521,X24520) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24522,X24522)),hAPP(hAPP(c_Product__Type_OPair(X24522,X24522),X24519),X24518)),X24520))
| hAPP(c_Relation_OImage(X24522,X24522,X24520),hAPP(hAPP(c_Set_Oinsert(X24522),X24519),c_Orderings_Obot__class_Obot(tc_fun(X24522,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X24522,X24522,X24520),hAPP(hAPP(c_Set_Oinsert(X24522),X24518),c_Orderings_Obot__class_Obot(tc_fun(X24522,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(X24522),X24518),X24521))
| ~ hBOOL(hAPP(hAPP(c_member(X24522),X24519),X24521))
| ~ c_Equiv__Relations_Oequiv(X24522,X24521,X24520) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__equiv__class__iff])])]) ).
fof(i_0_7139,plain,
! [X27519,X27520,X27521] :
( ( hBOOL(hAPP(hAPP(c_member(X27521),esk250_3(X27519,X27520,X27521)),X27520))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27521,tc_Int_Oint),X27519),X27520) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27521,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X27521),c_Int_Onat),X27519)),X27520)) )
& ( ~ c_Nat__Transfer_Ois__nat(hAPP(X27519,esk250_3(X27519,X27520,X27521)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27521,tc_Int_Oint),X27519),X27520) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27521,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X27521),c_Int_Onat),X27519)),X27520)) ) ),
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_7140,plain,
! [X25785,X25786,X25787] :
( ( hBOOL(hAPP(hAPP(c_member(X25787),esk157_3(X25785,X25786,X25787)),X25786))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25787,tc_Int_Oint),X25785),X25786) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25787,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X25787),c_Int_Onat),X25785)),X25786)) )
& ( ~ c_Nat__Transfer_Ois__nat(hAPP(X25785,esk157_3(X25785,X25786,X25787)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25787,tc_Int_Oint),X25785),X25786) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25787,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X25787),c_Int_Onat),X25785)),X25786)) ) ),
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_7141,plain,
! [X33226,X33227,X33228,X33229] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33229),tc_List_Olist(X33229))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33229),tc_List_Olist(X33229)),X33228),X33227)),c_List_Olistrel1(X33229,X33226)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33229)),X33228) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33229)),X33227) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1__eq__len])]) ).
fof(i_0_7142,plain,
! [X32250,X32251,X32252,X32253] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32253),tc_List_Olist(X32253))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32253),tc_List_Olist(X32253)),X32252),X32251)),c_List_Olistrel(X32253,X32250)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32253)),X32252) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32253)),X32251) ),
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,
! [X31318,X31319,X31320,X31321] : hAPP(hAPP(c_Product__Type_OSigma(X31321,X31320),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31321,tc_HOL_Obool),X31319)),X31318) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X31321,tc_HOL_Obool),tc_fun(tc_prod(X31321,X31320),tc_HOL_Obool)),X31319),hAPP(hAPP(c_COMBC(tc_fun(X31321,tc_HOL_Obool),tc_fun(X31321,tc_fun(X31320,tc_HOL_Obool)),tc_fun(tc_prod(X31321,X31320),tc_HOL_Obool)),c_Product__Type_OSigma(X31321,X31320)),X31318)),
inference(variable_rename,[status(thm)],[fact_Sigma__Union]) ).
fof(i_0_7146,plain,
! [X26709,X26710,X26711,X26712] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk210_4(X26709,X26710,X26711,X26712)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26711)))
| X26712 = X26710
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26712),X26711) != X26710
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X26710),X26709))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26711)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk211_4(X26709,X26710,X26711,X26712)),X26709))
| X26712 = X26710
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26712),X26711) != X26710
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X26710),X26709))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26711)) )
& ( X26712 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk211_4(X26709,X26710,X26711,X26712)),esk210_4(X26709,X26710,X26711,X26712))
| X26712 = X26710
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26712),X26711) != X26710
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X26710),X26709))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26711)) ) ),
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,
! [X26703,X26704,X26705,X26706] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk208_4(X26703,X26704,X26705,X26706)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26705)))
| X26706 = X26704
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26706),X26705) != X26704
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X26704),X26703))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26705)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk209_4(X26703,X26704,X26705,X26706)),X26703))
| X26706 = X26704
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26706),X26705) != X26704
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X26704),X26703))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26705)) )
& ( X26706 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk209_4(X26703,X26704,X26705,X26706)),esk208_4(X26703,X26704,X26705,X26706))
| X26706 = X26704
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26706),X26705) != X26704
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X26704),X26703))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26705)) ) ),
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,
! [X30656,X30657,X30658,X30659,X30660] : hAPP(hAPP(c_Finite__Set_Ofold(X30660,X30659,X30658),X30657),X30656) = c_HOL_OThe(X30659,c_Finite__Set_Ofold__graph(X30660,X30659,X30658,X30657,X30656)),
inference(variable_rename,[status(thm)],[fact_fold__def]) ).
fof(i_0_7149,plain,
! [X22105,X22106,X22107,X22109,X22110,X22111,X22112,X22113,X22116] :
( ( ~ hBOOL(hAPP(X22107,esk89_3(X22105,X22106,X22107)))
| hBOOL(hAPP(X22107,hAPP(hAPP(c_Product__Type_OPair(X22106,X22105),X22109),X22110))) )
& ( ~ hBOOL(hAPP(X22113,hAPP(hAPP(c_Product__Type_OPair(X22112,X22111),esk90_3(X22111,X22112,X22113)),esk91_3(X22111,X22112,X22113))))
| hBOOL(hAPP(X22113,X22116)) ) ),
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,
! [X31944,X31945,X31946,X31947] :
( ( hAPP(c_Map_Omap__of(X31947,X31946,X31945),X31944) != c_Option_Ooption_ONone(X31946)
| ~ hBOOL(hAPP(hAPP(c_member(X31947),X31944),hAPP(c_Set_Oimage(tc_prod(X31947,X31946),X31947,c_Product__Type_Ofst(X31947,X31946)),hAPP(c_List_Oset(tc_prod(X31947,X31946)),X31945)))) )
& ( hBOOL(hAPP(hAPP(c_member(X31947),X31944),hAPP(c_Set_Oimage(tc_prod(X31947,X31946),X31947,c_Product__Type_Ofst(X31947,X31946)),hAPP(c_List_Oset(tc_prod(X31947,X31946)),X31945))))
| hAPP(c_Map_Omap__of(X31947,X31946,X31945),X31944) = c_Option_Ooption_ONone(X31946) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5517])]) ).
fof(i_0_7151,plain,
! [X23051,X23052,X23053,X23054,X23055] :
( ~ hBOOL(hAPP(X23055,hAPP(hAPP(c_Product__Type_OPair(X23054,X23053),X23052),X23051)))
| hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X23054,X23053,tc_HOL_Obool,X23055),X23052),X23051)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_curryI])]) ).
fof(i_0_7152,plain,
! [X25497,X25498,X25499] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25499),X25498))
| 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(X25499),X25497)),hAPP(c_Finite__Set_Ocard(X25499),X25498))),hAPP(c_Finite__Set_Ocard(X25499),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25499,tc_HOL_Obool)),X25497),X25498)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__card__le__card__Diff])]) ).
fof(i_0_7153,plain,
! [X31452,X31453,X31454,X31455] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X31454,tc_HOL_Obool)),esk411_4(X31452,X31453,X31454,X31455)),X31455))
| c_Fun_Oinj__on(X31454,X31453,X31452,c_Complete__Lattice_OInf__class_OInf(tc_fun(X31454,tc_HOL_Obool),X31455))
| X31455 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X31454,tc_HOL_Obool),tc_HOL_Obool)) )
& ( ~ c_Fun_Oinj__on(X31454,X31453,X31452,esk411_4(X31452,X31453,X31454,X31455))
| c_Fun_Oinj__on(X31454,X31453,X31452,c_Complete__Lattice_OInf__class_OInf(tc_fun(X31454,tc_HOL_Obool),X31455))
| X31455 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X31454,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,
! [X23769,X23770,X23771,X23772,X23773] :
( ( ~ c_Nitpick_Orefl_H(X23770,X23769)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X23770,X23770)),hAPP(hAPP(c_Product__Type_OPair(X23770,X23770),X23771),X23771)),X23769)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23773,X23773)),hAPP(hAPP(c_Product__Type_OPair(X23773,X23773),esk108_2(X23772,X23773)),esk108_2(X23772,X23773))),X23772))
| c_Nitpick_Orefl_H(X23773,X23772) ) ),
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,
! [X20618,X20619,X20620,X20622] :
( ( hBOOL(hAPP(X20619,esk75_3(X20618,X20619,X20620)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20618))
| ~ hBOOL(hAPP(X20619,X20622))
| hBOOL(hAPP(X20619,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20622),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20618),X20620))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20620)) )
& ( ~ hBOOL(hAPP(X20619,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk75_3(X20618,X20619,X20620)),X20620)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20618))
| ~ hBOOL(hAPP(X20619,X20622))
| hBOOL(hAPP(X20619,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20622),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20618),X20620))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20620)) ) ),
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,
! [X20244,X20245,X20246,X20248] :
( ( hBOOL(hAPP(X20245,esk71_3(X20244,X20245,X20246)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20244))
| ~ hBOOL(hAPP(X20245,X20248))
| hBOOL(hAPP(X20245,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20248),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20244),X20246))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20246)) )
& ( ~ hBOOL(hAPP(X20245,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk71_3(X20244,X20245,X20246)),X20246)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20244))
| ~ hBOOL(hAPP(X20245,X20248))
| hBOOL(hAPP(X20245,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20248),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20244),X20246))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20246)) ) ),
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,
! [X28027,X28028,X28029,X28030,X28031,X28032,X28033] :
( ~ c_Finite__Set_Ofolding__idem(X28033,X28032,X28031,X28030)
| hAPP(c_Fun_Ocomp(X28032,X28032,X28029,hAPP(X28031,X28028)),hAPP(c_Fun_Ocomp(X28032,X28032,X28029,hAPP(X28031,X28028)),X28027)) = hAPP(c_Fun_Ocomp(X28032,X28032,X28029,hAPP(X28031,X28028)),X28027) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Oidem__left__comp])]) ).
fof(i_0_7161,plain,
! [X23605,X23606,X23607,X23608,X23609,X23610,X23611] :
( ~ hBOOL(hAPP(hAPP(c_member(X23611),X23610),hAPP(hAPP(X23609,X23608),X23607)))
| hBOOL(hAPP(hAPP(c_member(X23611),X23610),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X23606,X23605,tc_fun(X23611,tc_HOL_Obool)),X23609),hAPP(hAPP(c_Product__Type_OPair(X23606,X23605),X23608),X23607)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__splitI])]) ).
fof(i_0_7162,plain,
! [X32940,X32941,X32942,X32943,X32944,X32945] :
( hBOOL(hAPP(hAPP(c_member(X32945),X32944),hAPP(c_List_Oset(X32945),X32943)))
| hAPP(c_Map_Omap__upds(X32945,X32942,X32941,X32943,X32940),X32944) = hAPP(X32941,X32944) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5519])]) ).
fof(i_0_7163,plain,
! [X32361,X32362,X32363,X32364] : hAPP(c_Relation_OImage(tc_List_Olist(X32364),tc_List_Olist(X32364),c_List_Olistrel(X32364,X32363)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X32364)),hAPP(hAPP(c_List_Olist_OCons(X32364),X32362),X32361)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X32364),tc_HOL_Obool)))) = c_List_Oset__Cons(X32364,hAPP(c_Relation_OImage(X32364,X32364,X32363),hAPP(hAPP(c_Set_Oinsert(X32364),X32362),c_Orderings_Obot__class_Obot(tc_fun(X32364,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(X32364),tc_List_Olist(X32364),c_List_Olistrel(X32364,X32363)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X32364)),X32361),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X32364),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_listrel__Cons]) ).
fof(i_0_7164,plain,
! [X26999,X27000,X27001,X27002] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X27002,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X27001)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X27002,tc_HOL_Obool),tc_Nat_Onat),X27000),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X26999))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X27002,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26999,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27001),X26999))),X27000),
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,
! [X33023,X33024,X33025,X33026,X33027,X33028] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33028)),X33027) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33026)),X33025)
| c_Map_Omap__upds(X33028,X33026,X33024,hAPP(hAPP(c_List_Oappend(X33028),X33027),X33023),X33025) = c_Map_Omap__upds(X33028,X33026,X33024,X33027,X33025) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upds__append__drop])]) ).
fof(i_0_7168,plain,
! [X33029,X33030,X33031,X33032,X33033,X33034] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33034)),X33033) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33032)),X33031)
| c_Map_Omap__upds(X33034,X33032,X33030,X33033,hAPP(hAPP(c_List_Oappend(X33032),X33031),X33029)) = c_Map_Omap__upds(X33034,X33032,X33030,X33033,X33031) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upds__append2__drop])]) ).
fof(i_0_7169,plain,
! [X31872,X31873,X31874,X31875,X31876,X31878,X31879,X31880,X31881,X31882,X31883] :
( ( X31873 = hAPP(c_Option_Ooption_OSome(X31876),esk438_5(X31872,X31873,X31874,X31875,X31876))
| hAPP(hAPP(c_Option_Omap(X31876,X31875),X31874),X31873) != hAPP(c_Option_Ooption_OSome(X31875),X31872) )
& ( hAPP(X31874,esk438_5(X31872,X31873,X31874,X31875,X31876)) = X31872
| hAPP(hAPP(c_Option_Omap(X31876,X31875),X31874),X31873) != hAPP(c_Option_Ooption_OSome(X31875),X31872) )
& ( X31879 != hAPP(c_Option_Ooption_OSome(X31882),X31883)
| hAPP(X31880,X31883) != X31878
| hAPP(hAPP(c_Option_Omap(X31882,X31881),X31880),X31879) = hAPP(c_Option_Ooption_OSome(X31881),X31878) ) ),
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,
! [X29312,X29313,X29314,X29315,X29316,X29317] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X29317),X29316),X29315))
| hAPP(c_Fun_Ooverride__on(X29317,X29314,X29313,X29312,X29315),X29316) = hAPP(X29312,X29316) )
& ( hBOOL(hAPP(hAPP(c_member(X29317),X29316),X29315))
| hAPP(c_Fun_Ooverride__on(X29317,X29314,X29313,X29312,X29315),X29316) = hAPP(X29313,X29316) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5520])]) ).
fof(i_0_7171,plain,
! [X29293,X29294,X29295,X29296,X29297,X29298] :
( ~ hBOOL(hAPP(hAPP(c_member(X29298),X29297),X29296))
| hAPP(c_Fun_Ooverride__on(X29298,X29295,X29294,X29293,X29296),X29297) = hAPP(X29293,X29297) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_override__on__apply__in])]) ).
fof(i_0_7172,plain,
! [X27264,X27265,X27266,X27267,X27268] : c_Map_Orestrict__map(X27268,X27267,X27266,hAPP(hAPP(c_Set_Oinsert(X27268),X27265),X27264)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27268,tc_Option_Ooption(X27267)),c_Map_Orestrict__map(X27268,X27267,X27266,X27264)),X27265),hAPP(X27266,X27265)),
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,
! [X33704,X33705,X33706,X33707,X33708,X33709] :
( X33707 != hAPP(hAPP(c_List_Olist_OCons(X33706),X33708),X33709)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33706),tc_List_Olist(X33706))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33706),tc_List_Olist(X33706)),X33705),hAPP(hAPP(c_List_Oappend(X33706),X33705),X33707))),c_List_Olexord(X33706,X33704))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__rightI])])]) ).
fof(i_0_7175,plain,
! [X32205,X32206,X32207,X32208,X32209,X32210,X32211] :
( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32205)),X32207) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32205)),X32206)
| X32207 != X32206 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32205,X32205)),X32208),hAPP(c_List_Oset(tc_prod(X32205,X32205)),hAPP(hAPP(c_List_Ozip(X32205,X32205),X32207),X32206))))
| hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X32205,X32205,tc_HOL_Obool),c_fequal),X32208))
| X32207 != X32206 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32209,X32209)),esk441_3(X32209,X32210,X32211)),hAPP(c_List_Oset(tc_prod(X32209,X32209)),hAPP(hAPP(c_List_Ozip(X32209,X32209),X32211),X32210))))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32209)),X32211) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32209)),X32210)
| X32211 = X32210 )
& ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X32209,X32209,tc_HOL_Obool),c_fequal),esk441_3(X32209,X32210,X32211)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32209)),X32211) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32209)),X32210)
| X32211 = X32210 ) ),
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,
! [X22285,X22286,X22287] :
( ( 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),esk96_3(X22285,X22286,X22287)),esk97_3(X22285,X22286,X22287))))
| hBOOL(hAPP(hAPP(X22285,X22287),X22286))
| ~ 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),X22287),X22286))) )
& ( esk97_3(X22285,X22286,X22287) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(X22285,esk97_3(X22285,X22286,X22287)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,esk96_3(X22285,X22286,X22287),esk97_3(X22285,X22286,X22287))))
| hBOOL(hAPP(hAPP(X22285,X22287),X22286))
| ~ 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),X22287),X22286))) )
& ( ~ hBOOL(hAPP(hAPP(X22285,esk96_3(X22285,X22286,X22287)),esk97_3(X22285,X22286,X22287)))
| hBOOL(hAPP(hAPP(X22285,X22287),X22286))
| ~ 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),X22287),X22286))) ) ),
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,
! [X26645,X26646,X26647,X26648,X26649] :
( ~ c_Fun_Oinj__on(X26649,X26648,X26647,X26646)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X26649,tc_HOL_Obool)),X26645),X26646))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X26648,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26649,X26648,X26647),X26645)),hAPP(c_Set_Oimage(X26649,X26648,X26647),X26646))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__strict__subset])]) ).
fof(i_0_7178,plain,
! [X17707,X17708,X17709,X17710] :
( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17710),X17708),esk12_4(X17707,X17708,X17709,X17710)))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X17710,X17709)),X17708),X17707)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17709),esk12_4(X17707,X17708,X17709,X17710)),X17707))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X17710,X17709)),X17708),X17707)) ) ),
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,
! [X17556,X17557,X17558,X17559,X17561,X17562,X17563,X17564,X17565] :
( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17559),X17557),esk11_4(X17556,X17557,X17558,X17559)))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X17559,X17558)),X17557),X17556)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17558),esk11_4(X17556,X17557,X17558,X17559)),X17556))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X17559,X17558)),X17557),X17556)) )
& ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17564),X17562),X17565))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17563),X17565),X17561))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X17564,X17563)),X17562),X17561)) ) ),
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,
! [X26650,X26651,X26652,X26653,X26654,X26655] :
( ~ c_Fun_Oinj__on(X26655,X26654,X26653,X26652)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26655,tc_HOL_Obool)),X26651),X26652))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26655,tc_HOL_Obool)),X26650),X26652))
| hAPP(c_Set_Oimage(X26655,X26654,X26653),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26655,tc_HOL_Obool)),X26651),X26650)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26654,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26655,X26654,X26653),X26651)),hAPP(c_Set_Oimage(X26655,X26654,X26653),X26650)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__image__Int])]) ).
fof(i_0_7181,plain,
! [X26656,X26657,X26658,X26659,X26660,X26661] :
( ~ c_Fun_Oinj__on(X26661,X26660,X26659,X26658)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26661,tc_HOL_Obool)),X26657),X26658))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26661,tc_HOL_Obool)),X26656),X26658))
| hAPP(c_Set_Oimage(X26661,X26660,X26659),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26661,tc_HOL_Obool)),X26657),X26656)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26660,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26661,X26660,X26659),X26657)),hAPP(c_Set_Oimage(X26661,X26660,X26659),X26656)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__image__set__diff])]) ).
fof(i_0_7182,plain,
! [X33944,X33945,X33946] :
( ~ hBOOL(hAPP(c_List_Odistinct(X33946),X33945))
| hAPP(c_List_Ofilter(X33946,hAPP(hAPP(c_COMBC(X33946,tc_fun(X33946,tc_HOL_Obool),tc_HOL_Obool),c_member(X33946)),hAPP(c_List_Oset(X33946),c_List_Osublist(X33946,X33945,X33944)))),X33945) = c_List_Osublist(X33946,X33945,X33944) ),
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)),esk369_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,
! [X26479,X26480,X26481] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26481),X26480))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26481,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26481,X26481,X26479),X26480)),X26480))
| ~ c_Fun_Oinj__on(X26481,X26481,X26479,X26480)
| hAPP(c_Set_Oimage(X26481,X26481,X26479),X26480) = X26480 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_endo__inj__surj])]) ).
fof(i_0_7186,plain,
! [X29299,X29300,X29301,X29302,X29303,X29304] :
( hBOOL(hAPP(hAPP(c_member(X29304),X29303),X29302))
| hAPP(c_Fun_Ooverride__on(X29304,X29301,X29300,X29299,X29302),X29303) = hAPP(X29300,X29303) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5524])]) ).
fof(i_0_7187,plain,
! [X32493,X32494,X32495,X32496,X32497] :
( ~ class_Orderings_Olinorder(X32497)
| ~ hBOOL(hAPP(hAPP(c_member(X32497),hAPP(X32496,X32495)),hAPP(c_Set_Oimage(X32494,X32497,X32496),hAPP(c_List_Oset(X32494),X32493))))
| c_List_Olinorder__class_Oinsort__insert__key(X32494,X32497,X32496,X32495,X32493) = X32493 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__insert__key__triv])]) ).
fof(i_0_7188,plain,
! [X32490,X32491,X32492] :
( ~ class_Orderings_Olinorder(X32492)
| hAPP(c_List_Oset(X32492),c_List_Olinorder__class_Oinsort__insert__key(X32492,X32492,c_COMBI(X32492),X32491,X32490)) = hAPP(hAPP(c_Set_Oinsert(X32492),X32491),hAPP(c_List_Oset(X32492),X32490)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__insort__insert])]) ).
fof(i_0_7189,plain,
! [X33269,X33270,X33271] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X33271,X33271),tc_HOL_Obool)),X33270),X33269))
| ~ c_Relation_Orefl__on(X33271,c_Orderings_Otop__class_Otop(tc_fun(X33271,tc_HOL_Obool)),X33269)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X33271),tc_List_Olist(X33271)),tc_HOL_Obool)),c_List_Olistrel1(X33271,X33270)),c_List_Olistrel(X33271,X33269))) ),
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,
! [X26303,X26304,X26305,X26306,X26307,X26308,X26309] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26308),X26304))
| hAPP(hAPP(X26305,X26303),X26304) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X26309,X26308,X26307),X26303),X26306),X26304)
| ~ c_Big__Operators_Ocomm__monoid__big(X26309,X26308,X26307,X26306,X26305) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X26308),X26304))
| hAPP(hAPP(X26305,X26303),X26304) = X26306
| ~ c_Big__Operators_Ocomm__monoid__big(X26309,X26308,X26307,X26306,X26305) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5525])])]) ).
fof(i_0_7192,plain,
! [X27965,X27966,X27967,X27968,X27969,X27970,X27971] :
( ~ c_Finite__Set_Ofolding__image(X27971,X27970,X27969,X27968,X27967)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27970),X27966))
| hAPP(hAPP(X27967,X27965),X27966) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X27971,X27970,X27969),X27965),X27968),X27966) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image_Oeq__fold])]) ).
fof(i_0_7193,plain,
! [X30769,X30770,X30771,X30772,X30773,X30774] :
( ~ c_Finite__Set_Ofun__left__comm(X30774,X30773,X30772)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30774),X30771))
| ~ hBOOL(hAPP(hAPP(c_member(X30774),X30770),X30771))
| hAPP(hAPP(c_Finite__Set_Ofold(X30774,X30773,X30772),X30769),X30771) = hAPP(hAPP(X30772,X30770),hAPP(hAPP(c_Finite__Set_Ofold(X30774,X30773,X30772),X30769),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30774,tc_HOL_Obool)),X30771),hAPP(hAPP(c_Set_Oinsert(X30774),X30770),c_Orderings_Obot__class_Obot(tc_fun(X30774,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__rec])]) ).
fof(i_0_7194,plain,
! [X29930,X29931,X29932,X29933,X29935,X29936,X29937,X29938,X29940] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X29932)),esk336_4(X29930,X29931,X29932,X29933)),X29931))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X29932)),X29935),X29930))
| c_Hoare__Mirabelle_Otriple__valid(X29932,X29933,X29935)
| ~ c_Hoare__Mirabelle_Ohoare__valids(X29932,X29931,X29930) )
& ( ~ c_Hoare__Mirabelle_Otriple__valid(X29932,X29933,esk336_4(X29930,X29931,X29932,X29933))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X29932)),X29935),X29930))
| c_Hoare__Mirabelle_Otriple__valid(X29932,X29933,X29935)
| ~ c_Hoare__Mirabelle_Ohoare__valids(X29932,X29931,X29930) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X29938)),X29940),X29937))
| c_Hoare__Mirabelle_Otriple__valid(X29938,esk337_3(X29936,X29937,X29938),X29940)
| c_Hoare__Mirabelle_Ohoare__valids(X29938,X29937,X29936) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X29938)),esk338_3(X29936,X29937,X29938)),X29936))
| c_Hoare__Mirabelle_Ohoare__valids(X29938,X29937,X29936) )
& ( ~ c_Hoare__Mirabelle_Otriple__valid(X29938,esk337_3(X29936,X29937,X29938),esk338_3(X29936,X29937,X29938))
| c_Hoare__Mirabelle_Ohoare__valids(X29938,X29937,X29936) ) ),
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,
! [X22875,X22876,X22877,X22878,X22879,X22880] : hAPP(c_Sum__Type_Osum_Osum__case(X22880,X22879,X22878,X22877,X22876),hAPP(c_Sum__Type_OInl(X22880,X22878),X22875)) = hAPP(X22877,X22875),
inference(variable_rename,[status(thm)],[fact_sum_Osimps_I5_J]) ).
fof(i_0_7196,plain,
! [X22869,X22870,X22871,X22872,X22873,X22874] : hAPP(c_Sum__Type_Osum_Osum__case(X22874,X22873,X22872,X22871,X22870),hAPP(c_Sum__Type_OInr(X22872,X22874),X22869)) = hAPP(X22870,X22869),
inference(variable_rename,[status(thm)],[fact_sum_Osimps_I6_J]) ).
fof(i_0_7197,plain,
! [X28393,X28394,X28395,X28396,X28397,X28398] : hAPP(c_Set_Ovimage(X28398,X28397,hAPP(c_Fun_Ocomp(X28396,X28397,X28398,X28395),X28394)),X28393) = hAPP(c_Set_Ovimage(X28398,X28396,X28394),hAPP(c_Set_Ovimage(X28396,X28397,X28395),X28393)),
inference(variable_rename,[status(thm)],[fact_vimage__compose]) ).
fof(i_0_7198,plain,
! [X27770,X27771,X27772,X27773,X27774,X27775] : hAPP(c_Set_Oimage(X27775,X27774,hAPP(c_Fun_Ocomp(X27773,X27774,X27775,X27772),X27771)),X27770) = hAPP(c_Set_Oimage(X27773,X27774,X27772),hAPP(c_Set_Oimage(X27775,X27773,X27771),X27770)),
inference(variable_rename,[status(thm)],[fact_image__compose]) ).
fof(i_0_7199,plain,
! [X30441,X30442,X30443,X30445,X30446,X30447,X30448] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30443,X30443)),X30442),c_Transitive__Closure_Ortrancl(X30443,X30441)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30443,X30443)),X30442),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30443,X30443),tc_HOL_Obool),esk368_3(X30441,X30442,X30443)),X30441))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30447,X30447)),X30446),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30447,X30447),tc_HOL_Obool),X30448),X30445)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30447,X30447)),X30446),c_Transitive__Closure_Ortrancl(X30447,X30445))) ) ),
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,
! [X22818,X22819,X22820,X22821,X22822,X22823,X22824] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X22824,X22823,X22822,X22821),X22820),X22819),X22818) = hAPP(hAPP(X22819,hAPP(c_Product__Type_Ofst(X22823,X22822),hAPP(X22820,X22818))),hAPP(c_Product__Type_Osnd(X22823,X22822),hAPP(X22820,X22818))),
inference(variable_rename,[status(thm)],[fact_scomp__unfold]) ).
fof(i_0_7201,plain,
! [X24513,X24514,X24515,X24516,X24517] :
( ( hAPP(c_Relation_OImage(X24517,X24517,X24515),hAPP(hAPP(c_Set_Oinsert(X24517),X24514),c_Orderings_Obot__class_Obot(tc_fun(X24517,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X24517,X24517,X24515),hAPP(hAPP(c_Set_Oinsert(X24517),X24513),c_Orderings_Obot__class_Obot(tc_fun(X24517,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24517,X24517)),hAPP(hAPP(c_Product__Type_OPair(X24517,X24517),X24514),X24513)),X24515))
| ~ c_Equiv__Relations_Oequiv(X24517,X24516,X24515) )
& ( hBOOL(hAPP(hAPP(c_member(X24517),X24514),X24516))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24517,X24517)),hAPP(hAPP(c_Product__Type_OPair(X24517,X24517),X24514),X24513)),X24515))
| ~ c_Equiv__Relations_Oequiv(X24517,X24516,X24515) )
& ( hBOOL(hAPP(hAPP(c_member(X24517),X24513),X24516))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24517,X24517)),hAPP(hAPP(c_Product__Type_OPair(X24517,X24517),X24514),X24513)),X24515))
| ~ c_Equiv__Relations_Oequiv(X24517,X24516,X24515) )
& ( hAPP(c_Relation_OImage(X24517,X24517,X24515),hAPP(hAPP(c_Set_Oinsert(X24517),X24514),c_Orderings_Obot__class_Obot(tc_fun(X24517,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(X24517,X24517,X24515),hAPP(hAPP(c_Set_Oinsert(X24517),X24513),c_Orderings_Obot__class_Obot(tc_fun(X24517,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(X24517),X24514),X24516))
| ~ hBOOL(hAPP(hAPP(c_member(X24517),X24513),X24516))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X24517,X24517)),hAPP(hAPP(c_Product__Type_OPair(X24517,X24517),X24514),X24513)),X24515))
| ~ c_Equiv__Relations_Oequiv(X24517,X24516,X24515) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__eq__iff])])]) ).
fof(i_0_7202,plain,
! [X18999,X19000,X19001] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19001),c_Groups_Ozero__class_Ozero(X19001)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19001),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19001),X19000),X19000)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19001),X18999),X18999))))
| X19000 != c_Groups_Ozero__class_Ozero(X19001)
| X18999 != c_Groups_Ozero__class_Ozero(X19001)
| ~ class_Rings_Olinordered__ring__strict(X19001) )
& ( X19000 = c_Groups_Ozero__class_Ozero(X19001)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19001),c_Groups_Ozero__class_Ozero(X19001)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19001),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19001),X19000),X19000)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19001),X18999),X18999))))
| ~ class_Rings_Olinordered__ring__strict(X19001) )
& ( X18999 = c_Groups_Ozero__class_Ozero(X19001)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19001),c_Groups_Ozero__class_Ozero(X19001)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19001),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19001),X19000),X19000)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19001),X18999),X18999))))
| ~ class_Rings_Olinordered__ring__strict(X19001) ) ),
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,
! [X30531,X30532] : c_Transitive__Closure_Ortrancl(X30532,X30531) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X30532,X30532),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(X30532,X30532),tc_HOL_Obool),tc_fun(tc_prod(X30532,X30532),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X30532,X30532),tc_HOL_Obool)),X30531)),
inference(variable_rename,[status(thm)],[fact_rtrancl__is__UN__rel__pow]) ).
fof(i_0_7204,plain,
! [X27776,X27777,X27778,X27779,X27780,X27781] :
( ~ c_Fun_Oinj__on(X27781,X27780,hAPP(c_Fun_Ocomp(X27779,X27780,X27781,X27778),X27777),X27776)
| c_Fun_Oinj__on(X27779,X27780,X27778,hAPP(c_Set_Oimage(X27781,X27779,X27777),X27776)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__imageI])]) ).
fof(i_0_7205,plain,
! [X27479,X27480,X27481,X27483,X27484] :
( ( hBOOL(hAPP(hAPP(c_member(X27481),esk246_3(X27479,X27480,X27481)),X27480))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27481,tc_Nat_Onat),X27479),X27480) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27481),X27480)) )
& ( hAPP(X27479,esk246_3(X27479,X27480,X27481)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27481,tc_Nat_Onat),X27479),X27480) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27481),X27480)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X27481),X27483),X27480))
| esk246_3(X27479,X27480,X27481) = X27483
| hAPP(X27479,X27483) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27481,tc_Nat_Onat),X27479),X27480) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27481),X27480)) )
& ( hBOOL(hAPP(hAPP(c_member(X27481),esk247_4(X27479,X27480,X27481,X27484)),X27480))
| ~ hBOOL(hAPP(hAPP(c_member(X27481),X27484),X27480))
| hAPP(X27479,X27484) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27481,tc_Nat_Onat),X27479),X27480) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27481),X27480)) )
& ( X27484 != esk247_4(X27479,X27480,X27481,X27484)
| ~ hBOOL(hAPP(hAPP(c_member(X27481),X27484),X27480))
| hAPP(X27479,X27484) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27481,tc_Nat_Onat),X27479),X27480) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27481),X27480)) )
& ( hAPP(X27479,esk247_4(X27479,X27480,X27481,X27484)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(X27481),X27484),X27480))
| hAPP(X27479,X27484) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27481,tc_Nat_Onat),X27479),X27480) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27481),X27480)) ) ),
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,
! [X34105,X34106,X34107] :
( ~ class_Orderings_Olinorder(X34107)
| ~ c_List_Olinorder__class_Osorted(X34107,X34106)
| c_List_Olinorder__class_Osorted(X34107,c_List_Olinorder__class_Oinsort__insert__key(X34107,X34107,c_COMBI(X34107),X34105,X34106)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__insort__insert])]) ).
fof(i_0_7207,plain,
! [X20719,X20720,X20721,X20722,X20723] :
( ~ class_Rings_Olinordered__idom(X20723)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20723),hAPP(c_Groups_Oabs__class_Oabs(X20723),X20722)),X20721))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20723),hAPP(c_Groups_Oabs__class_Oabs(X20723),X20720)),X20719))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20723),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20723),hAPP(c_Groups_Oabs__class_Oabs(X20723),X20722)),hAPP(c_Groups_Oabs__class_Oabs(X20723),X20720))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20723),X20721),X20719))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__less])]) ).
fof(i_0_7208,plain,
! [X30775,X30776,X30777,X30778,X30779,X30780] :
( ~ c_Finite__Set_Ofun__left__comm(X30780,X30779,X30778)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30780),X30777))
| hAPP(hAPP(c_Finite__Set_Ofold(X30780,X30779,X30778),X30776),hAPP(hAPP(c_Set_Oinsert(X30780),X30775),X30777)) = hAPP(hAPP(X30778,X30775),hAPP(hAPP(c_Finite__Set_Ofold(X30780,X30779,X30778),X30776),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30780,tc_HOL_Obool)),X30777),hAPP(hAPP(c_Set_Oinsert(X30780),X30775),c_Orderings_Obot__class_Obot(tc_fun(X30780,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,
! [X34369,X34370,X34371,X34372,X34373] : c_List_OtakeWhile(X34373,X34372,hAPP(hAPP(c_List_Omap(X34371,X34373),X34370),X34369)) = hAPP(hAPP(c_List_Omap(X34371,X34373),X34370),c_List_OtakeWhile(X34371,hAPP(c_Fun_Ocomp(X34373,tc_HOL_Obool,X34371,X34372),X34370),X34369)),
inference(variable_rename,[status(thm)],[fact_takeWhile__map]) ).
fof(i_0_7210,plain,
! [X27486,X27487,X27488,X27490,X27491] :
( ( hBOOL(hAPP(hAPP(c_member(X27488),esk248_3(X27486,X27487,X27488)),X27487))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27488,tc_Nat_Onat),X27486),X27487) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27488),X27487)) )
& ( hAPP(X27486,esk248_3(X27486,X27487,X27488)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27488,tc_Nat_Onat),X27486),X27487) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27488),X27487)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X27488),X27490),X27487))
| esk248_3(X27486,X27487,X27488) = X27490
| hAPP(X27486,X27490) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27488,tc_Nat_Onat),X27486),X27487) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27488),X27487)) )
& ( hBOOL(hAPP(hAPP(c_member(X27488),esk249_4(X27486,X27487,X27488,X27491)),X27487))
| ~ hBOOL(hAPP(hAPP(c_member(X27488),X27491),X27487))
| hAPP(X27486,X27491) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27488,tc_Nat_Onat),X27486),X27487) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27488),X27487)) )
& ( X27491 != esk249_4(X27486,X27487,X27488,X27491)
| ~ hBOOL(hAPP(hAPP(c_member(X27488),X27491),X27487))
| hAPP(X27486,X27491) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27488,tc_Nat_Onat),X27486),X27487) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27488),X27487)) )
& ( hAPP(X27486,esk249_4(X27486,X27487,X27488,X27491)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(X27488),X27491),X27487))
| hAPP(X27486,X27491) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27488,tc_Nat_Onat),X27486),X27487) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27488),X27487)) ) ),
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,
! [X30422,X30423,X30424] :
( ~ c_Relation_Orefl__on(X30424,X30423,X30422)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30424,X30424),tc_HOL_Obool)),X30422),hAPP(hAPP(c_Relation_Orel__comp(X30424,X30424,X30424),hAPP(c_Relation_Oconverse(X30424,X30424),X30422)),X30422))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__comp__subset])]) ).
fof(i_0_7212,plain,
! [X27782,X27783,X27784,X27785,X27786,X27787] :
( ~ c_Fun_Oinj__on(X27787,X27786,X27785,X27784)
| ~ c_Fun_Oinj__on(X27786,X27783,X27782,hAPP(c_Set_Oimage(X27787,X27786,X27785),X27784))
| c_Fun_Oinj__on(X27787,X27783,hAPP(c_Fun_Ocomp(X27786,X27783,X27787,X27782),X27785),X27784) ),
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,
! [X33659,X33660] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X33660),hAPP(c_List_Oset(tc_Nat_Onat),X33659)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33660),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)),X33659))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_elem__le__sum])]) ).
fof(i_0_7216,plain,
! [X24354,X24355,X24356,X24357,X24358,X24359] :
( ~ hBOOL(hAPP(hAPP(c_member(X24359),X24358),X24357))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24359,X24356)),hAPP(hAPP(c_Product__Type_OPair(X24359,X24356),X24358),X24355)),X24354))
| hBOOL(hAPP(hAPP(c_member(X24356),X24355),hAPP(c_Relation_OImage(X24359,X24356,X24354),X24357))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__ImageI])]) ).
fof(i_0_7217,plain,
! [X31846,X31847,X31848,X31849,X31850,X31851] : hAPP(hAPP(c_Option_Omap(X31851,X31850),X31849),hAPP(hAPP(c_Option_Omap(X31848,X31851),X31847),X31846)) = hAPP(hAPP(c_Option_Omap(X31848,X31850),hAPP(c_Fun_Ocomp(X31851,X31850,X31848,X31849),X31847)),X31846),
inference(variable_rename,[status(thm)],[fact_Option_Omap_Ocompositionality]) ).
fof(i_0_7218,plain,
! [X31840,X31841,X31842,X31843,X31844,X31845] : hAPP(hAPP(c_Option_Omap(X31845,X31844),X31843),hAPP(hAPP(c_Option_Omap(X31842,X31845),X31841),X31840)) = hAPP(hAPP(c_Option_Omap(X31842,X31844),hAPP(c_Fun_Ocomp(X31845,X31844,X31842,X31843),X31841)),X31840),
inference(variable_rename,[status(thm)],[fact_option__map__comp]) ).
fof(i_0_7219,plain,
! [X31776,X31777,X31778,X31779,X31780,X31781] : hAPP(hAPP(c_List_Omap(X31781,X31780),X31779),hAPP(hAPP(c_List_Omap(X31778,X31781),X31777),X31776)) = hAPP(hAPP(c_List_Omap(X31778,X31780),hAPP(c_Fun_Ocomp(X31781,X31780,X31778,X31779),X31777)),X31776),
inference(variable_rename,[status(thm)],[fact_map__map]) ).
fof(i_0_7220,plain,
! [X31770,X31771,X31772,X31773,X31774,X31775] : hAPP(hAPP(c_List_Omap(X31775,X31774),X31773),hAPP(hAPP(c_List_Omap(X31772,X31775),X31771),X31770)) = hAPP(hAPP(c_List_Omap(X31772,X31774),hAPP(c_Fun_Ocomp(X31775,X31774,X31772,X31773),X31771)),X31770),
inference(variable_rename,[status(thm)],[fact_List_Omap_Ocompositionality]) ).
fof(i_0_7221,plain,
! [X32701,X32702,X32703,X32704] : hAPP(hAPP(c_List_Otake(X32704),X32703),hAPP(hAPP(c_List_Olist_OCons(X32704),X32702),X32701)) = c_Nat_Onat_Onat__case(tc_List_Olist(X32704),c_List_Olist_ONil(X32704),hAPP(hAPP(c_COMBB(tc_List_Olist(X32704),tc_List_Olist(X32704),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X32704),X32702)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X32704),tc_List_Olist(X32704)),c_List_Otake(X32704)),X32701)),X32703),
inference(variable_rename,[status(thm)],[fact_take__Cons]) ).
fof(i_0_7222,plain,
! [X24339,X24340,X24341,X24342,X24343] : hAPP(c_Relation_OImage(X24343,X24342,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X24343,X24342),tc_HOL_Obool)),X24341),X24340)),X24339) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24342,tc_HOL_Obool)),hAPP(c_Relation_OImage(X24343,X24342,X24341),X24339)),hAPP(c_Relation_OImage(X24343,X24342,X24340),X24339)),
inference(variable_rename,[status(thm)],[fact_Un__Image]) ).
fof(i_0_7223,plain,
! [X22813,X22814,X22815,X22816,X22817] :
( ( X22817 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| hAPP(c_Random_Oiterate(X22816,X22815,X22817,X22814),X22813) = hAPP(c_Product__Type_OPair(X22816,X22815),X22813) )
& ( X22817 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| hAPP(c_Random_Oiterate(X22816,X22815,X22817,X22814),X22813) = hAPP(hAPP(c_Product__Type_Oscomp(X22815,X22816,X22815,tc_prod(X22816,X22815)),hAPP(X22814,X22813)),c_Random_Oiterate(X22816,X22815,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X22817),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X22814)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iterate_Osimps])]) ).
fof(i_0_7224,plain,
! [X24508,X24509,X24510,X24511,X24512] :
( ~ c_Equiv__Relations_Oequiv(X24512,X24511,X24510)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24512,X24512)),hAPP(hAPP(c_Product__Type_OPair(X24512,X24512),X24509),X24508)),X24510))
| hAPP(c_Relation_OImage(X24512,X24512,X24510),hAPP(hAPP(c_Set_Oinsert(X24512),X24509),c_Orderings_Obot__class_Obot(tc_fun(X24512,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X24512,X24512,X24510),hAPP(hAPP(c_Set_Oinsert(X24512),X24508),c_Orderings_Obot__class_Obot(tc_fun(X24512,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__eq])]) ).
fof(i_0_7225,plain,
! [X28730,X28731,X28732,X28733,X28734,X28735] :
( ( hBOOL(hAPP(hAPP(c_member(X28735),X28733),X28731))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28735,X28734)),hAPP(hAPP(c_Product__Type_OPair(X28735,X28734),X28733),X28732)),hAPP(hAPP(c_Product__Type_OSigma(X28735,X28734),X28731),X28730))) )
& ( hBOOL(hAPP(hAPP(c_member(X28734),X28732),hAPP(X28730,X28733)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28735,X28734)),hAPP(hAPP(c_Product__Type_OPair(X28735,X28734),X28733),X28732)),hAPP(hAPP(c_Product__Type_OSigma(X28735,X28734),X28731),X28730))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5528])])]) ).
fof(i_0_7226,plain,
! [X28712,X28713,X28714,X28715,X28716,X28717] :
( ( hBOOL(hAPP(hAPP(c_member(X28717),X28715),X28713))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28717,X28716)),hAPP(hAPP(c_Product__Type_OPair(X28717,X28716),X28715),X28714)),hAPP(hAPP(c_Product__Type_OSigma(X28717,X28716),X28713),X28712))) )
& ( hBOOL(hAPP(hAPP(c_member(X28716),X28714),hAPP(X28712,X28715)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28717,X28716)),hAPP(hAPP(c_Product__Type_OPair(X28717,X28716),X28715),X28714)),hAPP(hAPP(c_Product__Type_OSigma(X28717,X28716),X28713),X28712))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X28717),X28715),X28713))
| ~ hBOOL(hAPP(hAPP(c_member(X28716),X28714),hAPP(X28712,X28715)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X28717,X28716)),hAPP(hAPP(c_Product__Type_OPair(X28717,X28716),X28715),X28714)),hAPP(hAPP(c_Product__Type_OSigma(X28717,X28716),X28713),X28712))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__Sigma__iff])])]) ).
fof(i_0_7227,plain,
! [X28724,X28725,X28726,X28727,X28728,X28729] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28729,X28728)),hAPP(hAPP(c_Product__Type_OPair(X28729,X28728),X28727),X28726)),hAPP(hAPP(c_Product__Type_OSigma(X28729,X28728),X28725),X28724)))
| hBOOL(hAPP(hAPP(c_member(X28728),X28726),hAPP(X28724,X28727))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaD2])]) ).
fof(i_0_7228,plain,
! [X33211,X33212,X33213] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X33213,X33213),tc_HOL_Obool)),X33212),X33211))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X33213),tc_List_Olist(X33213)),tc_HOL_Obool)),c_List_Olistrel1(X33213,X33212)),c_List_Olistrel1(X33213,X33211))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1__mono])]) ).
fof(i_0_7229,plain,
! [X32259,X32260,X32261] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X32261,X32261),tc_HOL_Obool)),X32260),X32259))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X32261),tc_List_Olist(X32261)),tc_HOL_Obool)),c_List_Olistrel(X32261,X32260)),c_List_Olistrel(X32261,X32259))) ),
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,
! [X22881,X22882,X22883,X22884,X22885,X22886,X22887] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X22887,X22886,X22885,X22884),X22883),X22882),X22881) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22886,X22885,X22884),X22882),hAPP(X22883,X22881)),
inference(variable_rename,[status(thm)],[fact_scomp__def]) ).
fof(i_0_7232,plain,
! [X22862,X22863,X22864,X22865,X22866,X22867,X22868] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X22868,X22867,X22866,X22865),X22864),X22863),X22862) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22867,X22866,X22865),X22863),hAPP(X22864,X22862)),
inference(variable_rename,[status(thm)],[fact_scomp__apply]) ).
fof(i_0_7233,plain,
! [X24001,X24002,X24003,X24004] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24004,tc_HOL_Obool)),X24003),X24002))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24004,tc_HOL_Obool)),X24001),X24002))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24004,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24004,tc_HOL_Obool)),X24003),X24001)),X24002)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__least])]) ).
fof(i_0_7234,plain,
! [X25103,X25104,X25105,X25106,X25107] :
( ~ c_Finite__Set_Ofolding__one(X25107,X25106,X25105)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25107),X25104))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25107),X25103))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25107,tc_HOL_Obool)),X25104),X25103) = c_Orderings_Obot__class_Obot(tc_fun(X25107,tc_HOL_Obool))
| hAPP(hAPP(X25106,hAPP(X25105,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25107,tc_HOL_Obool)),X25104),X25103))),hAPP(X25105,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25107,tc_HOL_Obool)),X25104),X25103))) = hAPP(hAPP(X25106,hAPP(X25105,X25104)),hAPP(X25105,X25103)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Ounion__inter])]) ).
fof(i_0_7235,plain,
! [X27050,X27051,X27052,X27053,X27054] :
( ~ c_Fun_Oinj__on(X27054,X27053,X27052,X27051)
| ~ hBOOL(hAPP(hAPP(c_member(X27053),X27050),hAPP(c_Set_Oimage(X27054,X27053,X27052),X27051)))
| hAPP(X27052,hAPP(c_Fun_Othe__inv__into(X27054,X27053,X27051,X27052),X27050)) = X27050 ),
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,
! [X31235,X31236,X31237,X31238] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X31238,tc_HOL_Obool),tc_fun(X31237,tc_HOL_Obool)),X31236),hAPP(hAPP(c_COMBC(tc_fun(X31238,tc_HOL_Obool),tc_fun(X31238,tc_fun(X31237,tc_HOL_Obool)),tc_fun(X31237,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31238,tc_fun(X31237,tc_HOL_Obool))),X31235)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31238,tc_fun(X31237,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31238,tc_HOL_Obool),X31236)),X31235),
inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I8_J]) ).
fof(i_0_7239,plain,
! [X31322,X31323,X31324,X31325] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X31325,tc_HOL_Obool),tc_fun(X31324,tc_HOL_Obool)),X31323),hAPP(hAPP(c_COMBC(tc_fun(X31325,tc_HOL_Obool),tc_fun(X31325,tc_fun(X31324,tc_HOL_Obool)),tc_fun(X31324,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X31325,tc_fun(X31324,tc_HOL_Obool))),X31322)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X31325,tc_fun(X31324,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31325,tc_HOL_Obool),X31323)),X31322),
inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I8_J]) ).
fof(i_0_7240,plain,
! [X31239,X31240,X31241,X31242] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31242,tc_fun(X31241,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31242,tc_HOL_Obool),X31240)),X31239) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X31242,tc_HOL_Obool),tc_fun(X31241,tc_HOL_Obool)),X31240),hAPP(hAPP(c_COMBC(tc_fun(X31242,tc_HOL_Obool),tc_fun(X31242,tc_fun(X31241,tc_HOL_Obool)),tc_fun(X31241,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31242,tc_fun(X31241,tc_HOL_Obool))),X31239)),
inference(variable_rename,[status(thm)],[fact_INT__simps_I8_J]) ).
fof(i_0_7241,plain,
! [X31326,X31327,X31328,X31329] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X31329,tc_fun(X31328,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31329,tc_HOL_Obool),X31327)),X31326) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X31329,tc_HOL_Obool),tc_fun(X31328,tc_HOL_Obool)),X31327),hAPP(hAPP(c_COMBC(tc_fun(X31329,tc_HOL_Obool),tc_fun(X31329,tc_fun(X31328,tc_HOL_Obool)),tc_fun(X31328,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X31329,tc_fun(X31328,tc_HOL_Obool))),X31326)),
inference(variable_rename,[status(thm)],[fact_UN__simps_I8_J]) ).
fof(i_0_7242,plain,
! [X26588,X26589,X26590,X26591,X26592,X26593,X26594,X26595,X26596,X26597] :
( ( ~ c_Fun_Oinj__on(X26591,X26590,X26589,X26588)
| ~ hBOOL(hAPP(hAPP(c_member(X26591),X26592),X26588))
| ~ hBOOL(hAPP(hAPP(c_member(X26591),X26593),X26588))
| hAPP(X26589,X26592) != hAPP(X26589,X26593)
| X26592 = X26593 )
& ( hBOOL(hAPP(hAPP(c_member(X26597),esk194_4(X26594,X26595,X26596,X26597)),X26594))
| c_Fun_Oinj__on(X26597,X26596,X26595,X26594) )
& ( hBOOL(hAPP(hAPP(c_member(X26597),esk195_4(X26594,X26595,X26596,X26597)),X26594))
| c_Fun_Oinj__on(X26597,X26596,X26595,X26594) )
& ( hAPP(X26595,esk194_4(X26594,X26595,X26596,X26597)) = hAPP(X26595,esk195_4(X26594,X26595,X26596,X26597))
| c_Fun_Oinj__on(X26597,X26596,X26595,X26594) )
& ( esk194_4(X26594,X26595,X26596,X26597) != esk195_4(X26594,X26595,X26596,X26597)
| c_Fun_Oinj__on(X26597,X26596,X26595,X26594) ) ),
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,
! [X30217,X30218,X30219] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30219,X30219),tc_HOL_Obool)),X30218),X30217))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30219,X30219),tc_HOL_Obool)),X30217),c_Transitive__Closure_Ortrancl(X30219,X30218)))
| c_Transitive__Closure_Ortrancl(X30219,X30217) = c_Transitive__Closure_Ortrancl(X30219,X30218) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__subset])]) ).
fof(i_0_7244,plain,
! [X24523,X24524,X24525,X24526,X24527] :
( hAPP(c_Relation_OImage(X24527,X24527,X24526),hAPP(hAPP(c_Set_Oinsert(X24527),X24525),c_Orderings_Obot__class_Obot(tc_fun(X24527,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(X24527,X24527,X24526),hAPP(hAPP(c_Set_Oinsert(X24527),X24524),c_Orderings_Obot__class_Obot(tc_fun(X24527,tc_HOL_Obool))))
| ~ c_Equiv__Relations_Oequiv(X24527,X24523,X24526)
| ~ hBOOL(hAPP(hAPP(c_member(X24527),X24524),X24523))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X24527,X24527)),hAPP(hAPP(c_Product__Type_OPair(X24527,X24527),X24525),X24524)),X24526)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__equiv__class])]) ).
fof(i_0_7245,plain,
! [X32336,X32337,X32338,X32339,X32340,X32341] :
( ( X32341 != X32340
| hAPP(c_Map_Omap__of(X32339,X32338,hAPP(hAPP(c_List_Olist_OCons(tc_prod(X32339,X32338)),hAPP(hAPP(c_Product__Type_OPair(X32339,X32338),X32341),X32337)),X32336)),X32340) = hAPP(c_Option_Ooption_OSome(X32338),X32337) )
& ( X32341 = X32340
| hAPP(c_Map_Omap__of(X32339,X32338,hAPP(hAPP(c_List_Olist_OCons(tc_prod(X32339,X32338)),hAPP(hAPP(c_Product__Type_OPair(X32339,X32338),X32341),X32337)),X32336)),X32340) = hAPP(c_Map_Omap__of(X32339,X32338,X32336),X32340) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__Cons__code_I2_J])]) ).
fof(i_0_7246,plain,
! [X28718,X28719,X28720,X28721,X28722,X28723] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28723,X28722)),hAPP(hAPP(c_Product__Type_OPair(X28723,X28722),X28721),X28720)),hAPP(hAPP(c_Product__Type_OSigma(X28723,X28722),X28719),X28718)))
| hBOOL(hAPP(hAPP(c_member(X28723),X28721),X28719)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaD1])]) ).
fof(i_0_7247,plain,
! [X25607,X25608,X25609,X25610,X25612] :
( ( hBOOL(hAPP(hAPP(c_member(X25609),esk151_4(X25607,X25608,X25609,X25610)),X25608))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25609,X25610),X25607),X25608) != c_Groups_Ozero__class_Ozero(X25610)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25609),X25608))
| ~ class_Rings_Ocomm__semiring__1(X25610)
| ~ class_Rings_Ono__zero__divisors(X25610) )
& ( hAPP(X25607,esk151_4(X25607,X25608,X25609,X25610)) = c_Groups_Ozero__class_Ozero(X25610)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25609,X25610),X25607),X25608) != c_Groups_Ozero__class_Ozero(X25610)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25609),X25608))
| ~ class_Rings_Ocomm__semiring__1(X25610)
| ~ class_Rings_Ono__zero__divisors(X25610) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X25609),X25612),X25608))
| hAPP(X25607,X25612) != c_Groups_Ozero__class_Ozero(X25610)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25609,X25610),X25607),X25608) = c_Groups_Ozero__class_Ozero(X25610)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25609),X25608))
| ~ class_Rings_Ocomm__semiring__1(X25610)
| ~ class_Rings_Ono__zero__divisors(X25610) ) ),
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,
! [X25470,X25471,X25472,X25473] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25473),X25472))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25471),hAPP(c_Set_Oimage(X25473,X25471,X25470),X25472))),hAPP(c_Finite__Set_Ocard(X25473),X25472))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image__le])]) ).
fof(i_0_7249,plain,
! [X32473,X32474,X32475,X32476,X32477] :
( ~ class_Orderings_Olinorder(X32477)
| hBOOL(hAPP(hAPP(c_member(X32477),hAPP(X32476,X32475)),hAPP(c_Set_Oimage(X32474,X32477,X32476),hAPP(c_List_Oset(X32474),X32473))))
| c_List_Olinorder__class_Oinsort__insert__key(X32474,X32477,X32476,X32475,X32473) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32474,X32477,X32476),X32475),X32473) ),
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,
! [X30959,X30960,X30961,X30962,X30963,X30964,X30965,X30966,X30967] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30962,tc_fun(X30961,tc_HOL_Obool)),X30960),X30959) != c_Orderings_Otop__class_Otop(tc_fun(X30961,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X30962),X30963),X30960))
| hAPP(X30959,X30963) = c_Orderings_Otop__class_Otop(tc_fun(X30961,tc_HOL_Obool)) )
& ( hBOOL(hAPP(hAPP(c_member(X30967),esk393_4(X30964,X30965,X30966,X30967)),X30965))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30967,tc_fun(X30966,tc_HOL_Obool)),X30965),X30964) = c_Orderings_Otop__class_Otop(tc_fun(X30966,tc_HOL_Obool)) )
& ( hAPP(X30964,esk393_4(X30964,X30965,X30966,X30967)) != c_Orderings_Otop__class_Otop(tc_fun(X30966,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30967,tc_fun(X30966,tc_HOL_Obool)),X30965),X30964) = c_Orderings_Otop__class_Otop(tc_fun(X30966,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,
! [X25984,X25985,X25986,X25987,X25988,X25989,X25990,X25991,X25992] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25987,tc_fun(X25986,tc_HOL_Obool)),X25985),X25984) != c_Orderings_Obot__class_Obot(tc_fun(X25986,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X25987),X25988),X25985))
| hAPP(X25984,X25988) = c_Orderings_Obot__class_Obot(tc_fun(X25986,tc_HOL_Obool)) )
& ( hBOOL(hAPP(hAPP(c_member(X25992),esk167_4(X25989,X25990,X25991,X25992)),X25990))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25992,tc_fun(X25991,tc_HOL_Obool)),X25990),X25989) = c_Orderings_Obot__class_Obot(tc_fun(X25991,tc_HOL_Obool)) )
& ( hAPP(X25989,esk167_4(X25989,X25990,X25991,X25992)) != c_Orderings_Obot__class_Obot(tc_fun(X25991,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25992,tc_fun(X25991,tc_HOL_Obool)),X25990),X25989) = c_Orderings_Obot__class_Obot(tc_fun(X25991,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,
! [X30949,X30950,X30951,X30952,X30953,X30954,X30955,X30956,X30957] :
( ( c_Orderings_Otop__class_Otop(tc_fun(X30952,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30951,tc_fun(X30952,tc_HOL_Obool)),X30950),X30949)
| ~ hBOOL(hAPP(hAPP(c_member(X30951),X30953),X30950))
| hAPP(X30949,X30953) = c_Orderings_Otop__class_Otop(tc_fun(X30952,tc_HOL_Obool)) )
& ( hBOOL(hAPP(hAPP(c_member(X30956),esk392_4(X30954,X30955,X30956,X30957)),X30955))
| c_Orderings_Otop__class_Otop(tc_fun(X30957,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30956,tc_fun(X30957,tc_HOL_Obool)),X30955),X30954) )
& ( hAPP(X30954,esk392_4(X30954,X30955,X30956,X30957)) != c_Orderings_Otop__class_Otop(tc_fun(X30957,tc_HOL_Obool))
| c_Orderings_Otop__class_Otop(tc_fun(X30957,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30956,tc_fun(X30957,tc_HOL_Obool)),X30955),X30954) ) ),
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_7254,plain,
! [X25967,X25968,X25969,X25970,X25971,X25972,X25973,X25974,X25975] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X25970,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25969,tc_fun(X25970,tc_HOL_Obool)),X25968),X25967)
| ~ hBOOL(hAPP(hAPP(c_member(X25969),X25971),X25968))
| hAPP(X25967,X25971) = c_Orderings_Obot__class_Obot(tc_fun(X25970,tc_HOL_Obool)) )
& ( hBOOL(hAPP(hAPP(c_member(X25974),esk166_4(X25972,X25973,X25974,X25975)),X25973))
| c_Orderings_Obot__class_Obot(tc_fun(X25975,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25974,tc_fun(X25975,tc_HOL_Obool)),X25973),X25972) )
& ( hAPP(X25972,esk166_4(X25972,X25973,X25974,X25975)) != c_Orderings_Obot__class_Obot(tc_fun(X25975,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(X25975,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25974,tc_fun(X25975,tc_HOL_Obool)),X25973),X25972) ) ),
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_7255,plain,
! [X29976,X29977,X29978,X29979] :
( ( hBOOL(hAPP(hAPP(c_member(X29979),esk349_4(X29976,X29977,X29978,X29979)),X29977))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29979,tc_Nat_Onat),X29978),X29977) != hAPP(c_Nat_OSuc,X29976) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X29978,esk349_4(X29976,X29977,X29978,X29979))))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29979,tc_Nat_Onat),X29978),X29977) != hAPP(c_Nat_OSuc,X29976) ) ),
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,
! [X25365,X25366,X25367] :
( ~ class_Lattices_Olattice(X25367)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25367),X25366))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25367),X25365))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25367,tc_HOL_Obool)),X25366),X25365) = c_Orderings_Obot__class_Obot(tc_fun(X25367,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25367),c_Big__Operators_Olattice__class_OInf__fin(X25367,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25367,tc_HOL_Obool)),X25366),X25365))),c_Big__Operators_Olattice__class_OInf__fin(X25367,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25367,tc_HOL_Obool)),X25366),X25365))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25367),c_Big__Operators_Olattice__class_OInf__fin(X25367,X25366)),c_Big__Operators_Olattice__class_OInf__fin(X25367,X25365)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__inter])]) ).
fof(i_0_7257,plain,
! [X25015,X25016,X25017] :
( ~ class_Lattices_Olattice(X25017)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25017),X25016))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25017),X25015))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25017,tc_HOL_Obool)),X25016),X25015) = c_Orderings_Obot__class_Obot(tc_fun(X25017,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25017),c_Big__Operators_Olattice__class_OSup__fin(X25017,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25017,tc_HOL_Obool)),X25016),X25015))),c_Big__Operators_Olattice__class_OSup__fin(X25017,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25017,tc_HOL_Obool)),X25016),X25015))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25017),c_Big__Operators_Olattice__class_OSup__fin(X25017,X25016)),c_Big__Operators_Olattice__class_OSup__fin(X25017,X25015)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__inter])]) ).
fof(i_0_7258,plain,
! [X25380,X25381,X25382] :
( ~ class_Orderings_Olinorder(X25382)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25382),X25381))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25382),X25380))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25382,tc_HOL_Obool)),X25381),X25380) = c_Orderings_Obot__class_Obot(tc_fun(X25382,tc_HOL_Obool))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X25382),c_Big__Operators_Olinorder__class_OMax(X25382,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25382,tc_HOL_Obool)),X25381),X25380))),c_Big__Operators_Olinorder__class_OMax(X25382,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25382,tc_HOL_Obool)),X25381),X25380))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25382),c_Big__Operators_Olinorder__class_OMax(X25382,X25381)),c_Big__Operators_Olinorder__class_OMax(X25382,X25380)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Ounion__inter])]) ).
fof(i_0_7259,plain,
! [X25377,X25378,X25379] :
( ~ class_Orderings_Olinorder(X25379)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25379),X25378))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25379),X25377))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25379,tc_HOL_Obool)),X25378),X25377) = c_Orderings_Obot__class_Obot(tc_fun(X25379,tc_HOL_Obool))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X25379),c_Big__Operators_Olinorder__class_OMin(X25379,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25379,tc_HOL_Obool)),X25378),X25377))),c_Big__Operators_Olinorder__class_OMin(X25379,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25379,tc_HOL_Obool)),X25378),X25377))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25379),c_Big__Operators_Olinorder__class_OMin(X25379,X25378)),c_Big__Operators_Olinorder__class_OMin(X25379,X25377)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Ounion__inter])]) ).
fof(i_0_7260,plain,
! [X28521,X28522,X28523,X28524,X28525,X28526,X28527] :
( ( hAPP(X28524,X28522) != hAPP(X28524,X28521)
| X28522 = X28521
| ~ hBOOL(hAPP(hAPP(c_member(X28526),X28521),X28523))
| ~ hBOOL(hAPP(hAPP(c_member(X28526),X28522),X28523))
| ~ c_Typedef_Otype__definition(X28527,X28526,X28525,X28524,X28523) )
& ( X28522 != X28521
| hAPP(X28524,X28522) = hAPP(X28524,X28521)
| ~ hBOOL(hAPP(hAPP(c_member(X28526),X28521),X28523))
| ~ hBOOL(hAPP(hAPP(c_member(X28526),X28522),X28523))
| ~ c_Typedef_Otype__definition(X28527,X28526,X28525,X28524,X28523) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__inject])])]) ).
fof(i_0_7261,plain,
! [X24438,X24439,X24440,X24441] : hAPP(c_Relation_OField(X24441),hAPP(hAPP(c_Set_Oinsert(tc_prod(X24441,X24441)),hAPP(hAPP(c_Product__Type_OPair(X24441,X24441),X24440),X24439)),X24438)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24441,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X24441),X24440),hAPP(hAPP(c_Set_Oinsert(X24441),X24439),c_Orderings_Obot__class_Obot(tc_fun(X24441,tc_HOL_Obool))))),hAPP(c_Relation_OField(X24441),X24438)),
inference(variable_rename,[status(thm)],[fact_Field__insert]) ).
fof(i_0_7262,plain,
! [X33588,X33589,X33590] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33590),X33589))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33590),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33589),X33588))) ),
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,
! [X18226,X18227,X18228,X18229,X18230,X18231] : c_Nitpick_Opair__box_Opair__box__size(X18231,X18230,X18229,X18228,c_Nitpick_Opair__box_OPairBox(X18231,X18230,X18227,X18226)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X18229,X18227)),hAPP(X18228,X18226))),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,
! [X31434,X31435,X31436] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X31436,tc_HOL_Obool)),esk406_3(X31434,X31435,X31436)),X31435))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31434),hAPP(c_Finite__Set_Ocard(tc_fun(X31436,tc_HOL_Obool)),X31435)) = hAPP(c_Finite__Set_Ocard(X31436),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31436,tc_HOL_Obool),X31435))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X31436,tc_HOL_Obool)),esk405_3(X31434,X31435,X31436)),X31435))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31436),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31436,tc_HOL_Obool),X31435)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X31436,tc_HOL_Obool)),X31435)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(X31436,tc_HOL_Obool)),esk407_3(X31434,X31435,X31436)),X31435))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31434),hAPP(c_Finite__Set_Ocard(tc_fun(X31436,tc_HOL_Obool)),X31435)) = hAPP(c_Finite__Set_Ocard(X31436),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31436,tc_HOL_Obool),X31435))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X31436,tc_HOL_Obool)),esk405_3(X31434,X31435,X31436)),X31435))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31436),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31436,tc_HOL_Obool),X31435)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X31436,tc_HOL_Obool)),X31435)) )
& ( esk406_3(X31434,X31435,X31436) != esk407_3(X31434,X31435,X31436)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31434),hAPP(c_Finite__Set_Ocard(tc_fun(X31436,tc_HOL_Obool)),X31435)) = hAPP(c_Finite__Set_Ocard(X31436),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31436,tc_HOL_Obool),X31435))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X31436,tc_HOL_Obool)),esk405_3(X31434,X31435,X31436)),X31435))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31436),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31436,tc_HOL_Obool),X31435)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X31436,tc_HOL_Obool)),X31435)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31436,tc_HOL_Obool)),esk406_3(X31434,X31435,X31436)),esk407_3(X31434,X31435,X31436)) != c_Orderings_Obot__class_Obot(tc_fun(X31436,tc_HOL_Obool))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31434),hAPP(c_Finite__Set_Ocard(tc_fun(X31436,tc_HOL_Obool)),X31435)) = hAPP(c_Finite__Set_Ocard(X31436),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31436,tc_HOL_Obool),X31435))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X31436,tc_HOL_Obool)),esk405_3(X31434,X31435,X31436)),X31435))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31436),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31436,tc_HOL_Obool),X31435)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X31436,tc_HOL_Obool)),X31435)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(X31436,tc_HOL_Obool)),esk406_3(X31434,X31435,X31436)),X31435))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31434),hAPP(c_Finite__Set_Ocard(tc_fun(X31436,tc_HOL_Obool)),X31435)) = hAPP(c_Finite__Set_Ocard(X31436),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31436,tc_HOL_Obool),X31435))
| hAPP(c_Finite__Set_Ocard(X31436),esk405_3(X31434,X31435,X31436)) != X31434
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31436),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31436,tc_HOL_Obool),X31435)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X31436,tc_HOL_Obool)),X31435)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(X31436,tc_HOL_Obool)),esk407_3(X31434,X31435,X31436)),X31435))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31434),hAPP(c_Finite__Set_Ocard(tc_fun(X31436,tc_HOL_Obool)),X31435)) = hAPP(c_Finite__Set_Ocard(X31436),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31436,tc_HOL_Obool),X31435))
| hAPP(c_Finite__Set_Ocard(X31436),esk405_3(X31434,X31435,X31436)) != X31434
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31436),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31436,tc_HOL_Obool),X31435)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X31436,tc_HOL_Obool)),X31435)) )
& ( esk406_3(X31434,X31435,X31436) != esk407_3(X31434,X31435,X31436)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31434),hAPP(c_Finite__Set_Ocard(tc_fun(X31436,tc_HOL_Obool)),X31435)) = hAPP(c_Finite__Set_Ocard(X31436),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31436,tc_HOL_Obool),X31435))
| hAPP(c_Finite__Set_Ocard(X31436),esk405_3(X31434,X31435,X31436)) != X31434
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31436),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31436,tc_HOL_Obool),X31435)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X31436,tc_HOL_Obool)),X31435)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31436,tc_HOL_Obool)),esk406_3(X31434,X31435,X31436)),esk407_3(X31434,X31435,X31436)) != c_Orderings_Obot__class_Obot(tc_fun(X31436,tc_HOL_Obool))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31434),hAPP(c_Finite__Set_Ocard(tc_fun(X31436,tc_HOL_Obool)),X31435)) = hAPP(c_Finite__Set_Ocard(X31436),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31436,tc_HOL_Obool),X31435))
| hAPP(c_Finite__Set_Ocard(X31436),esk405_3(X31434,X31435,X31436)) != X31434
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31436),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31436,tc_HOL_Obool),X31435)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X31436,tc_HOL_Obool)),X31435)) ) ),
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,
! [X34016,X34017,X34018] :
( ~ class_Orderings_Olinorder(X34018)
| c_List_Olinorder__class_Osorted(X34018,hAPP(c_List_Ofilter(X34018,hAPP(hAPP(c_COMBC(X34018,X34018,tc_HOL_Obool),c_fequal),hAPP(X34017,X34016))),X34016)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__same])]) ).
fof(i_0_7267,plain,
! [X28215,X28216,X28217,X28218,X28219] :
( ~ c_Fun_Oinj__on(X28219,X28218,X28217,c_Orderings_Otop__class_Otop(tc_fun(X28219,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(X28216,X28219,X28215,c_Orderings_Otop__class_Otop(tc_fun(X28216,tc_HOL_Obool)))
| c_Fun_Oinj__on(X28216,X28218,hAPP(c_Fun_Ocomp(X28219,X28218,X28216,X28217),X28215),c_Orderings_Otop__class_Otop(tc_fun(X28216,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__comp])]) ).
fof(i_0_7268,plain,
! [X32831,X32832,X32833,X32834] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32834,tc_HOL_Obool)),hAPP(c_List_Oset(X32834),hAPP(hAPP(c_List_Olist__update(X32834,X32833),X32832),X32831))),hAPP(hAPP(c_Set_Oinsert(X32834),X32831),hAPP(c_List_Oset(X32834),X32833)))),
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,
! [X25404,X25405,X25406] :
( ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(X25406,tc_HOL_Obool))
| c_Big__Operators_Olattice_OInf__fin(X25406,c_Orderings_Oord__class_Omin(X25406),X25405) = X25404
| ~ hBOOL(hAPP(hAPP(c_member(X25406),X25404),X25405))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25406),X25405))
| ~ class_Orderings_Olinorder(X25406) )
& ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(X25406,tc_HOL_Obool))
| c_Big__Operators_Olattice_OInf__fin(X25406,c_Orderings_Oord__class_Omin(X25406),X25405) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25406),X25404),c_Big__Operators_Olattice_OInf__fin(X25406,c_Orderings_Oord__class_Omin(X25406),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))))))
| ~ hBOOL(hAPP(hAPP(c_member(X25406),X25404),X25405))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25406),X25405))
| ~ class_Orderings_Olinorder(X25406) ) ),
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,
! [X25251,X25252,X25253] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25253,tc_HOL_Obool)),X25252),hAPP(hAPP(c_Set_Oinsert(X25253),X25251),c_Orderings_Obot__class_Obot(tc_fun(X25253,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25253,tc_HOL_Obool))
| c_Big__Operators_Olattice_OSup__fin(X25253,c_Orderings_Oord__class_Omax(X25253),X25252) = X25251
| ~ hBOOL(hAPP(hAPP(c_member(X25253),X25251),X25252))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25253),X25252))
| ~ class_Orderings_Olinorder(X25253) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25253,tc_HOL_Obool)),X25252),hAPP(hAPP(c_Set_Oinsert(X25253),X25251),c_Orderings_Obot__class_Obot(tc_fun(X25253,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25253,tc_HOL_Obool))
| c_Big__Operators_Olattice_OSup__fin(X25253,c_Orderings_Oord__class_Omax(X25253),X25252) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25253),X25251),c_Big__Operators_Olattice_OSup__fin(X25253,c_Orderings_Oord__class_Omax(X25253),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25253,tc_HOL_Obool)),X25252),hAPP(hAPP(c_Set_Oinsert(X25253),X25251),c_Orderings_Obot__class_Obot(tc_fun(X25253,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(X25253),X25251),X25252))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25253),X25252))
| ~ class_Orderings_Olinorder(X25253) ) ),
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,
! [X27495,X27496,X27497] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27497,tc_Nat_Onat),X27496),X27495) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27497,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X27497),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X27496)),X27495)),
inference(variable_rename,[status(thm)],[fact_transfer__nat__int__sum__prod2_I1_J]) ).
fof(i_0_7273,plain,
! [X25590,X25591,X25592] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25592,tc_Nat_Onat),X25591),X25590) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25592,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X25592),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X25591)),X25590)),
inference(variable_rename,[status(thm)],[fact_transfer__nat__int__sum__prod2_I2_J]) ).
fof(i_0_7274,plain,
! [X28461,X28462,X28463,X28464,X28465] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X28465),X28464),hAPP(c_Set_Ovimage(X28465,X28463,X28462),hAPP(hAPP(c_Set_Oinsert(X28463),X28461),c_Orderings_Obot__class_Obot(tc_fun(X28463,tc_HOL_Obool))))))
| hAPP(X28462,X28464) = X28461 )
& ( hAPP(X28462,X28464) != X28461
| hBOOL(hAPP(hAPP(c_member(X28465),X28464),hAPP(c_Set_Ovimage(X28465,X28463,X28462),hAPP(hAPP(c_Set_Oinsert(X28463),X28461),c_Orderings_Obot__class_Obot(tc_fun(X28463,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,
! [X27757,X27758,X27759,X27760,X27761,X27762] :
( ~ c_Fun_Oinj__on(X27762,X27761,hAPP(c_Fun_Ocomp(X27760,X27761,X27762,X27759),X27758),X27757)
| c_Fun_Oinj__on(X27762,X27760,X27758,X27757) ),
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,
! [X24574,X24575,X24576,X24577] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24577),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24577,tc_HOL_Obool)),X24576),hAPP(hAPP(c_Set_Oinsert(X24577),X24575),X24574))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24577),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24577,tc_HOL_Obool)),X24576),X24574))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24577),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24577,tc_HOL_Obool)),X24576),X24574)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24577),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24577,tc_HOL_Obool)),X24576),hAPP(hAPP(c_Set_Oinsert(X24577),X24575),X24574)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Diff__insert])]) ).
fof(i_0_7279,plain,
! [X29213,X29214,X29215] : hAPP(hAPP(c_Set_Oinsert(X29215),X29214),X29213) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29215,tc_HOL_Obool)),hAPP(c_Set_OCollect(X29215),hAPP(hAPP(c_COMBC(X29215,X29215,tc_HOL_Obool),c_fequal),X29214))),X29213),
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,
! [X20410,X20411,X20412,X20413,X20414,X20415] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20415),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20415),X20414),X20413)),X20412) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20415),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20415),X20411),X20413)),X20410)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20415),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20415),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20415),X20414),X20411)),X20413)),X20412) = X20410
| ~ class_Rings_Oring(X20415) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20415),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20415),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20415),X20414),X20411)),X20413)),X20412) != X20410
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20415),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20415),X20414),X20413)),X20412) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20415),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20415),X20411),X20413)),X20410)
| ~ class_Rings_Oring(X20415) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff1])])]) ).
fof(i_0_7289,plain,
! [X20404,X20405,X20406,X20407,X20408,X20409] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20409),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20409),X20408),X20407)),X20406) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20409),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20409),X20405),X20407)),X20404)
| X20406 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20409),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20409),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20409),X20405),X20408)),X20407)),X20404)
| ~ class_Rings_Oring(X20409) )
& ( X20406 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20409),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20409),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20409),X20405),X20408)),X20407)),X20404)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20409),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20409),X20408),X20407)),X20406) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20409),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20409),X20405),X20407)),X20404)
| ~ class_Rings_Oring(X20409) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff2])])]) ).
fof(i_0_7290,plain,
! [X31177,X31178,X31179,X31180,X31181,X31182] :
( ~ c_Relation_Osingle__valued(X31182,X31181,hAPP(c_Relation_Oconverse(X31181,X31182),X31180))
| X31179 = c_Orderings_Obot__class_Obot(tc_fun(X31178,tc_HOL_Obool))
| hAPP(c_Relation_OImage(X31181,X31182,X31180),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31178,tc_fun(X31181,tc_HOL_Obool)),X31179),X31177)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31178,tc_fun(X31182,tc_HOL_Obool)),X31179),hAPP(hAPP(c_COMBB(tc_fun(X31181,tc_HOL_Obool),tc_fun(X31182,tc_HOL_Obool),X31178),c_Relation_OImage(X31181,X31182,X31180)),X31177)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__INT__eq])]) ).
fof(i_0_7291,plain,
! [X33925,X33926,X33927] : hAPP(c_Product__Type_Osnd(tc_List_Olist(X33927),tc_List_Olist(X33927)),c_List_Opartition(X33927,X33926,X33925)) = hAPP(c_List_Ofilter(X33927,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X33927,c_fNot),X33926)),X33925),
inference(variable_rename,[status(thm)],[fact_partition__filter2]) ).
fof(i_0_7292,plain,
! [X28443,X28444,X28445,X28446,X28447] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28447,tc_HOL_Obool)),X28446),X28445))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28444,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X28444,X28447,X28443),X28446)),hAPP(c_Set_Ovimage(X28444,X28447,X28443),X28445))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__mono])]) ).
fof(i_0_7293,plain,
! [X24268,X24269,X24270,X24271,X24272] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24272,tc_HOL_Obool)),X24271),X24270))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24269,tc_HOL_Obool)),hAPP(c_Set_Oimage(X24272,X24269,X24268),X24271)),hAPP(c_Set_Oimage(X24272,X24269,X24268),X24270))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__mono])]) ).
fof(i_0_7294,plain,
! [X26155,X26156,X26157,X26158,X26159,X26160] :
( ~ c_Equiv__Relations_Oequiv(X26160,X26159,X26158)
| ~ c_Equiv__Relations_Ocongruent(X26160,tc_fun(X26157,tc_HOL_Obool),X26158,X26156)
| ~ hBOOL(hAPP(hAPP(c_member(X26160),X26155),X26159))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26160,tc_fun(X26157,tc_HOL_Obool)),hAPP(c_Relation_OImage(X26160,X26160,X26158),hAPP(hAPP(c_Set_Oinsert(X26160),X26155),c_Orderings_Obot__class_Obot(tc_fun(X26160,tc_HOL_Obool))))),X26156) = hAPP(X26156,X26155) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__equiv__class])]) ).
fof(i_0_7295,plain,
! [X25433,X25434,X25435] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25435,tc_HOL_Obool)),X25434),hAPP(hAPP(c_Set_Oinsert(X25435),X25433),c_Orderings_Obot__class_Obot(tc_fun(X25435,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25435,tc_HOL_Obool))
| c_Big__Operators_Olattice_OInf__fin(X25435,c_Orderings_Oord__class_Omin(X25435),hAPP(hAPP(c_Set_Oinsert(X25435),X25433),X25434)) = X25433
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25435),X25434))
| ~ class_Orderings_Olinorder(X25435) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25435,tc_HOL_Obool)),X25434),hAPP(hAPP(c_Set_Oinsert(X25435),X25433),c_Orderings_Obot__class_Obot(tc_fun(X25435,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25435,tc_HOL_Obool))
| c_Big__Operators_Olattice_OInf__fin(X25435,c_Orderings_Oord__class_Omin(X25435),hAPP(hAPP(c_Set_Oinsert(X25435),X25433),X25434)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25435),X25433),c_Big__Operators_Olattice_OInf__fin(X25435,c_Orderings_Oord__class_Omin(X25435),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25435,tc_HOL_Obool)),X25434),hAPP(hAPP(c_Set_Oinsert(X25435),X25433),c_Orderings_Obot__class_Obot(tc_fun(X25435,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25435),X25434))
| ~ class_Orderings_Olinorder(X25435) ) ),
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,
! [X25341,X25342,X25343] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25343,tc_HOL_Obool)),X25342),hAPP(hAPP(c_Set_Oinsert(X25343),X25341),c_Orderings_Obot__class_Obot(tc_fun(X25343,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25343,tc_HOL_Obool))
| c_Big__Operators_Olattice_OSup__fin(X25343,c_Orderings_Oord__class_Omax(X25343),hAPP(hAPP(c_Set_Oinsert(X25343),X25341),X25342)) = X25341
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25343),X25342))
| ~ class_Orderings_Olinorder(X25343) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25343,tc_HOL_Obool)),X25342),hAPP(hAPP(c_Set_Oinsert(X25343),X25341),c_Orderings_Obot__class_Obot(tc_fun(X25343,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25343,tc_HOL_Obool))
| c_Big__Operators_Olattice_OSup__fin(X25343,c_Orderings_Oord__class_Omax(X25343),hAPP(hAPP(c_Set_Oinsert(X25343),X25341),X25342)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25343),X25341),c_Big__Operators_Olattice_OSup__fin(X25343,c_Orderings_Oord__class_Omax(X25343),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25343,tc_HOL_Obool)),X25342),hAPP(hAPP(c_Set_Oinsert(X25343),X25341),c_Orderings_Obot__class_Obot(tc_fun(X25343,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25343),X25342))
| ~ class_Orderings_Olinorder(X25343) ) ),
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,
! [X27732,X27733,X27734,X27735,X27736,X27737,X27738,X27739,X27740,X27741,X27742] :
( hAPP(X27742,hAPP(X27741,X27740)) != hAPP(X27739,hAPP(X27738,X27737))
| hAPP(hAPP(c_Fun_Ocomp(X27736,X27735,X27734,X27742),X27741),X27740) = hAPP(hAPP(c_Fun_Ocomp(X27733,X27735,X27732,X27739),X27738),X27737) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comp__cong])]) ).
fof(i_0_7298,plain,
! [X24589,X24590,X24591,X24592,X24593] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24593,tc_HOL_Obool)),X24590),hAPP(hAPP(c_Set_Oinsert(X24593),X24589),c_Orderings_Obot__class_Obot(tc_fun(X24593,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X24593,tc_HOL_Obool))
| hAPP(X24591,X24590) = X24589
| ~ hBOOL(hAPP(hAPP(c_member(X24593),X24589),X24590))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24593),X24590))
| ~ c_Finite__Set_Ofolding__one(X24593,X24592,X24591) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24593,tc_HOL_Obool)),X24590),hAPP(hAPP(c_Set_Oinsert(X24593),X24589),c_Orderings_Obot__class_Obot(tc_fun(X24593,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X24593,tc_HOL_Obool))
| hAPP(X24591,X24590) = hAPP(hAPP(X24592,X24589),hAPP(X24591,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24593,tc_HOL_Obool)),X24590),hAPP(hAPP(c_Set_Oinsert(X24593),X24589),c_Orderings_Obot__class_Obot(tc_fun(X24593,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(X24593),X24589),X24590))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24593),X24590))
| ~ c_Finite__Set_Ofolding__one(X24593,X24592,X24591) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Oremove])])]) ).
fof(i_0_7299,plain,
! [X25485,X25486,X25487] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25487),X25486))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25487),X25485))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25487),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25487,tc_HOL_Obool)),X25486),X25485))),hAPP(c_Finite__Set_Ocard(X25487),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25487,tc_HOL_Obool)),X25486),X25485))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25487),X25486)),hAPP(c_Finite__Set_Ocard(X25487),X25485)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Ounion__inter])]) ).
fof(i_0_7300,plain,
! [X25488,X25489,X25490] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25490),X25489))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25490),X25488))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25490),X25489)),hAPP(c_Finite__Set_Ocard(X25490),X25488)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25490),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25490,tc_HOL_Obool)),X25489),X25488))),hAPP(c_Finite__Set_Ocard(X25490),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25490,tc_HOL_Obool)),X25489),X25488))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Un__Int])]) ).
fof(i_0_7301,plain,
! [X29675,X29676,X29677,X29678] :
( ( hBOOL(hAPP(X29678,esk321_4(X29675,X29676,X29677,X29678)))
| c_Wellfounded_Owf(tc_prod(X29675,X29677),c_Recdef_Osame__fst(X29675,X29677,X29678,X29676)) )
& ( ~ c_Wellfounded_Owf(X29677,hAPP(X29676,esk321_4(X29675,X29676,X29677,X29678)))
| c_Wellfounded_Owf(tc_prod(X29675,X29677),c_Recdef_Osame__fst(X29675,X29677,X29678,X29676)) ) ),
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,
! [X23757,X23758,X23759,X23760,X23761] :
( ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X23761,X23760,X23759),X23758),X23757))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X23761,X23760)),hAPP(hAPP(c_Product__Type_OPair(X23761,X23760),X23758),X23757)),X23759)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23761,X23760)),hAPP(hAPP(c_Product__Type_OPair(X23761,X23760),X23758),X23757)),X23759))
| hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X23761,X23760,X23759),X23758),X23757)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rel__def])]) ).
fof(i_0_7303,plain,
! [X31957,X31958,X31959] :
( ~ hBOOL(hAPP(c_List_Odistinct(X31959),hAPP(hAPP(c_List_Omap(tc_prod(X31959,X31958),X31959),c_Product__Type_Ofst(X31959,X31958)),X31957)))
| c_Map_Oran(X31959,X31958,c_Map_Omap__of(X31959,X31958,X31957)) = hAPP(c_Set_Oimage(tc_prod(X31959,X31958),X31958,c_Product__Type_Osnd(X31959,X31958)),hAPP(c_List_Oset(tc_prod(X31959,X31958)),X31957)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ran__distinct])]) ).
fof(i_0_7304,plain,
! [X27442,X27443,X27444,X27445,X27446] : c_Map_Orestrict__map(X27446,X27445,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27446,tc_Option_Ooption(X27445)),X27444),X27443),hAPP(c_Option_Ooption_OSome(X27445),X27442)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27446,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X27446),X27443),c_Orderings_Obot__class_Obot(tc_fun(X27446,tc_HOL_Obool))))) = c_Map_Orestrict__map(X27446,X27445,X27444,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27446,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X27446),X27443),c_Orderings_Obot__class_Obot(tc_fun(X27446,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,
! [X30211,X30212,X30213] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30213,tc_HOL_Obool)),hAPP(c_Relation_OImage(X30213,X30213,X30212),X30211)),X30211))
| hAPP(c_Relation_OImage(X30213,X30213,c_Transitive__Closure_Ortrancl(X30213,X30212)),X30211) = X30211 ),
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,
! [X30297,X30298,X30299,X30300] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30300,X30300)),hAPP(hAPP(c_Product__Type_OPair(X30300,X30300),X30299),X30298)),c_Transitive__Closure_Ortrancl(X30300,X30297)))
| ~ hBOOL(hAPP(hAPP(c_member(X30300),X30298),c_Wellfounded_Oacc(X30300,X30297)))
| hBOOL(hAPP(hAPP(c_member(X30300),X30299),c_Wellfounded_Oacc(X30300,X30297))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downwards__aux])]) ).
fof(i_0_7309,plain,
! [X30293,X30294,X30295,X30296] :
( ~ hBOOL(hAPP(hAPP(c_member(X30296),X30295),c_Wellfounded_Oacc(X30296,X30294)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30296,X30296)),hAPP(hAPP(c_Product__Type_OPair(X30296,X30296),X30293),X30295)),c_Transitive__Closure_Ortrancl(X30296,X30294)))
| hBOOL(hAPP(hAPP(c_member(X30296),X30293),c_Wellfounded_Oacc(X30296,X30294))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downwards])]) ).
fof(i_0_7310,plain,
! [X25525,X25526,X25527,X25528] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25528),X25527))
| ~ hBOOL(hAPP(hAPP(c_member(X25528),X25526),X25527))
| hBOOL(hAPP(hAPP(c_member(X25528),X25526),X25525))
| hAPP(c_Finite__Set_Ocard(X25528),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25528,tc_HOL_Obool)),X25527),hAPP(hAPP(c_Set_Oinsert(X25528),X25526),X25525))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25528),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25528,tc_HOL_Obool)),X25527),X25525))),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,
! [X31142,X31143,X31144,X31145,X31146] :
( ( X31146 != c_Orderings_Obot__class_Obot(tc_fun(X31145,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31145,tc_fun(X31144,tc_HOL_Obool)),X31146),hAPP(hAPP(c_COMBB(tc_fun(X31144,tc_HOL_Obool),tc_fun(X31144,tc_HOL_Obool),X31145),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31144,tc_HOL_Obool)),X31143)),X31142)) = c_Orderings_Otop__class_Otop(tc_fun(X31144,tc_HOL_Obool)) )
& ( X31146 = c_Orderings_Obot__class_Obot(tc_fun(X31145,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31145,tc_fun(X31144,tc_HOL_Obool)),X31146),hAPP(hAPP(c_COMBB(tc_fun(X31144,tc_HOL_Obool),tc_fun(X31144,tc_HOL_Obool),X31145),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31144,tc_HOL_Obool)),X31143)),X31142)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31144,tc_HOL_Obool)),X31143),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31145,tc_fun(X31144,tc_HOL_Obool)),X31146),X31142)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__simps_I2_J])]) ).
fof(i_0_7313,plain,
! [X31172,X31173,X31174,X31175,X31176] :
( ( X31176 != c_Orderings_Obot__class_Obot(tc_fun(X31175,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31175,tc_fun(X31174,tc_HOL_Obool)),X31176),hAPP(hAPP(c_COMBB(tc_fun(X31174,tc_HOL_Obool),tc_fun(X31174,tc_HOL_Obool),X31175),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X31174,tc_HOL_Obool)),X31173)),X31172)) = c_Orderings_Otop__class_Otop(tc_fun(X31174,tc_HOL_Obool)) )
& ( X31176 = c_Orderings_Obot__class_Obot(tc_fun(X31175,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31175,tc_fun(X31174,tc_HOL_Obool)),X31176),hAPP(hAPP(c_COMBB(tc_fun(X31174,tc_HOL_Obool),tc_fun(X31174,tc_HOL_Obool),X31175),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X31174,tc_HOL_Obool)),X31173)),X31172)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X31174,tc_HOL_Obool)),X31173),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X31175,tc_fun(X31174,tc_HOL_Obool)),X31176),X31172)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__simps_I4_J])]) ).
fof(i_0_7314,plain,
! [X26135,X26136,X26137,X26138,X26139] :
( ( X26139 != c_Orderings_Obot__class_Obot(tc_fun(X26138,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26138,tc_fun(X26137,tc_HOL_Obool)),X26139),hAPP(hAPP(c_COMBB(tc_fun(X26137,tc_HOL_Obool),tc_fun(X26137,tc_HOL_Obool),X26138),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26137,tc_HOL_Obool)),X26136)),X26135)) = c_Orderings_Obot__class_Obot(tc_fun(X26137,tc_HOL_Obool)) )
& ( X26139 = c_Orderings_Obot__class_Obot(tc_fun(X26138,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26138,tc_fun(X26137,tc_HOL_Obool)),X26139),hAPP(hAPP(c_COMBB(tc_fun(X26137,tc_HOL_Obool),tc_fun(X26137,tc_HOL_Obool),X26138),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26137,tc_HOL_Obool)),X26136)),X26135)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26137,tc_HOL_Obool)),X26136),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26138,tc_fun(X26137,tc_HOL_Obool)),X26139),X26135)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__simps_I3_J])]) ).
fof(i_0_7315,plain,
! [X31077,X31078,X31079,X31080,X31081] :
( ( X31081 != c_Orderings_Obot__class_Obot(tc_fun(X31080,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31079,tc_HOL_Obool)),X31078),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31080,tc_fun(X31079,tc_HOL_Obool)),X31081),X31077)) = X31078 )
& ( X31081 = c_Orderings_Obot__class_Obot(tc_fun(X31080,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31079,tc_HOL_Obool)),X31078),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31080,tc_fun(X31079,tc_HOL_Obool)),X31081),X31077)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31080,tc_fun(X31079,tc_HOL_Obool)),X31081),hAPP(hAPP(c_COMBB(tc_fun(X31079,tc_HOL_Obool),tc_fun(X31079,tc_HOL_Obool),X31080),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31079,tc_HOL_Obool)),X31078)),X31077)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I2_J])]) ).
fof(i_0_7316,plain,
! [X26125,X26126,X26127,X26128,X26129] :
( ( X26129 != c_Orderings_Obot__class_Obot(tc_fun(X26128,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26127,tc_HOL_Obool)),X26126),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26128,tc_fun(X26127,tc_HOL_Obool)),X26129),X26125)) = X26126 )
& ( X26129 = c_Orderings_Obot__class_Obot(tc_fun(X26128,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26127,tc_HOL_Obool)),X26126),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26128,tc_fun(X26127,tc_HOL_Obool)),X26129),X26125)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26128,tc_fun(X26127,tc_HOL_Obool)),X26129),hAPP(hAPP(c_COMBB(tc_fun(X26127,tc_HOL_Obool),tc_fun(X26127,tc_HOL_Obool),X26128),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26127,tc_HOL_Obool)),X26126)),X26125)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I3_J])]) ).
fof(i_0_7317,plain,
! [X31162,X31163,X31164,X31165,X31166] :
( ( X31166 != c_Orderings_Obot__class_Obot(tc_fun(X31165,tc_HOL_Obool))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X31164,tc_HOL_Obool)),X31163),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X31165,tc_fun(X31164,tc_HOL_Obool)),X31166),X31162)) = X31163 )
& ( X31166 = c_Orderings_Obot__class_Obot(tc_fun(X31165,tc_HOL_Obool))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X31164,tc_HOL_Obool)),X31163),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X31165,tc_fun(X31164,tc_HOL_Obool)),X31166),X31162)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31165,tc_fun(X31164,tc_HOL_Obool)),X31166),hAPP(hAPP(c_COMBB(tc_fun(X31164,tc_HOL_Obool),tc_fun(X31164,tc_HOL_Obool),X31165),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X31164,tc_HOL_Obool)),X31163)),X31162)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I4_J])]) ).
fof(i_0_7318,plain,
! [X24651,X24652,X24653,X24654,X24655] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24655,tc_HOL_Obool)),X24652),hAPP(hAPP(c_Set_Oinsert(X24655),X24651),c_Orderings_Obot__class_Obot(tc_fun(X24655,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X24655,tc_HOL_Obool))
| hAPP(X24653,hAPP(hAPP(c_Set_Oinsert(X24655),X24651),X24652)) = X24651
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24655),X24652))
| ~ c_Finite__Set_Ofolding__one(X24655,X24654,X24653) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24655,tc_HOL_Obool)),X24652),hAPP(hAPP(c_Set_Oinsert(X24655),X24651),c_Orderings_Obot__class_Obot(tc_fun(X24655,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X24655,tc_HOL_Obool))
| hAPP(X24653,hAPP(hAPP(c_Set_Oinsert(X24655),X24651),X24652)) = hAPP(hAPP(X24654,X24651),hAPP(X24653,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24655,tc_HOL_Obool)),X24652),hAPP(hAPP(c_Set_Oinsert(X24655),X24651),c_Orderings_Obot__class_Obot(tc_fun(X24655,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24655),X24652))
| ~ c_Finite__Set_Ofolding__one(X24655,X24654,X24653) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Oinsert__remove])])]) ).
fof(i_0_7319,plain,
! [X25248,X25249,X25250] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25250,tc_HOL_Obool)),X25249),hAPP(hAPP(c_Set_Oinsert(X25250),X25248),c_Orderings_Obot__class_Obot(tc_fun(X25250,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25250,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMin(X25250,X25249) = X25248
| ~ hBOOL(hAPP(hAPP(c_member(X25250),X25248),X25249))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25250),X25249))
| ~ class_Orderings_Olinorder(X25250) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25250,tc_HOL_Obool)),X25249),hAPP(hAPP(c_Set_Oinsert(X25250),X25248),c_Orderings_Obot__class_Obot(tc_fun(X25250,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25250,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMin(X25250,X25249) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25250),X25248),c_Big__Operators_Olinorder__class_OMin(X25250,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25250,tc_HOL_Obool)),X25249),hAPP(hAPP(c_Set_Oinsert(X25250),X25248),c_Orderings_Obot__class_Obot(tc_fun(X25250,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(X25250),X25248),X25249))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25250),X25249))
| ~ class_Orderings_Olinorder(X25250) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oremove])])]) ).
fof(i_0_7320,plain,
! [X25245,X25246,X25247] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25247,tc_HOL_Obool)),X25246),hAPP(hAPP(c_Set_Oinsert(X25247),X25245),c_Orderings_Obot__class_Obot(tc_fun(X25247,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25247,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMax(X25247,X25246) = X25245
| ~ hBOOL(hAPP(hAPP(c_member(X25247),X25245),X25246))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25247),X25246))
| ~ class_Orderings_Olinorder(X25247) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25247,tc_HOL_Obool)),X25246),hAPP(hAPP(c_Set_Oinsert(X25247),X25245),c_Orderings_Obot__class_Obot(tc_fun(X25247,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25247,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMax(X25247,X25246) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25247),X25245),c_Big__Operators_Olinorder__class_OMax(X25247,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25247,tc_HOL_Obool)),X25246),hAPP(hAPP(c_Set_Oinsert(X25247),X25245),c_Orderings_Obot__class_Obot(tc_fun(X25247,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(X25247),X25245),X25246))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25247),X25246))
| ~ class_Orderings_Olinorder(X25247) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oremove])])]) ).
fof(i_0_7321,plain,
! [X25242,X25243,X25244] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25244,tc_HOL_Obool)),X25243),hAPP(hAPP(c_Set_Oinsert(X25244),X25242),c_Orderings_Obot__class_Obot(tc_fun(X25244,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25244,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OInf__fin(X25244,X25243) = X25242
| ~ hBOOL(hAPP(hAPP(c_member(X25244),X25242),X25243))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25244),X25243))
| ~ class_Lattices_Olattice(X25244) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25244,tc_HOL_Obool)),X25243),hAPP(hAPP(c_Set_Oinsert(X25244),X25242),c_Orderings_Obot__class_Obot(tc_fun(X25244,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25244,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OInf__fin(X25244,X25243) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25244),X25242),c_Big__Operators_Olattice__class_OInf__fin(X25244,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25244,tc_HOL_Obool)),X25243),hAPP(hAPP(c_Set_Oinsert(X25244),X25242),c_Orderings_Obot__class_Obot(tc_fun(X25244,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(X25244),X25242),X25243))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25244),X25243))
| ~ class_Lattices_Olattice(X25244) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oremove])])]) ).
fof(i_0_7322,plain,
! [X24682,X24683,X24684] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24684,tc_HOL_Obool)),X24683),hAPP(hAPP(c_Set_Oinsert(X24684),X24682),c_Orderings_Obot__class_Obot(tc_fun(X24684,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X24684,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OSup__fin(X24684,X24683) = X24682
| ~ hBOOL(hAPP(hAPP(c_member(X24684),X24682),X24683))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24684),X24683))
| ~ class_Lattices_Olattice(X24684) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24684,tc_HOL_Obool)),X24683),hAPP(hAPP(c_Set_Oinsert(X24684),X24682),c_Orderings_Obot__class_Obot(tc_fun(X24684,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X24684,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OSup__fin(X24684,X24683) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24684),X24682),c_Big__Operators_Olattice__class_OSup__fin(X24684,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24684,tc_HOL_Obool)),X24683),hAPP(hAPP(c_Set_Oinsert(X24684),X24682),c_Orderings_Obot__class_Obot(tc_fun(X24684,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(X24684),X24682),X24683))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24684),X24683))
| ~ class_Lattices_Olattice(X24684) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oremove])])]) ).
fof(i_0_7323,plain,
! [X28541,X28542,X28543,X28544,X28545,X28546] :
( ~ c_Typedef_Otype__definition(X28546,X28545,X28544,X28543,X28542)
| hBOOL(hAPP(hAPP(c_member(X28545),hAPP(X28544,X28541)),X28542)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep])]) ).
fof(i_0_7324,plain,
! [X28547,X28548,X28549,X28550,X28551,X28552] :
( ~ c_Typedef_Otype__definition(X28552,X28551,X28550,X28549,X28548)
| ~ hBOOL(hAPP(hAPP(c_member(X28551),X28547),X28548))
| hAPP(X28550,hAPP(X28549,X28547)) = X28547 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__inverse])]) ).
fof(i_0_7325,plain,
! [X34116,X34117,X34118,X34119,X34120] :
( ( ~ c_List_Olinorder__class_Osorted(X34120,hAPP(hAPP(c_List_Omap(X34119,X34120),X34118),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X34119,X34120,X34118),X34117),X34116)))
| c_List_Olinorder__class_Osorted(X34120,hAPP(hAPP(c_List_Omap(X34119,X34120),X34118),X34116))
| ~ class_Orderings_Olinorder(X34120) )
& ( ~ c_List_Olinorder__class_Osorted(X34120,hAPP(hAPP(c_List_Omap(X34119,X34120),X34118),X34116))
| c_List_Olinorder__class_Osorted(X34120,hAPP(hAPP(c_List_Omap(X34119,X34120),X34118),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X34119,X34120,X34118),X34117),X34116)))
| ~ class_Orderings_Olinorder(X34120) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__insort__key])])]) ).
fof(i_0_7326,plain,
! [X20633,X20634,X20635] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk77_3(X20633,X20634,X20635)),X20635))
| ~ hBOOL(hAPP(X20634,X20633))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20633),X20635))
| hBOOL(hAPP(X20634,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( hBOOL(hAPP(X20634,esk77_3(X20633,X20634,X20635)))
| ~ hBOOL(hAPP(X20634,X20633))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20633),X20635))
| hBOOL(hAPP(X20634,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( ~ hBOOL(hAPP(X20634,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,esk77_3(X20633,X20634,X20635)),X20635)))
| ~ hBOOL(hAPP(X20634,X20633))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20633),X20635))
| hBOOL(hAPP(X20634,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,
! [X20158,X20159,X20160] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20160),X20159)),X20158) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20160),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20159),X20158))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20160),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20159,X20158))),X20158)),
inference(variable_rename,[status(thm)],[fact_zdiv__zmult1__eq]) ).
fof(i_0_7328,plain,
! [X20001,X20002,X20003] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20003),X20002)),X20001) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20003),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20002),X20001))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20003),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20002,X20001))),X20001)),
inference(variable_rename,[status(thm)],[fact_div__mult1__eq]) ).
fof(i_0_7329,plain,
! [X20571,X20572,X20573,X20574,X20575] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20574),X20573)),X20572) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20575),X20573)),X20571)
| 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),X20574),X20575)),X20573)),X20572) = X20571
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20575),X20574)) )
& ( 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),X20574),X20575)),X20573)),X20572) != X20571
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20574),X20573)),X20572) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20575),X20573)),X20571)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20575),X20574)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff1])])]) ).
fof(i_0_7330,plain,
! [X20556,X20557,X20558,X20559,X20560] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20560),X20558)),X20557) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20559),X20558)),X20556)
| X20557 = 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),X20559),X20560)),X20558)),X20556)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20560),X20559)) )
& ( X20557 != 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),X20559),X20560)),X20558)),X20556)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20560),X20558)),X20557) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20559),X20558)),X20556)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20560),X20559)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff2])])]) ).
fof(i_0_7331,plain,
! [X26268,X26269,X26270,X26271,X26272,X26273] :
( ~ class_Groups_Oab__semigroup__mult(X26273)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26272),X26271))
| hBOOL(hAPP(hAPP(c_member(X26272),X26270),X26271))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X26273,X26272,c_Groups_Otimes__class_Otimes(X26273)),X26269),X26268),hAPP(hAPP(c_Set_Oinsert(X26272),X26270),X26271)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26273),hAPP(X26269,X26270)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X26273,X26272,c_Groups_Otimes__class_Otimes(X26273)),X26269),X26268),X26271)) ),
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,
! [X25029,X25030,X25031,X25032] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25032,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25032,tc_HOL_Obool)),X25031),X25030)),X25029) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25032,tc_HOL_Obool)),X25031),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25032,tc_HOL_Obool)),X25030),X25029))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25032,tc_HOL_Obool)),X25029),X25031)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25032,tc_HOL_Obool)),X25029),X25031))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25032,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25032,tc_HOL_Obool)),X25031),X25030)),X25029) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25032,tc_HOL_Obool)),X25031),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25032,tc_HOL_Obool)),X25030),X25029)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__Int__assoc__eq])]) ).
fof(i_0_7334,plain,
! [X31091,X31092,X31093,X31094,X31095] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31095,tc_fun(X31094,tc_HOL_Obool)),X31093),hAPP(hAPP(c_COMBB(tc_fun(X31094,tc_HOL_Obool),tc_fun(X31094,tc_HOL_Obool),X31095),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31094,tc_HOL_Obool)),X31092)),X31091)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31094,tc_HOL_Obool)),X31092),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31095,tc_fun(X31094,tc_HOL_Obool)),X31093),X31091)),
inference(variable_rename,[status(thm)],[fact_INT__simps_I7_J]) ).
fof(i_0_7335,plain,
! [X26034,X26035,X26036,X26037,X26038] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26038,tc_fun(X26037,tc_HOL_Obool)),X26036),hAPP(hAPP(c_COMBB(tc_fun(X26037,tc_HOL_Obool),tc_fun(X26037,tc_HOL_Obool),X26038),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26037,tc_HOL_Obool)),X26035)),X26034)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26037,tc_HOL_Obool)),X26035),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26038,tc_fun(X26037,tc_HOL_Obool)),X26036),X26034)),
inference(variable_rename,[status(thm)],[fact_UN__simps_I5_J]) ).
fof(i_0_7336,plain,
! [X30891,X30892,X30893,X30894,X30895] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30895,tc_fun(X30894,tc_HOL_Obool)),X30893),hAPP(hAPP(c_COMBB(tc_fun(X30894,tc_HOL_Obool),tc_fun(X30894,tc_HOL_Obool),X30895),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30894,tc_HOL_Obool)),X30892)),X30891)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30894,tc_HOL_Obool)),X30892),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30895,tc_fun(X30894,tc_HOL_Obool)),X30893),X30891)),
inference(variable_rename,[status(thm)],[fact_UN__simps_I7_J]) ).
fof(i_0_7337,plain,
! [X26049,X26050,X26051,X26052,X26053] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26053,tc_HOL_Obool)),X26052),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26051,tc_fun(X26053,tc_HOL_Obool)),X26050),X26049)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26051,tc_fun(X26053,tc_HOL_Obool)),X26050),hAPP(hAPP(c_COMBB(tc_fun(X26053,tc_HOL_Obool),tc_fun(X26053,tc_HOL_Obool),X26051),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26053,tc_HOL_Obool)),X26052)),X26049)),
inference(variable_rename,[status(thm)],[fact_Int__UN__distrib]) ).
fof(i_0_7338,plain,
! [X26044,X26045,X26046,X26047,X26048] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26048,tc_HOL_Obool)),X26047),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26046,tc_fun(X26048,tc_HOL_Obool)),X26045),X26044)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26046,tc_fun(X26048,tc_HOL_Obool)),X26045),hAPP(hAPP(c_COMBB(tc_fun(X26048,tc_HOL_Obool),tc_fun(X26048,tc_HOL_Obool),X26046),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26048,tc_HOL_Obool)),X26047)),X26044)),
inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I5_J]) ).
fof(i_0_7339,plain,
! [X31106,X31107,X31108,X31109,X31110] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31110,tc_HOL_Obool)),X31109),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31108,tc_fun(X31110,tc_HOL_Obool)),X31107),X31106)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31108,tc_fun(X31110,tc_HOL_Obool)),X31107),hAPP(hAPP(c_COMBB(tc_fun(X31110,tc_HOL_Obool),tc_fun(X31110,tc_HOL_Obool),X31108),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31110,tc_HOL_Obool)),X31109)),X31106)),
inference(variable_rename,[status(thm)],[fact_Un__INT__distrib]) ).
fof(i_0_7340,plain,
! [X31101,X31102,X31103,X31104,X31105] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31105,tc_HOL_Obool)),X31104),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31103,tc_fun(X31105,tc_HOL_Obool)),X31102),X31101)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31103,tc_fun(X31105,tc_HOL_Obool)),X31102),hAPP(hAPP(c_COMBB(tc_fun(X31105,tc_HOL_Obool),tc_fun(X31105,tc_HOL_Obool),X31103),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31105,tc_HOL_Obool)),X31104)),X31101)),
inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I7_J]) ).
fof(i_0_7341,plain,
! [X30896,X30897,X30898,X30899,X30900] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30900,tc_HOL_Obool)),X30899),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30898,tc_fun(X30900,tc_HOL_Obool)),X30897),X30896)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30898,tc_fun(X30900,tc_HOL_Obool)),X30897),hAPP(hAPP(c_COMBB(tc_fun(X30900,tc_HOL_Obool),tc_fun(X30900,tc_HOL_Obool),X30898),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30900,tc_HOL_Obool)),X30899)),X30896)),
inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I7_J]) ).
fof(i_0_7342,plain,
! [X29518,X29519,X29520,X29521] :
( hAPP(hAPP(c_Relation_Orel__comp(X29521,X29521,X29521),X29520),X29519) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29521,X29521),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(X29521,X29521,X29521),X29520),X29518) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29521,X29521),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(X29521,X29521,X29521),X29520),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29521,X29521),tc_HOL_Obool)),X29519),X29518)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29521,X29521),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,
! [X28511,X28512,X28513,X28514,X28515] :
( ~ c_Typedef_Otype__definition(X28515,X28514,X28513,X28512,X28511)
| hAPP(c_Set_Oimage(X28515,X28514,X28513),c_Orderings_Otop__class_Otop(tc_fun(X28515,tc_HOL_Obool))) = X28511 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__range])]) ).
fof(i_0_7346,plain,
! [X24617,X24618,X24619] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X24619),hAPP(hAPP(c_Set_Oinsert(X24619),X24618),c_Orderings_Obot__class_Obot(tc_fun(X24619,tc_HOL_Obool)))),X24617) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X24619,tc_HOL_Obool)),hAPP(c_Relation_OImage(X24619,X24619,X24617),hAPP(hAPP(c_Set_Oinsert(X24619),X24618),c_Orderings_Obot__class_Obot(tc_fun(X24619,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X24619,tc_HOL_Obool),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_singleton__quotient]) ).
fof(i_0_7347,plain,
! [X26172,X26173,X26174,X26175,X26176,X26177] :
( ~ c_Equiv__Relations_Ocongruent(X26177,X26176,X26175,X26174)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26177,X26177)),hAPP(hAPP(c_Product__Type_OPair(X26177,X26177),X26173),X26172)),X26175))
| hAPP(X26174,X26173) = hAPP(X26174,X26172) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruentD])]) ).
fof(i_0_7348,plain,
! [X30220,X30221,X30222] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30222,X30222),tc_HOL_Obool)),X30221),c_Transitive__Closure_Ortrancl(X30222,X30220)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30222,X30222),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X30222,X30221)),c_Transitive__Closure_Ortrancl(X30222,X30220))) ),
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,
! [X30449,X30450,X30451,X30452] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30452,X30452)),X30451),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30452,X30452),tc_HOL_Obool),X30450),X30449)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30452,X30452)),X30451),c_Transitive__Closure_Ortrancl(X30452,X30449))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__pow__imp__rtrancl])]) ).
fof(i_0_7352,plain,
! [X24496,X24497,X24498,X24499] :
( ~ hBOOL(hAPP(hAPP(c_member(X24499),X24498),c_Wellfounded_Oacc(X24499,X24497)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24499,X24499)),hAPP(hAPP(c_Product__Type_OPair(X24499,X24499),X24496),X24498)),X24497))
| hBOOL(hAPP(hAPP(c_member(X24499),X24496),c_Wellfounded_Oacc(X24499,X24497))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downward])]) ).
fof(i_0_7353,plain,
! [X25362,X25363,X25364] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25364,tc_HOL_Obool)),X25363),hAPP(hAPP(c_Set_Oinsert(X25364),X25362),c_Orderings_Obot__class_Obot(tc_fun(X25364,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25364,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMin(X25364,hAPP(hAPP(c_Set_Oinsert(X25364),X25362),X25363)) = X25362
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25364),X25363))
| ~ class_Orderings_Olinorder(X25364) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25364,tc_HOL_Obool)),X25363),hAPP(hAPP(c_Set_Oinsert(X25364),X25362),c_Orderings_Obot__class_Obot(tc_fun(X25364,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25364,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMin(X25364,hAPP(hAPP(c_Set_Oinsert(X25364),X25362),X25363)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25364),X25362),c_Big__Operators_Olinorder__class_OMin(X25364,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25364,tc_HOL_Obool)),X25363),hAPP(hAPP(c_Set_Oinsert(X25364),X25362),c_Orderings_Obot__class_Obot(tc_fun(X25364,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25364),X25363))
| ~ class_Orderings_Olinorder(X25364) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oinsert__remove])])]) ).
fof(i_0_7354,plain,
! [X25371,X25372,X25373] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25373,tc_HOL_Obool)),X25372),hAPP(hAPP(c_Set_Oinsert(X25373),X25371),c_Orderings_Obot__class_Obot(tc_fun(X25373,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25373,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMax(X25373,hAPP(hAPP(c_Set_Oinsert(X25373),X25371),X25372)) = X25371
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25373),X25372))
| ~ class_Orderings_Olinorder(X25373) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25373,tc_HOL_Obool)),X25372),hAPP(hAPP(c_Set_Oinsert(X25373),X25371),c_Orderings_Obot__class_Obot(tc_fun(X25373,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25373,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMax(X25373,hAPP(hAPP(c_Set_Oinsert(X25373),X25371),X25372)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25373),X25371),c_Big__Operators_Olinorder__class_OMax(X25373,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25373,tc_HOL_Obool)),X25372),hAPP(hAPP(c_Set_Oinsert(X25373),X25371),c_Orderings_Obot__class_Obot(tc_fun(X25373,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25373),X25372))
| ~ class_Orderings_Olinorder(X25373) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oinsert__remove])])]) ).
fof(i_0_7355,plain,
! [X25359,X25360,X25361] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25361,tc_HOL_Obool)),X25360),hAPP(hAPP(c_Set_Oinsert(X25361),X25359),c_Orderings_Obot__class_Obot(tc_fun(X25361,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25361,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OInf__fin(X25361,hAPP(hAPP(c_Set_Oinsert(X25361),X25359),X25360)) = X25359
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25361),X25360))
| ~ class_Lattices_Olattice(X25361) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25361,tc_HOL_Obool)),X25360),hAPP(hAPP(c_Set_Oinsert(X25361),X25359),c_Orderings_Obot__class_Obot(tc_fun(X25361,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25361,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OInf__fin(X25361,hAPP(hAPP(c_Set_Oinsert(X25361),X25359),X25360)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25361),X25359),c_Big__Operators_Olattice__class_OInf__fin(X25361,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25361,tc_HOL_Obool)),X25360),hAPP(hAPP(c_Set_Oinsert(X25361),X25359),c_Orderings_Obot__class_Obot(tc_fun(X25361,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25361),X25360))
| ~ class_Lattices_Olattice(X25361) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oinsert__remove])])]) ).
fof(i_0_7356,plain,
! [X25120,X25121,X25122] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25122,tc_HOL_Obool)),X25121),hAPP(hAPP(c_Set_Oinsert(X25122),X25120),c_Orderings_Obot__class_Obot(tc_fun(X25122,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25122,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OSup__fin(X25122,hAPP(hAPP(c_Set_Oinsert(X25122),X25120),X25121)) = X25120
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25122),X25121))
| ~ class_Lattices_Olattice(X25122) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25122,tc_HOL_Obool)),X25121),hAPP(hAPP(c_Set_Oinsert(X25122),X25120),c_Orderings_Obot__class_Obot(tc_fun(X25122,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25122,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OSup__fin(X25122,hAPP(hAPP(c_Set_Oinsert(X25122),X25120),X25121)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25122),X25120),c_Big__Operators_Olattice__class_OSup__fin(X25122,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25122,tc_HOL_Obool)),X25121),hAPP(hAPP(c_Set_Oinsert(X25122),X25120),c_Orderings_Obot__class_Obot(tc_fun(X25122,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25122),X25121))
| ~ class_Lattices_Olattice(X25122) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oinsert__remove])])]) ).
fof(i_0_7357,plain,
! [X28516,X28517,X28518,X28519,X28520] :
( ~ c_Typedef_Otype__definition(X28520,X28519,X28518,X28517,X28516)
| hAPP(c_Set_Oimage(X28519,X28520,X28517),X28516) = c_Orderings_Otop__class_Otop(tc_fun(X28520,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__image])]) ).
fof(i_0_7358,plain,
! [X31923,X31924,X31925,X31926] :
( ~ c_Fun_Oinj__on(X31926,X31925,X31924,c_Complete__Lattice_OSup__class_OSup(tc_fun(X31926,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(X31926),tc_fun(X31926,tc_HOL_Obool),c_List_Oset(X31926)),X31923)))
| c_Fun_Oinj__on(tc_List_Olist(X31926),tc_List_Olist(X31925),hAPP(c_List_Omap(X31926,X31925),X31924),X31923) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__mapI])]) ).
fof(i_0_7359,plain,
! [X21758,X21759,X21760,X21761] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21761),c_Groups_Ozero__class_Ozero(X21761)),X21759))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21761),X21760),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21761),X21758),X21759)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21761),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21761),X21760),X21759)),X21758))
| ~ class_Fields_Olinordered__field__inverse__zero(X21761) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21761),X21759),c_Groups_Ozero__class_Ozero(X21761)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21761),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21761),X21758),X21759)),X21760))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21761),c_Groups_Ozero__class_Ozero(X21761)),X21759))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21761),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21761),X21760),X21759)),X21758))
| ~ class_Fields_Olinordered__field__inverse__zero(X21761) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21761),X21759),c_Groups_Ozero__class_Ozero(X21761)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21761),c_Groups_Ozero__class_Ozero(X21761)),X21758))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21761),c_Groups_Ozero__class_Ozero(X21761)),X21759))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21761),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21761),X21760),X21759)),X21758))
| ~ class_Fields_Olinordered__field__inverse__zero(X21761) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21761),c_Groups_Ozero__class_Ozero(X21761)),X21759))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21761),c_Groups_Ozero__class_Ozero(X21761)),X21759))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21761),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21761),X21760),X21759)),X21758))
| ~ class_Fields_Olinordered__field__inverse__zero(X21761) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21761),X21759),c_Groups_Ozero__class_Ozero(X21761)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21761),X21759),c_Groups_Ozero__class_Ozero(X21761)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21761),c_Groups_Ozero__class_Ozero(X21761)),X21759))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21761),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21761),X21760),X21759)),X21758))
| ~ class_Fields_Olinordered__field__inverse__zero(X21761) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21761),c_Groups_Ozero__class_Ozero(X21761)),X21758))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21761),X21759),c_Groups_Ozero__class_Ozero(X21761)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21761),c_Groups_Ozero__class_Ozero(X21761)),X21759))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21761),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21761),X21760),X21759)),X21758))
| ~ class_Fields_Olinordered__field__inverse__zero(X21761) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21761),X21759),c_Groups_Ozero__class_Ozero(X21761)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21761),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21761),X21758),X21759)),X21760))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21761),c_Groups_Ozero__class_Ozero(X21761)),X21759))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21761),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21761),X21760),X21759)),X21758))
| ~ class_Fields_Olinordered__field__inverse__zero(X21761) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21761),c_Groups_Ozero__class_Ozero(X21761)),X21758))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21761),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21761),X21758),X21759)),X21760))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21761),c_Groups_Ozero__class_Ozero(X21761)),X21759))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21761),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21761),X21760),X21759)),X21758))
| ~ class_Fields_Olinordered__field__inverse__zero(X21761) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21761),c_Groups_Ozero__class_Ozero(X21761)),X21759))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21761),X21760),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21761),X21758),X21759)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21761),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21761),X21760),X21759)),X21758))
| ~ class_Fields_Olinordered__field__inverse__zero(X21761) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21761),X21759),c_Groups_Ozero__class_Ozero(X21761)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21761),X21759),c_Groups_Ozero__class_Ozero(X21761)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21761),X21760),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21761),X21758),X21759)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21761),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21761),X21760),X21759)),X21758))
| ~ class_Fields_Olinordered__field__inverse__zero(X21761) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21761),c_Groups_Ozero__class_Ozero(X21761)),X21758))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21761),X21759),c_Groups_Ozero__class_Ozero(X21761)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21761),X21760),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21761),X21758),X21759)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21761),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21761),X21760),X21759)),X21758))
| ~ class_Fields_Olinordered__field__inverse__zero(X21761) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21761),X21759),c_Groups_Ozero__class_Ozero(X21761)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21761),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21761),X21758),X21759)),X21760))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21761),X21760),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21761),X21758),X21759)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21761),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21761),X21760),X21759)),X21758))
| ~ class_Fields_Olinordered__field__inverse__zero(X21761) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21761),c_Groups_Ozero__class_Ozero(X21761)),X21758))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21761),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21761),X21758),X21759)),X21760))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21761),X21760),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21761),X21758),X21759)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21761),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21761),X21760),X21759)),X21758))
| ~ class_Fields_Olinordered__field__inverse__zero(X21761) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5548])])]) ).
fof(i_0_7360,plain,
! [X21678,X21679,X21680,X21681] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),c_Groups_Ozero__class_Ozero(X21681)),X21679))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),X21680),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21681),X21678),X21679)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21681),X21680),X21679)),X21678))
| ~ class_Fields_Olinordered__field__inverse__zero(X21681) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),X21679),c_Groups_Ozero__class_Ozero(X21681)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21681),X21678),X21679)),X21680))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),c_Groups_Ozero__class_Ozero(X21681)),X21679))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21681),X21680),X21679)),X21678))
| ~ class_Fields_Olinordered__field__inverse__zero(X21681) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),X21679),c_Groups_Ozero__class_Ozero(X21681)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),c_Groups_Ozero__class_Ozero(X21681)),X21678))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),c_Groups_Ozero__class_Ozero(X21681)),X21679))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21681),X21680),X21679)),X21678))
| ~ class_Fields_Olinordered__field__inverse__zero(X21681) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),c_Groups_Ozero__class_Ozero(X21681)),X21679))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),c_Groups_Ozero__class_Ozero(X21681)),X21679))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21681),X21680),X21679)),X21678))
| ~ class_Fields_Olinordered__field__inverse__zero(X21681) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),X21679),c_Groups_Ozero__class_Ozero(X21681)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),X21679),c_Groups_Ozero__class_Ozero(X21681)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),c_Groups_Ozero__class_Ozero(X21681)),X21679))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21681),X21680),X21679)),X21678))
| ~ class_Fields_Olinordered__field__inverse__zero(X21681) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),c_Groups_Ozero__class_Ozero(X21681)),X21678))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),X21679),c_Groups_Ozero__class_Ozero(X21681)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),c_Groups_Ozero__class_Ozero(X21681)),X21679))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21681),X21680),X21679)),X21678))
| ~ class_Fields_Olinordered__field__inverse__zero(X21681) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),X21679),c_Groups_Ozero__class_Ozero(X21681)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21681),X21678),X21679)),X21680))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),c_Groups_Ozero__class_Ozero(X21681)),X21679))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21681),X21680),X21679)),X21678))
| ~ class_Fields_Olinordered__field__inverse__zero(X21681) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),c_Groups_Ozero__class_Ozero(X21681)),X21678))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21681),X21678),X21679)),X21680))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),c_Groups_Ozero__class_Ozero(X21681)),X21679))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21681),X21680),X21679)),X21678))
| ~ class_Fields_Olinordered__field__inverse__zero(X21681) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),c_Groups_Ozero__class_Ozero(X21681)),X21679))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),X21680),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21681),X21678),X21679)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21681),X21680),X21679)),X21678))
| ~ class_Fields_Olinordered__field__inverse__zero(X21681) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),X21679),c_Groups_Ozero__class_Ozero(X21681)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),X21679),c_Groups_Ozero__class_Ozero(X21681)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),X21680),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21681),X21678),X21679)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21681),X21680),X21679)),X21678))
| ~ class_Fields_Olinordered__field__inverse__zero(X21681) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),c_Groups_Ozero__class_Ozero(X21681)),X21678))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),X21679),c_Groups_Ozero__class_Ozero(X21681)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),X21680),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21681),X21678),X21679)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21681),X21680),X21679)),X21678))
| ~ class_Fields_Olinordered__field__inverse__zero(X21681) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),X21679),c_Groups_Ozero__class_Ozero(X21681)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21681),X21678),X21679)),X21680))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),X21680),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21681),X21678),X21679)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21681),X21680),X21679)),X21678))
| ~ class_Fields_Olinordered__field__inverse__zero(X21681) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),c_Groups_Ozero__class_Ozero(X21681)),X21678))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21681),X21678),X21679)),X21680))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),X21680),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21681),X21678),X21679)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21681),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21681),X21680),X21679)),X21678))
| ~ class_Fields_Olinordered__field__inverse__zero(X21681) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5549])])]) ).
fof(i_0_7361,plain,
! [X32729,X32730,X32731,X32732,X32733,X32734] : hAPP(hAPP(c_List_Olist__update(tc_prod(X32734,X32733),hAPP(hAPP(c_List_Ozip(X32734,X32733),X32732),X32731)),X32730),X32729) = hAPP(hAPP(c_List_Ozip(X32734,X32733),hAPP(hAPP(c_List_Olist__update(X32734,X32732),X32730),hAPP(c_Product__Type_Ofst(X32734,X32733),X32729))),hAPP(hAPP(c_List_Olist__update(X32733,X32731),X32730),hAPP(c_Product__Type_Osnd(X32734,X32733),X32729))),
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,
! [X29128] : 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)),X29128)))),
inference(variable_rename,[status(thm)],[fact_finite__Collect__le__nat]) ).
fof(i_0_7369,plain,
! [X29127] : 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)),X29127)))),
inference(variable_rename,[status(thm)],[fact_finite__Collect__less__nat]) ).
fof(i_0_7370,plain,
! [X29511,X29512,X29513,X29514,X29515,X29516,X29517] : hAPP(hAPP(c_Relation_Orel__comp(X29517,X29516,X29515),hAPP(hAPP(c_Relation_Orel__comp(X29517,X29514,X29516),X29513),X29512)),X29511) = hAPP(hAPP(c_Relation_Orel__comp(X29517,X29514,X29515),X29513),hAPP(hAPP(c_Relation_Orel__comp(X29514,X29516,X29515),X29512),X29511)),
inference(variable_rename,[status(thm)],[fact_O__assoc]) ).
fof(i_0_7371,plain,
! [X27402,X27403,X27404,X27405,X27406] :
( ~ class_Groups_Ocomm__monoid__add(X27406)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27405),X27404))
| ~ hBOOL(hAPP(hAPP(c_member(X27405),X27403),X27404))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27405,X27406),X27402),X27404) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27406),hAPP(X27402,X27403)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27405,X27406),X27402),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27405,tc_HOL_Obool)),X27404),hAPP(hAPP(c_Set_Oinsert(X27405),X27403),c_Orderings_Obot__class_Obot(tc_fun(X27405,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oremove])]) ).
fof(i_0_7372,plain,
! [X27397,X27398,X27399,X27400,X27401] :
( ~ class_Groups_Ocomm__monoid__add(X27401)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27400),X27399))
| ~ hBOOL(hAPP(hAPP(c_member(X27400),X27398),X27399))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27400,X27401),X27397),X27399) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27401),hAPP(X27397,X27398)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27400,X27401),X27397),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27400,tc_HOL_Obool)),X27399),hAPP(hAPP(c_Set_Oinsert(X27400),X27398),c_Orderings_Obot__class_Obot(tc_fun(X27400,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff1_H])]) ).
fof(i_0_7373,plain,
! [X25753,X25754,X25755,X25756,X25757] :
( ~ class_Groups_Ocomm__monoid__mult(X25757)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25756),X25755))
| ~ hBOOL(hAPP(hAPP(c_member(X25756),X25754),X25755))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25756,X25757),X25753),X25755) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25757),hAPP(X25753,X25754)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25756,X25757),X25753),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25756,tc_HOL_Obool)),X25755),hAPP(hAPP(c_Set_Oinsert(X25756),X25754),c_Orderings_Obot__class_Obot(tc_fun(X25756,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oremove])]) ).
fof(i_0_7374,plain,
! [X30921,X30922,X30923,X30924] : hAPP(c_Set_OPow(X30924),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30923,tc_fun(X30924,tc_HOL_Obool)),X30922),X30921)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30923,tc_fun(tc_fun(X30924,tc_HOL_Obool),tc_HOL_Obool)),X30922),hAPP(hAPP(c_COMBB(tc_fun(X30924,tc_HOL_Obool),tc_fun(tc_fun(X30924,tc_HOL_Obool),tc_HOL_Obool),X30923),c_Set_OPow(X30924)),X30921)),
inference(variable_rename,[status(thm)],[fact_Pow__INT__eq]) ).
fof(i_0_7375,plain,
! [X19736,X19737,X19738] :
( ~ 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),X19738),X19737)),X19736)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19736),X19738))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19738))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19737)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_q__pos__lemma])]) ).
fof(i_0_7376,plain,
! [X27055,X27056,X27057] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X27057,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X27056)),X27055) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27057,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X27057,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X27056)),X27055)),hAPP(X27055,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[fact_UN__le__eq__Un0]) ).
fof(i_0_7377,plain,
! [X25494,X25495,X25496] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25496),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25496,tc_HOL_Obool)),X25495),X25494)))
| hAPP(c_Finite__Set_Ocard(X25496),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25496,tc_HOL_Obool)),X25495),X25494)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25496),X25495)),hAPP(c_Finite__Set_Ocard(X25496),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25496,tc_HOL_Obool)),X25495),X25494))) ),
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,
! [X31123,X31124,X31125,X31126,X31127] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31127,tc_fun(X31126,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31127,tc_HOL_Obool)),X31125),X31124)),X31123) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31126,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31127,tc_fun(X31126,tc_HOL_Obool)),X31125),X31123)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31127,tc_fun(X31126,tc_HOL_Obool)),X31124),X31123)),
inference(variable_rename,[status(thm)],[fact_INT__Un]) ).
fof(i_0_7380,plain,
! [X26029,X26030,X26031,X26032,X26033] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26033,tc_fun(X26032,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26033,tc_HOL_Obool)),X26031),X26030)),X26029) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26032,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26033,tc_fun(X26032,tc_HOL_Obool)),X26031),X26029)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26033,tc_fun(X26032,tc_HOL_Obool)),X26030),X26029)),
inference(variable_rename,[status(thm)],[fact_UN__Un]) ).
fof(i_0_7381,plain,
! [X30289,X30290,X30291,X30292] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30292,X30292)),hAPP(hAPP(c_Product__Type_OPair(X30292,X30292),X30291),X30289)),c_Transitive__Closure_Ortrancl(X30292,X30290)))
| X30291 = X30289
| hBOOL(hAPP(hAPP(c_member(X30292),X30291),hAPP(c_Relation_ODomain(X30292,X30292),X30290))) )
& ( X30291 != X30289
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30292,X30292)),hAPP(hAPP(c_Product__Type_OPair(X30292,X30292),X30291),X30289)),c_Transitive__Closure_Ortrancl(X30292,X30290)))
| hBOOL(hAPP(hAPP(c_member(X30292),X30291),hAPP(c_Relation_ODomain(X30292,X30292),X30290))) ) ),
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,
! [X27685,X27686,X27687,X27688,X27690,X27691,X27692,X27693,X27694] :
( ( c_Map_Odom(X27688,X27687,X27686) != hAPP(hAPP(c_Set_Oinsert(X27688),X27685),c_Orderings_Obot__class_Obot(tc_fun(X27688,tc_HOL_Obool)))
| X27686 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27688,tc_Option_Ooption(X27687)),hAPP(c_COMBK(tc_Option_Ooption(X27687),X27688),c_Option_Ooption_ONone(X27687))),X27685),hAPP(c_Option_Ooption_OSome(X27687),esk262_4(X27685,X27686,X27687,X27688))) )
& ( X27691 != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27693,tc_Option_Ooption(X27692)),hAPP(c_COMBK(tc_Option_Ooption(X27692),X27693),c_Option_Ooption_ONone(X27692))),X27690),hAPP(c_Option_Ooption_OSome(X27692),X27694))
| c_Map_Odom(X27693,X27692,X27691) = hAPP(hAPP(c_Set_Oinsert(X27693),X27690),c_Orderings_Obot__class_Obot(tc_fun(X27693,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,
! [X26320,X26321,X26322,X26323,X26324,X26325,X26326] :
( ~ c_Big__Operators_Ocomm__monoid__big(X26326,X26325,X26324,X26323,X26322)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X26325),X26321))
| hAPP(hAPP(X26322,X26320),X26321) = X26323 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5553])]) ).
fof(i_0_7385,plain,
! [X22360,X22361,X22362] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22362,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X22362,tc_HOL_Obool)),X22361)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X22362,tc_HOL_Obool)),X22360)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22362,tc_HOL_Obool)),X22360),X22361)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22362,tc_HOL_Obool)),X22360),X22361))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22362,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X22362,tc_HOL_Obool)),X22361)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X22362,tc_HOL_Obool)),X22360))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__subset__Compl__iff])]) ).
fof(i_0_7386,plain,
! [X31019,X31020,X31021,X31022,X31023] :
( ~ hBOOL(hAPP(hAPP(c_member(X31023),X31022),X31021))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31020,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31023,tc_fun(X31020,tc_HOL_Obool)),X31021),X31019)),hAPP(X31019,X31022))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__lower])]) ).
fof(i_0_7387,plain,
! [X30214,X30215,X30216] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30216,X30216),tc_HOL_Obool)),X30215),X30214))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30216,X30216),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X30216,X30215)),c_Transitive__Closure_Ortrancl(X30216,X30214))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__mono])]) ).
fof(i_0_7388,plain,
! [X30996,X30997,X30998,X30999,X31000,X31001] : hAPP(c_Set_Ovimage(X31001,X31000,X30999),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30998,tc_fun(X31000,tc_HOL_Obool)),X30997),X30996)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30998,tc_fun(X31001,tc_HOL_Obool)),X30997),hAPP(hAPP(c_COMBB(tc_fun(X31000,tc_HOL_Obool),tc_fun(X31001,tc_HOL_Obool),X30998),c_Set_Ovimage(X31001,X31000,X30999)),X30996)),
inference(variable_rename,[status(thm)],[fact_vimage__INT]) ).
fof(i_0_7389,plain,
! [X28448,X28449,X28450,X28451,X28452,X28453] : hAPP(c_Set_Ovimage(X28453,X28452,X28451),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28450,tc_fun(X28452,tc_HOL_Obool)),X28449),X28448)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28450,tc_fun(X28453,tc_HOL_Obool)),X28449),hAPP(hAPP(c_COMBB(tc_fun(X28452,tc_HOL_Obool),tc_fun(X28453,tc_HOL_Obool),X28450),c_Set_Ovimage(X28453,X28452,X28451)),X28448)),
inference(variable_rename,[status(thm)],[fact_vimage__UN]) ).
fof(i_0_7390,plain,
! [X25811,X25812,X25813,X25814,X25815,X25816] : hAPP(c_Relation_OImage(X25816,X25815,X25814),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25813,tc_fun(X25816,tc_HOL_Obool)),X25812),X25811)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25813,tc_fun(X25815,tc_HOL_Obool)),X25812),hAPP(hAPP(c_COMBB(tc_fun(X25816,tc_HOL_Obool),tc_fun(X25815,tc_HOL_Obool),X25813),c_Relation_OImage(X25816,X25815,X25814)),X25811)),
inference(variable_rename,[status(thm)],[fact_Image__UN]) ).
fof(i_0_7391,plain,
! [X26012,X26013,X26014,X26015,X26016,X26017] : hAPP(c_Set_Oimage(X26017,X26016,X26015),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26014,tc_fun(X26017,tc_HOL_Obool)),X26013),X26012)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26014,tc_fun(X26016,tc_HOL_Obool)),X26013),hAPP(hAPP(c_COMBB(tc_fun(X26017,tc_HOL_Obool),tc_fun(X26016,tc_HOL_Obool),X26014),c_Set_Oimage(X26017,X26016,X26015)),X26012)),
inference(variable_rename,[status(thm)],[fact_image__UN]) ).
fof(i_0_7392,plain,
! [X21708,X21709,X21710,X21711,X21712] :
( ~ class_Fields_Ofield(X21712)
| X21711 = c_Groups_Ozero__class_Ozero(X21712)
| X21710 = c_Groups_Ozero__class_Ozero(X21712)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21712),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21712),X21709),X21711)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21712),X21708),X21710)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21712),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21712),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21712),X21709),X21710)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21712),X21708),X21711))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21712),X21711),X21710)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__frac__eq])]) ).
fof(i_0_7393,plain,
! [X21687,X21688,X21689,X21690,X21691] :
( ~ class_Fields_Ofield(X21691)
| X21690 = c_Groups_Ozero__class_Ozero(X21691)
| X21689 = c_Groups_Ozero__class_Ozero(X21691)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21691),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21691),X21688),X21690)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21691),X21687),X21689)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21691),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21691),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21691),X21688),X21689)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21691),X21687),X21690))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21691),X21690),X21689)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__frac__eq])]) ).
fof(i_0_7394,plain,
! [X29216,X29217] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X29217,tc_HOL_Obool)),X29216) = hAPP(c_Set_OCollect(X29217),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29217),c_fNot),hAPP(hAPP(c_COMBC(X29217,tc_fun(X29217,tc_HOL_Obool),tc_HOL_Obool),c_member(X29217)),X29216))),
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,
! [X19037,X19038,X19039] :
( ( ~ 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,X19039)),X19038)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19039)),X19037)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19038),X19037)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19038),X19037))
| 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,X19039)),X19038)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19039)),X19037))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__le__cancel1])]) ).
fof(i_0_7397,plain,
! [X19497,X19498,X19499] :
( ( ~ 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,X19499)),X19498)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19499)),X19497)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19498),X19497)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19498),X19497))
| 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,X19499)),X19498)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19499)),X19497))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__less__cancel1])]) ).
fof(i_0_7398,plain,
! [X19960,X19961,X19962,X19963,X19964] :
( ( ~ hBOOL(hAPP(hAPP(X19961,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19960),X19962)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19960,X19962)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19964))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19964),X19962))
| X19960 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19962),X19963)),X19964)
| hBOOL(hAPP(hAPP(X19961,X19963),X19964))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19962)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk62_3(X19960,X19961,X19962)))
| hBOOL(hAPP(hAPP(X19961,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19960),X19962)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19960,X19962)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19962)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk62_3(X19960,X19961,X19962)),X19962))
| hBOOL(hAPP(hAPP(X19961,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19960),X19962)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19960,X19962)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19962)) )
& ( X19960 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19962),esk61_3(X19960,X19961,X19962))),esk62_3(X19960,X19961,X19962))
| hBOOL(hAPP(hAPP(X19961,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19960),X19962)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19960,X19962)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19962)) )
& ( ~ hBOOL(hAPP(hAPP(X19961,esk61_3(X19960,X19961,X19962)),esk62_3(X19960,X19961,X19962)))
| hBOOL(hAPP(hAPP(X19961,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19960),X19962)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19960,X19962)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19962)) ) ),
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,
! [X32185,X32186,X32187,X32188,X32189] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X32188),X32186),hAPP(c_List_Oset(X32188),X32185)))
| ~ hBOOL(hAPP(c_List_Odistinct(X32188),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32188,X32189,X32187),X32186),X32185)))
| ~ class_Orderings_Olinorder(X32189) )
& ( hBOOL(hAPP(c_List_Odistinct(X32188),X32185))
| ~ hBOOL(hAPP(c_List_Odistinct(X32188),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32188,X32189,X32187),X32186),X32185)))
| ~ class_Orderings_Olinorder(X32189) )
& ( hBOOL(hAPP(hAPP(c_member(X32188),X32186),hAPP(c_List_Oset(X32188),X32185)))
| ~ hBOOL(hAPP(c_List_Odistinct(X32188),X32185))
| hBOOL(hAPP(c_List_Odistinct(X32188),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32188,X32189,X32187),X32186),X32185)))
| ~ class_Orderings_Olinorder(X32189) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5555])])]) ).
fof(i_0_7400,plain,
! [X27916,X27917,X27918,X27919,X27920,X27921] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27921,tc_fun(X27920,tc_HOL_Obool)),X27919),hAPP(c_Fun_Ocomp(X27918,tc_fun(X27920,tc_HOL_Obool),X27921,X27917),X27916)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27918,tc_fun(X27920,tc_HOL_Obool)),hAPP(c_Set_Oimage(X27921,X27918,X27916),X27919)),X27917),
inference(variable_rename,[status(thm)],[fact_UN__o]) ).
fof(i_0_7401,plain,
! [X27357,X27358,X27359,X27360,X27361] :
( ~ class_Groups_Ocomm__monoid__add(X27361)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27360),X27359))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27360,X27361),X27358),hAPP(hAPP(c_Set_Oinsert(X27360),X27357),X27359)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27361),hAPP(X27358,X27357)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27360,X27361),X27358),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27360,tc_HOL_Obool)),X27359),hAPP(hAPP(c_Set_Oinsert(X27360),X27357),c_Orderings_Obot__class_Obot(tc_fun(X27360,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oinsert__remove])]) ).
fof(i_0_7402,plain,
! [X25734,X25735,X25736,X25737,X25738] :
( ~ class_Groups_Ocomm__monoid__mult(X25738)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25737),X25736))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25737,X25738),X25735),hAPP(hAPP(c_Set_Oinsert(X25737),X25734),X25736)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25738),hAPP(X25735,X25734)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25737,X25738),X25735),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25737,tc_HOL_Obool)),X25736),hAPP(hAPP(c_Set_Oinsert(X25737),X25734),c_Orderings_Obot__class_Obot(tc_fun(X25737,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oinsert__remove])]) ).
fof(i_0_7403,plain,
! [X26979,X26980,X26981,X26982,X26983,X26984] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26984,X26983),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26984,X26983),X26982),X26981),X26980)),X26981),X26979) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26984,X26983),X26982),X26981),X26979),
inference(variable_rename,[status(thm)],[fact_fun__upd__upd]) ).
fof(i_0_7404,plain,
! [X19967,X19968,X19969,X19970,X19971] :
( ( ~ hBOOL(hAPP(hAPP(X19968,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19967),X19969)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19967,X19969)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19969),X19971))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19971),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X19967 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19969),X19970)),X19971)
| hBOOL(hAPP(hAPP(X19968,X19970),X19971))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19969),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19969),esk64_3(X19967,X19968,X19969)))
| hBOOL(hAPP(hAPP(X19968,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19967),X19969)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19967,X19969)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19969),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk64_3(X19967,X19968,X19969)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(X19968,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19967),X19969)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19967,X19969)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19969),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( X19967 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19969),esk63_3(X19967,X19968,X19969))),esk64_3(X19967,X19968,X19969))
| hBOOL(hAPP(hAPP(X19968,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19967),X19969)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19967,X19969)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19969),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(X19968,esk63_3(X19967,X19968,X19969)),esk64_3(X19967,X19968,X19969)))
| hBOOL(hAPP(hAPP(X19968,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19967),X19969)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19967,X19969)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19969),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,
! [X32045,X32046] : hAPP(hAPP(c_List_Ozip(X32046,X32046),X32045),X32045) = hAPP(hAPP(c_List_Omap(X32046,tc_prod(X32046,X32046)),hAPP(hAPP(c_COMBS(X32046,X32046,tc_prod(X32046,X32046)),c_Product__Type_OPair(X32046,X32046)),c_COMBI(X32046))),X32045),
inference(variable_rename,[status(thm)],[fact_zip__same__conv__map]) ).
fof(i_0_7406,plain,
! [X25044,X25045] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X25045),X25044) = 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)),X25045)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X25044))),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J]) ).
fof(i_0_7407,plain,
! [X24405,X24406] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X24406),X24405) = 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)),X24406)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X24405))),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J]) ).
fof(i_0_7408,plain,
! [X25725,X25726,X25727,X25728] : c_Sum__Type_OPlus(X25728,X25727,X25726,X25725) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_sum(X25728,X25727),tc_HOL_Obool)),hAPP(c_Set_Oimage(X25728,tc_sum(X25728,X25727),c_Sum__Type_OInl(X25728,X25727)),X25726)),hAPP(c_Set_Oimage(X25727,tc_sum(X25728,X25727),c_Sum__Type_OInr(X25727,X25728)),X25725)),
inference(variable_rename,[status(thm)],[fact_Plus__def]) ).
fof(i_0_7409,plain,
! [X21037,X21038,X21039] :
( ~ class_Rings_Olinordered__semidom(X21039)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21039),c_Groups_Ozero__class_Ozero(X21039)),X21038))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21039),X21038),c_Groups_Oone__class_Oone(X21039)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21039),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21039),X21038),hAPP(hAPP(c_Power_Opower__class_Opower(X21039),X21038),X21037))),hAPP(hAPP(c_Power_Opower__class_Opower(X21039),X21038),X21037))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc__less])]) ).
fof(i_0_7410,plain,
! [X28534,X28535,X28536,X28537,X28538,X28539,X28540] :
( ( hAPP(X28538,X28535) != hAPP(X28538,X28534)
| X28535 = X28534
| ~ c_Typedef_Otype__definition(X28540,X28539,X28538,X28537,X28536) )
& ( X28535 != X28534
| hAPP(X28538,X28535) = hAPP(X28538,X28534)
| ~ c_Typedef_Otype__definition(X28540,X28539,X28538,X28537,X28536) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__inject])])]) ).
fof(i_0_7411,plain,
! [X28760,X28761,X28762,X28763] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28763,X28762)),hAPP(hAPP(c_Product__Type_OSigma(X28763,X28762),X28761),hAPP(c_COMBK(tc_fun(X28762,tc_HOL_Obool),X28763),X28760))))
| X28761 = c_Orderings_Obot__class_Obot(tc_fun(X28763,tc_HOL_Obool))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X28762),X28760)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__cartesian__productD2])]) ).
fof(i_0_7412,plain,
! [X28756,X28757,X28758,X28759] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28759,X28758)),hAPP(hAPP(c_Product__Type_OSigma(X28759,X28758),X28757),hAPP(c_COMBK(tc_fun(X28758,tc_HOL_Obool),X28759),X28756))))
| X28756 = c_Orderings_Obot__class_Obot(tc_fun(X28758,tc_HOL_Obool))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X28759),X28757)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__cartesian__productD1])]) ).
fof(i_0_7413,plain,
! [X28528,X28529,X28530,X28531,X28532,X28533] :
( ~ c_Typedef_Otype__definition(X28533,X28532,X28531,X28530,X28529)
| hAPP(X28530,hAPP(X28531,X28528)) = X28528 ),
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,
! [X20727,X20728,X20729] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20729)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20729),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20729),hAPP(c_Groups_Oabs__class_Oabs(X20729),X20728)),hAPP(c_Groups_Oabs__class_Oabs(X20729),X20727))),hAPP(c_Groups_Oabs__class_Oabs(X20729),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20729),X20728),X20727)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2])]) ).
fof(i_0_7416,plain,
! [X20730,X20731,X20732] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20732)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20732),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20732),hAPP(c_Groups_Oabs__class_Oabs(X20732),X20731)),hAPP(c_Groups_Oabs__class_Oabs(X20732),X20730))),hAPP(c_Groups_Oabs__class_Oabs(X20732),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20732),X20730),X20731)))) ),
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,
! [X28466,X28467,X28468,X28469,X28470] : hAPP(c_Set_Ovimage(X28470,X28469,X28468),hAPP(hAPP(c_Set_Oinsert(X28469),X28467),X28466)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28470,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X28470,X28469,X28468),hAPP(hAPP(c_Set_Oinsert(X28469),X28467),c_Orderings_Obot__class_Obot(tc_fun(X28469,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(X28470,X28469,X28468),X28466)),
inference(variable_rename,[status(thm)],[fact_vimage__insert]) ).
fof(i_0_7419,plain,
! [X29758,X29759,X29760,X29761,X29762] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29762,X29761)),hAPP(hAPP(c_Product__Type_OPair(X29762,X29761),X29760),X29759)),X29758))
| hBOOL(hAPP(hAPP(c_member(X29762),X29760),hAPP(c_Relation_ODomain(X29762,X29761),X29758))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainI])]) ).
fof(i_0_7420,plain,
! [X29683,X29684,X29685,X29686,X29687] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29687,X29686)),hAPP(hAPP(c_Product__Type_OPair(X29687,X29686),X29685),X29684)),X29683))
| hBOOL(hAPP(hAPP(c_member(X29686),X29684),hAPP(c_Relation_ORange(X29687,X29686),X29683))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeI])]) ).
fof(i_0_7421,plain,
! [X33369,X33370,X33371,X33372] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33372),X33371))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33370,tc_HOL_Obool)),hAPP(c_List_Oset(X33370),hAPP(hAPP(c_List_Odrop(X33370),X33371),X33369))),hAPP(c_List_Oset(X33370),hAPP(hAPP(c_List_Odrop(X33370),X33372),X33369)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__drop__subset__set__drop])]) ).
fof(i_0_7422,plain,
! [X32623,X32624,X32625,X32626] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32626),X32625))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32624,tc_HOL_Obool)),hAPP(c_List_Oset(X32624),hAPP(hAPP(c_List_Otake(X32624),X32626),X32623))),hAPP(c_List_Oset(X32624),hAPP(hAPP(c_List_Otake(X32624),X32625),X32623)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__take__subset__set__take])]) ).
fof(i_0_7423,plain,
! [X32108,X32109,X32110] :
( ~ class_Orderings_Olinorder(X32110)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32110),X32109))
| c_List_Olinorder__class_Osorted__list__of__set(X32110,hAPP(hAPP(c_Set_Oinsert(X32110),X32108),X32109)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32110,X32110,c_COMBI(X32110)),X32108),c_List_Olinorder__class_Osorted__list__of__set(X32110,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X32110,tc_HOL_Obool)),X32109),hAPP(hAPP(c_Set_Oinsert(X32110),X32108),c_Orderings_Obot__class_Obot(tc_fun(X32110,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__insert])]) ).
fof(i_0_7424,plain,
! [X21000,X21001,X21002,X21003] :
( ~ class_Rings_Olinordered__semidom(X21003)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21003),hAPP(hAPP(c_Power_Opower__class_Opower(X21003),X21002),hAPP(c_Nat_OSuc,X21001))),hAPP(hAPP(c_Power_Opower__class_Opower(X21003),X21000),hAPP(c_Nat_OSuc,X21001))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21003),c_Groups_Ozero__class_Ozero(X21003)),X21000))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21003),X21002),X21000)) ),
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,
! [X30702,X30703,X30704,X30705] :
( ~ class_Lattices_Osemilattice__sup(X30705)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30705),X30704))
| ~ hBOOL(hAPP(hAPP(c_member(X30705),X30703),X30704))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30705),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X30705),X30703),X30702)),hAPP(hAPP(c_Finite__Set_Ofold(X30705,X30705,c_Lattices_Osemilattice__sup__class_Osup(X30705)),X30702),X30704))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__le__fold__sup])]) ).
fof(i_0_7427,plain,
! [X30714,X30715,X30716,X30717] :
( ~ class_Orderings_Olinorder(X30717)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30717),X30716))
| ~ hBOOL(hAPP(hAPP(c_member(X30717),X30715),X30716))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30717),hAPP(hAPP(c_Orderings_Oord__class_Omax(X30717),X30715),X30714)),hAPP(hAPP(c_Finite__Set_Ofold(X30717,X30717,c_Orderings_Oord__class_Omax(X30717)),X30714),X30716))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__le__fold__sup])]) ).
fof(i_0_7428,plain,
! [X29782,X29783,X29784,X29785] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29785,X29784),tc_HOL_Obool)),X29783),X29782))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29785,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X29785,X29784),X29783)),hAPP(c_Relation_ODomain(X29785,X29784),X29782))) ),
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,
! [X21737,X21738,X21739] :
( ~ class_Fields_Olinordered__field(X21739)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21739),X21738),X21737))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21739),X21738),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21739),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21739),X21738),X21737)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21739),c_Groups_Oone__class_Oone(X21739)),c_Groups_Oone__class_Oone(X21739))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__half__sum])]) ).
fof(i_0_7431,plain,
! [X25069,X25070] :
( ~ c_Nat__Transfer_Onat__set(X25070)
| ~ c_Nat__Transfer_Onat__set(X25069)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X25070),X25069) = 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),X25070)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X25069))) ),
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,
! [X24455,X24456] :
( ~ c_Nat__Transfer_Onat__set(X24456)
| ~ c_Nat__Transfer_Onat__set(X24455)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X24456),X24455) = 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),X24456)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X24455))) ),
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,
! [X26516,X26517,X26518,X26519,X26520] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26520),X26517),X26519))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26520),X26519),X26518))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X26520,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26520,X26519,X26518)),c_SetInterval_Oord__class_OatLeastAtMost(X26520,X26517,X26516)))
| ~ class_Orderings_Oorder(X26520) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26520),X26518),X26516))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26520),X26519),X26518))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X26520,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26520,X26519,X26518)),c_SetInterval_Oord__class_OatLeastAtMost(X26520,X26517,X26516)))
| ~ class_Orderings_Oorder(X26520) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26520),X26517),X26519))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26520),X26518),X26516))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26520),X26519),X26518))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X26520,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26520,X26519,X26518)),c_SetInterval_Oord__class_OatLeastAtMost(X26520,X26517,X26516)))
| ~ class_Orderings_Oorder(X26520) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26520),X26517),X26516))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X26520,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26520,X26519,X26518)),c_SetInterval_Oord__class_OatLeastAtMost(X26520,X26517,X26516)))
| ~ class_Orderings_Oorder(X26520) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26520),X26519),X26518))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26520),X26517),X26516))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X26520,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26520,X26519,X26518)),c_SetInterval_Oord__class_OatLeastAtMost(X26520,X26517,X26516)))
| ~ class_Orderings_Oorder(X26520) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26520),X26517),X26519))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26520),X26517),X26519))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26520),X26518),X26516))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26520),X26517),X26516))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X26520,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26520,X26519,X26518)),c_SetInterval_Oord__class_OatLeastAtMost(X26520,X26517,X26516)))
| ~ class_Orderings_Oorder(X26520) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26520),X26518),X26516))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26520),X26517),X26519))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26520),X26518),X26516))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26520),X26517),X26516))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X26520,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26520,X26519,X26518)),c_SetInterval_Oord__class_OatLeastAtMost(X26520,X26517,X26516)))
| ~ class_Orderings_Oorder(X26520) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5560])])]) ).
fof(i_0_7434,plain,
! [X18858,X18859,X18860,X18861,X18862] :
( ~ class_Rings_Osemiring(X18862)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18862),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18862),X18861),X18860)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18862),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18862),X18859),X18860)),X18858)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18862),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18862),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18862),X18861),X18859)),X18860)),X18858) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_combine__common__factor])]) ).
fof(i_0_7435,plain,
! [X28708,X28709] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28709,X28709),tc_HOL_Obool)),c_Relation_OId__on(X28709,X28708)),hAPP(hAPP(c_Product__Type_OSigma(X28709,X28709),X28708),hAPP(c_COMBK(tc_fun(X28709,tc_HOL_Obool),X28709),X28708)))),
inference(variable_rename,[status(thm)],[fact_Id__on__subset__Times]) ).
fof(i_0_7436,plain,
! [X31951] :
( ( ~ c_Com_OWT__bodies
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),X31951),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)),X31951)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),esk439_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)),esk439_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,
! [X29680,X29681,X29682] : hAPP(c_Relation_ORange(X29682,X29681),hAPP(c_Set_OCollect(tc_prod(X29682,X29681)),hAPP(c_Product__Type_Oprod_Oprod__case(X29682,X29681,tc_HOL_Obool),X29680))) = hAPP(c_Set_OCollect(X29681),hAPP(hAPP(c_COMBB(tc_fun(X29682,tc_HOL_Obool),tc_HOL_Obool,X29681),c_HOL_OEx(X29682)),hAPP(c_COMBC(X29682,X29681,tc_HOL_Obool),X29680))),
inference(variable_rename,[status(thm)],[fact_Range__Collect__split]) ).
fof(i_0_7438,plain,
! [X28690,X28691,X28692] :
( ~ c_Equiv__Relations_Oequiv(X28692,X28691,X28690)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28692,X28692),tc_HOL_Obool)),X28690),hAPP(hAPP(c_Product__Type_OSigma(X28692,X28692),X28691),hAPP(c_COMBK(tc_fun(X28692,tc_HOL_Obool),X28692),X28691)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__type])]) ).
fof(i_0_7439,plain,
! [X31765,X31766,X31767,X31768,X31769] : hAPP(c_Fun_Ocomp(tc_List_Olist(X31769),tc_List_Olist(X31768),tc_List_Olist(X31767),hAPP(c_List_Omap(X31769,X31768),X31766)),hAPP(c_List_Omap(X31767,X31769),X31765)) = hAPP(c_List_Omap(X31767,X31768),hAPP(c_Fun_Ocomp(X31769,X31768,X31767,X31766),X31765)),
inference(variable_rename,[status(thm)],[fact_map__comp__map]) ).
fof(i_0_7440,plain,
! [X31760,X31761,X31762,X31763,X31764] : hAPP(c_Fun_Ocomp(tc_List_Olist(X31764),tc_List_Olist(X31763),tc_List_Olist(X31762),hAPP(c_List_Omap(X31764,X31763),X31761)),hAPP(c_List_Omap(X31762,X31764),X31760)) = hAPP(c_List_Omap(X31762,X31763),hAPP(c_Fun_Ocomp(X31764,X31763,X31762,X31761),X31760)),
inference(variable_rename,[status(thm)],[fact_List_Omap_Ocomp]) ).
fof(i_0_7441,plain,
! [X31852,X31853,X31854,X31855,X31856] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(X31856),tc_Option_Ooption(X31855),tc_Option_Ooption(X31854),hAPP(c_Option_Omap(X31856,X31855),X31853)),hAPP(c_Option_Omap(X31854,X31856),X31852)) = hAPP(c_Option_Omap(X31854,X31855),hAPP(c_Fun_Ocomp(X31856,X31855,X31854,X31853),X31852)),
inference(variable_rename,[status(thm)],[fact_Option_Omap_Ocomp]) ).
fof(i_0_7442,plain,
! [X29059,X29060,X29061,X29062,X29063] :
( ~ c_Relation_Orefl__on(X29063,X29062,X29061)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29063,X29063)),hAPP(hAPP(c_Product__Type_OPair(X29063,X29063),X29060),X29059)),X29061))
| hBOOL(hAPP(hAPP(c_member(X29063),X29060),X29062)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onD1])]) ).
fof(i_0_7443,plain,
! [X29064,X29065,X29066,X29067,X29068] :
( ~ c_Relation_Orefl__on(X29068,X29067,X29066)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29068,X29068)),hAPP(hAPP(c_Product__Type_OPair(X29068,X29068),X29065),X29064)),X29066))
| hBOOL(hAPP(hAPP(c_member(X29068),X29064),X29067)) ),
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,
! [X32848,X32849] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32849),tc_List_Olist(X32849))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32849),tc_List_Olist(X32849)),c_List_Olist_ONil(X32849)),c_List_Olist_ONil(X32849))),c_List_Olistrel(X32849,X32848))),
inference(variable_rename,[status(thm)],[fact_listrel_ONil]) ).
fof(i_0_7446,plain,
! [X31333,X31334,X31335] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31335,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31335,tc_HOL_Obool),X31334)),X31333) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X31335,tc_HOL_Obool),tc_fun(X31335,tc_HOL_Obool)),X31334),hAPP(hAPP(c_COMBC(tc_fun(X31335,tc_HOL_Obool),tc_fun(X31335,tc_HOL_Obool),tc_fun(X31335,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31335,tc_HOL_Obool))),X31333)),
inference(variable_rename,[status(thm)],[fact_Int__Union2]) ).
fof(i_0_7447,plain,
! [X26282,X26283,X26284,X26285] :
( ( X26284 = X26283
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26285,X26285)),hAPP(hAPP(c_Product__Type_OPair(X26285,X26285),X26284),X26283)),c_Relation_OId__on(X26285,X26282))) )
& ( hBOOL(hAPP(hAPP(c_member(X26285),X26284),X26282))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26285,X26285)),hAPP(hAPP(c_Product__Type_OPair(X26285,X26285),X26284),X26283)),c_Relation_OId__on(X26285,X26282))) )
& ( X26284 != X26283
| ~ hBOOL(hAPP(hAPP(c_member(X26285),X26284),X26282))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X26285,X26285)),hAPP(hAPP(c_Product__Type_OPair(X26285,X26285),X26284),X26283)),c_Relation_OId__on(X26285,X26282))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__on__iff])])]) ).
fof(i_0_7448,plain,
! [X25653,X25654,X25655,X25656] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X25656),X25654))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X25656,X25655)),c_Sum__Type_OPlus(X25656,X25655,X25654,X25653))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X25655),X25653))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X25656,X25655)),c_Sum__Type_OPlus(X25656,X25655,X25654,X25653))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25656),X25654))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25655),X25653))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X25656,X25655)),c_Sum__Type_OPlus(X25656,X25655,X25654,X25653))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus__iff])])]) ).
fof(i_0_7449,plain,
! [X25645,X25646,X25647,X25648] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X25648,X25647)),c_Sum__Type_OPlus(X25648,X25647,X25646,X25645)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X25648),X25646)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I1_J])]) ).
fof(i_0_7450,plain,
! [X25641,X25642,X25643,X25644] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X25644,X25643)),c_Sum__Type_OPlus(X25644,X25643,X25642,X25641)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X25643),X25641)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I2_J])]) ).
fof(i_0_7451,plain,
! [X28601,X28602,X28603,X28604,X28605,X28606] :
( ~ hBOOL(hAPP(hAPP(c_member(X28606),X28605),X28604))
| ~ hBOOL(hAPP(hAPP(c_member(X28603),X28602),hAPP(X28601,X28605)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X28606,X28603)),hAPP(hAPP(c_Product__Type_OPair(X28606,X28603),X28605),X28602)),hAPP(hAPP(c_Product__Type_OSigma(X28606,X28603),X28604),X28601))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaI])]) ).
fof(i_0_7452,plain,
! [X31447,X31448,X31449] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X31449,tc_HOL_Obool)),esk409_3(X31447,X31448,X31449)),hAPP(hAPP(c_Set_Oinsert(tc_fun(X31449,tc_HOL_Obool)),X31448),X31447)))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31449,tc_HOL_Obool)),X31448),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31449,tc_HOL_Obool),X31447)) = c_Orderings_Obot__class_Obot(tc_fun(X31449,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X31449,tc_HOL_Obool)),X31448),X31447)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(X31449,tc_HOL_Obool)),esk410_3(X31447,X31448,X31449)),hAPP(hAPP(c_Set_Oinsert(tc_fun(X31449,tc_HOL_Obool)),X31448),X31447)))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31449,tc_HOL_Obool)),X31448),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31449,tc_HOL_Obool),X31447)) = c_Orderings_Obot__class_Obot(tc_fun(X31449,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X31449,tc_HOL_Obool)),X31448),X31447)) )
& ( esk409_3(X31447,X31448,X31449) != esk410_3(X31447,X31448,X31449)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31449,tc_HOL_Obool)),X31448),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31449,tc_HOL_Obool),X31447)) = c_Orderings_Obot__class_Obot(tc_fun(X31449,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X31449,tc_HOL_Obool)),X31448),X31447)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31449,tc_HOL_Obool)),esk409_3(X31447,X31448,X31449)),esk410_3(X31447,X31448,X31449)) != c_Orderings_Obot__class_Obot(tc_fun(X31449,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31449,tc_HOL_Obool)),X31448),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31449,tc_HOL_Obool),X31447)) = c_Orderings_Obot__class_Obot(tc_fun(X31449,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X31449,tc_HOL_Obool)),X31448),X31447)) ) ),
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,
! [X33584,X33585,X33586,X33587] :
( ~ class_Groups_Osemigroup__add(X33587)
| hAPP(c_List_Ofoldl(X33587,X33587,c_Groups_Oplus__class_Oplus(X33587),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X33587),X33586),X33585)),X33584) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X33587),X33586),hAPP(c_List_Ofoldl(X33587,X33587,c_Groups_Oplus__class_Oplus(X33587),X33585),X33584)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__assoc])]) ).
fof(i_0_7454,plain,
! [X30485,X30486,X30487] : hBOOL(hAPP(hAPP(c_member(tc_prod(X30487,X30487)),hAPP(hAPP(c_Product__Type_OPair(X30487,X30487),X30486),X30486)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30487,X30487),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30485))),
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,
! [X33170,X33171,X33172,X33173,X33174] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33174),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33173)),X33172)))
| hAPP(hAPP(c_List_Olist__update(X33173,hAPP(hAPP(c_List_Oappend(X33173),X33172),X33171)),X33174),X33170) = hAPP(hAPP(c_List_Oappend(X33173),hAPP(hAPP(c_List_Olist__update(X33173,X33172),X33174),X33170)),X33171) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33174),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33173)),X33172)))
| hAPP(hAPP(c_List_Olist__update(X33173,hAPP(hAPP(c_List_Oappend(X33173),X33172),X33171)),X33174),X33170) = hAPP(hAPP(c_List_Oappend(X33173),X33172),hAPP(hAPP(c_List_Olist__update(X33173,X33171),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33174),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33173)),X33172))),X33170)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5564])]) ).
fof(i_0_7457,plain,
! [X25074,X25075,X25076,X25077,X25078] :
( ~ c_Equiv__Relations_Oequiv(X25078,X25077,X25076)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25078,tc_HOL_Obool)),X25075),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25078),X25077),X25076)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25078,tc_HOL_Obool)),X25074),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25078),X25077),X25076)))
| X25075 = X25074
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25078,tc_HOL_Obool)),X25075),X25074) = c_Orderings_Obot__class_Obot(tc_fun(X25078,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__disj])]) ).
fof(i_0_7458,plain,
! [X32604,X32605,X32606] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32606),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32605)),X32604)))
| hAPP(c_Random_Opick(X32605,hAPP(hAPP(c_List_Omap(X32605,tc_prod(tc_Code__Numeral_Ocode__numeral,X32605)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X32605),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X32604)),hAPP(c_Code__Numeral_Oof__nat,X32606)) = hAPP(hAPP(c_List_Onth(X32605),X32604),X32606) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pick__same])]) ).
fof(i_0_7459,plain,
! [X21754,X21755,X21756,X21757] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21757),c_Groups_Ozero__class_Ozero(X21757)),X21754))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21757),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21757),X21756),X21754)),X21755))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21757),X21756),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21757),X21755),X21754)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21757) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21757),X21754),c_Groups_Ozero__class_Ozero(X21757)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21757),X21755),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21757),X21756),X21754)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21757),c_Groups_Ozero__class_Ozero(X21757)),X21754))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21757),X21756),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21757),X21755),X21754)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21757) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21757),X21754),c_Groups_Ozero__class_Ozero(X21757)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21757),X21756),c_Groups_Ozero__class_Ozero(X21757)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21757),c_Groups_Ozero__class_Ozero(X21757)),X21754))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21757),X21756),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21757),X21755),X21754)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21757) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21757),c_Groups_Ozero__class_Ozero(X21757)),X21754))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21757),c_Groups_Ozero__class_Ozero(X21757)),X21754))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21757),X21756),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21757),X21755),X21754)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21757) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21757),X21754),c_Groups_Ozero__class_Ozero(X21757)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21757),X21754),c_Groups_Ozero__class_Ozero(X21757)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21757),c_Groups_Ozero__class_Ozero(X21757)),X21754))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21757),X21756),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21757),X21755),X21754)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21757) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21757),X21756),c_Groups_Ozero__class_Ozero(X21757)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21757),X21754),c_Groups_Ozero__class_Ozero(X21757)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21757),c_Groups_Ozero__class_Ozero(X21757)),X21754))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21757),X21756),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21757),X21755),X21754)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21757) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21757),X21754),c_Groups_Ozero__class_Ozero(X21757)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21757),X21755),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21757),X21756),X21754)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21757),c_Groups_Ozero__class_Ozero(X21757)),X21754))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21757),X21756),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21757),X21755),X21754)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21757) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21757),X21756),c_Groups_Ozero__class_Ozero(X21757)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21757),X21755),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21757),X21756),X21754)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21757),c_Groups_Ozero__class_Ozero(X21757)),X21754))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21757),X21756),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21757),X21755),X21754)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21757) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21757),c_Groups_Ozero__class_Ozero(X21757)),X21754))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21757),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21757),X21756),X21754)),X21755))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21757),X21756),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21757),X21755),X21754)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21757) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21757),X21754),c_Groups_Ozero__class_Ozero(X21757)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21757),X21754),c_Groups_Ozero__class_Ozero(X21757)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21757),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21757),X21756),X21754)),X21755))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21757),X21756),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21757),X21755),X21754)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21757) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21757),X21756),c_Groups_Ozero__class_Ozero(X21757)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21757),X21754),c_Groups_Ozero__class_Ozero(X21757)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21757),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21757),X21756),X21754)),X21755))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21757),X21756),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21757),X21755),X21754)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21757) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21757),X21754),c_Groups_Ozero__class_Ozero(X21757)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21757),X21755),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21757),X21756),X21754)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21757),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21757),X21756),X21754)),X21755))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21757),X21756),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21757),X21755),X21754)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21757) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21757),X21756),c_Groups_Ozero__class_Ozero(X21757)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21757),X21755),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21757),X21756),X21754)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21757),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21757),X21756),X21754)),X21755))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21757),X21756),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21757),X21755),X21754)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21757) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5565])])]) ).
fof(i_0_7460,plain,
! [X21682,X21683,X21684,X21685] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),c_Groups_Ozero__class_Ozero(X21685)),X21682))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21685),X21684),X21682)),X21683))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21684),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21685),X21683),X21682)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21685) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21682),c_Groups_Ozero__class_Ozero(X21685)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21685),X21684),X21682)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),c_Groups_Ozero__class_Ozero(X21685)),X21682))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21684),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21685),X21683),X21682)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21685) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21682),c_Groups_Ozero__class_Ozero(X21685)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21684),c_Groups_Ozero__class_Ozero(X21685)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),c_Groups_Ozero__class_Ozero(X21685)),X21682))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21684),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21685),X21683),X21682)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21685) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),c_Groups_Ozero__class_Ozero(X21685)),X21682))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),c_Groups_Ozero__class_Ozero(X21685)),X21682))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21684),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21685),X21683),X21682)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21685) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21682),c_Groups_Ozero__class_Ozero(X21685)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21682),c_Groups_Ozero__class_Ozero(X21685)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),c_Groups_Ozero__class_Ozero(X21685)),X21682))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21684),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21685),X21683),X21682)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21685) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21684),c_Groups_Ozero__class_Ozero(X21685)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21682),c_Groups_Ozero__class_Ozero(X21685)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),c_Groups_Ozero__class_Ozero(X21685)),X21682))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21684),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21685),X21683),X21682)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21685) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21682),c_Groups_Ozero__class_Ozero(X21685)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21685),X21684),X21682)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),c_Groups_Ozero__class_Ozero(X21685)),X21682))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21684),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21685),X21683),X21682)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21685) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21684),c_Groups_Ozero__class_Ozero(X21685)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21685),X21684),X21682)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),c_Groups_Ozero__class_Ozero(X21685)),X21682))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21684),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21685),X21683),X21682)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21685) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),c_Groups_Ozero__class_Ozero(X21685)),X21682))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21685),X21684),X21682)),X21683))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21684),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21685),X21683),X21682)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21685) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21682),c_Groups_Ozero__class_Ozero(X21685)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21682),c_Groups_Ozero__class_Ozero(X21685)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21685),X21684),X21682)),X21683))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21684),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21685),X21683),X21682)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21685) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21684),c_Groups_Ozero__class_Ozero(X21685)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21682),c_Groups_Ozero__class_Ozero(X21685)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21685),X21684),X21682)),X21683))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21684),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21685),X21683),X21682)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21685) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21682),c_Groups_Ozero__class_Ozero(X21685)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21685),X21684),X21682)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21685),X21684),X21682)),X21683))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21684),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21685),X21683),X21682)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21685) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21684),c_Groups_Ozero__class_Ozero(X21685)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21685),X21684),X21682)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21685),X21684),X21682)),X21683))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21685),X21684),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21685),X21683),X21682)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21685) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5566])])]) ).
fof(i_0_7461,plain,
! [X26862,X26863] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X26863),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26862),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26862),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X26863)))))
| X26863 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26862),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26862),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X26863))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__card__intvl__is__intvl])]) ).
fof(i_0_7462,plain,
! [X25205,X25206,X25207,X25208,X25209] :
( ( hBOOL(hAPP(hAPP(X25207,X25206),X25208))
| ~ hBOOL(hAPP(hAPP(c_member(X25209),X25208),c_SetInterval_Oord_OatLeastAtMost(X25209,X25207,X25206,X25205))) )
& ( hBOOL(hAPP(hAPP(X25207,X25208),X25205))
| ~ hBOOL(hAPP(hAPP(c_member(X25209),X25208),c_SetInterval_Oord_OatLeastAtMost(X25209,X25207,X25206,X25205))) )
& ( ~ hBOOL(hAPP(hAPP(X25207,X25206),X25208))
| ~ hBOOL(hAPP(hAPP(X25207,X25208),X25205))
| hBOOL(hAPP(hAPP(c_member(X25209),X25208),c_SetInterval_Oord_OatLeastAtMost(X25209,X25207,X25206,X25205))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeastAtMost__iff])])]) ).
fof(i_0_7463,plain,
! [X25149,X25150,X25151,X25152,X25153] :
( ( hBOOL(hAPP(hAPP(X25151,X25150),X25152))
| ~ hBOOL(hAPP(hAPP(c_member(X25153),X25152),c_SetInterval_Oord_OgreaterThanLessThan(X25153,X25151,X25150,X25149))) )
& ( hBOOL(hAPP(hAPP(X25151,X25152),X25149))
| ~ hBOOL(hAPP(hAPP(c_member(X25153),X25152),c_SetInterval_Oord_OgreaterThanLessThan(X25153,X25151,X25150,X25149))) )
& ( ~ hBOOL(hAPP(hAPP(X25151,X25150),X25152))
| ~ hBOOL(hAPP(hAPP(X25151,X25152),X25149))
| hBOOL(hAPP(hAPP(c_member(X25153),X25152),c_SetInterval_Oord_OgreaterThanLessThan(X25153,X25151,X25150,X25149))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanLessThan__iff])])]) ).
fof(i_0_7464,plain,
! [X32879,X32880] : c_List_Oset__Cons(X32880,X32879,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X32880)),c_List_Olist_ONil(X32880)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X32880),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(X32880,tc_List_Olist(X32880),hAPP(hAPP(c_COMBC(X32880,tc_List_Olist(X32880),tc_List_Olist(X32880)),c_List_Olist_OCons(X32880)),c_List_Olist_ONil(X32880))),X32879),
inference(variable_rename,[status(thm)],[fact_set__Cons__sing__Nil]) ).
fof(i_0_7465,plain,
! [X31024,X31025,X31026,X31027,X31028,X31029] :
( ~ hBOOL(hAPP(hAPP(c_member(X31029),X31028),X31027))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31029,tc_fun(X31026,tc_HOL_Obool)),X31027),hAPP(hAPP(c_COMBB(tc_fun(X31026,tc_HOL_Obool),tc_fun(X31026,tc_HOL_Obool),X31029),hAPP(c_Set_Oinsert(X31026),X31025)),X31024)) = hAPP(hAPP(c_Set_Oinsert(X31026),X31025),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31029,tc_fun(X31026,tc_HOL_Obool)),X31027),X31024)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__insert__distrib])]) ).
fof(i_0_7466,plain,
! [X26092,X26093,X26094,X26095,X26096,X26097] :
( ~ hBOOL(hAPP(hAPP(c_member(X26097),X26096),X26095))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26097,tc_fun(X26094,tc_HOL_Obool)),X26095),hAPP(hAPP(c_COMBB(tc_fun(X26094,tc_HOL_Obool),tc_fun(X26094,tc_HOL_Obool),X26097),hAPP(c_Set_Oinsert(X26094),X26093)),X26092)) = hAPP(hAPP(c_Set_Oinsert(X26094),X26093),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26097,tc_fun(X26094,tc_HOL_Obool)),X26095),X26092)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__insert__distrib])]) ).
fof(i_0_7467,plain,
! [X29449,X29450,X29453,X29454,X29455,X29456] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29450),X29449))
| X29449 = hAPP(c_Set_Oimage(tc_Nat_Onat,X29450,esk315_2(X29449,X29450)),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)),esk314_2(X29449,X29450)))) )
& ( X29453 != hAPP(c_Set_Oimage(tc_Nat_Onat,X29454,X29456),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)),X29455)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29454),X29453)) ) ),
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,
! [X29248,X29249,X29250,X29251] :
( X29251 != hAPP(c_Set_Oimage(tc_Nat_Onat,X29250,X29249),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)),X29248)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29250),X29251)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__seg__image__imp__finite])]) ).
fof(i_0_7469,plain,
! [X33439,X33440,X33441] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33441),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33440)),X33439)))
| hAPP(hAPP(c_List_Oappend(X33440),hAPP(hAPP(c_List_Otake(X33440),X33441),X33439)),hAPP(hAPP(c_List_Olist_OCons(X33440),hAPP(c_List_Ohd(X33440),hAPP(hAPP(c_List_Odrop(X33440),X33441),X33439))),c_List_Olist_ONil(X33440))) = hAPP(hAPP(c_List_Otake(X33440),hAPP(c_Nat_OSuc,X33441)),X33439) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__hd__drop])]) ).
fof(i_0_7470,plain,
! [X23298,X23299,X23300,X23301] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23301,tc_HOL_Obool)),X23300),hAPP(hAPP(c_Set_Oinsert(X23301),X23299),X23298)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23301,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23301,tc_HOL_Obool)),X23300),hAPP(hAPP(c_Set_Oinsert(X23301),X23299),c_Orderings_Obot__class_Obot(tc_fun(X23301,tc_HOL_Obool))))),X23298),
inference(variable_rename,[status(thm)],[fact_Diff__insert2]) ).
fof(i_0_7471,plain,
! [X32247,X32248,X32249] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32249),tc_List_Olist(X32249))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32249),tc_List_Olist(X32249)),X32248),X32248)),c_List_Olistrel(X32249,c_Transitive__Closure_Ortrancl(X32249,X32247)))),
inference(variable_rename,[status(thm)],[fact_listrel__rtrancl__refl]) ).
fof(i_0_7472,plain,
! [X25573,X25574,X25575,X25576,X25577] :
( ~ hBOOL(hAPP(hAPP(c_member(X25577),X25576),X25575))
| hBOOL(hAPP(hAPP(c_member(tc_sum(X25577,X25574)),hAPP(c_Sum__Type_OInl(X25577,X25574),X25576)),c_Sum__Type_OPlus(X25577,X25574,X25575,X25573))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_InlI])]) ).
fof(i_0_7473,plain,
! [X25568,X25569,X25570,X25571,X25572] :
( ~ hBOOL(hAPP(hAPP(c_member(X25572),X25571),X25570))
| hBOOL(hAPP(hAPP(c_member(tc_sum(X25569,X25572)),hAPP(c_Sum__Type_OInr(X25572,X25569),X25571)),c_Sum__Type_OPlus(X25569,X25572,X25568,X25570))) ),
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,
! [X31457,X31458,X31459] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X31459,tc_HOL_Obool)),esk412_3(X31457,X31458,X31459)),X31458))
| X31458 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X31459,tc_HOL_Obool),tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31459,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31459,tc_HOL_Obool),X31458)),X31457)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31459,tc_HOL_Obool)),esk412_3(X31457,X31458,X31459)),X31457))
| X31458 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X31459,tc_HOL_Obool),tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31459,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31459,tc_HOL_Obool),X31458)),X31457)) ) ),
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,
! [X19974,X19975,X19976] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19976))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X19975,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19974),X19976)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19974),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19975),X19974),X19976))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19975,X19974)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zmult2__eq])]) ).
fof(i_0_7477,plain,
! [X24716,X24717,X24718,X24719] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24719,tc_HOL_Obool)),X24718),X24717))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24719,tc_HOL_Obool)),X24718),X24716))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24719,tc_HOL_Obool)),X24718),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24719,tc_HOL_Obool)),X24717),X24716))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__greatest])]) ).
fof(i_0_7478,plain,
! [X22721,X22722] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X22722),hAPP(c_Nat_OSuc,X22721)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X22721),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)),X22721)),X22722),
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,
! [X30461,X30462,X30463,X30464] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30464,X30464),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30463),X30462)),X30461) = hAPP(hAPP(c_Relation_Orel__comp(X30464,X30464,X30464),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30464,X30464),tc_HOL_Obool),X30463),X30461)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30464,X30464),tc_HOL_Obool),X30462),X30461)),
inference(variable_rename,[status(thm)],[fact_rel__pow__add]) ).
fof(i_0_7481,plain,
! [X31292,X31293,X31294] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X31294,tc_HOL_Obool),tc_HOL_Obool)),X31293),X31292))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31294,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31294,tc_HOL_Obool),X31293)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31294,tc_HOL_Obool),X31292))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Union__mono])]) ).
fof(i_0_7482,plain,
! [X31254,X31255,X31256] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X31256,tc_HOL_Obool),tc_HOL_Obool)),X31255),X31254))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31256,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31256,tc_HOL_Obool),X31254)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31256,tc_HOL_Obool),X31255))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inter__anti__mono])]) ).
fof(i_0_7483,plain,
! [X20836,X20837,X20838] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20838)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20838),hAPP(c_Groups_Oabs__class_Oabs(X20838),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20838),X20837),X20836))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20838),hAPP(c_Groups_Oabs__class_Oabs(X20838),X20837)),hAPP(c_Groups_Oabs__class_Oabs(X20838),X20836)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq4])]) ).
fof(i_0_7484,plain,
! [X20716,X20717,X20718] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20718)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20718),hAPP(c_Groups_Oabs__class_Oabs(X20718),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20718),X20717),X20716))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20718),hAPP(c_Groups_Oabs__class_Oabs(X20718),X20717)),hAPP(c_Groups_Oabs__class_Oabs(X20718),X20716)))) ),
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,
! [X26457,X26458,X26459,X26460,X26461] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26461),X26458),X26460))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26461),X26460),X26459))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26461,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26461,X26460,X26459)),c_SetInterval_Oord__class_OatLeastAtMost(X26461,X26458,X26457)))
| ~ class_Orderings_Oorder(X26461) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26461),X26459),X26457))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26461),X26460),X26459))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26461,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26461,X26460,X26459)),c_SetInterval_Oord__class_OatLeastAtMost(X26461,X26458,X26457)))
| ~ class_Orderings_Oorder(X26461) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26461),X26460),X26459))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26461,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26461,X26460,X26459)),c_SetInterval_Oord__class_OatLeastAtMost(X26461,X26458,X26457)))
| ~ class_Orderings_Oorder(X26461) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26461),X26458),X26460))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26461),X26459),X26457))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26461,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26461,X26460,X26459)),c_SetInterval_Oord__class_OatLeastAtMost(X26461,X26458,X26457)))
| ~ class_Orderings_Oorder(X26461) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5569])])]) ).
fof(i_0_7487,plain,
! [X22556,X22557] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X22557),hAPP(c_Nat_OSuc,X22556)) = 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)),X22556)),X22557),
inference(variable_rename,[status(thm)],[fact_min__Suc2]) ).
fof(i_0_7488,plain,
! [X25532,X25533,X25534] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25534),X25533))
| ~ hBOOL(hAPP(hAPP(c_member(X25534),X25532),X25533))
| hAPP(c_Finite__Set_Ocard(X25534),X25533) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X25534),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25534,tc_HOL_Obool)),X25533),hAPP(hAPP(c_Set_Oinsert(X25534),X25532),c_Orderings_Obot__class_Obot(tc_fun(X25534,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oremove])]) ).
fof(i_0_7489,plain,
! [X32722,X32723,X32724,X32725,X32726,X32727,X32728] : hAPP(hAPP(c_List_Ozip(X32728,X32727),hAPP(hAPP(c_List_Olist__update(X32728,X32726),X32725),X32724)),hAPP(hAPP(c_List_Olist__update(X32727,X32723),X32725),X32722)) = hAPP(hAPP(c_List_Olist__update(tc_prod(X32728,X32727),hAPP(hAPP(c_List_Ozip(X32728,X32727),X32726),X32723)),X32725),hAPP(hAPP(c_Product__Type_OPair(X32728,X32727),X32724),X32722)),
inference(variable_rename,[status(thm)],[fact_zip__update]) ).
fof(i_0_7490,plain,
! [X28284,X28285,X28286,X28287,X28288] :
( ~ c_Fun_Oinj__on(X28288,X28287,X28286,c_Orderings_Otop__class_Otop(tc_fun(X28288,tc_HOL_Obool)))
| hAPP(c_Set_Oimage(X28288,X28287,X28286),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28288,tc_HOL_Obool)),X28285),X28284)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28287,tc_HOL_Obool)),hAPP(c_Set_Oimage(X28288,X28287,X28286),X28285)),hAPP(c_Set_Oimage(X28288,X28287,X28286),X28284)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__Int])]) ).
fof(i_0_7491,plain,
! [X28289,X28290,X28291,X28292,X28293] :
( ~ c_Fun_Oinj__on(X28293,X28292,X28291,c_Orderings_Otop__class_Otop(tc_fun(X28293,tc_HOL_Obool)))
| hAPP(c_Set_Oimage(X28293,X28292,X28291),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28293,tc_HOL_Obool)),X28290),X28289)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28292,tc_HOL_Obool)),hAPP(c_Set_Oimage(X28293,X28292,X28291),X28290)),hAPP(c_Set_Oimage(X28293,X28292,X28291),X28289)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__set__diff])]) ).
fof(i_0_7492,plain,
! [X27018,X27019,X27020,X27021] :
( ~ c_Fun_Oinj__on(X27021,X27020,X27019,X27018)
| hAPP(c_Set_Oimage(X27020,X27021,c_Fun_Othe__inv__into(X27021,X27020,X27018,X27019)),hAPP(c_Set_Oimage(X27021,X27020,X27019),X27018)) = X27018 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__onto])]) ).
fof(i_0_7493,plain,
! [X18404,X18405,X18406,X18407,X18408,X18409] : c_Nitpick_Opair__box_Opair__box__rec(X18409,X18408,X18407,X18406,c_Nitpick_Opair__box_OPairBox(X18409,X18408,X18405,X18404)) = hAPP(hAPP(X18406,X18405),X18404),
inference(variable_rename,[status(thm)],[fact_pair__box_Orecs]) ).
fof(i_0_7494,plain,
! [X18398,X18399,X18400,X18401,X18402,X18403] : c_Nitpick_Opair__box_Opair__box__case(X18403,X18402,X18401,X18400,c_Nitpick_Opair__box_OPairBox(X18403,X18402,X18399,X18398)) = hAPP(hAPP(X18400,X18399),X18398),
inference(variable_rename,[status(thm)],[fact_pair__box_Osimps_I2_J]) ).
fof(i_0_7495,plain,
! [X25680,X25681,X25682,X25683,X25684] :
( ~ class_Groups_Ocomm__monoid__mult(X25684)
| ~ class_Rings_Odvd(X25684)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25683),X25682))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25683,tc_HOL_Obool)),X25681),X25682))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X25684),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25683,X25684),X25680),X25681)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25683,X25684),X25680),X25682))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__dvd__setprod__subset])]) ).
fof(i_0_7496,plain,
! [X34380,X34381,X34382,X34383,X34384] : hAPP(hAPP(c_List_Ozip(X34384,X34383),c_List_OtakeWhile(X34384,X34382,X34381)),X34380) = c_List_OtakeWhile(tc_prod(X34384,X34383),hAPP(c_Fun_Ocomp(X34384,tc_HOL_Obool,tc_prod(X34384,X34383),X34382),c_Product__Type_Ofst(X34384,X34383)),hAPP(hAPP(c_List_Ozip(X34384,X34383),X34381),X34380)),
inference(variable_rename,[status(thm)],[fact_zip__takeWhile__fst]) ).
cnf(i_0_7497,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_7498,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_7499,plain,
( X2 = hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk389_2(X2,X1)),esk389_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_7500,plain,
! [X17511,X17512,X17513,X17514,X17515] :
( ( ~ hBOOL(hAPP(X17515,X17512))
| hBOOL(hAPP(X17515,X17512))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17515,X17514,X17513)),X17512),X17511)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17513),X17512),X17511))
| hBOOL(hAPP(X17515,X17512))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17515,X17514,X17513)),X17512),X17511)) )
& ( ~ hBOOL(hAPP(X17515,X17512))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17514),X17512),X17511))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17515,X17514,X17513)),X17512),X17511)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17513),X17512),X17511))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17514),X17512),X17511))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17515,X17514,X17513)),X17512),X17511)) )
& ( ~ hBOOL(hAPP(X17515,X17512))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17514),X17512),X17511))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17515,X17514,X17513)),X17512),X17511)) )
& ( hBOOL(hAPP(X17515,X17512))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17513),X17512),X17511))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17515,X17514,X17513)),X17512),X17511)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5573])])]) ).
fof(i_0_7501,plain,
! [X17506,X17507,X17508,X17509,X17510] :
( ( ~ hBOOL(hAPP(X17510,X17507))
| hBOOL(hAPP(X17510,X17507))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17510,X17509,X17508)),X17507),X17506)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17508),X17507),X17506))
| hBOOL(hAPP(X17510,X17507))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17510,X17509,X17508)),X17507),X17506)) )
& ( ~ hBOOL(hAPP(X17510,X17507))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17509),X17507),X17506))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17510,X17509,X17508)),X17507),X17506)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17508),X17507),X17506))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17509),X17507),X17506))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17510,X17509,X17508)),X17507),X17506)) )
& ( ~ hBOOL(hAPP(X17510,X17507))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17509),X17507),X17506))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17510,X17509,X17508)),X17507),X17506)) )
& ( hBOOL(hAPP(X17510,X17507))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17508),X17507),X17506))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17510,X17509,X17508)),X17507),X17506)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5574])])]) ).
fof(i_0_7502,plain,
! [X17493,X17494,X17495,X17496,X17497] :
( ( ~ hBOOL(hAPP(X17497,X17494))
| hBOOL(hAPP(X17497,X17494))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17497,X17496,X17495)),X17494),X17493)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17495),X17494),X17493))
| hBOOL(hAPP(X17497,X17494))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17497,X17496,X17495)),X17494),X17493)) )
& ( ~ hBOOL(hAPP(X17497,X17494))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17496),X17494),X17493))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17497,X17496,X17495)),X17494),X17493)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17495),X17494),X17493))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17496),X17494),X17493))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17497,X17496,X17495)),X17494),X17493)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5575])])]) ).
cnf(i_0_7503,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_7504,plain,
! [X18650,X18651,X18652] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18652),X18651))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18650))
| 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),X18650)),X18652)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18650)),X18651))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2__lemma])]) ).
cnf(i_0_7505,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_7506,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_7507,plain,
! [X24880,X24881,X24882,X24883] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24883,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24883,tc_HOL_Obool)),X24882),X24881)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24883,tc_HOL_Obool)),X24880),X24881)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24883,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24883,tc_HOL_Obool)),X24882),X24881)),X24880),
inference(variable_rename,[status(thm)],[fact_Diff__Int2]) ).
fof(i_0_7508,plain,
! [X24854,X24855,X24856,X24857] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24857,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24857,tc_HOL_Obool)),X24856),X24855)),X24854) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24857,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24857,tc_HOL_Obool)),X24856),X24854)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24857,tc_HOL_Obool)),X24855),X24854)),
inference(variable_rename,[status(thm)],[fact_Int__Un__distrib2]) ).
fof(i_0_7509,plain,
! [X24876,X24877,X24878,X24879] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24879,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24879,tc_HOL_Obool)),X24878),X24877)),X24876) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24879,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24879,tc_HOL_Obool)),X24878),X24876)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24879,tc_HOL_Obool)),X24877),X24876)),
inference(variable_rename,[status(thm)],[fact_Diff__Int__distrib2]) ).
fof(i_0_7510,plain,
! [X24858,X24859,X24860,X24861] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24861,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24861,tc_HOL_Obool)),X24860),X24859)),X24858) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24861,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24861,tc_HOL_Obool)),X24860),X24858)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24861,tc_HOL_Obool)),X24859),X24858)),
inference(variable_rename,[status(thm)],[fact_Un__Int__distrib2]) ).
fof(i_0_7511,plain,
! [X24136,X24137,X24138,X24139] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24139,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24139,tc_HOL_Obool)),X24138),X24137)),X24136) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24139,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24139,tc_HOL_Obool)),X24138),X24136)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24139,tc_HOL_Obool)),X24137),X24136)),
inference(variable_rename,[status(thm)],[fact_Un__Diff]) ).
fof(i_0_7512,plain,
! [X26698,X26699,X26700] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk206_3(X26698,X26699,X26700)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26700)))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26699),X26700) = X26699
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26699),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26698))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26700)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk207_3(X26698,X26699,X26700)),X26698))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26699),X26700) = X26699
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26699),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26698))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26700)) )
& ( X26699 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk207_3(X26698,X26699,X26700)),esk206_3(X26698,X26699,X26700))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26699),X26700) = X26699
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26699),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26698))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26700)) ) ),
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_7513,plain,
! [X26721,X26722,X26723] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk214_3(X26721,X26722,X26723)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26723)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26722),X26723) = X26722
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26722),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26721))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26723)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk215_3(X26721,X26722,X26723)),X26721))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26722),X26723) = X26722
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26722),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26721))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26723)) )
& ( X26722 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk215_3(X26721,X26722,X26723)),esk214_3(X26721,X26722,X26723))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26722),X26723) = X26722
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26722),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26721))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26723)) ) ),
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_7514,plain,
! [X33420,X33421,X33422,X33423] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33423),X33422)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33421)),X33420)))
| hAPP(hAPP(c_List_Otake(X33421),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33423),X33422)),X33420) = hAPP(hAPP(c_List_Oappend(X33421),hAPP(hAPP(c_List_Otake(X33421),X33423),X33420)),hAPP(hAPP(c_List_Otake(X33421),X33422),hAPP(hAPP(c_List_Odrop(X33421),X33423),X33420))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__add])]) ).
fof(i_0_7515,plain,
! [X25535,X25536,X25537] :
( ( hBOOL(hAPP(hAPP(c_member(X25537),esk147_3(X25535,X25536,X25537)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25537,tc_HOL_Obool)),X25536),X25535)))
| hAPP(c_Finite__Set_Ocard(X25537),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25537,tc_HOL_Obool)),X25536),X25535)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25537),X25536)),hAPP(c_Finite__Set_Ocard(X25537),X25535))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25537),X25535))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25537),X25536)) )
& ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Finite__Set_Ocard(X25537),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25537,tc_HOL_Obool)),X25536),X25535)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25537),X25536)),hAPP(c_Finite__Set_Ocard(X25537),X25535))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25537),X25535))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25537),X25536)) ) ),
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_7516,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_7517,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_7518,plain,
! [X31640,X31641,X31642,X31643] :
( ( ~ c_Fun_Oinj__on(X31643,tc_Option_Ooption(X31642),c_Map_Omap__add(X31643,X31642,X31641,X31640),c_Map_Odom(X31643,X31642,X31640))
| c_Fun_Oinj__on(X31643,tc_Option_Ooption(X31642),X31640,c_Map_Odom(X31643,X31642,X31640)) )
& ( ~ c_Fun_Oinj__on(X31643,tc_Option_Ooption(X31642),X31640,c_Map_Odom(X31643,X31642,X31640))
| c_Fun_Oinj__on(X31643,tc_Option_Ooption(X31642),c_Map_Omap__add(X31643,X31642,X31641,X31640),c_Map_Odom(X31643,X31642,X31640)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__map__add__dom])]) ).
fof(i_0_7519,plain,
! [X25515,X25516,X25517] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25517),X25516))
| ~ hBOOL(hAPP(hAPP(c_member(X25517),X25515),X25516))
| hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X25517),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25517,tc_HOL_Obool)),X25516),hAPP(hAPP(c_Set_Oinsert(X25517),X25515),c_Orderings_Obot__class_Obot(tc_fun(X25517,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(X25517),X25516) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Suc__Diff1])]) ).
fof(i_0_7520,plain,
! [X27945,X27946,X27947,X27948,X27949,X27950] :
( ~ c_Finite__Set_Ofolding(X27950,X27949,X27948,X27947)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27950),X27946))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27950),X27945))
| hAPP(c_Fun_Ocomp(X27949,X27949,X27949,hAPP(X27947,X27945)),hAPP(X27947,X27946)) = hAPP(c_Fun_Ocomp(X27949,X27949,X27949,hAPP(X27947,X27946)),hAPP(X27947,X27945)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp_H_H])]) ).
fof(i_0_7521,plain,
! [X30913,X30914,X30915,X30916] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X30916,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30915,tc_fun(X30916,tc_HOL_Obool)),X30914),X30913)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30915,tc_fun(X30916,tc_HOL_Obool)),X30914),hAPP(hAPP(c_COMBB(tc_fun(X30916,tc_HOL_Obool),tc_fun(X30916,tc_HOL_Obool),X30915),c_Groups_Ouminus__class_Ouminus(tc_fun(X30916,tc_HOL_Obool))),X30913)),
inference(variable_rename,[status(thm)],[fact_Compl__INT]) ).
fof(i_0_7522,plain,
! [X30917,X30918,X30919,X30920] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X30920,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30919,tc_fun(X30920,tc_HOL_Obool)),X30918),X30917)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30919,tc_fun(X30920,tc_HOL_Obool)),X30918),hAPP(hAPP(c_COMBB(tc_fun(X30920,tc_HOL_Obool),tc_fun(X30920,tc_HOL_Obool),X30919),c_Groups_Ouminus__class_Ouminus(tc_fun(X30920,tc_HOL_Obool))),X30917)),
inference(variable_rename,[status(thm)],[fact_Compl__UN]) ).
fof(i_0_7523,plain,
! [X28299,X28300,X28301,X28302] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X28302,X28301,hAPP(hAPP(c_Set_Oinsert(X28302),X28300),c_Orderings_Obot__class_Obot(tc_fun(X28302,tc_HOL_Obool)))),X28299))
| X28300 = X28299 )
& ( X28300 != X28299
| hBOOL(hAPP(c_Finite__Set_Ofold1Set(X28302,X28301,hAPP(hAPP(c_Set_Oinsert(X28302),X28300),c_Orderings_Obot__class_Obot(tc_fun(X28302,tc_HOL_Obool)))),X28299)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1Set__sing])]) ).
fof(i_0_7524,plain,
! [X32498,X32499,X32500] :
( ~ class_Orderings_Olinorder(X32500)
| hBOOL(hAPP(hAPP(c_member(X32500),X32499),hAPP(c_List_Oset(X32500),X32498)))
| c_List_Olinorder__class_Oinsort__insert__key(X32500,X32500,c_COMBI(X32500),X32499,X32498) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32500,X32500,c_COMBI(X32500)),X32499),X32498) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5580])]) ).
fof(i_0_7525,plain,
! [X24429,X24430,X24431,X24432,X24433] :
( ( ~ c_Relation_Oirrefl(X24430,X24429)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24430,X24430)),hAPP(hAPP(c_Product__Type_OPair(X24430,X24430),X24431),X24431)),X24429)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X24433,X24433)),hAPP(hAPP(c_Product__Type_OPair(X24433,X24433),esk120_2(X24432,X24433)),esk120_2(X24432,X24433))),X24432))
| c_Relation_Oirrefl(X24433,X24432) ) ),
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_7526,plain,
! [X27885,X27886,X27887,X27888,X27889,X27890] :
( ~ c_Finite__Set_Ofolding(X27890,X27889,X27888,X27887)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27890),X27886))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27890),X27885))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27890,tc_HOL_Obool)),X27886),X27885) != c_Orderings_Obot__class_Obot(tc_fun(X27890,tc_HOL_Obool))
| hAPP(X27887,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27890,tc_HOL_Obool)),X27886),X27885)) = hAPP(c_Fun_Ocomp(X27889,X27889,X27889,hAPP(X27887,X27886)),hAPP(X27887,X27885)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ounion])]) ).
fof(i_0_7527,plain,
! [X19986,X19987,X19988,X19990,X19991,X19992,X19993] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19986),esk65_3(X19986,X19987,X19988))),X19987))
| X19986 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X19988,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19987),X19986))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19987),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19986),hAPP(c_Nat_OSuc,esk65_3(X19986,X19987,X19988)))))
| X19986 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X19988,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19987),X19986))) )
& ( hBOOL(hAPP(X19988,esk65_3(X19986,X19987,X19988)))
| X19986 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X19988,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19987),X19986))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19986),esk65_3(X19986,X19987,X19988))),X19987))
| hBOOL(hAPP(X19988,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X19988,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19987),X19986))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19987),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19986),hAPP(c_Nat_OSuc,esk65_3(X19986,X19987,X19988)))))
| hBOOL(hAPP(X19988,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X19988,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19987),X19986))) )
& ( hBOOL(hAPP(X19988,esk65_3(X19986,X19987,X19988)))
| hBOOL(hAPP(X19988,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X19988,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19987),X19986))) )
& ( X19990 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X19992,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X19992,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19991),X19990))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19990),X19993)),X19991))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19991),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19990),hAPP(c_Nat_OSuc,X19993))))
| ~ hBOOL(hAPP(X19992,X19993))
| hBOOL(hAPP(X19992,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19991),X19990))) ) ),
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_7528,plain,
! [X25529,X25530,X25531] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25531),X25530))
| hAPP(c_Finite__Set_Ocard(X25531),hAPP(hAPP(c_Set_Oinsert(X25531),X25529),X25530)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X25531),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25531,tc_HOL_Obool)),X25530),hAPP(hAPP(c_Set_Oinsert(X25531),X25529),c_Orderings_Obot__class_Obot(tc_fun(X25531,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oinsert__remove])]) ).
fof(i_0_7529,plain,
! [X27717,X27718,X27719,X27720,X27721,X27722,X27723,X27724,X27725] :
( hAPP(c_Fun_Ocomp(X27724,X27723,X27722,X27721),X27720) != hAPP(c_Fun_Ocomp(X27719,X27723,X27722,X27718),X27717)
| hAPP(X27721,hAPP(X27720,X27725)) = hAPP(X27718,hAPP(X27717,X27725)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__eq__elim])])]) ).
fof(i_0_7530,plain,
! [X27708,X27709,X27710,X27711,X27712,X27713,X27714,X27715,X27716] :
( hAPP(c_Fun_Ocomp(X27716,X27715,X27714,X27713),X27712) != hAPP(c_Fun_Ocomp(X27711,X27715,X27714,X27710),X27709)
| hAPP(X27713,hAPP(X27712,X27708)) = hAPP(X27710,hAPP(X27709,X27708)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__eq__dest])]) ).
fof(i_0_7531,plain,
! [X32128,X32129,X32130,X32131] :
( ~ class_Orderings_Olinorder(X32131)
| hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32131,X32131,c_COMBI(X32131)),X32130),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32131,X32131,c_COMBI(X32131)),X32129),X32128)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32131,X32131,c_COMBI(X32131)),X32129),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32131,X32131,c_COMBI(X32131)),X32130),X32128)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__left__comm])]) ).
fof(i_0_7532,plain,
! [X29397,X29398,X29399,X29400,X29401,X29402,X29403] :
( hAPP(c_Fun_Ocomp(X29403,X29402,X29401,X29400),X29399) != hAPP(c_Fun_Ocomp(X29402,X29402,X29401,c_Fun_Oid(X29402)),X29398)
| hAPP(X29400,hAPP(X29399,X29397)) = hAPP(X29398,X29397) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__eq__id__dest])]) ).
fof(i_0_7533,plain,
! [X24492,X24493,X24494,X24495] :
( ~ c_Equiv__Relations_Oequiv(X24495,X24494,X24493)
| ~ hBOOL(hAPP(hAPP(c_member(X24495),X24492),X24494))
| hBOOL(hAPP(hAPP(c_member(X24495),X24492),hAPP(c_Relation_OImage(X24495,X24495,X24493),hAPP(hAPP(c_Set_Oinsert(X24495),X24492),c_Orderings_Obot__class_Obot(tc_fun(X24495,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__self])]) ).
fof(i_0_7534,plain,
! [X28262,X28263,X28264,X28265,X28266] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X28265),hAPP(X28264,X28263)),hAPP(c_Set_Oimage(X28266,X28265,X28264),X28262)))
| hBOOL(hAPP(hAPP(c_member(X28266),X28263),X28262))
| ~ c_Fun_Oinj__on(X28266,X28265,X28264,c_Orderings_Otop__class_Otop(tc_fun(X28266,tc_HOL_Obool))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X28266),X28263),X28262))
| hBOOL(hAPP(hAPP(c_member(X28265),hAPP(X28264,X28263)),hAPP(c_Set_Oimage(X28266,X28265,X28264),X28262)))
| ~ c_Fun_Oinj__on(X28266,X28265,X28264,c_Orderings_Otop__class_Otop(tc_fun(X28266,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_7535,plain,
! [X31133,X31134,X31135,X31136,X31137] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31137)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31136,tc_HOL_Obool)),X31135),X31134))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31137),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31136,X31137),X31134),X31133)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31136,X31137),X31135),X31133))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__subset])]) ).
fof(i_0_7536,plain,
! [X26082,X26083,X26084,X26085,X26086] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X26086)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26085,tc_HOL_Obool)),X26084),X26083))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26086),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26085,X26086),X26084),X26082)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26085,X26086),X26083),X26082))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__subset])]) ).
fof(i_0_7537,plain,
! [X29630,X29631,X29632] :
( ~ c_Wellfounded_Owf(X29632,X29631)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29632,X29632)),hAPP(hAPP(c_Product__Type_OPair(X29632,X29632),X29630),X29630)),X29631)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5582])]) ).
fof(i_0_7538,plain,
! [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),X29619)),X29620)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5583])]) ).
fof(i_0_7539,plain,
! [X31664,X31665,X31666] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X31666)),hAPP(c_Set_Oimage(X31665,tc_Option_Ooption(X31666),c_Map_Omap__of(X31665,X31666,X31664)),c_Orderings_Otop__class_Otop(tc_fun(X31665,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_finite__range__map__of]) ).
fof(i_0_7540,plain,
! [X26115,X26116,X26117,X26118,X26119] :
( ( X26119 != c_Orderings_Obot__class_Obot(tc_fun(X26118,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26118,tc_fun(X26117,tc_HOL_Obool)),X26119),hAPP(hAPP(c_COMBB(tc_fun(X26117,tc_HOL_Obool),tc_fun(X26117,tc_HOL_Obool),X26118),hAPP(c_Set_Oinsert(X26117),X26116)),X26115)) = c_Orderings_Obot__class_Obot(tc_fun(X26117,tc_HOL_Obool)) )
& ( X26119 = c_Orderings_Obot__class_Obot(tc_fun(X26118,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26118,tc_fun(X26117,tc_HOL_Obool)),X26119),hAPP(hAPP(c_COMBB(tc_fun(X26117,tc_HOL_Obool),tc_fun(X26117,tc_HOL_Obool),X26118),hAPP(c_Set_Oinsert(X26117),X26116)),X26115)) = hAPP(hAPP(c_Set_Oinsert(X26117),X26116),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26118,tc_fun(X26117,tc_HOL_Obool)),X26119),X26115)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__simps_I1_J])]) ).
fof(i_0_7541,plain,
! [X26108,X26109,X26110,X26111,X26112] :
( ( X26112 != c_Orderings_Obot__class_Obot(tc_fun(X26111,tc_HOL_Obool))
| hAPP(hAPP(c_Set_Oinsert(X26110),X26109),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26111,tc_fun(X26110,tc_HOL_Obool)),X26112),X26108)) = hAPP(hAPP(c_Set_Oinsert(X26110),X26109),c_Orderings_Obot__class_Obot(tc_fun(X26110,tc_HOL_Obool))) )
& ( X26112 = c_Orderings_Obot__class_Obot(tc_fun(X26111,tc_HOL_Obool))
| hAPP(hAPP(c_Set_Oinsert(X26110),X26109),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26111,tc_fun(X26110,tc_HOL_Obool)),X26112),X26108)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26111,tc_fun(X26110,tc_HOL_Obool)),X26112),hAPP(hAPP(c_COMBB(tc_fun(X26110,tc_HOL_Obool),tc_fun(X26110,tc_HOL_Obool),X26111),hAPP(c_Set_Oinsert(X26110),X26109)),X26108)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I1_J])]) ).
cnf(i_0_7542,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_7543,plain,
! [X27205,X27206,X27207,X27208,X27209] :
( ~ class_Rings_Osemiring__0(X27209)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27209),X27208),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27207,X27209),X27206),X27205)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27207,X27209),hAPP(hAPP(c_COMBB(X27209,X27209,X27207),hAPP(c_Groups_Otimes__class_Otimes(X27209),X27208)),X27206)),X27205) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__right__distrib])]) ).
fof(i_0_7544,plain,
! [X23802,X23803,X23804,X23805,X23806] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X23806,X23805)),hAPP(X23806,X23804)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X23803,X23803)),hAPP(hAPP(c_Product__Type_OPair(X23803,X23803),X23805),X23804)),c_Wellfounded_Omlex__prod(X23803,X23806,X23802))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__less])]) ).
fof(i_0_7545,plain,
! [X28132,X28133,X28134,X28135,X28136] : hAPP(c_Set_Oimage(X28136,X28135,hAPP(hAPP(c_COMBB(X28134,X28135,X28136),X28133),X28132)),c_Orderings_Otop__class_Otop(tc_fun(X28136,tc_HOL_Obool))) = hAPP(c_Set_Oimage(X28134,X28135,X28133),hAPP(c_Set_Oimage(X28136,X28134,X28132),c_Orderings_Otop__class_Otop(tc_fun(X28136,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_range__composition]) ).
fof(i_0_7546,plain,
! [X34177,X34178,X34179,X34180] :
( ( ~ c_List_Olinorder__class_Osorted(X34178,X34177)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34179),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34178)),X34177)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34180),X34179))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X34178),hAPP(hAPP(c_List_Onth(X34178),X34177),X34180)),hAPP(hAPP(c_List_Onth(X34178),X34177),X34179)))
| ~ class_Orderings_Olinorder(X34178) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk489_2(X34177,X34178)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34178)),X34177)))
| c_List_Olinorder__class_Osorted(X34178,X34177)
| ~ class_Orderings_Olinorder(X34178) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk490_2(X34177,X34178)),esk489_2(X34177,X34178)))
| c_List_Olinorder__class_Osorted(X34178,X34177)
| ~ class_Orderings_Olinorder(X34178) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X34178),hAPP(hAPP(c_List_Onth(X34178),X34177),esk490_2(X34177,X34178))),hAPP(hAPP(c_List_Onth(X34178),X34177),esk489_2(X34177,X34178))))
| c_List_Olinorder__class_Osorted(X34178,X34177)
| ~ class_Orderings_Olinorder(X34178) ) ),
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_7547,plain,
! [X30868,X30869,X30870,X30871,X30872,X30873] :
( ~ hBOOL(hAPP(hAPP(c_member(X30873),X30872),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30871,tc_fun(X30873,tc_HOL_Obool)),X30870),X30869)))
| ~ hBOOL(hAPP(hAPP(c_member(X30871),X30868),X30870))
| hBOOL(hAPP(hAPP(c_member(X30873),X30872),hAPP(X30869,X30868))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__D])]) ).
fof(i_0_7548,plain,
! [X30862,X30863,X30864,X30865,X30866,X30867] :
( ~ hBOOL(hAPP(hAPP(c_member(X30867),X30866),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30865,tc_fun(X30867,tc_HOL_Obool)),X30864),X30863)))
| hBOOL(hAPP(hAPP(c_member(X30867),X30866),hAPP(X30863,X30862)))
| ~ hBOOL(hAPP(hAPP(c_member(X30865),X30862),X30864)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5585])]) ).
fof(i_0_7549,plain,
! [X33581,X33582,X33583] :
( ~ class_Groups_Omonoid__add(X33583)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X33583),X33582),hAPP(c_List_Ofoldl(X33583,X33583,c_Groups_Oplus__class_Oplus(X33583),c_Groups_Ozero__class_Ozero(X33583)),X33581)) = hAPP(c_List_Ofoldl(X33583,X33583,c_Groups_Oplus__class_Oplus(X33583),X33582),X33581) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__absorb0])]) ).
fof(i_0_7550,plain,
! [X32782,X32783,X32784,X32785,X32786,X32787] :
( X32787 = X32786
| hAPP(hAPP(c_List_Olist__update(X32785,hAPP(hAPP(c_List_Olist__update(X32785,X32784),X32787),X32783)),X32786),X32782) = hAPP(hAPP(c_List_Olist__update(X32785,hAPP(hAPP(c_List_Olist__update(X32785,X32784),X32786),X32782)),X32787),X32783) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__swap])]) ).
fof(i_0_7551,plain,
! [X30455,X30456,X30457] : hAPP(hAPP(c_Relation_Orel__comp(X30457,X30457,X30457),X30456),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30457,X30457),tc_HOL_Obool),X30455),X30456)) = hAPP(hAPP(c_Relation_Orel__comp(X30457,X30457,X30457),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30457,X30457),tc_HOL_Obool),X30455),X30456)),X30456),
inference(variable_rename,[status(thm)],[fact_rel__pow__commute]) ).
fof(i_0_7552,plain,
! [X34509,X34510,X34511,X34512,X34513,X34514,X34515,X34516,X34517,X34518] :
( ( X34509 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(X34511,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ epred2_3(X34511,X34510,X34509) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34509))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34513))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34513),X34509))
| X34510 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34509),X34512)),X34513)
| hBOOL(hAPP(X34511,X34512))
| ~ epred2_3(X34511,X34510,X34509) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34509),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34509),X34515))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X34515),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X34510 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34509),X34514)),X34515)
| hBOOL(hAPP(X34511,X34514))
| ~ epred2_3(X34511,X34510,X34509) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34516),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)),X34516))
| X34516 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34518,X34517,X34516) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34516),esk504_3(X34516,X34517,X34518)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34516))
| X34516 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34518,X34517,X34516) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk504_3(X34516,X34517,X34518)),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)),X34516))
| X34516 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34518,X34517,X34516) )
& ( X34517 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34516),esk503_3(X34516,X34517,X34518))),esk504_3(X34516,X34517,X34518))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34516))
| X34516 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34518,X34517,X34516) )
& ( ~ hBOOL(hAPP(X34518,esk503_3(X34516,X34517,X34518)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34516))
| X34516 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34518,X34517,X34516) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34516),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)),esk502_3(X34516,X34517,X34518)))
| X34516 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34518,X34517,X34516) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34516),esk504_3(X34516,X34517,X34518)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk502_3(X34516,X34517,X34518)))
| X34516 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34518,X34517,X34516) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk504_3(X34516,X34517,X34518)),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)),esk502_3(X34516,X34517,X34518)))
| X34516 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34518,X34517,X34516) )
& ( X34517 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34516),esk503_3(X34516,X34517,X34518))),esk504_3(X34516,X34517,X34518))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk502_3(X34516,X34517,X34518)))
| X34516 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34518,X34517,X34516) )
& ( ~ hBOOL(hAPP(X34518,esk503_3(X34516,X34517,X34518)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk502_3(X34516,X34517,X34518)))
| X34516 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34518,X34517,X34516) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34516),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk502_3(X34516,X34517,X34518)),X34516))
| X34516 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34518,X34517,X34516) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34516),esk504_3(X34516,X34517,X34518)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk502_3(X34516,X34517,X34518)),X34516))
| X34516 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34518,X34517,X34516) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk504_3(X34516,X34517,X34518)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk502_3(X34516,X34517,X34518)),X34516))
| X34516 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34518,X34517,X34516) )
& ( X34517 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34516),esk503_3(X34516,X34517,X34518))),esk504_3(X34516,X34517,X34518))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk502_3(X34516,X34517,X34518)),X34516))
| X34516 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34518,X34517,X34516) )
& ( ~ hBOOL(hAPP(X34518,esk503_3(X34516,X34517,X34518)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk502_3(X34516,X34517,X34518)),X34516))
| X34516 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34518,X34517,X34516) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34516),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X34517 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34516),esk501_3(X34516,X34517,X34518))),esk502_3(X34516,X34517,X34518))
| X34516 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34518,X34517,X34516) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34516),esk504_3(X34516,X34517,X34518)))
| X34517 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34516),esk501_3(X34516,X34517,X34518))),esk502_3(X34516,X34517,X34518))
| X34516 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34518,X34517,X34516) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk504_3(X34516,X34517,X34518)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X34517 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34516),esk501_3(X34516,X34517,X34518))),esk502_3(X34516,X34517,X34518))
| X34516 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34518,X34517,X34516) )
& ( X34517 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34516),esk503_3(X34516,X34517,X34518))),esk504_3(X34516,X34517,X34518))
| X34517 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34516),esk501_3(X34516,X34517,X34518))),esk502_3(X34516,X34517,X34518))
| X34516 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34518,X34517,X34516) )
& ( ~ hBOOL(hAPP(X34518,esk503_3(X34516,X34517,X34518)))
| X34517 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34516),esk501_3(X34516,X34517,X34518))),esk502_3(X34516,X34517,X34518))
| X34516 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34518,X34517,X34516) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34516),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X34518,esk501_3(X34516,X34517,X34518)))
| X34516 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34518,X34517,X34516) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34516),esk504_3(X34516,X34517,X34518)))
| ~ hBOOL(hAPP(X34518,esk501_3(X34516,X34517,X34518)))
| X34516 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34518,X34517,X34516) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk504_3(X34516,X34517,X34518)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X34518,esk501_3(X34516,X34517,X34518)))
| X34516 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34518,X34517,X34516) )
& ( X34517 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34516),esk503_3(X34516,X34517,X34518))),esk504_3(X34516,X34517,X34518))
| ~ hBOOL(hAPP(X34518,esk501_3(X34516,X34517,X34518)))
| X34516 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34518,X34517,X34516) )
& ( ~ hBOOL(hAPP(X34518,esk503_3(X34516,X34517,X34518)))
| ~ hBOOL(hAPP(X34518,esk501_3(X34516,X34517,X34518)))
| X34516 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X34518,X34517,X34516) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34516),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)),X34516))
| ~ hBOOL(hAPP(X34518,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34518,X34517,X34516) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34516),esk504_3(X34516,X34517,X34518)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34516))
| ~ hBOOL(hAPP(X34518,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34518,X34517,X34516) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk504_3(X34516,X34517,X34518)),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)),X34516))
| ~ hBOOL(hAPP(X34518,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34518,X34517,X34516) )
& ( X34517 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34516),esk503_3(X34516,X34517,X34518))),esk504_3(X34516,X34517,X34518))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34516))
| ~ hBOOL(hAPP(X34518,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34518,X34517,X34516) )
& ( ~ hBOOL(hAPP(X34518,esk503_3(X34516,X34517,X34518)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34516))
| ~ hBOOL(hAPP(X34518,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34518,X34517,X34516) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34516),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)),esk502_3(X34516,X34517,X34518)))
| ~ hBOOL(hAPP(X34518,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34518,X34517,X34516) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34516),esk504_3(X34516,X34517,X34518)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk502_3(X34516,X34517,X34518)))
| ~ hBOOL(hAPP(X34518,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34518,X34517,X34516) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk504_3(X34516,X34517,X34518)),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)),esk502_3(X34516,X34517,X34518)))
| ~ hBOOL(hAPP(X34518,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34518,X34517,X34516) )
& ( X34517 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34516),esk503_3(X34516,X34517,X34518))),esk504_3(X34516,X34517,X34518))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk502_3(X34516,X34517,X34518)))
| ~ hBOOL(hAPP(X34518,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34518,X34517,X34516) )
& ( ~ hBOOL(hAPP(X34518,esk503_3(X34516,X34517,X34518)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk502_3(X34516,X34517,X34518)))
| ~ hBOOL(hAPP(X34518,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34518,X34517,X34516) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34516),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk502_3(X34516,X34517,X34518)),X34516))
| ~ hBOOL(hAPP(X34518,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34518,X34517,X34516) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34516),esk504_3(X34516,X34517,X34518)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk502_3(X34516,X34517,X34518)),X34516))
| ~ hBOOL(hAPP(X34518,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34518,X34517,X34516) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk504_3(X34516,X34517,X34518)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk502_3(X34516,X34517,X34518)),X34516))
| ~ hBOOL(hAPP(X34518,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34518,X34517,X34516) )
& ( X34517 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34516),esk503_3(X34516,X34517,X34518))),esk504_3(X34516,X34517,X34518))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk502_3(X34516,X34517,X34518)),X34516))
| ~ hBOOL(hAPP(X34518,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34518,X34517,X34516) )
& ( ~ hBOOL(hAPP(X34518,esk503_3(X34516,X34517,X34518)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk502_3(X34516,X34517,X34518)),X34516))
| ~ hBOOL(hAPP(X34518,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34518,X34517,X34516) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34516),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X34517 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34516),esk501_3(X34516,X34517,X34518))),esk502_3(X34516,X34517,X34518))
| ~ hBOOL(hAPP(X34518,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34518,X34517,X34516) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34516),esk504_3(X34516,X34517,X34518)))
| X34517 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34516),esk501_3(X34516,X34517,X34518))),esk502_3(X34516,X34517,X34518))
| ~ hBOOL(hAPP(X34518,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34518,X34517,X34516) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk504_3(X34516,X34517,X34518)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X34517 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34516),esk501_3(X34516,X34517,X34518))),esk502_3(X34516,X34517,X34518))
| ~ hBOOL(hAPP(X34518,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34518,X34517,X34516) )
& ( X34517 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34516),esk503_3(X34516,X34517,X34518))),esk504_3(X34516,X34517,X34518))
| X34517 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34516),esk501_3(X34516,X34517,X34518))),esk502_3(X34516,X34517,X34518))
| ~ hBOOL(hAPP(X34518,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34518,X34517,X34516) )
& ( ~ hBOOL(hAPP(X34518,esk503_3(X34516,X34517,X34518)))
| X34517 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34516),esk501_3(X34516,X34517,X34518))),esk502_3(X34516,X34517,X34518))
| ~ hBOOL(hAPP(X34518,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34518,X34517,X34516) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34516),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X34518,esk501_3(X34516,X34517,X34518)))
| ~ hBOOL(hAPP(X34518,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34518,X34517,X34516) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34516),esk504_3(X34516,X34517,X34518)))
| ~ hBOOL(hAPP(X34518,esk501_3(X34516,X34517,X34518)))
| ~ hBOOL(hAPP(X34518,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34518,X34517,X34516) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk504_3(X34516,X34517,X34518)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X34518,esk501_3(X34516,X34517,X34518)))
| ~ hBOOL(hAPP(X34518,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34518,X34517,X34516) )
& ( X34517 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34516),esk503_3(X34516,X34517,X34518))),esk504_3(X34516,X34517,X34518))
| ~ hBOOL(hAPP(X34518,esk501_3(X34516,X34517,X34518)))
| ~ hBOOL(hAPP(X34518,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34518,X34517,X34516) )
& ( ~ hBOOL(hAPP(X34518,esk503_3(X34516,X34517,X34518)))
| ~ hBOOL(hAPP(X34518,esk501_3(X34516,X34517,X34518)))
| ~ hBOOL(hAPP(X34518,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X34518,X34517,X34516) ) ),
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_7553,plain,
! [X25503,X25504,X25505] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25505),X25504))
| hAPP(c_Finite__Set_Ocard(X25505),hAPP(hAPP(c_Set_Oinsert(X25505),X25503),X25504)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X25505),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25505,tc_HOL_Obool)),X25504),hAPP(hAPP(c_Set_Oinsert(X25505),X25503),c_Orderings_Obot__class_Obot(tc_fun(X25505,tc_HOL_Obool)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__insert])]) ).
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__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_5586]) ).
cnf(i_0_7555,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_7556,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_7557,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_7558,plain,
! [X21786,X21787,X21788,X21789] :
( ~ class_Fields_Olinordered__field(X21789)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),X21788),X21787))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),c_Groups_Ozero__class_Ozero(X21789)),X21786))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21789),c_Groups_Ozero__class_Ozero(X21789)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21789),X21787),X21788)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21789),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21789),X21786),X21787)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21789),X21786),X21788))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__left__mono])]) ).
fof(i_0_7559,plain,
! [X21650,X21651,X21652,X21653] :
( ~ class_Fields_Olinordered__field(X21653)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21653),X21652),X21651))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21653),c_Groups_Ozero__class_Ozero(X21653)),X21650))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21653),c_Groups_Ozero__class_Ozero(X21653)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21653),X21651),X21652)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21653),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21653),X21650),X21651)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21653),X21650),X21652))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__left__mono])]) ).
fof(i_0_7560,plain,
! [X24449,X24450,X24451] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X24451,X24451),tc_HOL_Obool)),X24450),X24449))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24451,tc_HOL_Obool)),hAPP(c_Relation_OField(X24451),X24450)),hAPP(c_Relation_OField(X24451),X24449))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mono__Field])]) ).
fof(i_0_7561,plain,
! [X27959,X27960,X27961,X27962,X27963,X27964] :
( ~ c_Finite__Set_Ofolding(X27964,X27963,X27962,X27961)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27964),X27960))
| hAPP(c_Fun_Ocomp(X27963,X27963,X27963,hAPP(X27962,X27959)),hAPP(X27961,X27960)) = hAPP(c_Fun_Ocomp(X27963,X27963,X27963,hAPP(X27961,X27960)),hAPP(X27962,X27959)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp_H])]) ).
fof(i_0_7562,plain,
! [X34495,X34496,X34497,X34498,X34499,X34500,X34501,X34502,X34503,X34504] :
( ( X34495 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(X34497,X34496))
| ~ epred1_3(X34497,X34496,X34495) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34495))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34499))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34499),X34495))
| X34496 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34495),X34498)),X34499)
| hBOOL(hAPP(X34497,X34499))
| ~ epred1_3(X34497,X34496,X34495) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34495),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34495),X34501))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X34501),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X34496 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34495),X34500)),X34501)
| hBOOL(hAPP(X34497,X34501))
| ~ epred1_3(X34497,X34496,X34495) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34502),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)),X34502))
| X34502 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34504,X34503,X34502) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34502),esk500_3(X34502,X34503,X34504)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34502))
| X34502 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34504,X34503,X34502) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk500_3(X34502,X34503,X34504)),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)),X34502))
| X34502 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34504,X34503,X34502) )
& ( X34503 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34502),esk499_3(X34502,X34503,X34504))),esk500_3(X34502,X34503,X34504))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34502))
| X34502 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34504,X34503,X34502) )
& ( ~ hBOOL(hAPP(X34504,esk500_3(X34502,X34503,X34504)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34502))
| X34502 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34504,X34503,X34502) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34502),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)),esk498_3(X34502,X34503,X34504)))
| X34502 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34504,X34503,X34502) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34502),esk500_3(X34502,X34503,X34504)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk498_3(X34502,X34503,X34504)))
| X34502 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34504,X34503,X34502) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk500_3(X34502,X34503,X34504)),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)),esk498_3(X34502,X34503,X34504)))
| X34502 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34504,X34503,X34502) )
& ( X34503 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34502),esk499_3(X34502,X34503,X34504))),esk500_3(X34502,X34503,X34504))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk498_3(X34502,X34503,X34504)))
| X34502 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34504,X34503,X34502) )
& ( ~ hBOOL(hAPP(X34504,esk500_3(X34502,X34503,X34504)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk498_3(X34502,X34503,X34504)))
| X34502 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34504,X34503,X34502) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34502),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk498_3(X34502,X34503,X34504)),X34502))
| X34502 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34504,X34503,X34502) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34502),esk500_3(X34502,X34503,X34504)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk498_3(X34502,X34503,X34504)),X34502))
| X34502 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34504,X34503,X34502) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk500_3(X34502,X34503,X34504)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk498_3(X34502,X34503,X34504)),X34502))
| X34502 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34504,X34503,X34502) )
& ( X34503 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34502),esk499_3(X34502,X34503,X34504))),esk500_3(X34502,X34503,X34504))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk498_3(X34502,X34503,X34504)),X34502))
| X34502 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34504,X34503,X34502) )
& ( ~ hBOOL(hAPP(X34504,esk500_3(X34502,X34503,X34504)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk498_3(X34502,X34503,X34504)),X34502))
| X34502 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34504,X34503,X34502) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34502),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X34503 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34502),esk497_3(X34502,X34503,X34504))),esk498_3(X34502,X34503,X34504))
| X34502 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34504,X34503,X34502) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34502),esk500_3(X34502,X34503,X34504)))
| X34503 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34502),esk497_3(X34502,X34503,X34504))),esk498_3(X34502,X34503,X34504))
| X34502 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34504,X34503,X34502) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk500_3(X34502,X34503,X34504)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X34503 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34502),esk497_3(X34502,X34503,X34504))),esk498_3(X34502,X34503,X34504))
| X34502 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34504,X34503,X34502) )
& ( X34503 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34502),esk499_3(X34502,X34503,X34504))),esk500_3(X34502,X34503,X34504))
| X34503 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34502),esk497_3(X34502,X34503,X34504))),esk498_3(X34502,X34503,X34504))
| X34502 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34504,X34503,X34502) )
& ( ~ hBOOL(hAPP(X34504,esk500_3(X34502,X34503,X34504)))
| X34503 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34502),esk497_3(X34502,X34503,X34504))),esk498_3(X34502,X34503,X34504))
| X34502 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34504,X34503,X34502) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34502),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X34504,esk498_3(X34502,X34503,X34504)))
| X34502 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34504,X34503,X34502) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34502),esk500_3(X34502,X34503,X34504)))
| ~ hBOOL(hAPP(X34504,esk498_3(X34502,X34503,X34504)))
| X34502 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34504,X34503,X34502) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk500_3(X34502,X34503,X34504)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X34504,esk498_3(X34502,X34503,X34504)))
| X34502 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34504,X34503,X34502) )
& ( X34503 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34502),esk499_3(X34502,X34503,X34504))),esk500_3(X34502,X34503,X34504))
| ~ hBOOL(hAPP(X34504,esk498_3(X34502,X34503,X34504)))
| X34502 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34504,X34503,X34502) )
& ( ~ hBOOL(hAPP(X34504,esk500_3(X34502,X34503,X34504)))
| ~ hBOOL(hAPP(X34504,esk498_3(X34502,X34503,X34504)))
| X34502 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X34504,X34503,X34502) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34502),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)),X34502))
| ~ hBOOL(hAPP(X34504,X34503))
| epred1_3(X34504,X34503,X34502) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34502),esk500_3(X34502,X34503,X34504)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34502))
| ~ hBOOL(hAPP(X34504,X34503))
| epred1_3(X34504,X34503,X34502) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk500_3(X34502,X34503,X34504)),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)),X34502))
| ~ hBOOL(hAPP(X34504,X34503))
| epred1_3(X34504,X34503,X34502) )
& ( X34503 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34502),esk499_3(X34502,X34503,X34504))),esk500_3(X34502,X34503,X34504))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34502))
| ~ hBOOL(hAPP(X34504,X34503))
| epred1_3(X34504,X34503,X34502) )
& ( ~ hBOOL(hAPP(X34504,esk500_3(X34502,X34503,X34504)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34502))
| ~ hBOOL(hAPP(X34504,X34503))
| epred1_3(X34504,X34503,X34502) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34502),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)),esk498_3(X34502,X34503,X34504)))
| ~ hBOOL(hAPP(X34504,X34503))
| epred1_3(X34504,X34503,X34502) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34502),esk500_3(X34502,X34503,X34504)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk498_3(X34502,X34503,X34504)))
| ~ hBOOL(hAPP(X34504,X34503))
| epred1_3(X34504,X34503,X34502) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk500_3(X34502,X34503,X34504)),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)),esk498_3(X34502,X34503,X34504)))
| ~ hBOOL(hAPP(X34504,X34503))
| epred1_3(X34504,X34503,X34502) )
& ( X34503 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34502),esk499_3(X34502,X34503,X34504))),esk500_3(X34502,X34503,X34504))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk498_3(X34502,X34503,X34504)))
| ~ hBOOL(hAPP(X34504,X34503))
| epred1_3(X34504,X34503,X34502) )
& ( ~ hBOOL(hAPP(X34504,esk500_3(X34502,X34503,X34504)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk498_3(X34502,X34503,X34504)))
| ~ hBOOL(hAPP(X34504,X34503))
| epred1_3(X34504,X34503,X34502) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34502),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk498_3(X34502,X34503,X34504)),X34502))
| ~ hBOOL(hAPP(X34504,X34503))
| epred1_3(X34504,X34503,X34502) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34502),esk500_3(X34502,X34503,X34504)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk498_3(X34502,X34503,X34504)),X34502))
| ~ hBOOL(hAPP(X34504,X34503))
| epred1_3(X34504,X34503,X34502) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk500_3(X34502,X34503,X34504)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk498_3(X34502,X34503,X34504)),X34502))
| ~ hBOOL(hAPP(X34504,X34503))
| epred1_3(X34504,X34503,X34502) )
& ( X34503 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34502),esk499_3(X34502,X34503,X34504))),esk500_3(X34502,X34503,X34504))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk498_3(X34502,X34503,X34504)),X34502))
| ~ hBOOL(hAPP(X34504,X34503))
| epred1_3(X34504,X34503,X34502) )
& ( ~ hBOOL(hAPP(X34504,esk500_3(X34502,X34503,X34504)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk498_3(X34502,X34503,X34504)),X34502))
| ~ hBOOL(hAPP(X34504,X34503))
| epred1_3(X34504,X34503,X34502) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34502),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X34503 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34502),esk497_3(X34502,X34503,X34504))),esk498_3(X34502,X34503,X34504))
| ~ hBOOL(hAPP(X34504,X34503))
| epred1_3(X34504,X34503,X34502) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34502),esk500_3(X34502,X34503,X34504)))
| X34503 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34502),esk497_3(X34502,X34503,X34504))),esk498_3(X34502,X34503,X34504))
| ~ hBOOL(hAPP(X34504,X34503))
| epred1_3(X34504,X34503,X34502) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk500_3(X34502,X34503,X34504)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X34503 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34502),esk497_3(X34502,X34503,X34504))),esk498_3(X34502,X34503,X34504))
| ~ hBOOL(hAPP(X34504,X34503))
| epred1_3(X34504,X34503,X34502) )
& ( X34503 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34502),esk499_3(X34502,X34503,X34504))),esk500_3(X34502,X34503,X34504))
| X34503 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34502),esk497_3(X34502,X34503,X34504))),esk498_3(X34502,X34503,X34504))
| ~ hBOOL(hAPP(X34504,X34503))
| epred1_3(X34504,X34503,X34502) )
& ( ~ hBOOL(hAPP(X34504,esk500_3(X34502,X34503,X34504)))
| X34503 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34502),esk497_3(X34502,X34503,X34504))),esk498_3(X34502,X34503,X34504))
| ~ hBOOL(hAPP(X34504,X34503))
| epred1_3(X34504,X34503,X34502) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34502),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X34504,esk498_3(X34502,X34503,X34504)))
| ~ hBOOL(hAPP(X34504,X34503))
| epred1_3(X34504,X34503,X34502) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34502),esk500_3(X34502,X34503,X34504)))
| ~ hBOOL(hAPP(X34504,esk498_3(X34502,X34503,X34504)))
| ~ hBOOL(hAPP(X34504,X34503))
| epred1_3(X34504,X34503,X34502) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk500_3(X34502,X34503,X34504)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X34504,esk498_3(X34502,X34503,X34504)))
| ~ hBOOL(hAPP(X34504,X34503))
| epred1_3(X34504,X34503,X34502) )
& ( X34503 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34502),esk499_3(X34502,X34503,X34504))),esk500_3(X34502,X34503,X34504))
| ~ hBOOL(hAPP(X34504,esk498_3(X34502,X34503,X34504)))
| ~ hBOOL(hAPP(X34504,X34503))
| epred1_3(X34504,X34503,X34502) )
& ( ~ hBOOL(hAPP(X34504,esk500_3(X34502,X34503,X34504)))
| ~ hBOOL(hAPP(X34504,esk498_3(X34502,X34503,X34504)))
| ~ hBOOL(hAPP(X34504,X34503))
| epred1_3(X34504,X34503,X34502) ) ),
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_7563,plain,
! [X31030,X31031,X31032,X31033,X31034] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31034,tc_fun(X31033,tc_HOL_Obool)),X31032),hAPP(hAPP(c_COMBB(tc_fun(X31033,tc_HOL_Obool),tc_fun(X31033,tc_HOL_Obool),X31034),hAPP(c_Set_Oinsert(X31033),X31031)),X31030)) = hAPP(hAPP(c_Set_Oinsert(X31033),X31031),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31034,tc_fun(X31033,tc_HOL_Obool)),X31032),X31030)),
inference(variable_rename,[status(thm)],[fact_INT__simps_I5_J]) ).
fof(i_0_7564,plain,
! [X31035,X31036,X31037,X31038,X31039] : hAPP(hAPP(c_Set_Oinsert(X31039),X31038),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31037,tc_fun(X31039,tc_HOL_Obool)),X31036),X31035)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31037,tc_fun(X31039,tc_HOL_Obool)),X31036),hAPP(hAPP(c_COMBB(tc_fun(X31039,tc_HOL_Obool),tc_fun(X31039,tc_HOL_Obool),X31037),hAPP(c_Set_Oinsert(X31039),X31038)),X31035)),
inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I5_J]) ).
fof(i_0_7565,plain,
! [X19759,X19760,X19761,X19762] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19762),X19761)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19760),X19761)),X19759)) = 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),X19762),X19760)),X19761)),X19759),
inference(variable_rename,[status(thm)],[fact_left__add__mult__distrib]) ).
fof(i_0_7566,plain,
! [X34375,X34376,X34377,X34378,X34379] : hAPP(hAPP(c_List_Ozip(X34379,X34378),X34377),c_List_OtakeWhile(X34378,X34376,X34375)) = c_List_OtakeWhile(tc_prod(X34379,X34378),hAPP(c_Fun_Ocomp(X34378,tc_HOL_Obool,tc_prod(X34379,X34378),X34376),c_Product__Type_Osnd(X34379,X34378)),hAPP(hAPP(c_List_Ozip(X34379,X34378),X34377),X34375)),
inference(variable_rename,[status(thm)],[fact_zip__takeWhile__snd]) ).
cnf(i_0_7567,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_7568,plain,
! [X31895,X31896,X31897,X31898,X31899] : hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(X31899),tc_Option_Ooption(X31898),X31897,hAPP(c_Option_Omap(X31899,X31898),X31896)),hAPP(c_COMBK(tc_Option_Ooption(X31899),X31897),c_Option_Ooption_ONone(X31899))),X31895) = c_Option_Ooption_ONone(X31898),
inference(variable_rename,[status(thm)],[fact_option__map__o__empty]) ).
fof(i_0_7569,plain,
! [X22906,X22907,X22908,X22909,X22910] :
( ( X22910 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| hAPP(c_New__DSequence_Oneg__decr__bind(X22909,X22908,X22907,X22906),X22910) = c_Lazy__Sequence_Ohit__bound(X22908) )
& ( X22910 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| hAPP(c_New__DSequence_Oneg__decr__bind(X22909,X22908,X22907,X22906),X22910) = c_Lazy__Sequence_Ohb__bind(X22909,X22908,hAPP(X22907,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X22910),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X22909,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X22908))),X22906),X22910)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_New__DSequence_Oneg__decr__bind__def])]) ).
fof(i_0_7570,plain,
! [X28252,X28253,X28254,X28255] :
( ~ c_Fun_Oinj__on(X28255,X28254,X28253,c_Orderings_Otop__class_Otop(tc_fun(X28255,tc_HOL_Obool)))
| c_Fun_Oinj__on(X28255,tc_fun(X28252,X28254),hAPP(hAPP(c_COMBB(X28254,tc_fun(X28252,X28254),X28255),c_COMBK(X28254,X28252)),X28253),c_Orderings_Otop__class_Otop(tc_fun(X28255,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__fun])]) ).
fof(i_0_7571,plain,
! [X27022,X27023,X27024,X27025,X27026,X27027] :
( ~ c_Fun_Oinj__on(X27027,X27026,X27025,X27024)
| hBOOL(hAPP(hAPP(c_member(X27026),X27023),hAPP(c_Set_Oimage(X27027,X27026,X27025),X27024)))
| c_Fun_Oinj__on(X27027,X27026,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27027,X27026),X27025),X27022),X27023),X27024) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5591])]) ).
fof(i_0_7572,plain,
! [X31403,X31404,X31405] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31405,tc_HOL_Obool)),X31404),X31403) = c_Complete__Lattice_OInf__class_OInf(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_Int__eq__Inter]) ).
fof(i_0_7573,plain,
! [X31392,X31393,X31394] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31394,tc_HOL_Obool)),X31393),X31392) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X31394,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X31394,tc_HOL_Obool)),X31393),hAPP(hAPP(c_Set_Oinsert(tc_fun(X31394,tc_HOL_Obool)),X31392),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X31394,tc_HOL_Obool),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_Un__eq__Union]) ).
fof(i_0_7574,plain,
! [X21790,X21791,X21792,X21793] :
( ~ class_Fields_Olinordered__field__inverse__zero(X21793)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),X21792),X21791))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),X21790),c_Groups_Ozero__class_Ozero(X21793)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21793),c_Groups_Ozero__class_Ozero(X21793)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21793),X21792),X21791)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21793),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21793),X21790),X21792)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21793),X21790),X21791))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__left__mono__neg])]) ).
fof(i_0_7575,plain,
! [X21646,X21647,X21648,X21649] :
( ~ class_Fields_Olinordered__field(X21649)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21649),X21648),X21647))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21649),X21646),c_Groups_Ozero__class_Ozero(X21649)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21649),c_Groups_Ozero__class_Ozero(X21649)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21649),X21648),X21647)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21649),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21649),X21646),X21648)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21649),X21646),X21647))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__left__mono__neg])]) ).
fof(i_0_7576,plain,
! [X32511,X32512,X32513,X32514,X32515] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32515),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32514)),X32513)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32515),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32512)),X32511)))
| hAPP(hAPP(c_List_Onth(tc_prod(X32514,X32512)),hAPP(hAPP(c_List_Ozip(X32514,X32512),X32513),X32511)),X32515) = hAPP(hAPP(c_Product__Type_OPair(X32514,X32512),hAPP(hAPP(c_List_Onth(X32514),X32513),X32515)),hAPP(hAPP(c_List_Onth(X32512),X32511),X32515)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__zip])]) ).
fof(i_0_7577,plain,
! [X20004,X20005,X20006] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20006,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20005),X20004)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20005),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20006),X20005),X20004))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20006,X20005)),
inference(variable_rename,[status(thm)],[fact_mod__mult2__eq]) ).
fof(i_0_7578,plain,
! [X26764,X26765,X26766] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26766),X26765))
| 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)),X26766)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26764),X26765)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X26764),X26766)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X26765),X26766)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26764),X26765))
| 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)),X26766)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26764),X26765)) = 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),X26766),X26765)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26764),X26765))
| 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)),X26766)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26764),X26765)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26766),X26765)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5592])])]) ).
cnf(i_0_7579,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_7580,plain,
! [X33049,X33050,X33051,X33052,X33053] : hAPP(hAPP(c_List_Olist__update(X33053,hAPP(hAPP(c_List_Oappend(X33053),X33052),hAPP(hAPP(c_List_Olist_OCons(X33053),X33051),X33050))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33053)),X33052)),X33049) = hAPP(hAPP(c_List_Oappend(X33053),X33052),hAPP(hAPP(c_List_Olist_OCons(X33053),X33049),X33050)),
inference(variable_rename,[status(thm)],[fact_list__update__length]) ).
cnf(i_0_7581,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_7582,plain,
! [X33205,X33206] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X33206),tc_List_Olist(X33206)),tc_HOL_Obool)),c_List_Olistrel1(X33206,c_Transitive__Closure_Ortrancl(X33206,X33205))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X33206),c_List_Olistrel1(X33206,X33205)))),
inference(variable_rename,[status(thm)],[fact_listrel1__rtrancl__subset__rtrancl__listrel1]) ).
fof(i_0_7583,plain,
! [X30225,X30226,X30227] : c_Transitive__Closure_Ortrancl(X30227,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30227,X30227),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X30227,X30226)),c_Transitive__Closure_Ortrancl(X30227,X30225))) = c_Transitive__Closure_Ortrancl(X30227,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30227,X30227),tc_HOL_Obool)),X30226),X30225)),
inference(variable_rename,[status(thm)],[fact_rtrancl__Un__rtrancl]) ).
fof(i_0_7584,plain,
! [X23127,X23128,X23129,X23130] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23130),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23130),X23128),X23129)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23130),X23127),X23129)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23130),X23128),X23127))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23130),X23129),X23127))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23130),X23129),X23128))
| ~ class_Divides_Osemiring__div(X23130) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23130),X23128),X23127))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23130),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23130),X23128),X23129)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23130),X23127),X23129)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23130),X23129),X23127))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23130),X23129),X23128))
| ~ class_Divides_Osemiring__div(X23130) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__dvd__div])])]) ).
cnf(i_0_7585,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_7586,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_7587,plain,
! [X23420,X23421,X23422,X23423,X23425] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23422),X23420),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23422),esk100_3(X23420,X23421,X23422)),c_Groups_Ozero__class_Ozero(X23422))))
| ~ hBOOL(hAPP(X23421,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23422),X23420),X23423)))
| ~ class_Rings_Odvd(X23422)
| ~ class_Rings_Osemiring__0(X23422) )
& ( hBOOL(hAPP(X23421,esk100_3(X23420,X23421,X23422)))
| ~ hBOOL(hAPP(X23421,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23422),X23420),X23423)))
| ~ class_Rings_Odvd(X23422)
| ~ class_Rings_Osemiring__0(X23422) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23422),X23420),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23422),X23425),c_Groups_Ozero__class_Ozero(X23422))))
| ~ hBOOL(hAPP(X23421,X23425))
| hBOOL(hAPP(X23421,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23422),X23420),esk101_3(X23420,X23421,X23422))))
| ~ class_Rings_Odvd(X23422)
| ~ class_Rings_Osemiring__0(X23422) ) ),
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_7588,plain,
! [X32047,X32048,X32049] : hAPP(hAPP(c_List_Ozip(X32049,X32048),hAPP(hAPP(c_List_Omap(tc_prod(X32049,X32048),X32049),c_Product__Type_Ofst(X32049,X32048)),X32047)),hAPP(hAPP(c_List_Omap(tc_prod(X32049,X32048),X32048),c_Product__Type_Osnd(X32049,X32048)),X32047)) = X32047,
inference(variable_rename,[status(thm)],[fact_zip__map__fst__snd]) ).
fof(i_0_7589,plain,
! [X27823,X27824,X27825,X27826,X27827,X27828,X27829,X27830] :
( ~ class_Groups_Ocomm__monoid__mult(X27830)
| ~ c_Fun_Oinj__on(X27829,X27828,X27827,X27826)
| X27825 != hAPP(c_Set_Oimage(X27829,X27828,X27827),X27826)
| X27824 != hAPP(c_Fun_Ocomp(X27828,X27830,X27829,X27823),X27827)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27828,X27830),X27823),X27825) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27829,X27830),X27824),X27826) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__reindex__cong])]) ).
fof(i_0_7590,plain,
! [X19642,X19643,X19644] :
( ~ class_Rings_Olinordered__ring(X19644)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19644),c_Groups_Ozero__class_Ozero(X19644)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19644),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19644),X19643),X19643)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19644),X19642),X19642)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__ge__zero])]) ).
fof(i_0_7591,plain,
! [X30314,X30315] :
( ( ~ 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),X30315),X30314)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30315),X30314)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30315),X30314))
| 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),X30315),X30314)),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_7592,plain,
! [X27902,X27903,X27904,X27905,X27906,X27907] :
( ~ c_Finite__Set_Ofolding(X27907,X27906,X27905,X27904)
| hAPP(c_Fun_Ocomp(X27906,X27906,X27906,hAPP(X27905,X27903)),hAPP(X27905,X27902)) = hAPP(c_Fun_Ocomp(X27906,X27906,X27906,hAPP(X27905,X27902)),hAPP(X27905,X27903)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp])]) ).
fof(i_0_7593,plain,
! [X28693,X28694,X28695,X28696,X28697] : hAPP(hAPP(c_Product__Type_OSigma(X28697,X28696),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28697,tc_HOL_Obool)),X28695),X28694)),X28693) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X28697,X28696),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28697,X28696),X28695),X28693)),hAPP(hAPP(c_Product__Type_OSigma(X28697,X28696),X28694),X28693)),
inference(variable_rename,[status(thm)],[fact_Sigma__Int__distrib1]) ).
fof(i_0_7594,plain,
! [X28660,X28661,X28662,X28663,X28664] : hAPP(hAPP(c_Product__Type_OSigma(X28664,X28663),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28664,tc_HOL_Obool)),X28662),X28661)),X28660) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28664,X28663),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28664,X28663),X28662),X28660)),hAPP(hAPP(c_Product__Type_OSigma(X28664,X28663),X28661),X28660)),
inference(variable_rename,[status(thm)],[fact_Sigma__Un__distrib1]) ).
fof(i_0_7595,plain,
! [X28626,X28627,X28628,X28629,X28630] : hAPP(hAPP(c_Product__Type_OSigma(X28630,X28629),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28630,tc_HOL_Obool)),X28628),X28627)),X28626) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X28630,X28629),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28630,X28629),X28628),X28626)),hAPP(hAPP(c_Product__Type_OSigma(X28630,X28629),X28627),X28626)),
inference(variable_rename,[status(thm)],[fact_Sigma__Diff__distrib1]) ).
fof(i_0_7596,plain,
! [X33817,X33818,X33819,X33820] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X33820),X33819),hAPP(c_List_Oset(X33820),c_List_Obutlast(X33820,X33818))))
| hBOOL(hAPP(hAPP(c_member(X33820),X33819),hAPP(c_List_Oset(X33820),c_List_Obutlast(X33820,hAPP(hAPP(c_List_Oappend(X33820),X33818),X33817))))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X33820),X33819),hAPP(c_List_Oset(X33820),c_List_Obutlast(X33820,X33817))))
| hBOOL(hAPP(hAPP(c_member(X33820),X33819),hAPP(c_List_Oset(X33820),c_List_Obutlast(X33820,hAPP(hAPP(c_List_Oappend(X33820),X33818),X33817))))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__butlast__appendI])])]) ).
fof(i_0_7597,plain,
! [X24489,X24490,X24491] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X24491,X24491),tc_HOL_Obool)),X24490),X24489))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24491,tc_HOL_Obool)),c_Wellfounded_Oacc(X24491,X24489)),c_Wellfounded_Oacc(X24491,X24490))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__subset])]) ).
fof(i_0_7598,plain,
! [X32132,X32133,X32134,X32135,X32136,X32137] :
( ~ class_Orderings_Olinorder(X32137)
| hAPP(X32136,X32135) = hAPP(X32136,X32134)
| hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32133,X32137,X32136),X32134),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32133,X32137,X32136),X32135),X32132)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32133,X32137,X32136),X32135),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32133,X32137,X32136),X32134),X32132)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__key__left__comm])]) ).
fof(i_0_7599,plain,
! [X31936,X31937,X31938,X31939,X31940] :
( hAPP(c_Map_Omap__of(X31940,X31939,X31938),X31937) != hAPP(c_Option_Ooption_OSome(X31939),X31936)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X31940,X31939)),hAPP(hAPP(c_Product__Type_OPair(X31940,X31939),X31937),X31936)),hAPP(c_List_Oset(tc_prod(X31940,X31939)),X31938))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__SomeD])]) ).
fof(i_0_7600,plain,
! [X31931,X31932,X31933,X31934,X31935] :
( hAPP(c_Map_Omap__of(X31935,X31934,X31933),X31932) != hAPP(c_Option_Ooption_OSome(X31934),X31931)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X31935,X31934)),hAPP(hAPP(c_Product__Type_OPair(X31935,X31934),X31932),X31931)),hAPP(c_List_Oset(tc_prod(X31935,X31934)),X31933))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__is__SomeD])]) ).
fof(i_0_7601,plain,
! [X32032,X32033,X32034,X32035,X32036] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X32036),X32035),hAPP(c_List_Oset(X32036),X32034)))
| hAPP(c_Map_Omap__of(X32036,X32033,hAPP(hAPP(c_List_Ozip(X32036,X32033),X32034),hAPP(hAPP(c_List_Omap(X32036,X32033),X32032),X32034))),X32035) = hAPP(c_Option_Ooption_OSome(X32033),hAPP(X32032,X32035)) )
& ( hBOOL(hAPP(hAPP(c_member(X32036),X32035),hAPP(c_List_Oset(X32036),X32034)))
| hAPP(c_Map_Omap__of(X32036,X32033,hAPP(hAPP(c_List_Ozip(X32036,X32033),X32034),hAPP(hAPP(c_List_Omap(X32036,X32033),X32032),X32034))),X32035) = c_Option_Ooption_ONone(X32033) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5597])]) ).
fof(i_0_7602,plain,
! [X22241,X22242] :
( X22242 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22241,X22242),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22241),X22242)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X22241,X22242)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__div__mod])]) ).
fof(i_0_7603,plain,
! [X31002,X31003,X31004,X31005,X31006,X31007] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31007,tc_fun(X31006,tc_HOL_Obool)),X31005),hAPP(hAPP(c_COMBB(X31004,tc_fun(X31006,tc_HOL_Obool),X31007),X31003),X31002)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31004,tc_fun(X31006,tc_HOL_Obool)),hAPP(c_Set_Oimage(X31007,X31004,X31002),X31005)),X31003),
inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I10_J]) ).
fof(i_0_7604,plain,
! [X26018,X26019,X26020,X26021,X26022,X26023] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26023,tc_fun(X26022,tc_HOL_Obool)),X26021),hAPP(hAPP(c_COMBB(X26020,tc_fun(X26022,tc_HOL_Obool),X26023),X26019),X26018)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26020,tc_fun(X26022,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26023,X26020,X26018),X26021)),X26019),
inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I10_J]) ).
fof(i_0_7605,plain,
! [X31008,X31009,X31010,X31011,X31012,X31013] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31013,tc_fun(X31012,tc_HOL_Obool)),hAPP(c_Set_Oimage(X31011,X31013,X31010),X31009)),X31008) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31011,tc_fun(X31012,tc_HOL_Obool)),X31009),hAPP(hAPP(c_COMBB(X31013,tc_fun(X31012,tc_HOL_Obool),X31011),X31008),X31010)),
inference(variable_rename,[status(thm)],[fact_INT__simps_I10_J]) ).
fof(i_0_7606,plain,
! [X26006,X26007,X26008,X26009,X26010,X26011] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26011,tc_fun(X26010,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26009,X26011,X26008),X26007)),X26006) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26009,tc_fun(X26010,tc_HOL_Obool)),X26007),hAPP(hAPP(c_COMBB(X26011,tc_fun(X26010,tc_HOL_Obool),X26009),X26006),X26008)),
inference(variable_rename,[status(thm)],[fact_UN__simps_I10_J]) ).
fof(i_0_7607,plain,
! [X22022,X22023] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22023,X22022),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X22023),X22022)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X22023,X22022)))),
inference(variable_rename,[status(thm)],[fact_divmod__nat__rel]) ).
cnf(i_0_7608,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_7609,plain,
! [X22363,X22364,X22365] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22365,tc_HOL_Obool)),X22364),X22363))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22365,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X22365,tc_HOL_Obool)),X22363)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X22365,tc_HOL_Obool)),X22364))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__anti__mono])]) ).
fof(i_0_7610,plain,
! [X26476,X26477,X26478] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26478),X26477))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26478,tc_HOL_Obool)),X26477),hAPP(c_Set_Oimage(X26478,X26478,X26476),X26477)))
| c_Fun_Oinj__on(X26478,X26478,X26476,X26477) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj__inj])]) ).
fof(i_0_7611,plain,
! [X28651,X28652,X28653] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X28653,X28652),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28653,X28652),c_Orderings_Otop__class_Otop(tc_fun(X28653,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X28652,tc_HOL_Obool),X28653),X28651))) = hAPP(hAPP(c_Product__Type_OSigma(X28653,X28652),c_Orderings_Otop__class_Otop(tc_fun(X28653,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X28652,tc_HOL_Obool),X28653),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28652,tc_HOL_Obool)),X28651))),
inference(variable_rename,[status(thm)],[fact_Compl__Times__UNIV1]) ).
fof(i_0_7612,plain,
! [X28648,X28649,X28650] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X28650,X28649),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28650,X28649),X28648),hAPP(c_COMBK(tc_fun(X28649,tc_HOL_Obool),X28650),c_Orderings_Otop__class_Otop(tc_fun(X28649,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(X28650,X28649),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28650,tc_HOL_Obool)),X28648)),hAPP(c_COMBK(tc_fun(X28649,tc_HOL_Obool),X28650),c_Orderings_Otop__class_Otop(tc_fun(X28649,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_Compl__Times__UNIV2]) ).
fof(i_0_7613,plain,
! [X33201,X33202,X33203,X33204] :
( ~ hBOOL(hAPP(hAPP(c_member(X33204),X33203),c_Wellfounded_Oacc(X33204,X33202)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33204)),X33201),c_Wellfounded_Oacc(tc_List_Olist(X33204),c_List_Olistrel1(X33204,X33202))))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33204)),hAPP(hAPP(c_List_Olist_OCons(X33204),X33203),X33201)),c_Wellfounded_Oacc(tc_List_Olist(X33204),c_List_Olistrel1(X33204,X33202)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__acc__listrel1I])]) ).
fof(i_0_7614,plain,
! [X21782,X21783,X21784,X21785] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21785),X21783),X21784)),X21782))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21785),X21782),X21784)),X21783))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21785),X21784),c_Groups_Ozero__class_Ozero(X21785)))
| ~ class_Fields_Olinordered__field(X21785) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21785),X21782),X21784)),X21783))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21785),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21785),X21783),X21784)),X21782))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21785),X21784),c_Groups_Ozero__class_Ozero(X21785)))
| ~ class_Fields_Olinordered__field(X21785) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__divide__le__eq])])]) ).
fof(i_0_7615,plain,
! [X21654,X21655,X21656,X21657] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21657),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21657),X21655),X21656)),X21654))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21657),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21657),X21654),X21656)),X21655))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21657),X21656),c_Groups_Ozero__class_Ozero(X21657)))
| ~ class_Fields_Olinordered__field(X21657) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21657),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21657),X21654),X21656)),X21655))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21657),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21657),X21655),X21656)),X21654))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21657),X21656),c_Groups_Ozero__class_Ozero(X21657)))
| ~ class_Fields_Olinordered__field(X21657) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__divide__less__eq])])]) ).
fof(i_0_7616,plain,
! [X22911,X22912,X22913,X22914,X22915] :
( ( X22915 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| hAPP(c_New__DSequence_Opos__decr__bind(X22914,X22913,X22912,X22911),X22915) = c_Lazy__Sequence_Oempty(X22913) )
& ( X22915 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| hAPP(c_New__DSequence_Opos__decr__bind(X22914,X22913,X22912,X22911),X22915) = c_Lazy__Sequence_Obind(X22914,X22913,hAPP(X22912,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X22915),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X22914,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X22913)),X22911),X22915)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_New__DSequence_Opos__decr__bind__def])]) ).
cnf(i_0_7617,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_7618,plain,
! [X22045,X22046,X22047] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22047,tc_fun(X22047,tc_HOL_Obool))),X22046),X22045))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22047,tc_HOL_Obool)),c_Wellfounded_Oaccp(X22047,X22045)),c_Wellfounded_Oaccp(X22047,X22046))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__subset])]) ).
fof(i_0_7619,plain,
! [X28051,X28052,X28053,X28054,X28055,X28056] :
( ~ c_Finite__Set_Ofolding__idem(X28056,X28055,X28054,X28053)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28056),X28052))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28056,tc_HOL_Obool)),X28051),X28052))
| hAPP(c_Fun_Ocomp(X28055,X28055,X28055,hAPP(X28053,X28052)),hAPP(X28053,X28051)) = hAPP(X28053,X28052) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Osubset__comp__idem])]) ).
fof(i_0_7620,plain,
! [X32487,X32488,X32489] :
( ~ class_Orderings_Olinorder(X32489)
| ~ hBOOL(hAPP(hAPP(c_member(X32489),X32488),hAPP(c_List_Oset(X32489),X32487)))
| c_List_Olinorder__class_Oinsort__insert__key(X32489,X32489,c_COMBI(X32489),X32488,X32487) = X32487 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__insert__triv])]) ).
fof(i_0_7621,plain,
! [X20228,X20229,X20230] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20230),X20229)),X20228))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20228),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20230),hAPP(c_Nat_OSuc,X20229))))
| X20229 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20228),X20230)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20230)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20230),X20229)),X20228))
| X20229 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20228),X20230)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20230)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20228),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20230),hAPP(c_Nat_OSuc,X20229))))
| X20229 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20228),X20230)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20230)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__div__lemma])])]) ).
fof(i_0_7622,plain,
! [X27323,X27324,X27325,X27326,X27327] :
( ~ class_Groups_Oab__group__add(X27327)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27326),X27325))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27326,tc_HOL_Obool)),X27324),X27325))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27326,X27327),X27323),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27326,tc_HOL_Obool)),X27325),X27324)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27327),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27326,X27327),X27323),X27325)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27326,X27327),X27323),X27324)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff])]) ).
cnf(i_0_7623,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_7624,plain,
! [X33436,X33437,X33438] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33438),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33437)),X33436)))
| X33436 = hAPP(hAPP(c_List_Oappend(X33437),hAPP(hAPP(c_List_Otake(X33437),X33438),X33436)),hAPP(hAPP(c_List_Olist_OCons(X33437),hAPP(hAPP(c_List_Onth(X33437),X33436),X33438)),hAPP(hAPP(c_List_Odrop(X33437),hAPP(c_Nat_OSuc,X33438)),X33436))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_id__take__nth__drop])]) ).
fof(i_0_7625,plain,
! [X27064,X27065,X27066,X27067,X27068,X27069] :
( hBOOL(hAPP(hAPP(c_member(X27069),X27068),X27067))
| hAPP(c_Set_Oimage(X27069,tc_Option_Ooption(X27066),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27069,tc_Option_Ooption(X27066)),X27065),X27068),hAPP(c_Option_Ooption_OSome(X27066),X27064))),X27067) = hAPP(c_Set_Oimage(X27069,tc_Option_Ooption(X27066),X27065),X27067) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5600])]) ).
cnf(i_0_7626,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_7627,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_7628,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_7629,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_7630,plain,
! [X23914,X23915] :
( ( ~ 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),X23915),X23914)),c_Wellfounded_Oless__than))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23915),X23914)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23915),X23914))
| 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),X23915),X23914)),c_Wellfounded_Oless__than)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__than__iff])]) ).
cnf(i_0_7631,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_7632,plain,
! [X24285,X24286,X24287,X24288,X24289,X24290] : hAPP(c_Set_Oimage(X24290,X24289,X24288),hAPP(c_Set_Oimage(X24287,X24290,X24286),X24285)) = hAPP(c_Set_Oimage(X24287,X24289,hAPP(hAPP(c_COMBB(X24290,X24289,X24287),X24288),X24286)),X24285),
inference(variable_rename,[status(thm)],[fact_image__image]) ).
fof(i_0_7633,plain,
! [X25758,X25759,X25760,X25761,X25762] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25761),X25758),X25760))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25761,X25762),X25759),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25761,tc_HOL_Obool)),X25760),hAPP(hAPP(c_Set_Oinsert(X25761),X25758),c_Orderings_Obot__class_Obot(tc_fun(X25761,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25762),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25761,X25762),X25759),X25760)),hAPP(X25759,X25758))
| hAPP(X25759,X25758) = c_Groups_Ozero__class_Ozero(X25762)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25761),X25760))
| ~ class_Fields_Ofield(X25762) )
& ( hBOOL(hAPP(hAPP(c_member(X25761),X25758),X25760))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25761,X25762),X25759),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25761,tc_HOL_Obool)),X25760),hAPP(hAPP(c_Set_Oinsert(X25761),X25758),c_Orderings_Obot__class_Obot(tc_fun(X25761,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25761,X25762),X25759),X25760)
| hAPP(X25759,X25758) = c_Groups_Ozero__class_Ozero(X25762)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25761),X25760))
| ~ class_Fields_Ofield(X25762) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5602])])]) ).
cnf(i_0_7634,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_7635,plain,
! [X31912,X31913,X31914,X31915,X31916] :
( ( hAPP(hAPP(c_List_Omap(X31916,X31915),X31914),X31913) != hAPP(hAPP(c_List_Omap(X31916,X31915),X31914),X31912)
| X31913 = X31912
| ~ c_Fun_Oinj__on(X31916,X31915,X31914,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31916,tc_HOL_Obool)),hAPP(c_List_Oset(X31916),X31913)),hAPP(c_List_Oset(X31916),X31912))) )
& ( X31913 != X31912
| hAPP(hAPP(c_List_Omap(X31916,X31915),X31914),X31913) = hAPP(hAPP(c_List_Omap(X31916,X31915),X31914),X31912)
| ~ c_Fun_Oinj__on(X31916,X31915,X31914,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31916,tc_HOL_Obool)),hAPP(c_List_Oset(X31916),X31913)),hAPP(c_List_Oset(X31916),X31912))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__map__eq__map])])]) ).
fof(i_0_7636,plain,
! [X31907,X31908,X31909,X31910,X31911] :
( hAPP(hAPP(c_List_Omap(X31911,X31910),X31909),X31908) != hAPP(hAPP(c_List_Omap(X31911,X31910),X31909),X31907)
| ~ c_Fun_Oinj__on(X31911,X31910,X31909,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31911,tc_HOL_Obool)),hAPP(c_List_Oset(X31911),X31908)),hAPP(c_List_Oset(X31911),X31907)))
| X31908 = X31907 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__inj__on])]) ).
fof(i_0_7637,plain,
! [X20395,X20396,X20397] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20395),X20396))
| hBOOL(hAPP(X20397,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20396)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20395))))
| ~ hBOOL(hAPP(X20397,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20396),X20395)))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20396),X20395))
| hBOOL(hAPP(X20397,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X20397,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20396),X20395)))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20396),X20395))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20395),X20396))
| hBOOL(hAPP(X20397,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20396),X20395)))) )
& ( ~ hBOOL(hAPP(X20397,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20395),X20396))
| hBOOL(hAPP(X20397,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20396),X20395)))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20396),X20395))
| ~ hBOOL(hAPP(X20397,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20396)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20395))))
| hBOOL(hAPP(X20397,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20396),X20395)))) )
& ( ~ hBOOL(hAPP(X20397,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X20397,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20396)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20395))))
| hBOOL(hAPP(X20397,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20396),X20395)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiff__int__split])])]) ).
fof(i_0_7638,plain,
! [X23378,X23379,X23380,X23381,X23382] :
( ~ class_Rings_Ocomm__semiring__1(X23382)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23382),hAPP(hAPP(c_Power_Opower__class_Opower(X23382),X23381),X23380)),X23379))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23378),X23380))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23382),hAPP(hAPP(c_Power_Opower__class_Opower(X23382),X23381),X23378)),X23379)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__le__dvd])]) ).
cnf(i_0_7639,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_7640,plain,
! [X31610,X31611,X31612,X31613,X31614] : c_Map_Omap__add(X31614,X31613,X31612,c_Map_Omap__add(X31614,X31613,X31611,X31610)) = c_Map_Omap__add(X31614,X31613,c_Map_Omap__add(X31614,X31613,X31612,X31611),X31610),
inference(variable_rename,[status(thm)],[fact_map__add__assoc]) ).
fof(i_0_7641,plain,
! [X30551,X30552,X30553,X30554,X30555] :
( ~ c_Relation_Osingle__valued(X30555,X30554,hAPP(c_Relation_Oconverse(X30554,X30555),X30553))
| hAPP(c_Relation_OImage(X30554,X30555,X30553),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30554,tc_HOL_Obool)),X30552),X30551)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30555,tc_HOL_Obool)),hAPP(c_Relation_OImage(X30554,X30555,X30553),X30552)),hAPP(c_Relation_OImage(X30554,X30555,X30553),X30551)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__Int__eq])]) ).
fof(i_0_7642,plain,
! [X21625,X21626,X21627,X21628,X21629] :
( ~ class_Fields_Olinordered__field(X21629)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21629),c_Groups_Ozero__class_Ozero(X21629)),X21628))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21629),X21628),X21627))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21629),c_Groups_Ozero__class_Ozero(X21629)),X21626))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21629),X21626),X21625))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21629),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21629),X21628),X21625)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21629),X21627),X21626))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__le])]) ).
fof(i_0_7643,plain,
! [X19409,X19410,X19411,X19412,X19413] :
( ~ class_Rings_Oordered__semiring(X19413)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19413),X19412),X19411))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19413),X19410),X19409))
| ~ 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),c_Groups_Ozero__class_Ozero(X19413)),X19410))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19413),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19413),X19412),X19410)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19413),X19411),X19409))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono_H])]) ).
fof(i_0_7644,plain,
! [X19404,X19405,X19406,X19407,X19408] :
( ~ class_Rings_Oordered__semiring(X19408)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19408),X19407),X19406))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19408),X19405),X19404))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19408),c_Groups_Ozero__class_Ozero(X19408)),X19406))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19408),c_Groups_Ozero__class_Ozero(X19408)),X19405))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19408),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19408),X19407),X19405)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19408),X19406),X19404))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono])]) ).
fof(i_0_7645,plain,
! [X21630,X21631,X21632,X21633,X21634] :
( ~ class_Fields_Olinordered__field(X21634)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21634),c_Groups_Ozero__class_Ozero(X21634)),X21633))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21634),X21633),X21632))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21634),c_Groups_Ozero__class_Ozero(X21634)),X21631))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21634),X21631),X21630))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21634),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21634),X21633),X21630)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21634),X21632),X21631))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__less])]) ).
fof(i_0_7646,plain,
! [X21635,X21636,X21637,X21638,X21639] :
( ~ class_Fields_Olinordered__field(X21639)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21639),c_Groups_Ozero__class_Ozero(X21639)),X21638))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21639),X21638),X21637))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21639),c_Groups_Ozero__class_Ozero(X21639)),X21636))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21639),X21636),X21635))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21639),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21639),X21638),X21635)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21639),X21637),X21636))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__less2])]) ).
fof(i_0_7647,plain,
! [X19619,X19620,X19621,X19622,X19623] :
( ~ class_Rings_Olinordered__semiring__strict(X19623)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19623),X19622),X19621))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19623),X19620),X19619))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19623),c_Groups_Ozero__class_Ozero(X19623)),X19622))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19623),c_Groups_Ozero__class_Ozero(X19623)),X19620))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19623),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19623),X19622),X19620)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19623),X19621),X19619))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__le__imp__less])]) ).
fof(i_0_7648,plain,
! [X19614,X19615,X19616,X19617,X19618] :
( ~ class_Rings_Olinordered__semiring__strict(X19618)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19618),X19617),X19616))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19618),X19615),X19614))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19618),c_Groups_Ozero__class_Ozero(X19618)),X19617))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19618),c_Groups_Ozero__class_Ozero(X19618)),X19615))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19618),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19618),X19617),X19615)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19618),X19616),X19614))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__less__imp__less])]) ).
fof(i_0_7649,plain,
! [X19624,X19625,X19626,X19627,X19628] :
( ~ class_Rings_Olinordered__semiring__strict(X19628)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19628),X19627),X19626))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19628),X19625),X19624))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19628),c_Groups_Ozero__class_Ozero(X19628)),X19627))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19628),c_Groups_Ozero__class_Ozero(X19628)),X19625))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19628),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19628),X19627),X19625)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19628),X19626),X19624))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__mono_H])]) ).
fof(i_0_7650,plain,
! [X19629,X19630,X19631,X19632,X19633] :
( ~ class_Rings_Olinordered__semiring__strict(X19633)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19633),X19632),X19631))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19633),X19630),X19629))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19633),c_Groups_Ozero__class_Ozero(X19633)),X19631))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19633),c_Groups_Ozero__class_Ozero(X19633)),X19630))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19633),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19633),X19632),X19630)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19633),X19631),X19629))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__mono])]) ).
fof(i_0_7651,plain,
! [X27412,X27413,X27414,X27415,X27416] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X27415),X27413),X27414))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27415,X27416),X27412),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27415,tc_HOL_Obool)),X27414),hAPP(hAPP(c_Set_Oinsert(X27415),X27413),c_Orderings_Obot__class_Obot(tc_fun(X27415,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27416),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27415,X27416),X27412),X27414)),hAPP(X27412,X27413))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27415),X27414))
| ~ class_Groups_Oab__group__add(X27416) )
& ( hBOOL(hAPP(hAPP(c_member(X27415),X27413),X27414))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27415,X27416),X27412),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27415,tc_HOL_Obool)),X27414),hAPP(hAPP(c_Set_Oinsert(X27415),X27413),c_Orderings_Obot__class_Obot(tc_fun(X27415,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27415,X27416),X27412),X27414)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27415),X27414))
| ~ class_Groups_Oab__group__add(X27416) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5604])])]) ).
fof(i_0_7652,plain,
! [X27407,X27408,X27409,X27410,X27411] :
( ~ class_Rings_Oring(X27411)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27410),X27409))
| ~ hBOOL(hAPP(hAPP(c_member(X27410),X27408),X27409))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27410,X27411),X27407),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27410,tc_HOL_Obool)),X27409),hAPP(hAPP(c_Set_Oinsert(X27410),X27408),c_Orderings_Obot__class_Obot(tc_fun(X27410,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27411),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27410,X27411),X27407),X27409)),hAPP(X27407,X27408)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff1__ring])]) ).
fof(i_0_7653,plain,
! [X27417,X27418,X27419] :
( ~ class_Fields_Ofield(X27419)
| X27418 = c_Groups_Oone__class_Oone(X27419)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27419),hAPP(c_Power_Opower__class_Opower(X27419),X27418)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27417)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27419),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27419),hAPP(hAPP(c_Power_Opower__class_Opower(X27419),X27418),X27417)),c_Groups_Oone__class_Oone(X27419))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27419),X27418),c_Groups_Oone__class_Oone(X27419))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_geometric__sum])]) ).
fof(i_0_7654,plain,
! [X32435,X32436] :
( ~ class_Groups_Oordered__ab__group__add__abs(X32436)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32436),hAPP(c_Groups_Oabs__class_Oabs(X32436),hAPP(c_List_Omonoid__add__class_Olistsum(X32436),X32435))),hAPP(c_List_Omonoid__add__class_Olistsum(X32436),hAPP(hAPP(c_List_Omap(X32436,X32436),c_Groups_Oabs__class_Oabs(X32436)),X32435)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__abs])]) ).
cnf(i_0_7655,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_7656,plain,
! [X17721,X17722,X17723,X17724,X17725,X17726] :
( ~ c_Natural_Oevaln(X17726,hAPP(hAPP(hAPP(c_Natural_Oupdate,X17725),c_Com_Ovname_OLoc(X17724)),hAPP(X17723,X17725)),X17722,X17721)
| c_Natural_Oevaln(c_Com_Ocom_OLocal(X17724,X17723,X17726),X17725,X17722,hAPP(hAPP(hAPP(c_Natural_Oupdate,X17721),c_Com_Ovname_OLoc(X17724)),hAPP(hAPP(c_Natural_Ogetlocs,X17725),X17724))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln_OLocal])]) ).
fof(i_0_7657,plain,
! [X26842,X26843,X26844] : 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)),X26844)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26843),X26842)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26843),X26844)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26842),X26844)),
inference(variable_rename,[status(thm)],[fact_image__add__atLeastLessThan]) ).
fof(i_0_7658,plain,
! [X27274,X27275,X27276,X27277,X27278] :
( ~ class_Groups_Oab__group__add(X27278)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X27277),X27276))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X27276),X27275))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27278),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27278),X27274),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X27277),X27275))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27278),X27274),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X27277),X27276))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27278),X27274),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X27276),X27275)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff__nat__ivl])]) ).
fof(i_0_7659,plain,
! [X27269,X27270,X27271,X27272,X27273] :
( ~ class_Groups_Ocomm__monoid__add(X27273)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X27272),X27271))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X27271),X27270))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27273),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27273),X27269),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X27272),X27271))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27273),X27269),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X27271),X27270))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27273),X27269),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X27272),X27270)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__add__nat__ivl])]) ).
fof(i_0_7660,plain,
! [X19594,X19595,X19596,X19597] :
( ~ class_Rings_Olinordered__semiring__strict(X19597)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19597),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19597),X19596),X19595)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19597),X19594),X19595)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19597),c_Groups_Ozero__class_Ozero(X19597)),X19595))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19597),X19596),X19594)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__le__imp__le])]) ).
fof(i_0_7661,plain,
! [X19590,X19591,X19592,X19593] :
( ~ class_Rings_Olinordered__semiring__strict(X19593)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19593),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19593),X19592),X19591)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19593),X19592),X19590)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19593),c_Groups_Ozero__class_Ozero(X19593)),X19592))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19593),X19591),X19590)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__imp__le])]) ).
fof(i_0_7662,plain,
! [X19638,X19639,X19640,X19641] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19641),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19641),X19640),X19639)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19641),X19640),X19638)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19641),X19639),X19638))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19641),c_Groups_Ozero__class_Ozero(X19641)),X19640))
| ~ class_Rings_Olinordered__ring__strict(X19641) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19641),X19639),X19638))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19641),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19641),X19640),X19639)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19641),X19640),X19638)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19641),c_Groups_Ozero__class_Ozero(X19641)),X19640))
| ~ class_Rings_Olinordered__ring__strict(X19641) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__pos])])]) ).
fof(i_0_7663,plain,
! [X19610,X19611,X19612,X19613] :
( ~ class_Rings_Olinordered__semiring(X19613)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19613),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19613),X19612),X19611)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19613),X19610),X19611)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19613),c_Groups_Ozero__class_Ozero(X19613)),X19611))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19613),X19612),X19610)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__less__imp__less])]) ).
fof(i_0_7664,plain,
! [X19606,X19607,X19608,X19609] :
( ~ class_Rings_Olinordered__semiring__strict(X19609)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19609),X19608),X19607)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19609),X19606),X19607)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19609),c_Groups_Ozero__class_Ozero(X19609)),X19607))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19609),X19608),X19606)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__right])]) ).
fof(i_0_7665,plain,
! [X20992,X20993,X20994,X20995] :
( ~ class_Rings_Olinordered__semidom(X20995)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20995),hAPP(hAPP(c_Power_Opower__class_Opower(X20995),X20994),X20993)),hAPP(hAPP(c_Power_Opower__class_Opower(X20995),X20992),X20993)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20995),c_Groups_Ozero__class_Ozero(X20995)),X20992))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20995),X20994),X20992)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__base])]) ).
fof(i_0_7666,plain,
! [X19602,X19603,X19604,X19605] :
( ~ class_Rings_Olinordered__semiring(X19605)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19605),X19604),X19603)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19605),X19604),X19602)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19605),c_Groups_Ozero__class_Ozero(X19605)),X19604))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19605),X19603),X19602)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__less__imp__less])]) ).
fof(i_0_7667,plain,
! [X19598,X19599,X19600,X19601] :
( ~ class_Rings_Olinordered__semiring__strict(X19601)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19601),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19601),X19600),X19599)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19601),X19600),X19598)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19601),c_Groups_Ozero__class_Ozero(X19601)),X19600))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19601),X19599),X19598)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__left])]) ).
fof(i_0_7668,plain,
! [X18907,X18908,X18909,X18910] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18910),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18910),X18909),X18908)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18910),X18909),X18907)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18910),X18908),X18907))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18910),c_Groups_Ozero__class_Ozero(X18910)),X18909))
| ~ class_Rings_Olinordered__ring__strict(X18910) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18910),X18908),X18907))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18910),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18910),X18909),X18908)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18910),X18909),X18907)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18910),c_Groups_Ozero__class_Ozero(X18910)),X18909))
| ~ class_Rings_Olinordered__ring__strict(X18910) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__pos])])]) ).
cnf(i_0_7669,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_7670,plain,
! [X27498,X27499,X27500,X27501] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27501),X27500))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27501,tc_HOL_Obool)),X27500),X27499))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27501,tc_Nat_Onat),X27498),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27501,tc_HOL_Obool)),X27499),X27500)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27501,tc_Nat_Onat),X27498),X27499)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27501,tc_Nat_Onat),X27498),X27500)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff__nat])]) ).
fof(i_0_7671,plain,
! [X28844,X28845,X28846,X28848] :
( ( hBOOL(hAPP(hAPP(c_member(X28846),esk286_3(X28844,X28845,X28846)),X28845))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X28846),hAPP(c_Finite__Set_Ofold1(X28846,c_Orderings_Oord__class_Omin(X28846)),X28845)),X28844))
| X28845 = c_Orderings_Obot__class_Obot(tc_fun(X28846,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28846),X28845))
| ~ class_Orderings_Olinorder(X28846) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X28846),esk286_3(X28844,X28845,X28846)),X28844))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X28846),hAPP(c_Finite__Set_Ofold1(X28846,c_Orderings_Oord__class_Omin(X28846)),X28845)),X28844))
| X28845 = c_Orderings_Obot__class_Obot(tc_fun(X28846,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28846),X28845))
| ~ class_Orderings_Olinorder(X28846) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X28846),X28848),X28845))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X28846),X28848),X28844))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X28846),hAPP(c_Finite__Set_Ofold1(X28846,c_Orderings_Oord__class_Omin(X28846)),X28845)),X28844))
| X28845 = c_Orderings_Obot__class_Obot(tc_fun(X28846,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28846),X28845))
| ~ class_Orderings_Olinorder(X28846) ) ),
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_7672,plain,
! [X28826,X28827,X28828,X28830] :
( ( hBOOL(hAPP(hAPP(c_member(X28828),esk283_3(X28826,X28827,X28828)),X28827))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28828),hAPP(c_Finite__Set_Ofold1(X28828,c_Orderings_Oord__class_Omin(X28828)),X28827)),X28826))
| X28827 = c_Orderings_Obot__class_Obot(tc_fun(X28828,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28828),X28827))
| ~ class_Orderings_Olinorder(X28828) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28828),esk283_3(X28826,X28827,X28828)),X28826))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28828),hAPP(c_Finite__Set_Ofold1(X28828,c_Orderings_Oord__class_Omin(X28828)),X28827)),X28826))
| X28827 = c_Orderings_Obot__class_Obot(tc_fun(X28828,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28828),X28827))
| ~ class_Orderings_Olinorder(X28828) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X28828),X28830),X28827))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28828),X28830),X28826))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28828),hAPP(c_Finite__Set_Ofold1(X28828,c_Orderings_Oord__class_Omin(X28828)),X28827)),X28826))
| X28827 = c_Orderings_Obot__class_Obot(tc_fun(X28828,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28828),X28827))
| ~ class_Orderings_Olinorder(X28828) ) ),
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_7673,plain,
! [X30880,X30881,X30882,X30883,X30884,X30885] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30885,tc_fun(X30884,tc_HOL_Obool)),X30883),X30882),X30881))
| ~ hBOOL(hAPP(hAPP(c_member(X30885),X30880),X30883))
| hBOOL(hAPP(hAPP(X30882,X30880),X30881)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF1__D])]) ).
fof(i_0_7674,plain,
! [X30874,X30875,X30876,X30877,X30878,X30879] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30879,tc_fun(X30878,tc_HOL_Obool)),X30877),X30876),X30875))
| hBOOL(hAPP(hAPP(X30876,X30874),X30875))
| ~ hBOOL(hAPP(hAPP(c_member(X30879),X30874),X30877)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5607])]) ).
fof(i_0_7675,plain,
! [X20876,X20877,X20878,X20879] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20879),hAPP(hAPP(c_Power_Opower__class_Opower(X20879),X20878),X20877)),hAPP(hAPP(c_Power_Opower__class_Opower(X20879),X20878),X20876)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20877),X20876))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20879),c_Groups_Oone__class_Oone(X20879)),X20878))
| ~ class_Rings_Olinordered__semidom(X20879) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20877),X20876))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20879),hAPP(hAPP(c_Power_Opower__class_Opower(X20879),X20878),X20877)),hAPP(hAPP(c_Power_Opower__class_Opower(X20879),X20878),X20876)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20879),c_Groups_Oone__class_Oone(X20879)),X20878))
| ~ class_Rings_Olinordered__semidom(X20879) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__increasing__iff])])]) ).
fof(i_0_7676,plain,
! [X20872,X20873,X20874,X20875] :
( ~ class_Rings_Olinordered__semidom(X20875)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20875),c_Groups_Oone__class_Oone(X20875)),X20874))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20875),hAPP(hAPP(c_Power_Opower__class_Opower(X20875),X20874),X20873)),hAPP(hAPP(c_Power_Opower__class_Opower(X20875),X20874),X20872)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20873),X20872)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__exp])]) ).
fof(i_0_7677,plain,
! [X21019,X21020,X21021,X21022] :
( ~ class_Rings_Olinordered__semidom(X21022)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21022),c_Groups_Oone__class_Oone(X21022)),X21021))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21022),hAPP(hAPP(c_Power_Opower__class_Opower(X21022),X21021),X21020)),hAPP(hAPP(c_Power_Opower__class_Opower(X21022),X21021),X21019)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21020),X21019)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__exp])]) ).
fof(i_0_7678,plain,
! [X21015,X21016,X21017,X21018] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21018),hAPP(hAPP(c_Power_Opower__class_Opower(X21018),X21017),X21016)),hAPP(hAPP(c_Power_Opower__class_Opower(X21018),X21017),X21015)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21016),X21015))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21018),c_Groups_Oone__class_Oone(X21018)),X21017))
| ~ class_Rings_Olinordered__semidom(X21018) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21016),X21015))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21018),hAPP(hAPP(c_Power_Opower__class_Opower(X21018),X21017),X21016)),hAPP(hAPP(c_Power_Opower__class_Opower(X21018),X21017),X21015)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21018),c_Groups_Oone__class_Oone(X21018)),X21017))
| ~ class_Rings_Olinordered__semidom(X21018) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing__iff])])]) ).
fof(i_0_7679,plain,
! [X32874,X32875,X32876] :
( X32876 = c_List_Olist_ONil(X32875)
| hBOOL(hAPP(hAPP(c_member(X32875),hAPP(c_Product__Type_Ofst(X32875,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(X32875,X32876),X32874))),hAPP(c_List_Oset(X32875),X32876))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_select])]) ).
fof(i_0_7680,plain,
! [X28740,X28741,X28742,X28743] : hAPP(c_Finite__Set_Ocard(tc_prod(X28743,X28742)),hAPP(hAPP(c_Product__Type_OSigma(X28743,X28742),hAPP(hAPP(c_Set_Oinsert(X28743),X28741),c_Orderings_Obot__class_Obot(tc_fun(X28743,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(X28742,tc_HOL_Obool),X28743),X28740))) = hAPP(c_Finite__Set_Ocard(X28742),X28740),
inference(variable_rename,[status(thm)],[fact_card__cartesian__product__singleton]) ).
fof(i_0_7681,plain,
! [X17907,X17908,X17909] :
( ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X17909)),X17908),X17907))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X17909))),X17908),X17907)) )
& ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X17909))),X17908),X17907))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X17909)),X17908),X17907)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc_Oequations_I9_J])]) ).
fof(i_0_7682,plain,
! [X17753,X17754,X17755] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X17755))),X17754),X17753))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X17755)),X17754),X17753)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc_OBody])]) ).
fof(i_0_7683,plain,
! [X22135,X22136,X22137,X22138,X22139] :
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22139,X22138,tc_HOL_Obool),X22137),hAPP(hAPP(c_Product__Type_OPair(X22139,X22138),X22136),X22135)))
| hBOOL(hAPP(hAPP(X22137,X22136),X22135)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_splitD])]) ).
fof(i_0_7684,plain,
! [X26585,X26586,X26587] : c_Fun_Oinj__on(tc_prod(X26587,X26586),tc_prod(X26586,X26587),hAPP(c_Product__Type_Oprod_Oprod__case(X26587,X26586,tc_prod(X26586,X26587)),hAPP(c_COMBC(X26586,X26587,tc_prod(X26586,X26587)),c_Product__Type_OPair(X26586,X26587))),X26585),
inference(variable_rename,[status(thm)],[fact_swap__inj__on]) ).
fof(i_0_7685,plain,
! [X29073,X29074,X29075] :
( ( hBOOL(hAPP(hAPP(c_member(X29075),esk303_3(X29073,X29074,X29075)),X29074))
| 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(X29075,tc_Nat_Onat),X29073),X29074)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29075),X29074)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X29073,esk303_3(X29073,X29074,X29075))))
| 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(X29075,tc_Nat_Onat),X29073),X29074)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29075),X29074)) ) ),
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_7686,plain,
! [X25675,X25676,X25677,X25678] :
( ( ~ 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(X25677,tc_Nat_Onat),X25675),X25676)))
| ~ hBOOL(hAPP(hAPP(c_member(X25677),X25678),X25676))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X25675,X25678)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25677),X25676)) )
& ( hBOOL(hAPP(hAPP(c_member(X25677),esk153_3(X25675,X25676,X25677)),X25676))
| 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(X25677,tc_Nat_Onat),X25675),X25676)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25677),X25676)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X25675,esk153_3(X25675,X25676,X25677))))
| 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(X25677,tc_Nat_Onat),X25675),X25676)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25677),X25676)) ) ),
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_7687,plain,
! [X27250,X27251,X27252,X27253] :
( ~ class_Groups_Ocomm__monoid__add(X27253)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27253),X27252),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X27251),hAPP(c_Nat_OSuc,X27250))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27253),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X27253,tc_Nat_Onat),X27252),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X27251,X27250)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__cl__Suc__ivl])]) ).
fof(i_0_7688,plain,
! [X19634,X19635,X19636,X19637] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19637),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19637),X19636),X19635)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19637),X19636),X19634)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19637),X19634),X19635))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19637),X19636),c_Groups_Ozero__class_Ozero(X19637)))
| ~ class_Rings_Olinordered__ring__strict(X19637) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19637),X19634),X19635))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19637),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19637),X19636),X19635)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19637),X19636),X19634)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19637),X19636),c_Groups_Ozero__class_Ozero(X19637)))
| ~ class_Rings_Olinordered__ring__strict(X19637) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__neg])])]) ).
fof(i_0_7689,plain,
! [X18926,X18927,X18928,X18929] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18929),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18929),X18928),X18927)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18929),X18928),X18926)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18929),X18926),X18927))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18929),X18928),c_Groups_Ozero__class_Ozero(X18929)))
| ~ class_Rings_Olinordered__ring__strict(X18929) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18929),X18926),X18927))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18929),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18929),X18928),X18927)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18929),X18928),X18926)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18929),X18928),c_Groups_Ozero__class_Ozero(X18929)))
| ~ class_Rings_Olinordered__ring__strict(X18929) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__neg])])]) ).
fof(i_0_7690,plain,
! [X27117,X27118,X27119,X27120] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27120,tc_Option_Ooption(X27119)),hAPP(c_COMBK(tc_Option_Ooption(X27119),X27120),c_Option_Ooption_ONone(X27119))),X27118),c_Option_Ooption_ONone(X27119)),X27117) = c_Option_Ooption_ONone(X27119),
inference(variable_rename,[status(thm)],[fact_empty__upd__none]) ).
fof(i_0_7691,plain,
! [X24729,X24730,X24731] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24731,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24731,tc_HOL_Obool)),X24730),X24729)),X24730)),
inference(variable_rename,[status(thm)],[fact_Int__lower1]) ).
fof(i_0_7692,plain,
! [X24726,X24727,X24728] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24728,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24728,tc_HOL_Obool)),X24727),X24726)),X24726)),
inference(variable_rename,[status(thm)],[fact_Int__lower2]) ).
fof(i_0_7693,plain,
! [X22348,X22349,X22350] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22350,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22350,tc_HOL_Obool)),X22349),X22348)),X22349)),
inference(variable_rename,[status(thm)],[fact_Diff__subset]) ).
fof(i_0_7694,plain,
! [X32461,X32462,X32463,X32464,X32465] :
( ~ class_Groups_Ocomm__monoid__add(X32465)
| ~ hBOOL(hAPP(hAPP(c_member(X32464),X32463),hAPP(c_List_Oset(X32464),X32462)))
| hAPP(c_List_Omonoid__add__class_Olistsum(X32465),hAPP(hAPP(c_List_Omap(X32464,X32465),X32461),X32462)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X32465),hAPP(X32461,X32463)),hAPP(c_List_Omonoid__add__class_Olistsum(X32465),hAPP(hAPP(c_List_Omap(X32464,X32465),X32461),c_List_Oremove1(X32464,X32463,X32462)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__map__remove1])]) ).
fof(i_0_7695,plain,
! [X24846,X24847,X24848,X24849] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24849,tc_HOL_Obool)),X24848),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24849,tc_HOL_Obool)),X24847),X24846)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24849,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24849,tc_HOL_Obool)),X24848),X24847)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24849,tc_HOL_Obool)),X24848),X24846)),
inference(variable_rename,[status(thm)],[fact_Int__Un__distrib]) ).
fof(i_0_7696,plain,
! [X24868,X24869,X24870,X24871] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24871,tc_HOL_Obool)),X24870),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24871,tc_HOL_Obool)),X24869),X24868)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24871,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24871,tc_HOL_Obool)),X24870),X24869)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24871,tc_HOL_Obool)),X24870),X24868)),
inference(variable_rename,[status(thm)],[fact_Diff__Int__distrib]) ).
fof(i_0_7697,plain,
! [X24850,X24851,X24852,X24853] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24853,tc_HOL_Obool)),X24852),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24853,tc_HOL_Obool)),X24851),X24850)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24853,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24853,tc_HOL_Obool)),X24852),X24851)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24853,tc_HOL_Obool)),X24852),X24850)),
inference(variable_rename,[status(thm)],[fact_Un__Int__distrib]) ).
fof(i_0_7698,plain,
! [X25033,X25034,X25035,X25036] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25036,tc_HOL_Obool)),X25035),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25036,tc_HOL_Obool)),X25034),X25033)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25036,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25036,tc_HOL_Obool)),X25035),X25034)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25036,tc_HOL_Obool)),X25035),X25033)),
inference(variable_rename,[status(thm)],[fact_Diff__Int]) ).
fof(i_0_7699,plain,
! [X25037,X25038,X25039,X25040] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25040,tc_HOL_Obool)),X25039),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25040,tc_HOL_Obool)),X25038),X25037)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25040,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25040,tc_HOL_Obool)),X25039),X25038)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25040,tc_HOL_Obool)),X25039),X25037)),
inference(variable_rename,[status(thm)],[fact_Diff__Un]) ).
fof(i_0_7700,plain,
! [X22564,X22565,X22566,X22567,X22568,X22569] : c_Product__Type_Oprod_Oprod__rec(X22569,X22568,X22567,X22566,hAPP(hAPP(c_Product__Type_OPair(X22569,X22568),X22565),X22564)) = hAPP(hAPP(X22566,X22565),X22564),
inference(variable_rename,[status(thm)],[fact_prod_Orecs]) ).
fof(i_0_7701,plain,
! [X22966,X22967,X22968,X22969,X22970] : hAPP(c_New__DSequence_Oneg__bind(X22970,X22969,X22968,X22967),X22966) = c_Lazy__Sequence_Ohb__bind(X22970,X22969,hAPP(X22968,X22966),hAPP(hAPP(c_COMBC(X22970,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X22969))),X22967),X22966)),
inference(variable_rename,[status(thm)],[fact_New__DSequence_Oneg__bind__def]) ).
fof(i_0_7702,plain,
! [X27241,X27242,X27243,X27244] :
( ~ class_Groups_Ocomm__monoid__add(X27244)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27244),X27243),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X27242)),hAPP(c_Nat_OSuc,X27241))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27244),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X27244,tc_Nat_Onat),X27243),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X27242),X27241)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__Suc__ivl])]) ).
fof(i_0_7703,plain,
! [X26431,X26432,X26433] : 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)),X26433)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26432,X26431)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26432),X26433),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26431),X26433)),
inference(variable_rename,[status(thm)],[fact_image__add__atLeastAtMost]) ).
cnf(i_0_7704,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_7705,plain,
! [X29191,X29192,X29193,X29194] :
( ( hBOOL(hAPP(hAPP(c_member(X29194),X29193),X29192))
| ~ hBOOL(hAPP(hAPP(c_member(X29194),X29193),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29194,tc_HOL_Obool)),X29192),hAPP(c_Set_OCollect(X29194),X29191)))) )
& ( hBOOL(hAPP(X29191,X29193))
| ~ hBOOL(hAPP(hAPP(c_member(X29194),X29193),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29194,tc_HOL_Obool)),X29192),hAPP(c_Set_OCollect(X29194),X29191)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X29194),X29193),X29192))
| ~ hBOOL(hAPP(X29191,X29193))
| hBOOL(hAPP(hAPP(c_member(X29194),X29193),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29194,tc_HOL_Obool)),X29192),hAPP(c_Set_OCollect(X29194),X29191)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__Collect])])]) ).
fof(i_0_7706,plain,
! [X33928,X33929,X33930,X33931] :
( ~ hBOOL(hAPP(hAPP(c_member(X33931),X33930),hAPP(c_List_Oset(X33931),X33929)))
| hBOOL(hAPP(X33928,X33930))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33931)),hAPP(c_List_Ofilter(X33931,X33928),X33929))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33931)),X33929))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5609])]) ).
fof(i_0_7707,plain,
! [X26823,X26824,X26825,X26826,X26827] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26827),X26824),X26826))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26827),X26825),X26826))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26827,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26827,X26826),X26825)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26827,X26824),X26823)))
| ~ class_Orderings_Olinorder(X26827) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26827),X26825),X26823))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26827),X26825),X26826))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26827,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26827,X26826),X26825)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26827,X26824),X26823)))
| ~ class_Orderings_Olinorder(X26827) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__subset__iff])])]) ).
fof(i_0_7708,plain,
! [X18237,X18238,X18239,X18240,X18241] : c_Sum__Type_Osum_Osum__size(X18241,X18240,X18239,X18238,hAPP(c_Sum__Type_OInl(X18241,X18240),X18237)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X18239,X18237)),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_7709,plain,
! [X18232,X18233,X18234,X18235,X18236] : c_Sum__Type_Osum_Osum__size(X18236,X18235,X18234,X18233,hAPP(c_Sum__Type_OInr(X18235,X18236),X18232)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X18233,X18232)),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_7710,plain,
! [X28021,X28022,X28023,X28024,X28025,X28026] :
( ~ c_Finite__Set_Ofolding__idem(X28026,X28025,X28024,X28023)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28026),X28022))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28026),X28021))
| hAPP(X28023,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28026,tc_HOL_Obool)),X28022),X28021)) = hAPP(c_Fun_Ocomp(X28025,X28025,X28025,hAPP(X28023,X28022)),hAPP(X28023,X28021)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Ounion__idem])]) ).
cnf(i_0_7711,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_7712,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_7713,plain,
! [X29752,X29753,X29754] :
( ~ c_Wellfounded_Owf(X29754,X29753)
| ~ c_Wellfounded_Owf(X29754,X29752)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29754,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X29754,X29754),X29753)),hAPP(c_Relation_ORange(X29754,X29754),X29752)) != c_Orderings_Obot__class_Obot(tc_fun(X29754,tc_HOL_Obool))
| c_Wellfounded_Owf(X29754,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29754,X29754),tc_HOL_Obool)),X29753),X29752)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__Un])]) ).
fof(i_0_7714,plain,
! [X20370,X20371,X20372] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20371),X20372)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20370),X20372)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20371),X20370))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20372),X20370))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20372),X20371)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20371),X20370))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20371),X20372)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20370),X20372)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20372),X20370))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20372),X20371)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__iff])])]) ).
fof(i_0_7715,plain,
! [X20451,X20452,X20453] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20452),X20453)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20451),X20453)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20452),X20451))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20453),X20451))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20453),X20452)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20452),X20451))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20452),X20453)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20451),X20453)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20453),X20451))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20453),X20452)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__iff])])]) ).
cnf(i_0_7716,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_7717,plain,
! [X18903,X18904,X18905,X18906] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18906),X18905),c_Groups_Ozero__class_Ozero(X18906)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18906),c_Groups_Ozero__class_Ozero(X18906)),X18905))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18906),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18906),X18905),X18904)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18906),X18905),X18903)))
| ~ class_Rings_Olinordered__ring__strict(X18906) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18906),X18903),X18904))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18906),c_Groups_Ozero__class_Ozero(X18906)),X18905))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18906),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18906),X18905),X18904)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18906),X18905),X18903)))
| ~ class_Rings_Olinordered__ring__strict(X18906) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18906),X18905),c_Groups_Ozero__class_Ozero(X18906)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18906),X18904),X18903))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18906),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18906),X18905),X18904)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18906),X18905),X18903)))
| ~ class_Rings_Olinordered__ring__strict(X18906) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18906),X18903),X18904))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18906),X18904),X18903))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18906),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18906),X18905),X18904)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18906),X18905),X18903)))
| ~ class_Rings_Olinordered__ring__strict(X18906) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18906),c_Groups_Ozero__class_Ozero(X18906)),X18905))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18906),X18904),X18903))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18906),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18906),X18905),X18904)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18906),X18905),X18903)))
| ~ class_Rings_Olinordered__ring__strict(X18906) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18906),X18905),c_Groups_Ozero__class_Ozero(X18906)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18906),X18903),X18904))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18906),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18906),X18905),X18904)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18906),X18905),X18903)))
| ~ class_Rings_Olinordered__ring__strict(X18906) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__disj])])]) ).
fof(i_0_7718,plain,
! [X18899,X18900,X18901,X18902] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18902),X18900),c_Groups_Ozero__class_Ozero(X18902)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18902),c_Groups_Ozero__class_Ozero(X18902)),X18900))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18902),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18902),X18901),X18900)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18902),X18899),X18900)))
| ~ class_Rings_Olinordered__ring__strict(X18902) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18902),X18899),X18901))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18902),c_Groups_Ozero__class_Ozero(X18902)),X18900))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18902),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18902),X18901),X18900)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18902),X18899),X18900)))
| ~ class_Rings_Olinordered__ring__strict(X18902) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18902),X18900),c_Groups_Ozero__class_Ozero(X18902)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18902),X18901),X18899))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18902),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18902),X18901),X18900)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18902),X18899),X18900)))
| ~ class_Rings_Olinordered__ring__strict(X18902) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18902),X18899),X18901))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18902),X18901),X18899))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18902),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18902),X18901),X18900)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18902),X18899),X18900)))
| ~ class_Rings_Olinordered__ring__strict(X18902) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18902),c_Groups_Ozero__class_Ozero(X18902)),X18900))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18902),X18901),X18899))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18902),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18902),X18901),X18900)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18902),X18899),X18900)))
| ~ class_Rings_Olinordered__ring__strict(X18902) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18902),X18900),c_Groups_Ozero__class_Ozero(X18902)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18902),X18899),X18901))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18902),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18902),X18901),X18900)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18902),X18899),X18900)))
| ~ class_Rings_Olinordered__ring__strict(X18902) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__right__disj])])]) ).
fof(i_0_7719,plain,
! [X23728,X23729,X23730,X23731] :
( ( hBOOL(hAPP(hAPP(c_member(X23731),X23730),X23728))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23731,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X23731),X23730),X23729)),X23728)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23731,tc_HOL_Obool)),X23729),X23728))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23731,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X23731),X23730),X23729)),X23728)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X23731),X23730),X23728))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23731,tc_HOL_Obool)),X23729),X23728))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23731,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X23731),X23730),X23729)),X23728)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__subset])])]) ).
fof(i_0_7720,plain,
! [X27513,X27514,X27515] :
( ~ class_Groups_Ocomm__monoid__add(X27515)
| ~ class_Groups_Ocomm__monoid__mult(X27515)
| ~ c_Nat__Transfer_Onat__set(X27514)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X27515),X27513),X27514) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27515),hAPP(hAPP(c_COMBB(tc_Int_Oint,X27515,tc_Nat_Onat),X27513),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X27514)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod_I1_J])]) ).
fof(i_0_7721,plain,
! [X25657,X25658,X25659] :
( ~ class_Groups_Ocomm__monoid__add(X25659)
| ~ class_Groups_Ocomm__monoid__mult(X25659)
| ~ c_Nat__Transfer_Onat__set(X25658)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X25659),X25657),X25658) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X25659),hAPP(hAPP(c_COMBB(tc_Int_Oint,X25659,tc_Nat_Onat),X25657),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X25658)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod_I2_J])]) ).
fof(i_0_7722,plain,
! [X32351,X32352,X32353,X32354] : c_Map_Omap__of(X32354,X32353,hAPP(hAPP(c_List_Olist_OCons(tc_prod(X32354,X32353)),X32352),X32351)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X32354,tc_Option_Ooption(X32353)),c_Map_Omap__of(X32354,X32353,X32351)),hAPP(c_Product__Type_Ofst(X32354,X32353),X32352)),hAPP(c_Option_Ooption_OSome(X32353),hAPP(c_Product__Type_Osnd(X32354,X32353),X32352))),
inference(variable_rename,[status(thm)],[fact_map__of_Osimps_I2_J]) ).
fof(i_0_7723,plain,
! [X27362,X27363,X27364,X27365,X27366] :
( ~ class_Groups_Ocomm__monoid__add(X27366)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27365),X27364))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27365),X27363))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27365,tc_HOL_Obool)),X27364),X27363) != c_Orderings_Obot__class_Obot(tc_fun(X27365,tc_HOL_Obool))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27365,X27366),X27362),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27365,tc_HOL_Obool)),X27364),X27363)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27366),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27365,X27366),X27362),X27364)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27365,X27366),X27362),X27363)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Un__disjoint])]) ).
fof(i_0_7724,plain,
! [X25744,X25745,X25746,X25747,X25748] :
( ~ class_Groups_Ocomm__monoid__mult(X25748)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25747),X25746))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25747),X25745))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25747,tc_HOL_Obool)),X25746),X25745) != c_Orderings_Obot__class_Obot(tc_fun(X25747,tc_HOL_Obool))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25747,X25748),X25744),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25747,tc_HOL_Obool)),X25746),X25745)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25748),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25747,X25748),X25744),X25746)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25747,X25748),X25744),X25745)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__Un__disjoint])]) ).
fof(i_0_7725,plain,
! [X25739,X25740,X25741,X25742,X25743] :
( ~ class_Groups_Ocomm__monoid__mult(X25743)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25742),X25741))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25742),X25740))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25742,tc_HOL_Obool)),X25741),X25740) != c_Orderings_Obot__class_Obot(tc_fun(X25742,tc_HOL_Obool))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25742,X25743),X25739),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25742,tc_HOL_Obool)),X25741),X25740)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25743),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25742,X25743),X25739),X25741)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25742,X25743),X25739),X25740)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__disjoint])]) ).
fof(i_0_7726,plain,
! [X27502,X27503,X27504] :
( ~ class_Groups_Ocomm__monoid__add(X27504)
| ~ class_Groups_Ocomm__monoid__mult(X27504)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27504),X27503),X27502) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X27504),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X27504,tc_Int_Oint),X27503),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X27502)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod_I1_J])]) ).
fof(i_0_7727,plain,
! [X25604,X25605,X25606] :
( ~ class_Groups_Ocomm__monoid__add(X25606)
| ~ class_Groups_Ocomm__monoid__mult(X25606)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X25606),X25605),X25604) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X25606),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X25606,tc_Int_Oint),X25605),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X25604)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod_I2_J])]) ).
cnf(i_0_7728,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_7729,plain,
! [X33214,X33215] : 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_Olistrel(X33215,X33214)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X33215),c_List_Olistrel1(X33215,X33214)))),
inference(variable_rename,[status(thm)],[fact_listrel__subset__rtrancl__listrel1]) ).
fof(i_0_7730,plain,
! [X22263,X22264,X22265,X22266] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22265))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22265))
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22266,X22265),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22264),X22263)))
| X22266 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22265),X22264)),X22263) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22265),X22263))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22263),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)),X22265))
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22266,X22265),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22264),X22263)))
| X22266 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22265),X22264)),X22263) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22265))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22263))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22263),X22265))
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22266,X22265),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22264),X22263)))
| X22266 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22265),X22264)),X22263) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22265),X22263))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22263),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)),X22263))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22263),X22265))
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22266,X22265),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22264),X22263)))
| X22266 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22265),X22264)),X22263) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5614])])]) ).
fof(i_0_7731,plain,
! [X26916,X26917] : 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)),X26917)),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),X26916),X26917))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X26917),X26916),
inference(variable_rename,[status(thm)],[fact_image__add__int__atLeastLessThan]) ).
fof(i_0_7732,plain,
! [X33385,X33386,X33387,X33388] : hAPP(hAPP(c_List_Odrop(X33388),X33387),hAPP(hAPP(c_List_Oappend(X33388),X33386),X33385)) = hAPP(hAPP(c_List_Oappend(X33388),hAPP(hAPP(c_List_Odrop(X33388),X33387),X33386)),hAPP(hAPP(c_List_Odrop(X33388),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33387),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33388)),X33386))),X33385)),
inference(variable_rename,[status(thm)],[fact_drop__append]) ).
fof(i_0_7733,plain,
! [X33129,X33130,X33131,X33132] : hAPP(hAPP(c_List_Otake(X33132),X33131),hAPP(hAPP(c_List_Oappend(X33132),X33130),X33129)) = hAPP(hAPP(c_List_Oappend(X33132),hAPP(hAPP(c_List_Otake(X33132),X33131),X33130)),hAPP(hAPP(c_List_Otake(X33132),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33131),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33132)),X33130))),X33129)),
inference(variable_rename,[status(thm)],[fact_take__append]) ).
fof(i_0_7734,plain,
! [X32400,X32401,X32402] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32402,tc_HOL_Obool)),hAPP(c_List_Oset(X32402),c_List_Osublist(X32402,X32401,X32400))),hAPP(c_List_Oset(X32402),X32401))),
inference(variable_rename,[status(thm)],[fact_set__sublist__subset]) ).
fof(i_0_7735,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_7736,plain,
! [X27014,X27015,X27016,X27017] :
( ~ c_Fun_Oinj__on(X27017,X27016,X27015,X27014)
| c_Fun_Oinj__on(X27016,X27017,c_Fun_Othe__inv__into(X27017,X27016,X27014,X27015),hAPP(c_Set_Oimage(X27017,X27016,X27015),X27014)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__the__inv__into])]) ).
fof(i_0_7737,plain,
! [X29825,X29826,X29827] : hAPP(c_Relation_ODomain(X29827,X29826),hAPP(c_Set_OCollect(tc_prod(X29827,X29826)),hAPP(c_Product__Type_Oprod_Oprod__case(X29827,X29826,tc_HOL_Obool),X29825))) = hAPP(c_Set_OCollect(X29827),hAPP(hAPP(c_COMBB(tc_fun(X29826,tc_HOL_Obool),tc_HOL_Obool,X29827),c_HOL_OEx(X29826)),X29825)),
inference(variable_rename,[status(thm)],[fact_Domain__Collect__split]) ).
cnf(i_0_7738,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_7739,plain,
! [X33609,X33610,X33611,X33612,X33613] :
( ~ c_Finite__Set_Ofun__left__comm__idem(X33613,X33612,X33611)
| hAPP(hAPP(c_Finite__Set_Ofold(X33613,X33612,X33611),X33610),hAPP(c_List_Oset(X33613),X33609)) = hAPP(c_List_Ofoldl(X33612,X33613,hAPP(c_COMBC(X33613,X33612,X33612),X33611),X33610),X33609) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__set])]) ).
fof(i_0_7740,plain,
! [X27505,X27506,X27507,X27508] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X27508),X27507),X27506))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27508,tc_Nat_Onat),X27505),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27508,tc_HOL_Obool)),X27506),hAPP(hAPP(c_Set_Oinsert(X27508),X27507),c_Orderings_Obot__class_Obot(tc_fun(X27508,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27508,tc_Nat_Onat),X27505),X27506)),hAPP(X27505,X27507)) )
& ( hBOOL(hAPP(hAPP(c_member(X27508),X27507),X27506))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27508,tc_Nat_Onat),X27505),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27508,tc_HOL_Obool)),X27506),hAPP(hAPP(c_Set_Oinsert(X27508),X27507),c_Orderings_Obot__class_Obot(tc_fun(X27508,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27508,tc_Nat_Onat),X27505),X27506) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5616])]) ).
fof(i_0_7741,plain,
! [X27184,X27185,X27186,X27187] :
( ~ class_Groups_Oab__group__add(X27187)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27186,X27187),hAPP(hAPP(c_COMBB(X27187,X27187,X27186),c_Groups_Ouminus__class_Ouminus(X27187)),X27185)),X27184) = hAPP(c_Groups_Ouminus__class_Ouminus(X27187),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27186,X27187),X27185),X27184)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__negf])]) ).
fof(i_0_7742,plain,
! [X25600,X25601,X25602,X25603] :
( ~ class_Fields_Olinordered__field(X25603)
| hAPP(c_Groups_Oabs__class_Oabs(X25603),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25602,X25603),X25601),X25600)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25602,X25603),hAPP(hAPP(c_COMBB(X25603,X25603,X25602),c_Groups_Oabs__class_Oabs(X25603)),X25601)),X25600) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__setprod])]) ).
fof(i_0_7743,plain,
! [X32534,X32535,X32536,X32538,X32539,X32540,X32541,X32543] :
( ( hBOOL(hAPP(hAPP(c_member(X32536),esk449_3(X32534,X32535,X32536)),hAPP(c_List_Oset(X32536),X32535)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32538),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32536)),X32535)))
| hBOOL(hAPP(X32534,hAPP(hAPP(c_List_Onth(X32536),X32535),X32538))) )
& ( ~ hBOOL(hAPP(X32534,esk449_3(X32534,X32535,X32536)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32538),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32536)),X32535)))
| hBOOL(hAPP(X32534,hAPP(hAPP(c_List_Onth(X32536),X32535),X32538))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk450_3(X32539,X32540,X32541)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32541)),X32540)))
| ~ hBOOL(hAPP(hAPP(c_member(X32541),X32543),hAPP(c_List_Oset(X32541),X32540)))
| hBOOL(hAPP(X32539,X32543)) )
& ( ~ hBOOL(hAPP(X32539,hAPP(hAPP(c_List_Onth(X32541),X32540),esk450_3(X32539,X32540,X32541))))
| ~ hBOOL(hAPP(hAPP(c_member(X32541),X32543),hAPP(c_List_Oset(X32541),X32540)))
| hBOOL(hAPP(X32539,X32543)) ) ),
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_7744,plain,
! [X23065,X23066,X23067,X23068] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23068,tc_HOL_Obool)),X23067),X23066))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23068,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X23068),X23065),X23067)),hAPP(hAPP(c_Set_Oinsert(X23068),X23065),X23066))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__mono])]) ).
cnf(i_0_7745,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_7746,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_7747,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_7748,plain,
! [X34037,X34038,X34039,X34040,X34041] :
( ( c_List_Olinorder__class_Osorted(X34039,X34038)
| ~ c_List_Olinorder__class_Osorted(X34039,hAPP(hAPP(c_List_Oappend(X34039),X34038),X34037))
| ~ class_Orderings_Olinorder(X34039) )
& ( c_List_Olinorder__class_Osorted(X34039,X34037)
| ~ c_List_Olinorder__class_Osorted(X34039,hAPP(hAPP(c_List_Oappend(X34039),X34038),X34037))
| ~ class_Orderings_Olinorder(X34039) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X34039),X34040),hAPP(c_List_Oset(X34039),X34038)))
| ~ hBOOL(hAPP(hAPP(c_member(X34039),X34041),hAPP(c_List_Oset(X34039),X34037)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X34039),X34040),X34041))
| ~ c_List_Olinorder__class_Osorted(X34039,hAPP(hAPP(c_List_Oappend(X34039),X34038),X34037))
| ~ class_Orderings_Olinorder(X34039) )
& ( hBOOL(hAPP(hAPP(c_member(X34039),esk485_3(X34037,X34038,X34039)),hAPP(c_List_Oset(X34039),X34038)))
| ~ c_List_Olinorder__class_Osorted(X34039,X34038)
| ~ c_List_Olinorder__class_Osorted(X34039,X34037)
| c_List_Olinorder__class_Osorted(X34039,hAPP(hAPP(c_List_Oappend(X34039),X34038),X34037))
| ~ class_Orderings_Olinorder(X34039) )
& ( hBOOL(hAPP(hAPP(c_member(X34039),esk486_3(X34037,X34038,X34039)),hAPP(c_List_Oset(X34039),X34037)))
| ~ c_List_Olinorder__class_Osorted(X34039,X34038)
| ~ c_List_Olinorder__class_Osorted(X34039,X34037)
| c_List_Olinorder__class_Osorted(X34039,hAPP(hAPP(c_List_Oappend(X34039),X34038),X34037))
| ~ class_Orderings_Olinorder(X34039) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X34039),esk485_3(X34037,X34038,X34039)),esk486_3(X34037,X34038,X34039)))
| ~ c_List_Olinorder__class_Osorted(X34039,X34038)
| ~ c_List_Olinorder__class_Osorted(X34039,X34037)
| c_List_Olinorder__class_Osorted(X34039,hAPP(hAPP(c_List_Oappend(X34039),X34038),X34037))
| ~ class_Orderings_Olinorder(X34039) ) ),
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_7749,plain,
! [X21004,X21005,X21006] :
( ~ class_Rings_Olinordered__semidom(X21006)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21006),c_Groups_Oone__class_Oone(X21006)),X21005))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21006),hAPP(hAPP(c_Power_Opower__class_Opower(X21006),X21005),X21004)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21006),X21005),hAPP(hAPP(c_Power_Opower__class_Opower(X21006),X21005),X21004)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__power__Suc])]) ).
fof(i_0_7750,plain,
! [X22356,X22357,X22358,X22359] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22359,tc_HOL_Obool)),X22358),X22357))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22359,tc_HOL_Obool)),X22357),X22356))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22359,tc_HOL_Obool)),X22357),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22359,tc_HOL_Obool)),X22356),X22358)) = X22358 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__diff])]) ).
fof(i_0_7751,plain,
! [X26394,X26395,X26396] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26396,tc_HOL_Obool)),X26395),X26394))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X26396,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X26396),X26395)),hAPP(c_Set_OPow(X26396),X26394))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pow__mono])]) ).
fof(i_0_7752,plain,
! [X28373,X28374,X28375,X28376,X28377,X28378] : hAPP(hAPP(c_Fun_Ocomp(X28378,X28377,X28376,hAPP(c_COMBK(X28377,X28378),X28375)),X28374),X28373) = X28375,
inference(variable_rename,[status(thm)],[fact_K__record__comp]) ).
fof(i_0_7753,plain,
! [X33340,X33341,X33342] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33342,tc_HOL_Obool)),hAPP(c_List_Oset(X33342),hAPP(hAPP(c_List_Odrop(X33342),X33341),X33340))),hAPP(c_List_Oset(X33342),X33340))),
inference(variable_rename,[status(thm)],[fact_set__drop__subset]) ).
fof(i_0_7754,plain,
! [X32631,X32632,X32633] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32633,tc_HOL_Obool)),hAPP(c_List_Oset(X32633),hAPP(hAPP(c_List_Otake(X32633),X32632),X32631))),hAPP(c_List_Oset(X32633),X32631))),
inference(variable_rename,[status(thm)],[fact_set__take__subset]) ).
fof(i_0_7755,plain,
! [X21762,X21763,X21764,X21765] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21765),X21763),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21765),X21762),X21764)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21765),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21765),X21763),X21764)),X21762))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21765),c_Groups_Ozero__class_Ozero(X21765)),X21764))
| ~ class_Fields_Olinordered__field(X21765) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21765),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21765),X21763),X21764)),X21762))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21765),X21763),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21765),X21762),X21764)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21765),c_Groups_Ozero__class_Ozero(X21765)),X21764))
| ~ class_Fields_Olinordered__field(X21765) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__le__divide__eq])])]) ).
fof(i_0_7756,plain,
! [X21766,X21767,X21768,X21769] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21769),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21769),X21767),X21768)),X21766))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21769),X21767),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21769),X21766),X21768)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21769),c_Groups_Ozero__class_Ozero(X21769)),X21768))
| ~ class_Fields_Olinordered__field(X21769) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21769),X21767),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21769),X21766),X21768)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21769),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21769),X21767),X21768)),X21766))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21769),c_Groups_Ozero__class_Ozero(X21769)),X21768))
| ~ class_Fields_Olinordered__field(X21769) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__divide__le__eq])])]) ).
fof(i_0_7757,plain,
! [X21774,X21775,X21776,X21777] :
( ~ class_Fields_Olinordered__field(X21777)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21777),c_Groups_Ozero__class_Ozero(X21777)),X21776))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21777),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21777),X21775),X21776)),X21774))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21777),X21775),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21777),X21774),X21776))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__le__div__pos])]) ).
fof(i_0_7758,plain,
! [X21674,X21675,X21676,X21677] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21677),X21675),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21677),X21674),X21676)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21677),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21677),X21675),X21676)),X21674))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21677),c_Groups_Ozero__class_Ozero(X21677)),X21676))
| ~ class_Fields_Olinordered__field(X21677) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21677),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21677),X21675),X21676)),X21674))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21677),X21675),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21677),X21674),X21676)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21677),c_Groups_Ozero__class_Ozero(X21677)),X21676))
| ~ class_Fields_Olinordered__field(X21677) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__less__divide__eq])])]) ).
fof(i_0_7759,plain,
! [X21670,X21671,X21672,X21673] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21673),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21673),X21671),X21672)),X21670))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21673),X21671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21673),X21670),X21672)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21673),c_Groups_Ozero__class_Ozero(X21673)),X21672))
| ~ class_Fields_Olinordered__field(X21673) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21673),X21671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21673),X21670),X21672)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21673),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21673),X21671),X21672)),X21670))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21673),c_Groups_Ozero__class_Ozero(X21673)),X21672))
| ~ class_Fields_Olinordered__field(X21673) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__divide__less__eq])])]) ).
fof(i_0_7760,plain,
! [X21662,X21663,X21664,X21665] :
( ~ class_Fields_Olinordered__field(X21665)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21665),c_Groups_Ozero__class_Ozero(X21665)),X21664))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21665),X21663),X21664)),X21662))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21665),X21663),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21665),X21662),X21664))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__less__div__pos])]) ).
fof(i_0_7761,plain,
! [X31676,X31677,X31678] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X31678),X31677))
| c_Smallcheck_Osmall_H(X31676,X31678,X31677) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X31678),X31677))
| c_Smallcheck_Osmall_H(X31676,X31678,X31677) = 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(X31676,X31678,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X31677),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(X31676,X31677)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5618])]) ).
fof(i_0_7762,plain,
! [X25593,X25594,X25595,X25596] :
( ~ class_Groups_Ocomm__monoid__mult(X25596)
| ~ class_Rings_Oring__1(X25596)
| hAPP(c_Int_Oring__1__class_Oof__int(X25596),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25595,tc_Int_Oint),X25594),X25593)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25595,X25596),hAPP(hAPP(c_COMBB(tc_Int_Oint,X25596,X25595),c_Int_Oring__1__class_Oof__int(X25596)),X25594)),X25593) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__setprod])]) ).
fof(i_0_7763,plain,
! [X25583,X25584,X25585,X25586] :
( ~ class_Groups_Ocomm__monoid__mult(X25586)
| ~ class_Rings_Osemiring__1(X25586)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25586),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25585,tc_Nat_Onat),X25584),X25583)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25585,X25586),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X25586,X25585),c_Nat_Osemiring__1__class_Oof__nat(X25586)),X25584)),X25583) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__setprod])]) ).
cnf(i_0_7764,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_7765,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_7766,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_7767,plain,
! [X30364,X30365,X30366,X30367] : hAPP(c_Relation_Oconverse(X30367,X30366),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X30367,X30366),tc_HOL_Obool)),X30365),X30364)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X30366,X30367),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X30367,X30366),X30365)),hAPP(c_Relation_Oconverse(X30367,X30366),X30364)),
inference(variable_rename,[status(thm)],[fact_converse__Int]) ).
fof(i_0_7768,plain,
! [X30386,X30387,X30388,X30389] : hAPP(c_Relation_Oconverse(X30389,X30388),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30389,X30388),tc_HOL_Obool)),X30387),X30386)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30388,X30389),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X30389,X30388),X30387)),hAPP(c_Relation_Oconverse(X30389,X30388),X30386)),
inference(variable_rename,[status(thm)],[fact_converse__Un]) ).
fof(i_0_7769,plain,
! [X34397,X34398,X34399] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34399)),c_List_OtakeWhile(X34399,X34398,X34397))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34399)),X34397))),
inference(variable_rename,[status(thm)],[fact_length__takeWhile__le]) ).
fof(i_0_7770,plain,
! [X30507,X30508,X30509,X30510] : hAPP(hAPP(c_Nat_Ocompow(X30510,X30510),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30509),X30508)),X30507) = hAPP(c_Fun_Ocomp(X30510,X30510,X30510,hAPP(hAPP(c_Nat_Ocompow(X30510,X30510),X30509),X30507)),hAPP(hAPP(c_Nat_Ocompow(X30510,X30510),X30508),X30507)),
inference(variable_rename,[status(thm)],[fact_funpow__add]) ).
fof(i_0_7771,plain,
! [X27195,X27196,X27197,X27198] :
( ~ class_Rings_Oring__1(X27198)
| hAPP(c_Int_Oring__1__class_Oof__int(X27198),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27197,tc_Int_Oint),X27196),X27195)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27197,X27198),hAPP(hAPP(c_COMBB(tc_Int_Oint,X27198,X27197),c_Int_Oring__1__class_Oof__int(X27198)),X27196)),X27195) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__setsum])]) ).
fof(i_0_7772,plain,
! [X27191,X27192,X27193,X27194] :
( ~ class_Rings_Osemiring__1(X27194)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27194),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27193,tc_Nat_Onat),X27192),X27191)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27193,X27194),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X27194,X27193),c_Nat_Osemiring__1__class_Oof__nat(X27194)),X27192)),X27191) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__setsum])]) ).
fof(i_0_7773,plain,
! [X28310] : c_Fun_Oinj__on(X28310,tc_fun(X28310,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X28310,tc_fun(X28310,tc_HOL_Obool),tc_fun(X28310,tc_HOL_Obool)),c_Set_Oinsert(X28310)),c_Orderings_Obot__class_Obot(tc_fun(X28310,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X28310,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_inj__singleton]) ).
fof(i_0_7774,plain,
! [X22984,X22985,X22986,X22987,X22988] : hAPP(c_New__DSequence_Opos__bind(X22988,X22987,X22986,X22985),X22984) = c_Lazy__Sequence_Obind(X22988,X22987,hAPP(X22986,X22984),hAPP(hAPP(c_COMBC(X22988,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X22987)),X22985),X22984)),
inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__bind__def]) ).
fof(i_0_7775,plain,
! [X28679,X28680,X28681,X28682] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28682),X28681))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28680),X28679))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28682,X28680)),hAPP(hAPP(c_Product__Type_OSigma(X28682,X28680),X28681),hAPP(c_COMBK(tc_fun(X28680,tc_HOL_Obool),X28682),X28679)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__cartesian__product])]) ).
fof(i_0_7776,plain,
! [X25500,X25501,X25502] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25502),X25501))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25502,tc_HOL_Obool)),X25500),X25501))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25502),X25500)),hAPP(c_Finite__Set_Ocard(X25502),X25501)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25502,tc_HOL_Obool)),X25500),X25501)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__psubset])]) ).
fof(i_0_7777,plain,
! [X24569,X24570,X24571,X24572,X24573] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24573),X24572))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24571,tc_HOL_Obool)),X24570),hAPP(c_Set_Oimage(X24573,X24571,X24569),X24572)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24571),X24570)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj])]) ).
cnf(i_0_7778,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_7779,plain,
! [X26627,X26628,X26629,X26630,X26631] :
( ~ c_Fun_Oinj__on(X26631,X26630,X26629,X26628)
| ~ c_Fun_Oinj__on(X26631,X26630,X26629,X26627)
| c_Fun_Oinj__on(X26631,X26630,X26629,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26631,tc_HOL_Obool)),X26628),X26627)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__Int])]) ).
fof(i_0_7780,plain,
! [X33400,X33401,X33402,X33403] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33403),X33402)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33401)),X33400)))
| hAPP(hAPP(c_List_Onth(X33401),hAPP(hAPP(c_List_Odrop(X33401),X33403),X33400)),X33402) = hAPP(hAPP(c_List_Onth(X33401),X33400),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33403),X33402)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__drop])]) ).
fof(i_0_7781,plain,
! [X27376,X27377,X27378,X27379] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X27378)),X27377))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27379),X27376),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X27377,hAPP(c_Nat_OSuc,X27378))) = c_Groups_Ozero__class_Ozero(X27379)
| ~ class_Groups_Ocomm__monoid__add(X27379) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X27378)),X27377))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27379),X27376),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X27377,hAPP(c_Nat_OSuc,X27378))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27379),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27379),X27376),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X27377,X27378))),hAPP(X27376,hAPP(c_Nat_OSuc,X27378)))
| ~ class_Groups_Ocomm__monoid__add(X27379) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5622])])]) ).
fof(i_0_7782,plain,
! [X34345,X34346,X34347,X34348] :
( ~ class_Orderings_Olinorder(X34348)
| ~ c_List_Olinorder__class_Osorted(X34348,hAPP(c_List_Orev(X34348),X34347))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34346),X34345))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34345),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34348)),X34347)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X34348),hAPP(hAPP(c_List_Onth(X34348),X34347),X34345)),hAPP(hAPP(c_List_Onth(X34348),X34347),X34346))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__rev__nth__mono])]) ).
fof(i_0_7783,plain,
! [X33066,X33067,X33068,X33069,X33070,X33071] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33071)),X33070) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33069)),X33068)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33071)),X33067) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33069)),X33066)
| hAPP(hAPP(c_List_Ozip(X33071,X33069),hAPP(hAPP(c_List_Oappend(X33071),X33070),X33067)),hAPP(hAPP(c_List_Oappend(X33069),X33068),X33066)) = hAPP(hAPP(c_List_Oappend(tc_prod(X33071,X33069)),hAPP(hAPP(c_List_Ozip(X33071,X33069),X33070),X33068)),hAPP(hAPP(c_List_Ozip(X33071,X33069),X33067),X33066)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__append])]) ).
fof(i_0_7784,plain,
! [X33573,X33574,X33575,X33576,X33577] : c_List_Olist_Olist__size(X33577,X33576,hAPP(hAPP(c_List_Omap(X33575,X33577),X33574),X33573)) = c_List_Olist_Olist__size(X33575,hAPP(c_Fun_Ocomp(X33577,tc_Nat_Onat,X33575,X33576),X33574),X33573),
inference(variable_rename,[status(thm)],[fact_list__size__map]) ).
fof(i_0_7785,plain,
! [X29055,X29056,X29057,X29058] :
( ~ c_Relation_Orefl__on(X29058,X29057,X29056)
| ~ hBOOL(hAPP(hAPP(c_member(X29058),X29055),X29057))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X29058,X29058)),hAPP(hAPP(c_Product__Type_OPair(X29058,X29058),X29055),X29055)),X29056)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onD])]) ).
fof(i_0_7786,plain,
! [X26098,X26099,X26100,X26101,X26102] :
( ~ hBOOL(hAPP(hAPP(c_member(X26102),X26101),X26100))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26099,tc_HOL_Obool)),hAPP(X26098,X26101)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26102,tc_fun(X26099,tc_HOL_Obool)),X26100),X26098))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__upper])]) ).
fof(i_0_7787,plain,
! [X32881,X32882,X32883,X32884] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X32884) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Otake(X32883),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X32884)),hAPP(hAPP(c_List_Olist_OCons(X32883),X32882),X32881)) = c_List_Olist_ONil(X32883) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X32884) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Otake(X32883),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X32884)),hAPP(hAPP(c_List_Olist_OCons(X32883),X32882),X32881)) = hAPP(hAPP(c_List_Olist_OCons(X32883),X32882),hAPP(hAPP(c_List_Otake(X32883),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X32884)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X32881)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__Cons__number__of])]) ).
fof(i_0_7788,plain,
! [X17828,X17829,X17830,X17832,X17833,X17834,X17835] :
( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17829),X17828),esk19_3(X17828,X17829,X17830)))
| ~ hBOOL(hAPP(X17830,X17828))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17830,X17829)),X17828),X17828)) )
& ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17830,X17829)),esk19_3(X17828,X17829,X17830)),X17828))
| ~ hBOOL(hAPP(X17830,X17828))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17830,X17829)),X17828),X17828)) )
& ( hBOOL(hAPP(X17834,X17832))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17834,X17833)),X17832),X17832)) )
& ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17833),X17832),X17835))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17834,X17833)),X17835),X17832))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17834,X17833)),X17832),X17832)) ) ),
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_7789,plain,
! [X22922,X22923,X22924,X22925,X22926,X22927] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22927,tc_fun(X22926,tc_HOL_Obool))),X22925),X22924))
| ~ hBOOL(hAPP(hAPP(X22925,X22923),X22922))
| hBOOL(hAPP(hAPP(X22924,X22923),X22922)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate2D])]) ).
fof(i_0_7790,plain,
! [X22916,X22917,X22918,X22919,X22920,X22921] :
( ~ hBOOL(hAPP(hAPP(X22921,X22920),X22919))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22918,tc_fun(X22917,tc_HOL_Obool))),X22921),X22916))
| hBOOL(hAPP(hAPP(X22916,X22920),X22919)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate2D])]) ).
fof(i_0_7791,plain,
! [X28858,X28859,X28860] :
( ~ class_Orderings_Olinorder(X28860)
| X28859 = c_Orderings_Obot__class_Obot(tc_fun(X28860,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28860,tc_HOL_Obool)),X28859),X28858))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28860),X28858))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28860),hAPP(c_Finite__Set_Ofold1(X28860,c_Orderings_Oord__class_Omin(X28860)),X28858)),hAPP(c_Finite__Set_Ofold1(X28860,c_Orderings_Oord__class_Omin(X28860)),X28859))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__antimono])]) ).
fof(i_0_7792,plain,
! [X24165,X24166,X24167,X24168] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X24168),X24167),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24168,tc_HOL_Obool)),X24166),X24165)))
| hBOOL(hAPP(hAPP(c_member(X24168),X24167),X24166))
| hBOOL(hAPP(hAPP(c_member(X24168),X24167),X24165)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X24168),X24167),X24166))
| hBOOL(hAPP(hAPP(c_member(X24168),X24167),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24168,tc_HOL_Obool)),X24166),X24165))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X24168),X24167),X24165))
| hBOOL(hAPP(hAPP(c_member(X24168),X24167),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24168,tc_HOL_Obool)),X24166),X24165))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__iff])])]) ).
fof(i_0_7793,plain,
! [X23924,X23925,X23926,X23927] :
( ~ hBOOL(hAPP(hAPP(c_member(X23927),X23926),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23927,tc_HOL_Obool)),X23925),X23924)))
| hBOOL(hAPP(hAPP(c_member(X23927),X23926),X23925))
| hBOOL(hAPP(hAPP(c_member(X23927),X23926),X23924)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5623])]) ).
fof(i_0_7794,plain,
! [X21839,X21840,X21841] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21841),c_Groups_Ozero__class_Ozero(X21841)),esk84_3(X21839,X21840,X21841)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21841),X21840),X21839))
| ~ class_Fields_Olinordered__field(X21841) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21841),X21840),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21841),X21839),esk84_3(X21839,X21840,X21841))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21841),X21840),X21839))
| ~ class_Fields_Olinordered__field(X21841) ) ),
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_7795,plain,
! [X27156,X27157,X27158,X27159,X27160] : c_Map_Orestrict__map(X27160,X27159,c_Map_Orestrict__map(X27160,X27159,X27158,X27157),X27156) = c_Map_Orestrict__map(X27160,X27159,X27158,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27160,tc_HOL_Obool)),X27157),X27156)),
inference(variable_rename,[status(thm)],[fact_restrict__restrict]) ).
fof(i_0_7796,plain,
! [X33560,X33561,X33562,X33563,X33564,X33565] : hAPP(c_List_Ofoldl(X33565,X33564,X33563,X33562),hAPP(hAPP(c_List_Olist_OCons(X33564),X33561),X33560)) = hAPP(c_List_Ofoldl(X33565,X33564,X33563,hAPP(hAPP(X33563,X33562),X33561)),X33560),
inference(variable_rename,[status(thm)],[fact_foldl__Cons]) ).
fof(i_0_7797,plain,
! [X34356,X34357] :
( ( X34356 != c_List_Olist_ONil(tc_List_Olist(X34357))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34357))),c_List_Otranspose(X34357,X34356)) = 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(X34357),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X34357))),X34356))) )
& ( X34356 = c_List_Olist_ONil(tc_List_Olist(X34357))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X34357))),c_List_Otranspose(X34357,X34356)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34357)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X34357)),X34356),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(X34357),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X34357))),X34356))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__transpose__sorted])])]) ).
fof(i_0_7798,plain,
! [X20865,X20866,X20867,X20868] :
( ~ class_Rings_Olinordered__semidom(X20868)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20868),X20867),X20866))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20868),c_Groups_Ozero__class_Ozero(X20868)),X20867))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20865))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20868),hAPP(hAPP(c_Power_Opower__class_Opower(X20868),X20867),X20865)),hAPP(hAPP(c_Power_Opower__class_Opower(X20868),X20866),X20865))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__mono])]) ).
fof(i_0_7799,plain,
! [X20880,X20881,X20882,X20883] :
( ~ class_Rings_Olinordered__semidom(X20883)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20882),X20881))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20883),c_Groups_Ozero__class_Ozero(X20883)),X20880))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20883),X20880),c_Groups_Oone__class_Oone(X20883)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20883),hAPP(hAPP(c_Power_Opower__class_Opower(X20883),X20880),X20881)),hAPP(hAPP(c_Power_Opower__class_Opower(X20883),X20880),X20882))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__decreasing])]) ).
fof(i_0_7800,plain,
! [X20884,X20885,X20886,X20887] :
( ~ class_Rings_Olinordered__semidom(X20887)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20886),X20885))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20887),c_Groups_Ozero__class_Ozero(X20887)),X20884))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20887),X20884),c_Groups_Oone__class_Oone(X20887)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20887),hAPP(hAPP(c_Power_Opower__class_Opower(X20887),X20884),X20885)),hAPP(hAPP(c_Power_Opower__class_Opower(X20887),X20884),X20886))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__decreasing])]) ).
fof(i_0_7801,plain,
! [X28438,X28439,X28440,X28441,X28442] : hAPP(c_Set_Ovimage(X28442,X28441,X28440),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28441,tc_HOL_Obool)),X28439),X28438)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28442,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X28442,X28441,X28440),X28439)),hAPP(c_Set_Ovimage(X28442,X28441,X28440),X28438)),
inference(variable_rename,[status(thm)],[fact_vimage__Int]) ).
fof(i_0_7802,plain,
! [X28433,X28434,X28435,X28436,X28437] : hAPP(c_Set_Ovimage(X28437,X28436,X28435),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28436,tc_HOL_Obool)),X28434),X28433)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28437,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X28437,X28436,X28435),X28434)),hAPP(c_Set_Ovimage(X28437,X28436,X28435),X28433)),
inference(variable_rename,[status(thm)],[fact_vimage__Un]) ).
fof(i_0_7803,plain,
! [X28399,X28400,X28401,X28402,X28403] : hAPP(c_Set_Ovimage(X28403,X28402,X28401),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28402,tc_HOL_Obool)),X28400),X28399)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28403,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X28403,X28402,X28401),X28400)),hAPP(c_Set_Ovimage(X28403,X28402,X28401),X28399)),
inference(variable_rename,[status(thm)],[fact_vimage__Diff]) ).
fof(i_0_7804,plain,
! [X24263,X24264,X24265,X24266,X24267] : hAPP(c_Relation_OImage(X24267,X24266,X24265),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24267,tc_HOL_Obool)),X24264),X24263)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24266,tc_HOL_Obool)),hAPP(c_Relation_OImage(X24267,X24266,X24265),X24264)),hAPP(c_Relation_OImage(X24267,X24266,X24265),X24263)),
inference(variable_rename,[status(thm)],[fact_Image__Un]) ).
fof(i_0_7805,plain,
! [X24258,X24259,X24260,X24261,X24262] : hAPP(c_Set_Oimage(X24262,X24261,X24260),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24262,tc_HOL_Obool)),X24259),X24258)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24261,tc_HOL_Obool)),hAPP(c_Set_Oimage(X24262,X24261,X24260),X24259)),hAPP(c_Set_Oimage(X24262,X24261,X24260),X24258)),
inference(variable_rename,[status(thm)],[fact_image__Un]) ).
fof(i_0_7806,plain,
! [X33682,X33683,X33684,X33685] :
( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33685)),X33684),c_List_Olists(X33685,X33682)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33685)),hAPP(hAPP(c_List_Oappend(X33685),X33684),X33683)),c_List_Olists(X33685,X33682))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33685)),X33683),c_List_Olists(X33685,X33682)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33685)),hAPP(hAPP(c_List_Oappend(X33685),X33684),X33683)),c_List_Olists(X33685,X33682))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33685)),X33684),c_List_Olists(X33685,X33682)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33685)),X33683),c_List_Olists(X33685,X33682)))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33685)),hAPP(hAPP(c_List_Oappend(X33685),X33684),X33683)),c_List_Olists(X33685,X33682))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__in__lists__conv])])]) ).
fof(i_0_7807,plain,
! [X26500,X26501,X26502] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26502,tc_HOL_Obool)),X26501),X26500))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X26502,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(X26502,X26501)),c_Predicate_OPowp(X26502,X26500))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Powp__mono])]) ).
fof(i_0_7808,plain,
! [X31644,X31645,X31646,X31647] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31647,tc_HOL_Obool)),c_Map_Odom(X31647,X31646,X31645)),c_Map_Odom(X31647,X31646,X31644)) != c_Orderings_Obot__class_Obot(tc_fun(X31647,tc_HOL_Obool))
| c_Map_Omap__add(X31647,X31646,X31645,X31644) = c_Map_Omap__add(X31647,X31646,X31644,X31645) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__add__comm])]) ).
fof(i_0_7809,plain,
! [X25649,X25650,X25651,X25652] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25652),X25651))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25650),X25649))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X25652,X25650)),c_Sum__Type_OPlus(X25652,X25650,X25651,X25649))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus])]) ).
fof(i_0_7810,plain,
! [X27972,X27973,X27974,X27975,X27976,X27977] :
( ~ c_Finite__Set_Ofolding(X27977,X27976,X27975,X27974)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27977),X27973))
| hBOOL(hAPP(hAPP(c_member(X27977),X27972),X27973))
| hAPP(X27974,hAPP(hAPP(c_Set_Oinsert(X27977),X27972),X27973)) = hAPP(c_Fun_Ocomp(X27976,X27976,X27976,hAPP(X27974,X27973)),hAPP(X27975,X27972)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5624])]) ).
fof(i_0_7811,plain,
! [X26286,X26287,X26288,X26289] :
( X26289 != X26288
| ~ hBOOL(hAPP(hAPP(c_member(X26287),X26289),X26286))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X26287,X26287)),hAPP(hAPP(c_Product__Type_OPair(X26287,X26287),X26289),X26288)),c_Relation_OId__on(X26287,X26286))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__on__eqI])]) ).
fof(i_0_7812,plain,
! [X29086,X29087] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X29087),c_Int_OInteg))
| ~ hBOOL(hAPP(X29086,hAPP(c_Int_ORep__Integ,esk307_2(X29086,X29087))))
| hBOOL(hAPP(X29086,X29087)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Rep__Integ__induct])])]) ).
fof(i_0_7813,plain,
! [X33054,X33055,X33056,X33057,X33058] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33058),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33057)),X33056)))
| hAPP(hAPP(c_List_Olist__update(X33057,hAPP(hAPP(c_List_Oappend(X33057),X33056),X33055)),X33058),X33054) = hAPP(hAPP(c_List_Oappend(X33057),hAPP(hAPP(c_List_Olist__update(X33057,X33056),X33058),X33054)),X33055) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__append1])]) ).
fof(i_0_7814,plain,
! [X23470,X23471,X23472] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23472),X23471)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23472),X23470)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23471),X23470))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23472)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23471),X23470))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23472),X23471)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23472),X23470)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23472)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__dvd__cancel1])])]) ).
fof(i_0_7815,plain,
! [X23467,X23468,X23469] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23469),X23468)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23469),X23467)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23469))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23468),X23467)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel])]) ).
fof(i_0_7816,plain,
! [X19149,X19150,X19151] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19151),X19150)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19149),X19150)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19150))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19151),X19149)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19150))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19151),X19150)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19149),X19150))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19151),X19149))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19151),X19150)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19149),X19150))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel2])])]) ).
fof(i_0_7817,plain,
! [X23048,X23049,X23050] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X23050),X23049)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X23050),X23048)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X23050))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23049),X23048)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__dvd__imp__le])]) ).
fof(i_0_7818,plain,
! [X19739,X19740,X19741] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19741),X19740)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19741),X19739)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19740),X19739))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19741)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19740),X19739))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19741),X19740)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19741),X19739)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19741)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__le__cancel1])])]) ).
fof(i_0_7819,plain,
! [X19146,X19147,X19148] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19148),X19147)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19148),X19146)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19148))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19147),X19146)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19148))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19148),X19147)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19148),X19146))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19147),X19146))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19148),X19147)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19148),X19146))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel1])])]) ).
fof(i_0_7820,plain,
! [X20904,X20905,X20906] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20906))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20906),X20905)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20906),X20904)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20905),X20904)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__less__imp__less])]) ).
fof(i_0_7821,plain,
! [X19766,X19767,X19768] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19768),X19767)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19768),X19766)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19767),X19766))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19768)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19767),X19766))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19768),X19767)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19768),X19766)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19768)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__less__cancel1])])]) ).
fof(i_0_7822,plain,
! [X29642,X29643,X29644] :
( ~ c_Wellfounded_Owf(X29644,X29643)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29644,tc_HOL_Obool)),X29642),hAPP(c_Relation_OImage(X29644,X29644,X29643),X29642)))
| X29642 = c_Orderings_Obot__class_Obot(tc_fun(X29644,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfE__pf])]) ).
fof(i_0_7823,plain,
! [X27476,X27477,X27478] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27478,tc_Nat_Onat),X27477),X27476)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27478,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X27478),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X27477)),X27476),
inference(variable_rename,[status(thm)],[fact_int__setsum]) ).
fof(i_0_7824,plain,
! [X25587,X25588,X25589] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25589,tc_Nat_Onat),X25588),X25587)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25589,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X25589),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X25588)),X25587),
inference(variable_rename,[status(thm)],[fact_int__setprod]) ).
fof(i_0_7825,plain,
! [X29305,X29306,X29307,X29308] : c_Fun_Ooverride__on(X29308,X29307,X29306,X29305,c_Orderings_Obot__class_Obot(tc_fun(X29308,tc_HOL_Obool))) = X29306,
inference(variable_rename,[status(thm)],[fact_override__on__emptyset]) ).
fof(i_0_7826,plain,
! [X30800,X30801,X30802,X30803,X30804] :
( ~ c_Finite__Set_Ofun__left__comm(X30804,X30803,X30802)
| hAPP(c_Fun_Ocomp(X30803,X30803,X30803,hAPP(X30802,X30801)),hAPP(X30802,X30800)) = hAPP(c_Fun_Ocomp(X30803,X30803,X30803,hAPP(X30802,X30800)),hAPP(X30802,X30801)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__comp__comm])]) ).
fof(i_0_7827,plain,
! [X23117,X23118,X23119] : c_Hoare__Mirabelle_Ohoare__derivs(X23119,X23118,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X23119)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X23119),X23117),c_Com_Ocom_OSKIP),X23117)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X23119),tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_hoare__derivs_OSkip]) ).
fof(i_0_7828,plain,
! [X23114,X23115,X23116] : c_Hoare__Mirabelle_Ohoare__derivs(X23116,X23115,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X23116)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X23116),X23114),c_Com_Ocom_OSKIP),X23114)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X23116),tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_hoare__derivs_Oequations_I7_J]) ).
fof(i_0_7829,plain,
! [X18166,X18167,X18168,X18169,X18170] : c_Option_Ooption_Ooption__rec(X18170,X18169,X18168,X18167,hAPP(c_Option_Ooption_OSome(X18169),X18166)) = hAPP(X18167,X18166),
inference(variable_rename,[status(thm)],[fact_option_Orecs_I2_J]) ).
fof(i_0_7830,plain,
! [X32859,X32860,X32861,X32862] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32862),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32861)),X32860)))
| hBOOL(hAPP(hAPP(c_member(X32861),X32859),hAPP(c_List_Oset(X32861),hAPP(hAPP(c_List_Olist__update(X32861,X32860),X32862),X32859)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__update__memI])]) ).
fof(i_0_7831,plain,
! [X25867,X25868,X25869,X25870,X25871,X25872] :
( ~ hBOOL(hAPP(hAPP(c_member(X25872),X25871),X25870))
| ~ hBOOL(hAPP(hAPP(c_member(X25869),X25868),hAPP(X25867,X25871)))
| hBOOL(hAPP(hAPP(c_member(X25869),X25868),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25872,tc_fun(X25869,tc_HOL_Obool)),X25870),X25867))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__I])]) ).
fof(i_0_7832,plain,
! [X22209,X22210,X22211,X22212,X22213,X22214] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22214,X22213),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22212),X22211)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22214,X22213),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22210),X22209)))
| X22213 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X22212 = X22210 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient])]) ).
fof(i_0_7833,plain,
! [X22215,X22216,X22217,X22218,X22219,X22220] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22220,X22219),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22218),X22217)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22220,X22219),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22216),X22215)))
| X22219 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X22217 = X22215 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__remainder])]) ).
fof(i_0_7834,plain,
! [X26436,X26437,X26438,X26439] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26439),hAPP(c_Set_Oimage(X26438,X26439,X26437),X26436)))
| ~ c_Fun_Oinj__on(X26438,X26439,X26437,X26436)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X26438),X26436)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageD])]) ).
fof(i_0_7835,plain,
! [X23326,X23327,X23328,X23329] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23329),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23329),X23328),X23327)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23329),X23328),X23326)))
| X23328 = c_Groups_Ozero__class_Ozero(X23329)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23329),X23327),X23326))
| ~ class_Rings_Oidom(X23329) )
& ( X23328 != c_Groups_Ozero__class_Ozero(X23329)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23329),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23329),X23328),X23327)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23329),X23328),X23326)))
| ~ class_Rings_Oidom(X23329) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23329),X23327),X23326))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23329),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23329),X23328),X23327)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23329),X23328),X23326)))
| ~ class_Rings_Oidom(X23329) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel__left])])]) ).
fof(i_0_7836,plain,
! [X23330,X23331,X23332,X23333] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23333),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23333),X23332),X23331)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23333),X23330),X23331)))
| X23331 = c_Groups_Ozero__class_Ozero(X23333)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23333),X23332),X23330))
| ~ class_Rings_Oidom(X23333) )
& ( X23331 != c_Groups_Ozero__class_Ozero(X23333)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23333),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23333),X23332),X23331)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23333),X23330),X23331)))
| ~ class_Rings_Oidom(X23333) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23333),X23332),X23330))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23333),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23333),X23332),X23331)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23333),X23330),X23331)))
| ~ class_Rings_Oidom(X23333) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel__right])])]) ).
fof(i_0_7837,plain,
! [X30565,X30566,X30567,X30568] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30568,X30567),tc_HOL_Obool)),X30566),X30565))
| ~ c_Relation_Osingle__valued(X30568,X30567,X30565)
| c_Relation_Osingle__valued(X30568,X30567,X30566) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__subset])]) ).
cnf(i_0_7838,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_7839,plain,
! [X19246,X19247,X19248,X19249] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19249),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19249),X19248),X19247)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19249),X19246),X19247)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19249),X19248),X19246))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X19249) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19249),X19248),X19246))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19249),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19249),X19248),X19247)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19249),X19246),X19247)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X19249) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right])])]) ).
fof(i_0_7840,plain,
! [X19225,X19226,X19227,X19228] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X19228)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19228),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19228),X19227),X19226)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19228),X19225),X19226)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19228),X19227),X19225)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right])]) ).
fof(i_0_7841,plain,
! [X19242,X19243,X19244,X19245] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19245),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19245),X19244),X19243)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19245),X19244),X19242)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19245),X19243),X19242))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X19245) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19245),X19243),X19242))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19245),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19245),X19244),X19243)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19245),X19244),X19242)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X19245) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left])])]) ).
fof(i_0_7842,plain,
! [X19221,X19222,X19223,X19224] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X19224)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19224),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19224),X19223),X19222)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19224),X19223),X19221)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19224),X19222),X19221)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left])]) ).
fof(i_0_7843,plain,
! [X18295,X18296,X18297,X18298] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18298)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18298),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18298),X18297),X18296)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18298),X18295),X18296)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18298),X18297),X18295)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right])]) ).
fof(i_0_7844,plain,
! [X18274,X18275,X18276,X18277] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18277),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18277),X18276),X18275)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18277),X18274),X18275)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18277),X18276),X18274))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18277) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18277),X18276),X18274))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18277),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18277),X18276),X18275)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18277),X18274),X18275)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18277) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right])])]) ).
fof(i_0_7845,plain,
! [X18299,X18300,X18301,X18302] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18302)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18302),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18302),X18301),X18300)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18302),X18301),X18299)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18302),X18300),X18299)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left])]) ).
fof(i_0_7846,plain,
! [X18278,X18279,X18280,X18281] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18281),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18281),X18280),X18279)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18281),X18280),X18278)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18281),X18279),X18278))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18281) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18281),X18279),X18278))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18281),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18281),X18280),X18279)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18281),X18280),X18278)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18281) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left])])]) ).
fof(i_0_7847,plain,
! [X17796,X17797,X17798,X17799,X17801,X17802,X17803,X17804,X17805] :
( ( c_Natural_Oevaln(X17798,X17797,X17796,esk16_4(X17796,X17797,X17798,X17799))
| ~ hBOOL(hAPP(X17799,X17797))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17799,X17798),X17797,X17796,X17797) )
& ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X17799,X17798),esk16_4(X17796,X17797,X17798,X17799),X17796,X17797)
| ~ hBOOL(hAPP(X17799,X17797))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17799,X17798),X17797,X17796,X17797) )
& ( hBOOL(hAPP(X17804,X17802))
| c_Natural_Oevaln(c_Com_Ocom_OWhile(X17804,X17803),X17802,X17801,X17802) )
& ( ~ c_Natural_Oevaln(X17803,X17802,X17801,X17805)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17804,X17803),X17805,X17801,X17802)
| c_Natural_Oevaln(c_Com_Ocom_OWhile(X17804,X17803),X17802,X17801,X17802) ) ),
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_7848,plain,
! [X18002,X18003,X18004,X18005] :
( ( X18003 = hAPP(c_Nat_OSuc,esk27_4(X18002,X18003,X18004,X18005))
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X18005),X18004,X18003,X18002) )
& ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X18005)),X18004,esk27_4(X18002,X18003,X18004,X18005),X18002)
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X18005),X18004,X18003,X18002) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5626])])])]) ).
fof(i_0_7849,plain,
! [X34183,X34184,X34185,X34186] :
( ~ class_Orderings_Olinorder(X34186)
| ~ c_List_Olinorder__class_Osorted(X34186,X34185)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34184),X34183))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34183),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34186)),X34185)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X34186),hAPP(hAPP(c_List_Onth(X34186),X34185),X34184)),hAPP(hAPP(c_List_Onth(X34186),X34185),X34183))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__nth__mono])]) ).
fof(i_0_7850,plain,
! [X30458,X30459,X30460] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30460,X30460),tc_HOL_Obool),hAPP(c_Nat_OSuc,X30459)),X30458) = hAPP(hAPP(c_Relation_Orel__comp(X30460,X30460,X30460),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30460,X30460),tc_HOL_Obool),X30459),X30458)),X30458),
inference(variable_rename,[status(thm)],[fact_relpow_Osimps_I2_J]) ).
fof(i_0_7851,plain,
! [X21717,X21718,X21719,X21720] :
( ~ class_Fields_Ofield(X21720)
| X21719 = c_Groups_Ozero__class_Ozero(X21720)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21720),X21718),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21720),X21717),X21719)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21720),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21720),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21720),X21719),X21718)),X21717)),X21719) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__divide__eq__iff])]) ).
fof(i_0_7852,plain,
! [X21700,X21701,X21702,X21703] :
( ~ class_Fields_Ofield(X21703)
| X21702 = c_Groups_Ozero__class_Ozero(X21703)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21703),X21701),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21703),X21700),X21702)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21703),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21703),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21703),X21702),X21701)),X21700)),X21702) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__divide__eq__iff])]) ).
fof(i_0_7853,plain,
! [X34135,X34136,X34137,X34138,X34139,X34140] :
( ~ class_Orderings_Olinorder(X34140)
| ~ c_List_Olinorder__class_Osorted(X34140,hAPP(hAPP(c_List_Omap(X34139,X34140),X34138),X34137))
| ~ hBOOL(hAPP(X34136,X34135))
| hAPP(c_List_Ofilter(X34139,X34136),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X34139,X34140,X34138),X34135),X34137)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X34139,X34140,X34138),X34135),hAPP(c_List_Ofilter(X34139,X34136),X34137)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_filter__insort])]) ).
cnf(i_0_7854,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_7855,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_7856,plain,
! [X23104,X23105,X23106] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23106,tc_HOL_Obool)),X23105),hAPP(hAPP(c_Set_Oinsert(X23106),X23104),c_Orderings_Obot__class_Obot(tc_fun(X23106,tc_HOL_Obool)))))
| X23105 = c_Orderings_Obot__class_Obot(tc_fun(X23106,tc_HOL_Obool))
| X23105 = hAPP(hAPP(c_Set_Oinsert(X23106),X23104),c_Orderings_Obot__class_Obot(tc_fun(X23106,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__singletonD])]) ).
fof(i_0_7857,plain,
! [X23697,X23698,X23699,X23700] :
( ( hBOOL(hAPP(hAPP(c_member(X23700),X23699),X23698))
| ~ hBOOL(hAPP(hAPP(c_member(X23700),X23699),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23700,tc_HOL_Obool)),X23698),X23697))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X23700),X23699),X23697))
| ~ hBOOL(hAPP(hAPP(c_member(X23700),X23699),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23700,tc_HOL_Obool)),X23698),X23697))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X23700),X23699),X23698))
| hBOOL(hAPP(hAPP(c_member(X23700),X23699),X23697))
| hBOOL(hAPP(hAPP(c_member(X23700),X23699),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23700,tc_HOL_Obool)),X23698),X23697))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5628])])]) ).
fof(i_0_7858,plain,
! [X23598,X23599,X23600,X23601] :
( ( hBOOL(hAPP(hAPP(c_member(X23601),X23600),X23599))
| ~ hBOOL(hAPP(hAPP(c_member(X23601),X23600),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23601,tc_HOL_Obool)),X23599),X23598))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X23601),X23600),X23598))
| ~ hBOOL(hAPP(hAPP(c_member(X23601),X23600),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23601,tc_HOL_Obool)),X23599),X23598))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DiffE])])]) ).
fof(i_0_7859,plain,
! [X23689,X23690,X23691,X23692] :
( ~ hBOOL(hAPP(hAPP(c_member(X23692),X23691),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23692,tc_HOL_Obool)),X23690),X23689)))
| ~ hBOOL(hAPP(hAPP(c_member(X23692),X23691),X23689)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5629])]) ).
fof(i_0_7860,plain,
! [X25539,X25540,X25541,X25544,X25545,X25546,X25547,X25548] :
( ( X25540 = hAPP(hAPP(c_Set_Oinsert(X25541),esk148_3(X25539,X25540,X25541)),esk149_3(X25539,X25540,X25541))
| hAPP(c_Finite__Set_Ocard(X25541),X25540) != hAPP(c_Nat_OSuc,X25539) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X25541),esk148_3(X25539,X25540,X25541)),esk149_3(X25539,X25540,X25541)))
| hAPP(c_Finite__Set_Ocard(X25541),X25540) != hAPP(c_Nat_OSuc,X25539) )
& ( hAPP(c_Finite__Set_Ocard(X25541),esk149_3(X25539,X25540,X25541)) = X25539
| hAPP(c_Finite__Set_Ocard(X25541),X25540) != hAPP(c_Nat_OSuc,X25539) )
& ( X25539 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| esk149_3(X25539,X25540,X25541) = c_Orderings_Obot__class_Obot(tc_fun(X25541,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(X25541),X25540) != hAPP(c_Nat_OSuc,X25539) )
& ( X25544 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X25545 != hAPP(hAPP(c_Set_Oinsert(X25546),X25547),X25548)
| hBOOL(hAPP(hAPP(c_member(X25546),X25547),X25548))
| hAPP(c_Finite__Set_Ocard(X25546),X25548) != X25544
| hAPP(c_Finite__Set_Ocard(X25546),X25545) = hAPP(c_Nat_OSuc,X25544) )
& ( X25548 != c_Orderings_Obot__class_Obot(tc_fun(X25546,tc_HOL_Obool))
| X25545 != hAPP(hAPP(c_Set_Oinsert(X25546),X25547),X25548)
| hBOOL(hAPP(hAPP(c_member(X25546),X25547),X25548))
| hAPP(c_Finite__Set_Ocard(X25546),X25548) != X25544
| hAPP(c_Finite__Set_Ocard(X25546),X25545) = hAPP(c_Nat_OSuc,X25544) ) ),
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_7861,plain,
! [X28039,X28040,X28041,X28042,X28043,X28044] :
( ~ c_Finite__Set_Ofolding__idem(X28044,X28043,X28042,X28041)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28044),X28040))
| ~ hBOOL(hAPP(hAPP(c_member(X28044),X28039),X28040))
| hAPP(c_Fun_Ocomp(X28043,X28043,X28043,hAPP(X28041,X28040)),hAPP(X28042,X28039)) = hAPP(X28041,X28040) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Oin__comp__idem])]) ).
fof(i_0_7862,plain,
! [X33186,X33187,X33188] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33188),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33187)),X33186)))
| hAPP(hAPP(c_List_Otake(X33187),hAPP(c_Nat_OSuc,X33188)),X33186) = hAPP(hAPP(c_List_Oappend(X33187),hAPP(hAPP(c_List_Otake(X33187),X33188),X33186)),hAPP(hAPP(c_List_Olist_OCons(X33187),hAPP(hAPP(c_List_Onth(X33187),X33186),X33188)),c_List_Olist_ONil(X33187))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__Suc__conv__app__nth])]) ).
fof(i_0_7863,plain,
! [X25436,X25437,X25438] :
( ~ class_Orderings_Olinorder(X25438)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25438),X25437))
| X25437 = c_Orderings_Obot__class_Obot(tc_fun(X25438,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25438),X25436))
| X25436 = c_Orderings_Obot__class_Obot(tc_fun(X25438,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25438,tc_HOL_Obool)),X25437),X25436) != c_Orderings_Obot__class_Obot(tc_fun(X25438,tc_HOL_Obool))
| c_Big__Operators_Olattice_OInf__fin(X25438,c_Orderings_Oord__class_Omin(X25438),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25438,tc_HOL_Obool)),X25437),X25436)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25438),c_Big__Operators_Olattice_OInf__fin(X25438,c_Orderings_Oord__class_Omin(X25438),X25437)),c_Big__Operators_Olattice_OInf__fin(X25438,c_Orderings_Oord__class_Omin(X25438),X25436)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__disjoint])]) ).
fof(i_0_7864,plain,
! [X25347,X25348,X25349] :
( ~ class_Orderings_Olinorder(X25349)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25349),X25348))
| X25348 = c_Orderings_Obot__class_Obot(tc_fun(X25349,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25349),X25347))
| X25347 = c_Orderings_Obot__class_Obot(tc_fun(X25349,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25349,tc_HOL_Obool)),X25348),X25347) != c_Orderings_Obot__class_Obot(tc_fun(X25349,tc_HOL_Obool))
| c_Big__Operators_Olattice_OSup__fin(X25349,c_Orderings_Oord__class_Omax(X25349),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25349,tc_HOL_Obool)),X25348),X25347)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25349),c_Big__Operators_Olattice_OSup__fin(X25349,c_Orderings_Oord__class_Omax(X25349),X25348)),c_Big__Operators_Olattice_OSup__fin(X25349,c_Orderings_Oord__class_Omax(X25349),X25347)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__disjoint])]) ).
fof(i_0_7865,plain,
! [X30476,X30477,X30478,X30479] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(X30479,X30478),tc_fun(X30479,X30478)),X30477),c_Fun_Ocomp(X30478,X30478,X30479,X30476)) = c_Fun_Ocomp(X30478,X30478,X30479,hAPP(hAPP(c_Nat_Ocompow(X30478,X30478),X30477),X30476)),
inference(variable_rename,[status(thm)],[fact_comp__funpow]) ).
fof(i_0_7866,plain,
! [X23427,X23428,X23429,X23430,X23431,X23432] : hAPP(hAPP(c_Product__Type_Ocurry(X23432,X23431,X23430,X23429),X23428),X23427) = hAPP(X23429,hAPP(hAPP(c_Product__Type_OPair(X23432,X23431),X23428),X23427)),
inference(variable_rename,[status(thm)],[fact_curry__conv]) ).
fof(i_0_7867,plain,
! [X23042,X23043,X23044,X23045,X23046,X23047] : hAPP(hAPP(c_Product__Type_Ocurry(X23047,X23046,X23045,X23044),X23043),X23042) = hAPP(X23044,hAPP(hAPP(c_Product__Type_OPair(X23047,X23046),X23043),X23042)),
inference(variable_rename,[status(thm)],[fact_curry__def]) ).
fof(i_0_7868,plain,
! [X26640,X26641,X26642,X26643,X26644] :
( ( hAPP(c_Set_Oimage(X26644,X26643,X26642),X26641) != hAPP(c_Set_Oimage(X26644,X26643,X26642),X26640)
| X26641 = X26640
| ~ c_Fun_Oinj__on(X26644,X26643,X26642,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26644,tc_HOL_Obool)),X26641),X26640)) )
& ( X26641 != X26640
| hAPP(c_Set_Oimage(X26644,X26643,X26642),X26641) = hAPP(c_Set_Oimage(X26644,X26643,X26642),X26640)
| ~ c_Fun_Oinj__on(X26644,X26643,X26642,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26644,tc_HOL_Obool)),X26641),X26640)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__Un__image__eq__iff])])]) ).
fof(i_0_7869,plain,
! [X21770,X21771,X21772,X21773] :
( ~ class_Fields_Olinordered__field(X21773)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21773),c_Groups_Ozero__class_Ozero(X21773)),X21772))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21773),X21771),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21773),X21770),X21772)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21773),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21773),X21771),X21772)),X21770)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__div__pos__le])]) ).
fof(i_0_7870,plain,
! [X21666,X21667,X21668,X21669] :
( ~ class_Fields_Olinordered__field(X21669)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21669),c_Groups_Ozero__class_Ozero(X21669)),X21668))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21669),X21667),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21669),X21666),X21668)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21669),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21669),X21667),X21668)),X21666)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__div__pos__less])]) ).
fof(i_0_7871,plain,
! [X29050,X29051,X29052,X29053,X29054] :
( ~ c_Relation_Orefl__on(X29054,X29053,X29052)
| ~ c_Relation_Orefl__on(X29054,X29051,X29050)
| c_Relation_Orefl__on(X29054,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29054,tc_HOL_Obool)),X29053),X29051),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X29054,X29054),tc_HOL_Obool)),X29052),X29050)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__Int])]) ).
fof(i_0_7872,plain,
! [X29045,X29046,X29047,X29048,X29049] :
( ~ c_Relation_Orefl__on(X29049,X29048,X29047)
| ~ c_Relation_Orefl__on(X29049,X29046,X29045)
| c_Relation_Orefl__on(X29049,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29049,tc_HOL_Obool)),X29048),X29046),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29049,X29049),tc_HOL_Obool)),X29047),X29045)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__Un])]) ).
fof(i_0_7873,plain,
! [X32936,X32937,X32938,X32939] : c_Map_Omap__upds(X32939,X32938,X32937,c_List_Olist_ONil(X32939),X32936) = X32937,
inference(variable_rename,[status(thm)],[fact_map__upds__Nil1]) ).
fof(i_0_7874,plain,
! [X32932,X32933,X32934,X32935] : c_Map_Omap__upds(X32935,X32934,X32933,X32932,c_List_Olist_ONil(X32934)) = X32933,
inference(variable_rename,[status(thm)],[fact_map__upds__Nil2]) ).
fof(i_0_7875,plain,
! [X18175,X18176,X18177,X18178] : c_Option_Ooption_Ooption__rec(X18178,X18177,X18176,X18175,c_Option_Ooption_ONone(X18177)) = X18176,
inference(variable_rename,[status(thm)],[fact_option_Orecs_I1_J]) ).
fof(i_0_7876,plain,
! [X29806,X29807,X29808,X29809,X29810] : hAPP(c_Relation_ODomain(X29810,X29809),hAPP(hAPP(c_Set_Oinsert(tc_prod(X29810,X29809)),hAPP(hAPP(c_Product__Type_OPair(X29810,X29809),X29808),X29807)),X29806)) = hAPP(hAPP(c_Set_Oinsert(X29810),X29808),hAPP(c_Relation_ODomain(X29810,X29809),X29806)),
inference(variable_rename,[status(thm)],[fact_Domain__insert]) ).
fof(i_0_7877,plain,
! [X29715,X29716,X29717,X29718,X29719] : hAPP(c_Relation_ORange(X29719,X29718),hAPP(hAPP(c_Set_Oinsert(tc_prod(X29719,X29718)),hAPP(hAPP(c_Product__Type_OPair(X29719,X29718),X29717),X29716)),X29715)) = hAPP(hAPP(c_Set_Oinsert(X29718),X29716),hAPP(c_Relation_ORange(X29719,X29718),X29715)),
inference(variable_rename,[status(thm)],[fact_Range__insert]) ).
fof(i_0_7878,plain,
! [X22377,X22378,X22379,X22380] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22380,tc_HOL_Obool)),X22379),X22378))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22380,tc_HOL_Obool)),X22378),X22377))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22380,tc_HOL_Obool)),X22379),X22377)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__trans])]) ).
fof(i_0_7879,plain,
! [X22393,X22394,X22395,X22396] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22396,tc_HOL_Obool)),X22395),X22394))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22396,tc_HOL_Obool)),X22394),X22393))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22396,tc_HOL_Obool)),X22395),X22393)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__subset__trans])]) ).
fof(i_0_7880,plain,
! [X22397,X22398,X22399,X22400] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22400,tc_HOL_Obool)),X22399),X22398))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22400,tc_HOL_Obool)),X22398),X22397))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22400,tc_HOL_Obool)),X22399),X22397)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__psubset__trans])]) ).
fof(i_0_7881,plain,
! [X22436,X22437,X22438,X22439] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22439,tc_HOL_Obool)),X22438),X22437))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22439,tc_HOL_Obool)),X22437),X22436))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22439,tc_HOL_Obool)),X22438),X22436)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__trans])]) ).
fof(i_0_7882,plain,
! [X24414,X24415] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X24415),X24414))
| hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24415)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X24414))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24415)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X24414)))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X24415),X24414)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I2_J])]) ).
fof(i_0_7883,plain,
! [X22857,X22858,X22859,X22860,X22861] : hAPP(hAPP(c_Product__Type_Oscomp(X22861,X22860,X22861,X22859),hAPP(c_Product__Type_OPair(X22860,X22861),X22858)),X22857) = hAPP(X22857,X22858),
inference(variable_rename,[status(thm)],[fact_Pair__scomp]) ).
cnf(i_0_7884,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_7885,plain,
! [X20187,X20188,X20189] :
( ~ class_Divides_Osemiring__div(X20189)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20189),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20189),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20189),X20188),X20187)),X20187)),c_Divides_Odiv__class_Omod(X20189,X20188,X20187)) = X20188 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__equality])]) ).
fof(i_0_7886,plain,
! [X20239,X20240,X20241] :
( ~ class_Divides_Osemiring__div(X20241)
| X20240 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20241),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20241),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20241),X20240),X20239)),X20239)),c_Divides_Odiv__class_Omod(X20241,X20240,X20239)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__decomp])]) ).
cnf(i_0_7887,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_7888,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_7889,plain,
! [X17756,X17757,X17758] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X17758)),X17757),X17756))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X17758))),X17757),X17756)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc__elim__cases_I6_J])]) ).
fof(i_0_7890,plain,
! [X26113,X26114] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26114,tc_fun(X26114,tc_HOL_Obool)),X26113),hAPP(hAPP(c_COMBC(X26114,tc_fun(X26114,tc_HOL_Obool),tc_fun(X26114,tc_HOL_Obool)),c_Set_Oinsert(X26114)),c_Orderings_Obot__class_Obot(tc_fun(X26114,tc_HOL_Obool)))) = X26113,
inference(variable_rename,[status(thm)],[fact_UN__singleton]) ).
fof(i_0_7891,plain,
! [X33308,X33309,X33310,X33311] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33311),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33310)),X33309)))
| hAPP(hAPP(c_List_Olist__update(X33310,X33309),X33311),X33308) = hAPP(hAPP(c_List_Oappend(X33310),hAPP(hAPP(c_List_Otake(X33310),X33311),X33309)),hAPP(hAPP(c_List_Olist_OCons(X33310),X33308),hAPP(hAPP(c_List_Odrop(X33310),hAPP(c_Nat_OSuc,X33311)),X33309))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upd__conv__take__nth__drop])]) ).
fof(i_0_7892,plain,
! [X32327,X32328,X32329,X32330,X32331,X32332] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32332),hAPP(X32331,X32330)),hAPP(X32331,X32329)))
| hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32328,X32332,X32331),X32330),hAPP(hAPP(c_List_Olist_OCons(X32328),X32329),X32327)) = hAPP(hAPP(c_List_Olist_OCons(X32328),X32330),hAPP(hAPP(c_List_Olist_OCons(X32328),X32329),X32327))
| ~ class_Orderings_Olinorder(X32332) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32332),hAPP(X32331,X32330)),hAPP(X32331,X32329)))
| hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32328,X32332,X32331),X32330),hAPP(hAPP(c_List_Olist_OCons(X32328),X32329),X32327)) = hAPP(hAPP(c_List_Olist_OCons(X32328),X32329),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32328,X32332,X32331),X32330),X32327))
| ~ class_Orderings_Olinorder(X32332) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5634])])]) ).
fof(i_0_7893,plain,
! [X32872,X32873] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X32873)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X32872)))
| c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X32873),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X32872)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X32873)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X32873)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X32872))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X32873)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X32872)))
| c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X32873),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X32872)) = c_List_Olist_ONil(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5635])]) ).
fof(i_0_7894,plain,
! [X26388,X26389,X26390] : hAPP(c_Set_OPow(X26390),hAPP(hAPP(c_Set_Oinsert(X26390),X26389),X26388)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X26390,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X26390),X26388)),hAPP(c_Set_Oimage(tc_fun(X26390,tc_HOL_Obool),tc_fun(X26390,tc_HOL_Obool),hAPP(c_Set_Oinsert(X26390),X26389)),hAPP(c_Set_OPow(X26390),X26388))),
inference(variable_rename,[status(thm)],[fact_Pow__insert]) ).
fof(i_0_7895,plain,
! [X17488,X17489,X17490,X17491,X17492] :
( ~ hBOOL(hAPP(X17492,X17491))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17490),X17491),X17489))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17492,X17490,X17488)),X17491),X17489)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc_OIfTrue])]) ).
fof(i_0_7896,plain,
! [X28471,X28472,X28473,X28474] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28474),hAPP(c_Set_Ovimage(X28474,X28473,X28472),X28471)))
| hAPP(c_Set_Oimage(X28474,X28473,X28472),c_Orderings_Otop__class_Otop(tc_fun(X28474,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X28473,tc_HOL_Obool))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X28473),X28471)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__vimageD])]) ).
fof(i_0_7897,plain,
! [X33686,X33687,X33688,X33689] :
( ( hBOOL(hAPP(hAPP(c_member(X33689),X33688),X33686))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33689)),hAPP(hAPP(c_List_Olist_OCons(X33689),X33688),X33687)),c_List_Olists(X33689,X33686))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33689)),X33687),c_List_Olists(X33689,X33686)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33689)),hAPP(hAPP(c_List_Olist_OCons(X33689),X33688),X33687)),c_List_Olists(X33689,X33686))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X33689),X33688),X33686))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33689)),X33687),c_List_Olists(X33689,X33686)))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33689)),hAPP(hAPP(c_List_Olist_OCons(X33689),X33688),X33687)),c_List_Olists(X33689,X33686))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__in__lists__iff])])]) ).
fof(i_0_7898,plain,
! [X23724,X23725,X23726,X23727] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23727,tc_HOL_Obool)),X23725),hAPP(hAPP(c_Set_Oinsert(X23727),X23726),X23724)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23727,tc_HOL_Obool)),X23725),X23724))
| hBOOL(hAPP(hAPP(c_member(X23727),X23726),X23725)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23727,tc_HOL_Obool)),X23725),X23724))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23727,tc_HOL_Obool)),X23725),hAPP(hAPP(c_Set_Oinsert(X23727),X23726),X23724)))
| hBOOL(hAPP(hAPP(c_member(X23727),X23726),X23725)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5636])])]) ).
fof(i_0_7899,plain,
! [X22561,X22562] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X22562))
| 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(X22562),X22561))),X22562)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range])]) ).
fof(i_0_7900,plain,
! [X24816,X24817,X24818,X24819] :
( ~ hBOOL(hAPP(hAPP(c_member(X24819),X24818),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24819,tc_HOL_Obool)),X24817),X24816)))
| hBOOL(hAPP(hAPP(c_member(X24819),X24818),X24817)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntD1])]) ).
fof(i_0_7901,plain,
! [X24812,X24813,X24814,X24815] :
( ( hBOOL(hAPP(hAPP(c_member(X24815),X24814),X24813))
| ~ hBOOL(hAPP(hAPP(c_member(X24815),X24814),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24815,tc_HOL_Obool)),X24813),X24812))) )
& ( hBOOL(hAPP(hAPP(c_member(X24815),X24814),X24812))
| ~ hBOOL(hAPP(hAPP(c_member(X24815),X24814),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24815,tc_HOL_Obool)),X24813),X24812))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X24815),X24814),X24813))
| ~ hBOOL(hAPP(hAPP(c_member(X24815),X24814),X24812))
| hBOOL(hAPP(hAPP(c_member(X24815),X24814),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24815,tc_HOL_Obool)),X24813),X24812))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__iff])])]) ).
fof(i_0_7902,plain,
! [X24693,X24694,X24695,X24696] :
( ( hBOOL(hAPP(hAPP(c_member(X24696),X24695),X24694))
| ~ hBOOL(hAPP(hAPP(c_member(X24696),X24695),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24696,tc_HOL_Obool)),X24694),X24693))) )
& ( hBOOL(hAPP(hAPP(c_member(X24696),X24695),X24693))
| ~ hBOOL(hAPP(hAPP(c_member(X24696),X24695),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24696,tc_HOL_Obool)),X24694),X24693))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5637])])]) ).
fof(i_0_7903,plain,
! [X23693,X23694,X23695,X23696] :
( ~ hBOOL(hAPP(hAPP(c_member(X23696),X23695),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23696,tc_HOL_Obool)),X23694),X23693)))
| hBOOL(hAPP(hAPP(c_member(X23696),X23695),X23694)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DiffD1])]) ).
fof(i_0_7904,plain,
! [X24820,X24821,X24822,X24823] :
( ~ hBOOL(hAPP(hAPP(c_member(X24823),X24822),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24823,tc_HOL_Obool)),X24821),X24820)))
| hBOOL(hAPP(hAPP(c_member(X24823),X24822),X24820)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntD2])]) ).
fof(i_0_7905,plain,
! [X23302,X23303,X23304,X23305] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23305,tc_HOL_Obool)),X23304),hAPP(hAPP(c_Set_Oinsert(X23305),X23303),X23302)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23305,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23305,tc_HOL_Obool)),X23304),X23302)),hAPP(hAPP(c_Set_Oinsert(X23305),X23303),c_Orderings_Obot__class_Obot(tc_fun(X23305,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_Diff__insert]) ).
fof(i_0_7906,plain,
! [X32889,X32890] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X32890),X32889))
| c_List_Oupto(X32890,X32889) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X32890),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X32890),c_Groups_Oone__class_Oone(tc_Int_Oint)),X32889))
| ~ 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),X32890),X32889))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X32890),X32889))
| c_List_Oupto(X32890,X32889) = 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),X32890),X32889))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5638])])]) ).
fof(i_0_7907,plain,
! [X28598,X28599,X28600] :
( ~ class_Groups_Oab__semigroup__mult(X28600)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28600),X28599))
| X28599 = c_Orderings_Obot__class_Obot(tc_fun(X28600,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28600),X28598))
| X28598 = c_Orderings_Obot__class_Obot(tc_fun(X28600,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28600,tc_HOL_Obool)),X28599),X28598) != c_Orderings_Obot__class_Obot(tc_fun(X28600,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ofold1(X28600,c_Groups_Otimes__class_Otimes(X28600)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28600,tc_HOL_Obool)),X28599),X28598)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X28600),hAPP(c_Finite__Set_Ofold1(X28600,c_Groups_Otimes__class_Otimes(X28600)),X28599)),hAPP(c_Finite__Set_Ofold1(X28600,c_Groups_Otimes__class_Otimes(X28600)),X28598)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__Un])]) ).
fof(i_0_7908,plain,
! [X30828,X30829,X30830,X30831,X30832,X30833] :
( ~ c_Finite__Set_Ofun__left__comm(X30833,X30832,X30831)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30833),X30830))
| hBOOL(hAPP(hAPP(c_member(X30833),X30829),X30830))
| hAPP(hAPP(c_Finite__Set_Ofold(X30833,X30832,X30831),X30828),hAPP(hAPP(c_Set_Oinsert(X30833),X30829),X30830)) = hAPP(hAPP(X30831,X30829),hAPP(hAPP(c_Finite__Set_Ofold(X30833,X30832,X30831),X30828),X30830)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5639])]) ).
cnf(i_0_7909,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_7910,plain,
! [X17483,X17484,X17485,X17486,X17487] :
( hBOOL(hAPP(X17487,X17486))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17485),X17486),X17484))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17487,X17483,X17485)),X17486),X17484)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5640])]) ).
fof(i_0_7911,plain,
! [X23568,X23569] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),esk104_2(X23568,X23569)),esk105_2(X23568,X23569)))
| c_Orderings_Oorder_Omono(tc_Nat_Onat,X23569,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23568)
| ~ class_Orderings_Oorder(X23569) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23569),hAPP(X23568,esk104_2(X23568,X23569))),hAPP(X23568,esk105_2(X23568,X23569))))
| c_Orderings_Oorder_Omono(tc_Nat_Onat,X23569,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23568)
| ~ class_Orderings_Oorder(X23569) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_OmonoI])])])]) ).
fof(i_0_7912,plain,
! [X28045,X28046,X28047,X28048,X28049,X28050] :
( ~ c_Finite__Set_Ofolding__idem(X28050,X28049,X28048,X28047)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28050),X28046))
| hAPP(X28047,hAPP(hAPP(c_Set_Oinsert(X28050),X28045),X28046)) = hAPP(c_Fun_Ocomp(X28049,X28049,X28049,hAPP(X28047,X28046)),hAPP(X28048,X28045)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Oinsert__idem])]) ).
fof(i_0_7913,plain,
! [X32213,X32214,X32215,X32216,X32217] :
( ( hAPP(c_Map_Omap__of(X32217,X32215,hAPP(hAPP(c_List_Ozip(X32217,X32215),X32216),X32214)),X32213) != c_Option_Ooption_ONone(X32215)
| ~ hBOOL(hAPP(hAPP(c_member(X32217),X32213),hAPP(c_List_Oset(X32217),X32216)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32217)),X32216) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32215)),X32214) )
& ( hBOOL(hAPP(hAPP(c_member(X32217),X32213),hAPP(c_List_Oset(X32217),X32216)))
| hAPP(c_Map_Omap__of(X32217,X32215,hAPP(hAPP(c_List_Ozip(X32217,X32215),X32216),X32214)),X32213) = c_Option_Ooption_ONone(X32215)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32217)),X32216) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32215)),X32214) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5641])])]) ).
fof(i_0_7914,plain,
! [X22853,X22854,X22855,X22856] : hAPP(hAPP(c_Product__Type_Oscomp(X22856,X22855,X22854,tc_prod(X22855,X22854)),X22853),c_Product__Type_OPair(X22855,X22854)) = X22853,
inference(variable_rename,[status(thm)],[fact_scomp__Pair]) ).
fof(i_0_7915,plain,
! [X29291,X29292] : hAPP(c_Set_OPow(X29292),X29291) = hAPP(c_Set_OCollect(tc_fun(X29292,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X29292,tc_HOL_Obool),tc_fun(X29292,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X29292,tc_HOL_Obool))),X29291)),
inference(variable_rename,[status(thm)],[fact_Pow__def]) ).
fof(i_0_7916,plain,
! [X34259,X34260] : hAPP(c_List_Orev(X34260),X34259) = hAPP(c_List_Ofoldl(tc_List_Olist(X34260),X34260,hAPP(c_COMBC(X34260,tc_List_Olist(X34260),tc_List_Olist(X34260)),c_List_Olist_OCons(X34260)),c_List_Olist_ONil(X34260)),X34259),
inference(variable_rename,[status(thm)],[fact_rev__foldl__cons]) ).
cnf(i_0_7917,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_7918,plain,
! [X27420,X27421] :
( ~ class_Rings_Ocomm__semiring__1(X27421)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27421),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27421),c_Groups_Oone__class_Oone(X27421)),c_Groups_Oone__class_Oone(X27421))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27421),c_Nat_Osemiring__1__class_Oof__nat(X27421)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X27420))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27421),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27421),X27420)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27421),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27421),X27420)),c_Groups_Oone__class_Oone(X27421))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gauss__sum])]) ).
cnf(i_0_7919,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_7920,plain,
! [X31917,X31918,X31919,X31920,X31921,X31922] :
( hBOOL(hAPP(hAPP(c_member(X31922),X31921),hAPP(c_List_Oset(X31922),X31920)))
| hAPP(hAPP(c_List_Omap(X31922,X31919),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X31922,X31919),X31918),X31921),X31917)),X31920) = hAPP(hAPP(c_List_Omap(X31922,X31919),X31918),X31920) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5642])]) ).
fof(i_0_7921,plain,
! [X29860,X29861,X29862] :
( ~ c_Wellfounded_Oacyclic(X29862,X29861)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29862,X29862),tc_HOL_Obool)),X29860),X29861))
| c_Wellfounded_Oacyclic(X29862,X29860) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acyclic__subset])]) ).
fof(i_0_7922,plain,
! [X29616,X29617,X29618] :
( ~ c_Wellfounded_Owf(X29618,X29617)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29618,X29618),tc_HOL_Obool)),X29616),X29617))
| c_Wellfounded_Owf(X29618,X29616) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__subset])]) ).
fof(i_0_7923,plain,
! [X32015,X32016,X32017,X32018] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X32016),X32018),hAPP(c_List_Oset(X32016),c_List_Oremove1(X32016,X32017,X32015))))
| hBOOL(hAPP(hAPP(c_member(X32016),X32018),hAPP(c_List_Oset(X32016),X32015)))
| X32018 = X32017 )
& ( ~ hBOOL(hAPP(hAPP(c_member(X32016),X32018),hAPP(c_List_Oset(X32016),X32015)))
| hBOOL(hAPP(hAPP(c_member(X32016),X32018),hAPP(c_List_Oset(X32016),c_List_Oremove1(X32016,X32017,X32015))))
| X32018 = X32017 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__remove1])])]) ).
fof(i_0_7924,plain,
! [X24952,X24953,X24954,X24955] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24955,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24955,tc_HOL_Obool)),X24954),X24953)),X24952) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24955,tc_HOL_Obool)),X24954),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24955,tc_HOL_Obool)),X24953),X24952)),
inference(variable_rename,[status(thm)],[fact_Int__assoc]) ).
fof(i_0_7925,plain,
! [X24056,X24057,X24058,X24059] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24059,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24059,tc_HOL_Obool)),X24058),X24057)),X24056) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24059,tc_HOL_Obool)),X24058),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24059,tc_HOL_Obool)),X24057),X24056)),
inference(variable_rename,[status(thm)],[fact_Un__assoc]) ).
fof(i_0_7926,plain,
! [X24872,X24873,X24874,X24875] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24875,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24875,tc_HOL_Obool)),X24874),X24873)),X24872) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24875,tc_HOL_Obool)),X24874),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24875,tc_HOL_Obool)),X24873),X24872)),
inference(variable_rename,[status(thm)],[fact_Int__Diff]) ).
fof(i_0_7927,plain,
! [X20479,X20480,X20481] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20481),X20480))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20479),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20480),X20479)),X20481))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff])]) ).
fof(i_0_7928,plain,
! [X34385,X34386,X34387,X34388] :
( ( hBOOL(hAPP(hAPP(c_member(X34388),X34387),hAPP(c_List_Oset(X34388),X34385)))
| ~ hBOOL(hAPP(hAPP(c_member(X34388),X34387),hAPP(c_List_Oset(X34388),c_List_OtakeWhile(X34388,X34386,X34385)))) )
& ( hBOOL(hAPP(X34386,X34387))
| ~ hBOOL(hAPP(hAPP(c_member(X34388),X34387),hAPP(c_List_Oset(X34388),c_List_OtakeWhile(X34388,X34386,X34385)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__takeWhileD])])]) ).
fof(i_0_7929,plain,
! [X32396,X32397,X32398,X32399] :
( hBOOL(hAPP(hAPP(c_member(X32399),X32398),hAPP(c_List_Oset(X32399),X32397)))
| ~ hBOOL(hAPP(hAPP(c_member(X32399),X32398),hAPP(c_List_Oset(X32399),c_List_Osublist(X32399,X32397,X32396)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5643])]) ).
fof(i_0_7930,plain,
! [X32392,X32393,X32394,X32395] :
( ~ hBOOL(hAPP(hAPP(c_member(X32395),X32394),hAPP(c_List_Oset(X32395),c_List_Osublist(X32395,X32393,X32392))))
| hBOOL(hAPP(hAPP(c_member(X32395),X32394),hAPP(c_List_Oset(X32395),X32393))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__sublistD])]) ).
fof(i_0_7931,plain,
! [X32011,X32012,X32013,X32014] :
( hBOOL(hAPP(hAPP(c_member(X32014),X32013),hAPP(c_List_Oset(X32014),X32012)))
| ~ hBOOL(hAPP(hAPP(c_member(X32014),X32013),hAPP(c_List_Oset(X32014),c_List_Oremove1(X32014,X32011,X32012)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5644])]) ).
fof(i_0_7932,plain,
! [X17784,X17785,X17786,X17787,X17788,X17789] :
( ~ hBOOL(hAPP(X17789,X17788))
| ~ c_Natural_Oevaln(X17787,X17788,X17786,X17785)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17789,X17787),X17785,X17786,X17784)
| c_Natural_Oevaln(c_Com_Ocom_OWhile(X17789,X17787),X17788,X17786,X17784) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln_OWhileTrue])]) ).
fof(i_0_7933,plain,
! [X33858,X33859,X33860] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33860,tc_HOL_Obool)),hAPP(c_List_Oset(X33860),hAPP(c_List_Ofilter(X33860,X33859),X33858))),hAPP(c_List_Oset(X33860),X33858))),
inference(variable_rename,[status(thm)],[fact_filter__is__subset]) ).
fof(i_0_7934,plain,
! [X18849,X18850,X18851,X18852,X18853] :
( ( X18852 = X18851
| X18850 = X18849
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18853),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18853),X18852),X18850)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18853),X18851),X18849)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18853),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18853),X18852),X18849)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18853),X18851),X18850))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18853) )
& ( X18852 != X18851
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18853),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18853),X18852),X18850)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18853),X18851),X18849)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18853),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18853),X18852),X18849)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18853),X18851),X18850))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18853) )
& ( X18850 != X18849
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18853),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18853),X18852),X18850)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18853),X18851),X18849)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18853),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18853),X18852),X18849)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18853),X18851),X18850))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18853) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__noteq])])]) ).
fof(i_0_7935,plain,
! [X18836,X18837,X18838,X18839,X18840] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18840),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18840),X18839),X18838)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18840),X18837),X18836)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18840),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18840),X18839),X18836)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18840),X18837),X18838))
| X18839 = X18837
| X18838 = X18836
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18840) )
& ( X18839 != X18837
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18840),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18840),X18839),X18838)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18840),X18837),X18836)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18840),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18840),X18839),X18836)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18840),X18837),X18838))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18840) )
& ( X18838 != X18836
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18840),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18840),X18839),X18838)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18840),X18837),X18836)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18840),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18840),X18839),X18836)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18840),X18837),X18838))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18840) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__eq])])]) ).
cnf(i_0_7936,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_7937,plain,
! [X29331,X29332] :
( ( ~ c_Predicate_Oreflp(X29332,X29331)
| c_Relation_Orefl__on(X29332,c_Orderings_Otop__class_Otop(tc_fun(X29332,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X29332,X29332)),hAPP(c_Product__Type_Oprod_Oprod__case(X29332,X29332,tc_HOL_Obool),X29331))) )
& ( ~ c_Relation_Orefl__on(X29332,c_Orderings_Otop__class_Otop(tc_fun(X29332,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X29332,X29332)),hAPP(c_Product__Type_Oprod_Oprod__case(X29332,X29332,tc_HOL_Obool),X29331)))
| c_Predicate_Oreflp(X29332,X29331) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reflp__def])]) ).
fof(i_0_7938,plain,
! [X20471,X20472,X20473] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20471),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20472),X20473)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20471),X20473)),X20472))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20473),X20472)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20471),X20473)),X20472))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20471),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20472),X20473)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20473),X20472)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv2])])]) ).
cnf(i_0_7939,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_7940,plain,
! [X28423,X28424,X28425,X28426,X28427] :
( ~ hBOOL(hAPP(hAPP(c_member(X28427),X28426),hAPP(c_Set_Ovimage(X28427,X28425,X28424),X28423)))
| hBOOL(hAPP(hAPP(c_member(X28425),hAPP(X28424,X28426)),X28423)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimageD])]) ).
fof(i_0_7941,plain,
! [X28418,X28419,X28420,X28421,X28422] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X28422),X28421),hAPP(c_Set_Ovimage(X28422,X28420,X28419),X28418)))
| hBOOL(hAPP(hAPP(c_member(X28420),hAPP(X28419,X28421)),X28418)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X28420),hAPP(X28419,X28421)),X28418))
| hBOOL(hAPP(hAPP(c_member(X28422),X28421),hAPP(c_Set_Ovimage(X28422,X28420,X28419),X28418))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__eq])]) ).
fof(i_0_7942,plain,
! [X19752,X19753,X19754,X19755] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19754,X19755)),X19753),X19752))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X19754,X19755)),X19753),X19752))
| ~ class_Orderings_Oord(X19755) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19754,X19755)),X19752),X19753))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X19754,X19755)),X19753),X19752))
| ~ class_Orderings_Oord(X19755) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19754,X19755)),X19753),X19752))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19754,X19755)),X19752),X19753))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X19754,X19755)),X19753),X19752))
| ~ class_Orderings_Oord(X19755) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5647])])]) ).
fof(i_0_7943,plain,
! [X33392,X33393,X33394,X33395] : hAPP(hAPP(c_List_Odrop(X33395),X33394),hAPP(hAPP(c_List_Olist_OCons(X33395),X33393),X33392)) = c_Nat_Onat_Onat__case(tc_List_Olist(X33395),hAPP(hAPP(c_List_Olist_OCons(X33395),X33393),X33392),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X33395),tc_List_Olist(X33395)),c_List_Odrop(X33395)),X33392),X33394),
inference(variable_rename,[status(thm)],[fact_drop__Cons]) ).
fof(i_0_7944,plain,
! [X19651,X19652,X19653] :
( ~ class_Rings_Olinordered__idom(X19653)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19653),c_Groups_Ozero__class_Ozero(X19653)),X19652))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19653),c_Groups_Ozero__class_Ozero(X19653)),X19651))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19653),X19651),c_Groups_Oone__class_Oone(X19653)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19653),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19653),X19652),X19651)),X19652)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__le__one__le])]) ).
fof(i_0_7945,plain,
! [X19648,X19649,X19650] :
( ~ class_Rings_Olinordered__idom(X19650)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19650),c_Groups_Ozero__class_Ozero(X19650)),X19649))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19650),c_Groups_Ozero__class_Ozero(X19650)),X19648))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19650),X19648),c_Groups_Oone__class_Oone(X19650)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19650),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19650),X19648),X19649)),X19649)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__one__le])]) ).
fof(i_0_7946,plain,
! [X32385,X32386,X32387,X32388] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X32388),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X32387),X32386)))
| hAPP(c_Random_Opick(X32387,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X32387)),X32386),X32385)),X32388) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X32387),X32386) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X32388),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X32387),X32386)))
| hAPP(c_Random_Opick(X32387,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X32387)),X32386),X32385)),X32388) = hAPP(c_Random_Opick(X32387,X32385),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X32388),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X32387),X32386))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5648])]) ).
cnf(i_0_7947,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_7948,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_7949,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_7950,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_7951,plain,
! [X31268,X31269,X31270,X31271,X31272,X31273,X31274] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31270,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31270,tc_HOL_Obool),X31269)),X31268) != c_Orderings_Obot__class_Obot(tc_fun(X31270,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X31270,tc_HOL_Obool)),X31271),X31269))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31270,tc_HOL_Obool)),X31271),X31268) = c_Orderings_Obot__class_Obot(tc_fun(X31270,tc_HOL_Obool)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(X31274,tc_HOL_Obool)),esk399_3(X31272,X31273,X31274)),X31273))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31274,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31274,tc_HOL_Obool),X31273)),X31272) = c_Orderings_Obot__class_Obot(tc_fun(X31274,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31274,tc_HOL_Obool)),esk399_3(X31272,X31273,X31274)),X31272) != c_Orderings_Obot__class_Obot(tc_fun(X31274,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31274,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31274,tc_HOL_Obool),X31273)),X31272) = c_Orderings_Obot__class_Obot(tc_fun(X31274,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_7952,plain,
! [X20124,X20125,X20126] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20126))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20125))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20125),X20124))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20126),X20124)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20126),X20125))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2])]) ).
fof(i_0_7953,plain,
! [X29786,X29787,X29788,X29789] : hAPP(c_Relation_ODomain(X29789,X29788),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29789,X29788),tc_HOL_Obool)),X29787),X29786)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29789,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X29789,X29788),X29787)),hAPP(c_Relation_ODomain(X29789,X29788),X29786)),
inference(variable_rename,[status(thm)],[fact_Domain__Un__eq]) ).
fof(i_0_7954,plain,
! [X29695,X29696,X29697,X29698] : hAPP(c_Relation_ORange(X29698,X29697),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29698,X29697),tc_HOL_Obool)),X29696),X29695)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29697,tc_HOL_Obool)),hAPP(c_Relation_ORange(X29698,X29697),X29696)),hAPP(c_Relation_ORange(X29698,X29697),X29695)),
inference(variable_rename,[status(thm)],[fact_Range__Un__eq]) ).
fof(i_0_7955,plain,
! [X32709,X32710,X32711,X32712,X32713,X32714] : hAPP(hAPP(c_List_Omap(X32714,X32713),X32712),hAPP(hAPP(c_List_Olist__update(X32714,X32711),X32710),X32709)) = hAPP(hAPP(c_List_Olist__update(X32713,hAPP(hAPP(c_List_Omap(X32714,X32713),X32712),X32711)),X32710),hAPP(X32712,X32709)),
inference(variable_rename,[status(thm)],[fact_map__update]) ).
fof(i_0_7956,plain,
! [X31588,X31589,X31590,X31591,X31592] : hAPP(c_Map_Omap__add(X31592,X31591,X31590,X31589),X31588) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X31591),X31591,hAPP(X31590,X31588),c_Option_Ooption_OSome(X31591)),hAPP(X31589,X31588)),
inference(variable_rename,[status(thm)],[fact_map__add__def]) ).
fof(i_0_7957,plain,
! [X32273,X32274,X32275,X32276] :
( ~ hBOOL(hAPP(hAPP(c_member(X32276),X32275),hAPP(c_List_Oset(X32276),hAPP(hAPP(c_List_Olist_OCons(X32276),X32274),X32273))))
| X32275 = X32274
| hBOOL(hAPP(hAPP(c_member(X32276),X32275),hAPP(c_List_Oset(X32276),X32273))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__ConsD])]) ).
fof(i_0_7958,plain,
! [X22743] :
( X22743 = 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,X22743)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,X22743))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral__decr])]) ).
fof(i_0_7959,plain,
! [X33334,X33335,X33336,X33337] :
( ~ hBOOL(hAPP(hAPP(c_member(X33337),X33336),hAPP(c_List_Oset(X33337),hAPP(hAPP(c_List_Odrop(X33337),X33335),X33334))))
| hBOOL(hAPP(hAPP(c_member(X33337),X33336),hAPP(c_List_Oset(X33337),X33334))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__dropD])]) ).
fof(i_0_7960,plain,
! [X32619,X32620,X32621,X32622] :
( ~ hBOOL(hAPP(hAPP(c_member(X32622),X32621),hAPP(c_List_Oset(X32622),hAPP(hAPP(c_List_Otake(X32622),X32620),X32619))))
| hBOOL(hAPP(hAPP(c_member(X32622),X32621),hAPP(c_List_Oset(X32622),X32619))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__takeD])]) ).
fof(i_0_7961,plain,
! [X27866,X27867,X27868,X27869,X27870] :
( ( X27870 != c_Option_Ooption_ONone(X27869)
| c_Map_Odom(X27868,X27869,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27868,tc_Option_Ooption(X27869)),X27867),X27866),X27870)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27868,tc_HOL_Obool)),c_Map_Odom(X27868,X27869,X27867)),hAPP(hAPP(c_Set_Oinsert(X27868),X27866),c_Orderings_Obot__class_Obot(tc_fun(X27868,tc_HOL_Obool)))) )
& ( X27870 = c_Option_Ooption_ONone(X27869)
| c_Map_Odom(X27868,X27869,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27868,tc_Option_Ooption(X27869)),X27867),X27866),X27870)) = hAPP(hAPP(c_Set_Oinsert(X27868),X27866),c_Map_Odom(X27868,X27869,X27867)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dom__fun__upd])]) ).
fof(i_0_7962,plain,
! [X20888,X20889,X20890] :
( ~ class_Rings_Olinordered__semidom(X20890)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20890),c_Groups_Ozero__class_Ozero(X20890)),X20889))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20890),X20889),c_Groups_Oone__class_Oone(X20890)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20890),hAPP(hAPP(c_Power_Opower__class_Opower(X20890),X20889),hAPP(c_Nat_OSuc,X20888))),c_Groups_Oone__class_Oone(X20890))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc__less__one])]) ).
fof(i_0_7963,plain,
! [X31560,X31561,X31562] :
( ( hBOOL(hAPP(hAPP(c_member(X31562),X31561),esk426_3(X31560,X31561,X31562)))
| ~ hBOOL(hAPP(hAPP(c_member(X31562),X31561),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31562,tc_HOL_Obool),X31560))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(X31562,tc_HOL_Obool)),esk426_3(X31560,X31561,X31562)),X31560))
| ~ hBOOL(hAPP(hAPP(c_member(X31562),X31561),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31562,tc_HOL_Obool),X31560))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5649])])])]) ).
fof(i_0_7964,plain,
! [X20135,X20136,X20137] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20137),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)),X20136))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20136),X20135))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20137),X20136)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20137),X20135))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg])]) ).
fof(i_0_7965,plain,
! [X26316,X26317,X26318] :
( ( hBOOL(hAPP(hAPP(c_member(X26318),esk178_3(X26316,X26317,X26318)),X26316))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26318,X26318)),X26317),c_Relation_OId__on(X26318,X26316))) )
& ( X26317 = hAPP(hAPP(c_Product__Type_OPair(X26318,X26318),esk178_3(X26316,X26317,X26318)),esk178_3(X26316,X26317,X26318))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26318,X26318)),X26317),c_Relation_OId__on(X26318,X26316))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__onE])])])]) ).
fof(i_0_7966,plain,
! [X28242,X28243,X28244,X28245] :
( ~ c_Fun_Oinj__on(X28245,X28244,X28243,c_Orderings_Otop__class_Otop(tc_fun(X28245,tc_HOL_Obool)))
| hAPP(c_Fun_Othe__inv__into(X28245,X28244,c_Orderings_Otop__class_Otop(tc_fun(X28245,tc_HOL_Obool)),X28243),hAPP(X28243,X28242)) = X28242 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__f__f])]) ).
fof(i_0_7967,plain,
! [X30805,X30806,X30807,X30808,X30809,X30810] :
( ~ c_Finite__Set_Ofun__left__comm(X30810,X30809,X30808)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30810),X30807))
| hAPP(hAPP(X30808,X30806),hAPP(hAPP(c_Finite__Set_Ofold(X30810,X30809,X30808),X30805),X30807)) = hAPP(hAPP(c_Finite__Set_Ofold(X30810,X30809,X30808),hAPP(hAPP(X30808,X30806),X30805)),X30807) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__fun__comm])]) ).
fof(i_0_7968,plain,
! [X29774,X29775,X29776] :
( ~ c_Wellfounded_OwfP(X29776,X29775)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29776,tc_fun(X29776,tc_HOL_Obool))),X29774),X29775))
| c_Wellfounded_OwfP(X29776,X29774) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__subset])]) ).
fof(i_0_7969,plain,
! [X23668,X23669,X23670] :
( ( hAPP(hAPP(c_COMBC(X23670,tc_fun(X23670,tc_HOL_Obool),tc_HOL_Obool),c_member(X23670)),X23669) != hAPP(hAPP(c_COMBC(X23670,tc_fun(X23670,tc_HOL_Obool),tc_HOL_Obool),c_member(X23670)),X23668)
| X23669 = X23668 )
& ( X23669 != X23668
| hAPP(hAPP(c_COMBC(X23670,tc_fun(X23670,tc_HOL_Obool),tc_HOL_Obool),c_member(X23670)),X23669) = hAPP(hAPP(c_COMBC(X23670,tc_fun(X23670,tc_HOL_Obool),tc_HOL_Obool),c_member(X23670)),X23668) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq])]) ).
fof(i_0_7970,plain,
! [X19492,X19493,X19494] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19494))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19494),X19493)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19494),X19492))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19493),X19492))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19494),X19493)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19494),X19492))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19494))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19493),X19492))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19494),X19493)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19494),X19492))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel1])])]) ).
fof(i_0_7971,plain,
! [X19489,X19490,X19491] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19490))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19491),X19490)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19489),X19490))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19491),X19489))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19491),X19490)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19489),X19490))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19490))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19491),X19489))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19491),X19490)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19489),X19490))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel2])])]) ).
fof(i_0_7972,plain,
! [X21523,X21524,X21525,X21526] :
( ~ class_Fields_Olinordered__field__inverse__zero(X21526)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21526),X21525),X21524))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21526),c_Groups_Ozero__class_Ozero(X21526)),X21523))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21526),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21526),X21525),X21523)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21526),X21524),X21523))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__right__mono])]) ).
fof(i_0_7973,plain,
! [X20958,X20959,X20960,X20961] :
( ~ class_Rings_Olinordered__semidom(X20961)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20961),X20960),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),hAPP(hAPP(c_Power_Opower__class_Opower(X20961),X20960),X20958)),hAPP(hAPP(c_Power_Opower__class_Opower(X20961),X20959),X20958))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mono])]) ).
fof(i_0_7974,plain,
! [X19430,X19431,X19432,X19433] :
( ~ class_Rings_Oordered__semiring(X19433)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19433),X19432),X19431))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19433),c_Groups_Ozero__class_Ozero(X19433)),X19430))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19433),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19433),X19432),X19430)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19433),X19431),X19430))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono])]) ).
fof(i_0_7975,plain,
! [X19422,X19423,X19424,X19425] :
( ~ class_Rings_Oordered__comm__semiring(X19425)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19425),X19424),X19423))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19425),c_Groups_Ozero__class_Ozero(X19425)),X19422))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19425),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19425),X19422),X19424)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19425),X19422),X19423))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__left__mono])]) ).
fof(i_0_7976,plain,
! [X19426,X19427,X19428,X19429] :
( ~ class_Rings_Oordered__semiring(X19429)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19429),X19428),X19427))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19429),c_Groups_Ozero__class_Ozero(X19429)),X19426))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19429),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19429),X19426),X19428)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19429),X19426),X19427))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono])]) ).
fof(i_0_7977,plain,
! [X21535,X21536,X21537,X21538] :
( ~ class_Fields_Olinordered__field(X21538)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21538),X21537),X21536))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21538),c_Groups_Ozero__class_Ozero(X21538)),X21535))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21538),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21538),X21537),X21535)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21538),X21536),X21535))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono])]) ).
fof(i_0_7978,plain,
! [X18936,X18937,X18938,X18939] :
( ~ class_Rings_Olinordered__semiring__strict(X18939)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18939),X18938),X18937))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18939),c_Groups_Ozero__class_Ozero(X18939)),X18936))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18939),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18939),X18938),X18936)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18939),X18937),X18936))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono])]) ).
fof(i_0_7979,plain,
! [X18944,X18945,X18946,X18947] :
( ~ class_Rings_Olinordered__comm__semiring__strict(X18947)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18947),X18946),X18945))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18947),c_Groups_Ozero__class_Ozero(X18947)),X18944))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18947),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18947),X18944),X18946)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18947),X18944),X18945))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__strict__left__mono])]) ).
fof(i_0_7980,plain,
! [X18940,X18941,X18942,X18943] :
( ~ class_Rings_Olinordered__semiring__strict(X18943)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18943),X18942),X18941))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18943),c_Groups_Ozero__class_Ozero(X18943)),X18940))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18943),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18943),X18940),X18942)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18943),X18940),X18941))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono])]) ).
fof(i_0_7981,plain,
! [X32277,X32278,X32279,X32280,X32281,X32282] : hAPP(hAPP(c_List_Ozip(X32282,X32281),hAPP(hAPP(c_List_Olist_OCons(X32282),X32280),X32279)),hAPP(hAPP(c_List_Olist_OCons(X32281),X32278),X32277)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(X32282,X32281)),hAPP(hAPP(c_Product__Type_OPair(X32282,X32281),X32280),X32278)),hAPP(hAPP(c_List_Ozip(X32282,X32281),X32279),X32277)),
inference(variable_rename,[status(thm)],[fact_zip__Cons__Cons]) ).
fof(i_0_7982,plain,
! [X21520,X21521,X21522] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21522),X21521),c_Groups_Ozero__class_Ozero(X21522)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21522),c_Groups_Ozero__class_Ozero(X21522)),X21521))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21522),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21522),X21521),X21520)),c_Groups_Ozero__class_Ozero(X21522)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21522) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21522),c_Groups_Ozero__class_Ozero(X21522)),X21520))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21522),c_Groups_Ozero__class_Ozero(X21522)),X21521))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21522),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21522),X21521),X21520)),c_Groups_Ozero__class_Ozero(X21522)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21522) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21522),X21521),c_Groups_Ozero__class_Ozero(X21522)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21522),X21520),c_Groups_Ozero__class_Ozero(X21522)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21522),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21522),X21521),X21520)),c_Groups_Ozero__class_Ozero(X21522)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21522) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21522),c_Groups_Ozero__class_Ozero(X21522)),X21520))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21522),X21520),c_Groups_Ozero__class_Ozero(X21522)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21522),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21522),X21521),X21520)),c_Groups_Ozero__class_Ozero(X21522)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21522) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21522),c_Groups_Ozero__class_Ozero(X21522)),X21521))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21522),X21520),c_Groups_Ozero__class_Ozero(X21522)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21522),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21522),X21521),X21520)),c_Groups_Ozero__class_Ozero(X21522)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21522) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21522),X21521),c_Groups_Ozero__class_Ozero(X21522)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21522),c_Groups_Ozero__class_Ozero(X21522)),X21520))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21522),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21522),X21521),X21520)),c_Groups_Ozero__class_Ozero(X21522)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21522) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__le__0__iff])])]) ).
fof(i_0_7983,plain,
! [X19449,X19450,X19451] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19451),X19450),c_Groups_Ozero__class_Ozero(X19451)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19451),c_Groups_Ozero__class_Ozero(X19451)),X19450))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19451),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19451),X19450),X19449)),c_Groups_Ozero__class_Ozero(X19451)))
| ~ class_Rings_Olinordered__ring__strict(X19451) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19451),c_Groups_Ozero__class_Ozero(X19451)),X19449))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19451),c_Groups_Ozero__class_Ozero(X19451)),X19450))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19451),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19451),X19450),X19449)),c_Groups_Ozero__class_Ozero(X19451)))
| ~ class_Rings_Olinordered__ring__strict(X19451) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19451),X19450),c_Groups_Ozero__class_Ozero(X19451)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19451),X19449),c_Groups_Ozero__class_Ozero(X19451)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19451),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19451),X19450),X19449)),c_Groups_Ozero__class_Ozero(X19451)))
| ~ class_Rings_Olinordered__ring__strict(X19451) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19451),c_Groups_Ozero__class_Ozero(X19451)),X19449))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19451),X19449),c_Groups_Ozero__class_Ozero(X19451)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19451),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19451),X19450),X19449)),c_Groups_Ozero__class_Ozero(X19451)))
| ~ class_Rings_Olinordered__ring__strict(X19451) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19451),c_Groups_Ozero__class_Ozero(X19451)),X19450))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19451),X19449),c_Groups_Ozero__class_Ozero(X19451)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19451),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19451),X19450),X19449)),c_Groups_Ozero__class_Ozero(X19451)))
| ~ class_Rings_Olinordered__ring__strict(X19451) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19451),X19450),c_Groups_Ozero__class_Ozero(X19451)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19451),c_Groups_Ozero__class_Ozero(X19451)),X19449))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19451),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19451),X19450),X19449)),c_Groups_Ozero__class_Ozero(X19451)))
| ~ class_Rings_Olinordered__ring__strict(X19451) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__0__iff])])]) ).
fof(i_0_7984,plain,
! [X21551,X21552,X21553] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21553),X21552),c_Groups_Ozero__class_Ozero(X21553)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21553),c_Groups_Ozero__class_Ozero(X21553)),X21552))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21553),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21553),X21552),X21551)),c_Groups_Ozero__class_Ozero(X21553)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21553) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21553),c_Groups_Ozero__class_Ozero(X21553)),X21551))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21553),c_Groups_Ozero__class_Ozero(X21553)),X21552))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21553),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21553),X21552),X21551)),c_Groups_Ozero__class_Ozero(X21553)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21553) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21553),X21552),c_Groups_Ozero__class_Ozero(X21553)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21553),X21551),c_Groups_Ozero__class_Ozero(X21553)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21553),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21553),X21552),X21551)),c_Groups_Ozero__class_Ozero(X21553)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21553) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21553),c_Groups_Ozero__class_Ozero(X21553)),X21551))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21553),X21551),c_Groups_Ozero__class_Ozero(X21553)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21553),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21553),X21552),X21551)),c_Groups_Ozero__class_Ozero(X21553)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21553) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21553),c_Groups_Ozero__class_Ozero(X21553)),X21552))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21553),X21551),c_Groups_Ozero__class_Ozero(X21553)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21553),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21553),X21552),X21551)),c_Groups_Ozero__class_Ozero(X21553)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21553) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21553),X21552),c_Groups_Ozero__class_Ozero(X21553)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21553),c_Groups_Ozero__class_Ozero(X21553)),X21551))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21553),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21553),X21552),X21551)),c_Groups_Ozero__class_Ozero(X21553)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21553) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__less__0__iff])])]) ).
fof(i_0_7985,plain,
! [X24461,X24462] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24462),X24461))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X24462)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X24461)))
| ~ c_Nat__Transfer_Onat__set(X24461)
| ~ c_Nat__Transfer_Ois__nat(X24462) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X24462)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X24461)))
| hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24462),X24461))
| ~ c_Nat__Transfer_Onat__set(X24461)
| ~ c_Nat__Transfer_Ois__nat(X24462) ) ),
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_7986,plain,
! [X30066,X30067,X30068] :
( ( hBOOL(hAPP(hAPP(c_member(X30068),esk361_3(X30066,X30067,X30068)),X30067))
| ~ hBOOL(hAPP(hAPP(c_member(X30068),X30066),X30067))
| c_Big__Operators_Olinorder__class_OMax(X30068,X30067) = X30066
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30068),X30067))
| ~ class_Orderings_Olinorder(X30068) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30068),esk361_3(X30066,X30067,X30068)),X30066))
| ~ hBOOL(hAPP(hAPP(c_member(X30068),X30066),X30067))
| c_Big__Operators_Olinorder__class_OMax(X30068,X30067) = X30066
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30068),X30067))
| ~ class_Orderings_Olinorder(X30068) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__eqI])])])]) ).
fof(i_0_7987,plain,
! [X23516,X23517,X23518] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23517),X23516))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23518),X23517)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23518),X23516)))
| X23518 = 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),X23518),X23517)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23518),X23516)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23517),X23516))
| X23518 = 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_7988,plain,
! [X23513,X23514,X23515] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23515),X23514)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23515),X23513)))
| X23515 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23514),X23513)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__mult__cancel])]) ).
fof(i_0_7989,plain,
! [X23391,X23392,X23393] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23393),X23392)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23393),X23391)))
| X23393 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23392),X23391)) )
& ( X23393 != 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),X23393),X23392)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23393),X23391))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23392),X23391))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23393),X23392)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23393),X23391))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__dvd__cancel__disj])])]) ).
fof(i_0_7990,plain,
! [X22172] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22172)),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),X22172)) = 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),X22172))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__neg__1__number__of])]) ).
fof(i_0_7991,plain,
! [X26622,X26623,X26624,X26625,X26626] :
( ~ c_Fun_Oinj__on(X26626,X26625,X26624,X26623)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26626,tc_HOL_Obool)),X26622),X26623))
| c_Fun_Oinj__on(X26626,X26625,X26624,X26622) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__inj__on])]) ).
fof(i_0_7992,plain,
! [X33855,X33856,X33857] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33857)),hAPP(c_List_Ofilter(X33857,X33856),X33855))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33857)),X33855))),
inference(variable_rename,[status(thm)],[fact_length__filter__le]) ).
fof(i_0_7993,plain,
! [X30165,X30166,X30167] : hBOOL(hAPP(hAPP(c_member(tc_prod(X30167,X30167)),hAPP(hAPP(c_Product__Type_OPair(X30167,X30167),X30166),X30166)),c_Transitive__Closure_Ortrancl(X30167,X30165))),
inference(variable_rename,[status(thm)],[fact_rtrancl_Ortrancl__refl]) ).
cnf(i_0_7994,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_7995,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_7996,plain,
! [X19324,X19325,X19326] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19326),X19325)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19326),X19324)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19325),X19324)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19325),X19324))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19326),X19325)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19326),X19324))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le])]) ).
cnf(i_0_7997,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_7998,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_7999,plain,
! [X18352,X18353,X18354] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18354),X18353)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18354),X18352)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18353),X18352)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18353),X18352))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18354),X18353)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18354),X18352))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less])]) ).
fof(i_0_8000,plain,
! [X23519,X23520,X23521] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23521),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23520),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23521),X23519))))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23521),X23520)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23521),X23520))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23521),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23520),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23521),X23519)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__reduce])]) ).
fof(i_0_8001,plain,
! [X27003,X27004,X27005,X27006,X27007] :
( ~ c_Fun_Oinj__on(X27007,X27006,X27005,X27004)
| ~ hBOOL(hAPP(hAPP(c_member(X27007),X27003),X27004))
| hAPP(c_Fun_Othe__inv__into(X27007,X27006,X27004,X27005),hAPP(X27005,X27003)) = X27003 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__f__f])]) ).
fof(i_0_8002,plain,
! [X22284] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22284)),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),X22284)) = 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),X22284))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__neg__1__number__of])]) ).
fof(i_0_8003,plain,
! [X27008,X27009,X27010,X27011,X27012,X27013] :
( ~ c_Fun_Oinj__on(X27013,X27012,X27011,X27010)
| hAPP(X27011,X27009) != X27008
| ~ hBOOL(hAPP(hAPP(c_member(X27013),X27009),X27010))
| hAPP(c_Fun_Othe__inv__into(X27013,X27012,X27010,X27011),X27008) = X27009 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__f__eq])]) ).
fof(i_0_8004,plain,
! [X30886,X30887,X30888,X30889,X30890] :
( ~ hBOOL(hAPP(hAPP(c_member(X30889),X30890),X30888))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30887),hAPP(X30886,X30890)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X30887),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30889,tc_fun(X30887,tc_HOL_Obool)),X30888),X30886))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__INT])])]) ).
fof(i_0_8005,plain,
! [X21030,X21031,X21032,X21033] :
( ~ class_Rings_Olinordered__semidom(X21033)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21032),X21031))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21033),c_Groups_Oone__class_Oone(X21033)),X21030))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21033),hAPP(hAPP(c_Power_Opower__class_Opower(X21033),X21030),X21032)),hAPP(hAPP(c_Power_Opower__class_Opower(X21033),X21030),X21031))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__increasing])]) ).
fof(i_0_8006,plain,
! [X21023,X21024,X21025,X21026] :
( ~ class_Rings_Olinordered__semidom(X21026)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21025),X21024))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21026),c_Groups_Oone__class_Oone(X21026)),X21023))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21026),hAPP(hAPP(c_Power_Opower__class_Opower(X21026),X21023),X21025)),hAPP(hAPP(c_Power_Opower__class_Opower(X21026),X21023),X21024))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing])]) ).
fof(i_0_8007,plain,
! [X21527,X21528,X21529,X21530] :
( ~ class_Fields_Olinordered__field__inverse__zero(X21530)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21530),X21529),X21528))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21530),X21527),c_Groups_Ozero__class_Ozero(X21530)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21530),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21530),X21528),X21527)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21530),X21529),X21527))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__right__mono__neg])]) ).
fof(i_0_8008,plain,
! [X19418,X19419,X19420,X19421] :
( ~ class_Rings_Oordered__ring(X19421)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19421),X19420),X19419))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19421),X19418),c_Groups_Ozero__class_Ozero(X19421)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19421),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19421),X19419),X19418)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19421),X19420),X19418))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono__neg])]) ).
fof(i_0_8009,plain,
! [X19414,X19415,X19416,X19417] :
( ~ class_Rings_Oordered__ring(X19417)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19417),X19416),X19415))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19417),X19414),c_Groups_Ozero__class_Ozero(X19417)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19417),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19417),X19414),X19415)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19417),X19414),X19416))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono__neg])]) ).
fof(i_0_8010,plain,
! [X21531,X21532,X21533,X21534] :
( ~ class_Fields_Olinordered__field(X21534)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21534),X21533),X21532))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21534),X21531),c_Groups_Ozero__class_Ozero(X21534)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21534),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21534),X21532),X21531)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21534),X21533),X21531))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono__neg])]) ).
fof(i_0_8011,plain,
! [X18948,X18949,X18950,X18951] :
( ~ class_Rings_Olinordered__ring__strict(X18951)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18951),X18950),X18949))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18951),X18948),c_Groups_Ozero__class_Ozero(X18951)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18951),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18951),X18949),X18948)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18951),X18950),X18948))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono__neg])]) ).
fof(i_0_8012,plain,
! [X18952,X18953,X18954,X18955] :
( ~ class_Rings_Olinordered__ring__strict(X18955)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18955),X18954),X18953))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18955),X18952),c_Groups_Ozero__class_Ozero(X18955)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18955),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18955),X18952),X18953)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18955),X18952),X18954))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono__neg])]) ).
fof(i_0_8013,plain,
! [X25449,X25450,X25451] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25451),X25450))
| ~ hBOOL(hAPP(hAPP(c_member(X25451),X25449),X25450))
| hAPP(c_Finite__Set_Ocard(X25451),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25451,tc_HOL_Obool)),X25450),hAPP(hAPP(c_Set_Oinsert(X25451),X25449),c_Orderings_Obot__class_Obot(tc_fun(X25451,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25451),X25450)),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_8014,plain,
! [X25446,X25447,X25448] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25448),X25446),X25447))
| hAPP(c_Finite__Set_Ocard(X25448),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25448,tc_HOL_Obool)),X25447),hAPP(hAPP(c_Set_Oinsert(X25448),X25446),c_Orderings_Obot__class_Obot(tc_fun(X25448,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25448),X25447)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25448),X25447)) )
& ( hBOOL(hAPP(hAPP(c_member(X25448),X25446),X25447))
| hAPP(c_Finite__Set_Ocard(X25448),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25448,tc_HOL_Obool)),X25447),hAPP(hAPP(c_Set_Oinsert(X25448),X25446),c_Orderings_Obot__class_Obot(tc_fun(X25448,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(X25448),X25447)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25448),X25447)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5654])])]) ).
fof(i_0_8015,plain,
! [X24566,X24567,X24568] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24568),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24568,tc_HOL_Obool)),X24566),X24567)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24568),X24566))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24568),X24567)) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24568),X24566))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24568),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24568,tc_HOL_Obool)),X24566),X24567)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24568),X24567)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Diff2])])]) ).
cnf(i_0_8016,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_8017,plain,
! [X20747,X20748,X20749] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20749),hAPP(c_Int_Onumber__class_Onumber__of(X20749),X20748)),hAPP(c_Int_Onumber__class_Onumber__of(X20749),X20747)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20749),hAPP(c_Int_Onumber__class_Onumber__of(X20749),X20747)),hAPP(c_Int_Onumber__class_Onumber__of(X20749),X20748)))
| ~ class_Int_Onumber(X20749)
| ~ class_Orderings_Olinorder(X20749) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20749),hAPP(c_Int_Onumber__class_Onumber__of(X20749),X20747)),hAPP(c_Int_Onumber__class_Onumber__of(X20749),X20748)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20749),hAPP(c_Int_Onumber__class_Onumber__of(X20749),X20748)),hAPP(c_Int_Onumber__class_Onumber__of(X20749),X20747)))
| ~ class_Int_Onumber(X20749)
| ~ class_Orderings_Olinorder(X20749) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5656])])]) ).
fof(i_0_8018,plain,
! [X23778,X23779,X23780,X23781] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X23781,tc_fun(X23780,tc_HOL_Obool))),X23779),X23778)),
inference(variable_rename,[status(thm)],[i_0_5657]) ).
fof(i_0_8019,plain,
! [X32664,X32665,X32666] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32666),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X32665)))
| hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,X32665),X32666),X32664)) = 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),X32665)),X32664)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X32665),X32666)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__update__nat])]) ).
fof(i_0_8020,plain,
! [X27726,X27727,X27728,X27729,X27730,X27731] : hAPP(hAPP(c_Fun_Ocomp(X27731,X27730,X27729,X27728),X27727),X27726) = hAPP(X27728,hAPP(X27727,X27726)),
inference(variable_rename,[status(thm)],[fact_o__def]) ).
fof(i_0_8021,plain,
! [X27702,X27703,X27704,X27705,X27706,X27707] : hAPP(hAPP(c_Fun_Ocomp(X27707,X27706,X27705,X27704),X27703),X27702) = hAPP(X27704,hAPP(X27703,X27702)),
inference(variable_rename,[status(thm)],[fact_o__apply]) ).
fof(i_0_8022,plain,
! [X23252,X23253,X23254,X23255,X23256] :
( ~ class_Rings_Ocomm__semiring__1(X23256)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23256),X23255),X23254))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23256),X23253),X23252))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23256),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23256),X23255),X23253)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23256),X23254),X23252))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__dvd__mono])]) ).
fof(i_0_8023,plain,
! [X24773,X24774,X24775,X24776,X24777] :
( ~ class_Lattices_Osemilattice__inf(X24777)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24777),X24776),X24775))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24777),X24774),X24773))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24777),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24777),X24776),X24774)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24777),X24775),X24773))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__mono])]) ).
fof(i_0_8024,plain,
! [X23987,X23988,X23989,X23990,X23991] :
( ~ class_Lattices_Osemilattice__sup(X23991)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23991),X23990),X23989))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23991),X23988),X23987))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23991),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23991),X23990),X23988)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23991),X23989),X23987))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__mono])]) ).
fof(i_0_8025,plain,
! [X22662,X22663,X22664,X22665,X22666] :
( ~ class_Orderings_Olinorder(X22666)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22666),X22665),X22664))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22666),X22663),X22662))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22666),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22666),X22665),X22663)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22666),X22664),X22662))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__mono])]) ).
fof(i_0_8026,plain,
! [X22475,X22476,X22477,X22478,X22479] :
( ~ class_Orderings_Olinorder(X22479)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22479),X22478),X22477))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22479),X22476),X22475))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22479),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22479),X22478),X22476)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22479),X22477),X22475))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__mono])]) ).
fof(i_0_8027,plain,
! [X19229,X19230,X19231,X19232,X19233] :
( ~ class_Groups_Oordered__ab__semigroup__add(X19233)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19233),X19232),X19231))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19233),X19230),X19229))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19233),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19233),X19232),X19230)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19233),X19231),X19229))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__mono])]) ).
fof(i_0_8028,plain,
! [X19462,X19463,X19464,X19465,X19466] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X19466)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19466),X19465),X19464))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19466),X19463),X19462))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19466),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19466),X19465),X19463)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19466),X19464),X19462))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__le__mono])]) ).
fof(i_0_8029,plain,
! [X19457,X19458,X19459,X19460,X19461] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X19461)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19461),X19460),X19459))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19461),X19458),X19457))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19461),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19461),X19460),X19458)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19461),X19459),X19457))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__less__mono])]) ).
fof(i_0_8030,plain,
! [X18290,X18291,X18292,X18293,X18294] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X18294)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18294),X18293),X18292))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18294),X18291),X18290))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18294),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18294),X18293),X18291)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18294),X18292),X18290))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__mono])]) ).
fof(i_0_8031,plain,
! [X20767,X20768,X20769,X20770] :
( ~ class_Int_Onumber(X20770)
| ~ class_Rings_Oring(X20770)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20770),hAPP(c_Int_Onumber__class_Onumber__of(X20770),X20769)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20770),X20768),X20767)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20770),hAPP(c_Int_Onumber__class_Onumber__of(X20770),X20769)),X20768)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20770),hAPP(c_Int_Onumber__class_Onumber__of(X20770),X20769)),X20767)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__diff__distrib__number__of])]) ).
fof(i_0_8032,plain,
! [X20750,X20751,X20752,X20753] :
( ~ class_Int_Onumber(X20753)
| ~ class_Rings_Osemiring(X20753)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20753),hAPP(c_Int_Onumber__class_Onumber__of(X20753),X20752)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20753),X20751),X20750)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20753),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20753),hAPP(c_Int_Onumber__class_Onumber__of(X20753),X20752)),X20751)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20753),hAPP(c_Int_Onumber__class_Onumber__of(X20753),X20752)),X20750)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__distrib__number__of])]) ).
fof(i_0_8033,plain,
! [X23344,X23345,X23346,X23347,X23348] :
( ~ class_Divides_Osemiring__div(X23348)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23348),X23347),X23346))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23348),X23345),X23344))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23348),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23348),X23346),X23347)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23348),X23344),X23345)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23348),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23348),X23346),X23344)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23348),X23347),X23345)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__div__if__dvd])]) ).
fof(i_0_8034,plain,
! [X30668,X30669,X30670,X30671] :
( ~ class_Lattices_Osemilattice__inf(X30671)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30671),X30670))
| hAPP(hAPP(c_Finite__Set_Ofold(X30671,X30671,c_Lattices_Osemilattice__inf__class_Oinf(X30671)),X30669),hAPP(hAPP(c_Set_Oinsert(X30671),X30668),X30670)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X30671),X30668),hAPP(hAPP(c_Finite__Set_Ofold(X30671,X30671,c_Lattices_Osemilattice__inf__class_Oinf(X30671)),X30669),X30670)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__inf__insert])]) ).
fof(i_0_8035,plain,
! [X30664,X30665,X30666,X30667] :
( ~ class_Lattices_Osemilattice__sup(X30667)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30667),X30666))
| hAPP(hAPP(c_Finite__Set_Ofold(X30667,X30667,c_Lattices_Osemilattice__sup__class_Osup(X30667)),X30665),hAPP(hAPP(c_Set_Oinsert(X30667),X30664),X30666)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X30667),X30664),hAPP(hAPP(c_Finite__Set_Ofold(X30667,X30667,c_Lattices_Osemilattice__sup__class_Osup(X30667)),X30665),X30666)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__sup__insert])]) ).
fof(i_0_8036,plain,
! [X30676,X30677,X30678,X30679] :
( ~ class_Orderings_Olinorder(X30679)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30679),X30678))
| hAPP(hAPP(c_Finite__Set_Ofold(X30679,X30679,c_Orderings_Oord__class_Omax(X30679)),X30677),hAPP(hAPP(c_Set_Oinsert(X30679),X30676),X30678)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X30679),X30676),hAPP(hAPP(c_Finite__Set_Ofold(X30679,X30679,c_Orderings_Oord__class_Omax(X30679)),X30677),X30678)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__sup__insert])]) ).
fof(i_0_8037,plain,
! [X30672,X30673,X30674,X30675] :
( ~ class_Orderings_Olinorder(X30675)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30675),X30674))
| hAPP(hAPP(c_Finite__Set_Ofold(X30675,X30675,c_Orderings_Oord__class_Omin(X30675)),X30673),hAPP(hAPP(c_Set_Oinsert(X30675),X30672),X30674)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X30675),X30672),hAPP(hAPP(c_Finite__Set_Ofold(X30675,X30675,c_Orderings_Oord__class_Omin(X30675)),X30673),X30674)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__inf__insert])]) ).
fof(i_0_8038,plain,
! [X28484,X28485,X28486,X28487] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28487),X28486))
| ~ c_Fun_Oinj__on(X28485,X28487,X28484,c_Orderings_Otop__class_Otop(tc_fun(X28485,tc_HOL_Obool)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X28485),hAPP(c_Set_Ovimage(X28485,X28487,X28484),X28486))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__vimageI])]) ).
fof(i_0_8039,plain,
! [X31167,X31168,X31169,X31170,X31171] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31171)
| ~ hBOOL(hAPP(hAPP(c_member(X31170),X31169),X31168))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31171),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31170,X31171),X31168),X31167)),hAPP(X31167,X31169))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__leI])]) ).
fof(i_0_8040,plain,
! [X20861,X20862,X20863,X20864] :
( ~ class_Int_Onumber__ring(X20864)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20864),hAPP(c_Int_Onumber__class_Onumber__of(X20864),X20863)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20864),X20862),hAPP(c_Int_Onumber__class_Onumber__of(X20864),X20861))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20864),hAPP(c_Int_Onumber__class_Onumber__of(X20864),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20863),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20861)))),X20862) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__diff2])]) ).
fof(i_0_8041,plain,
! [X21966,X21967] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21967)),X21966))
| hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21967),X21966)) )
& ( ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21967),X21966))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21967)),X21966)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__nat_Osimps_I2_J])]) ).
fof(i_0_8042,plain,
! [X25799,X25800,X25801,X25802,X25803,X25804] :
( ~ hBOOL(hAPP(hAPP(c_member(X25804),X25803),X25802))
| ~ hBOOL(hAPP(hAPP(X25801,X25803),X25800))
| hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25804,tc_fun(X25799,tc_HOL_Obool)),X25802),X25801),X25800)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP1__I])]) ).
fof(i_0_8043,plain,
! [X31276,X31277,X31278,X31279] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31278),c_Complete__Lattice_OSup__class_OSup(X31278,X31277)),X31276))
| ~ hBOOL(hAPP(hAPP(c_member(X31278),X31279),X31277))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31278),X31279),X31276))
| ~ class_Complete__Lattice_Ocomplete__lattice(X31278) )
& ( hBOOL(hAPP(hAPP(c_member(X31278),esk400_3(X31276,X31277,X31278)),X31277))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31278),c_Complete__Lattice_OSup__class_OSup(X31278,X31277)),X31276))
| ~ class_Complete__Lattice_Ocomplete__lattice(X31278) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31278),esk400_3(X31276,X31277,X31278)),X31276))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31278),c_Complete__Lattice_OSup__class_OSup(X31278,X31277)),X31276))
| ~ class_Complete__Lattice_Ocomplete__lattice(X31278) ) ),
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_8044,plain,
! [X30680,X30681,X30682,X30683,X30684,X30685] :
( ~ c_Finite__Set_Ofun__left__comm__idem(X30685,X30684,X30683)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30685),X30682))
| hAPP(hAPP(c_Finite__Set_Ofold(X30685,X30684,X30683),X30681),hAPP(hAPP(c_Set_Oinsert(X30685),X30680),X30682)) = hAPP(hAPP(X30683,X30680),hAPP(hAPP(c_Finite__Set_Ofold(X30685,X30684,X30683),X30681),X30682)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__insert__idem])]) ).
fof(i_0_8045,plain,
! [X33601,X33602,X33603,X33604,X33605] :
( ( X33602 = 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),X33602),X33601) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X33603),hAPP(c_List_Oset(tc_Nat_Onat),X33601)))
| X33603 = 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),X33602),X33601) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk470_2(X33604,X33605)),hAPP(c_List_Oset(tc_Nat_Onat),X33604)))
| X33605 != 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),X33605),X33604) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( esk470_2(X33604,X33605) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X33605 != 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),X33605),X33604) = 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_8046,plain,
! [X17579,X17580,X17581,X17582,X17583,X17584] :
( ( ~ hBOOL(hAPP(X17584,X17581))
| hBOOL(hAPP(X17584,X17581))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17584,X17583,X17582),X17581,X17580,X17579) )
& ( c_Natural_Oevaln(X17582,X17581,X17580,X17579)
| hBOOL(hAPP(X17584,X17581))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17584,X17583,X17582),X17581,X17580,X17579) )
& ( ~ hBOOL(hAPP(X17584,X17581))
| c_Natural_Oevaln(X17583,X17581,X17580,X17579)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17584,X17583,X17582),X17581,X17580,X17579) )
& ( c_Natural_Oevaln(X17582,X17581,X17580,X17579)
| c_Natural_Oevaln(X17583,X17581,X17580,X17579)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17584,X17583,X17582),X17581,X17580,X17579) )
& ( ~ hBOOL(hAPP(X17584,X17581))
| ~ c_Natural_Oevaln(X17583,X17581,X17580,X17579)
| c_Natural_Oevaln(c_Com_Ocom_OCond(X17584,X17583,X17582),X17581,X17580,X17579) )
& ( hBOOL(hAPP(X17584,X17581))
| ~ c_Natural_Oevaln(X17582,X17581,X17580,X17579)
| c_Natural_Oevaln(c_Com_Ocom_OCond(X17584,X17583,X17582),X17581,X17580,X17579) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5658])])]) ).
fof(i_0_8047,plain,
! [X17573,X17574,X17575,X17576,X17577,X17578] :
( ( ~ hBOOL(hAPP(X17578,X17575))
| hBOOL(hAPP(X17578,X17575))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17578,X17577,X17576),X17575,X17574,X17573) )
& ( c_Natural_Oevaln(X17576,X17575,X17574,X17573)
| hBOOL(hAPP(X17578,X17575))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17578,X17577,X17576),X17575,X17574,X17573) )
& ( ~ hBOOL(hAPP(X17578,X17575))
| c_Natural_Oevaln(X17577,X17575,X17574,X17573)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17578,X17577,X17576),X17575,X17574,X17573) )
& ( c_Natural_Oevaln(X17576,X17575,X17574,X17573)
| c_Natural_Oevaln(X17577,X17575,X17574,X17573)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17578,X17577,X17576),X17575,X17574,X17573) )
& ( ~ hBOOL(hAPP(X17578,X17575))
| ~ c_Natural_Oevaln(X17577,X17575,X17574,X17573)
| c_Natural_Oevaln(c_Com_Ocom_OCond(X17578,X17577,X17576),X17575,X17574,X17573) )
& ( hBOOL(hAPP(X17578,X17575))
| ~ c_Natural_Oevaln(X17576,X17575,X17574,X17573)
| c_Natural_Oevaln(c_Com_Ocom_OCond(X17578,X17577,X17576),X17575,X17574,X17573) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5659])])]) ).
fof(i_0_8048,plain,
! [X17450,X17451,X17452,X17453,X17454,X17455] :
( ( ~ hBOOL(hAPP(X17455,X17452))
| hBOOL(hAPP(X17455,X17452))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17455,X17454,X17453),X17452,X17451,X17450) )
& ( c_Natural_Oevaln(X17453,X17452,X17451,X17450)
| hBOOL(hAPP(X17455,X17452))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17455,X17454,X17453),X17452,X17451,X17450) )
& ( ~ hBOOL(hAPP(X17455,X17452))
| c_Natural_Oevaln(X17454,X17452,X17451,X17450)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17455,X17454,X17453),X17452,X17451,X17450) )
& ( c_Natural_Oevaln(X17453,X17452,X17451,X17450)
| c_Natural_Oevaln(X17454,X17452,X17451,X17450)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17455,X17454,X17453),X17452,X17451,X17450) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5660])])]) ).
fof(i_0_8049,plain,
! [X17330,X17331,X17332,X17333,X17334,X17335] :
( ~ c_Natural_Oevaln(X17335,X17334,X17333,X17332)
| ~ c_Natural_Oevaln(X17331,X17332,X17333,X17330)
| c_Natural_Oevaln(c_Com_Ocom_OSemi(X17335,X17331),X17334,X17333,X17330) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln_OSemi])]) ).
fof(i_0_8050,plain,
! [X19144,X19145] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19145))
| ~ 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),X19145),X19144))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19144))
| ~ 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),X19145),X19144))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19145))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19144))
| 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),X19145),X19144))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__mult__iff])])]) ).
fof(i_0_8051,plain,
! [X19658,X19659] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19659))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19658))
| 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),X19658),X19659))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__mult])]) ).
fof(i_0_8052,plain,
! [X20153,X20154,X20155] : 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),X20155),X20154)),X20153)),X20154) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X20153),X20154),
inference(variable_rename,[status(thm)],[fact_mod__mult__self4]) ).
fof(i_0_8053,plain,
! [X31348,X31349,X31350] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X31350,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X31350,tc_HOL_Obool),tc_HOL_Obool)),X31349),X31348)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31350,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31350,tc_HOL_Obool),X31349)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31350,tc_HOL_Obool),X31348)),
inference(variable_rename,[status(thm)],[fact_Union__Un__distrib]) ).
fof(i_0_8054,plain,
! [X31370,X31371,X31372] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X31372,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X31372,tc_HOL_Obool),tc_HOL_Obool)),X31371),X31370)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31372,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31372,tc_HOL_Obool),X31371)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31372,tc_HOL_Obool),X31370)),
inference(variable_rename,[status(thm)],[fact_Inter__Un__distrib]) ).
fof(i_0_8055,plain,
! [X20208,X20209,X20210,X20211,X20212,X20213,X20214,X20215] :
( ( X20208 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X20210,X20209))
| ~ hBOOL(hAPP(X20210,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20209,X20208))) )
& ( X20208 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20212),X20208))
| X20209 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20208),X20211)),X20212)
| hBOOL(hAPP(X20210,X20212))
| ~ hBOOL(hAPP(X20210,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20209,X20208))) )
& ( X20213 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X20213 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X20215,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20214,X20213))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk70_3(X20213,X20214,X20215)),X20213))
| X20213 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X20215,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20214,X20213))) )
& ( X20214 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20213),esk69_3(X20213,X20214,X20215))),esk70_3(X20213,X20214,X20215))
| X20213 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X20215,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20214,X20213))) )
& ( ~ hBOOL(hAPP(X20215,esk70_3(X20213,X20214,X20215)))
| X20213 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X20215,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20214,X20213))) )
& ( X20213 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X20215,X20214))
| hBOOL(hAPP(X20215,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20214,X20213))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk70_3(X20213,X20214,X20215)),X20213))
| ~ hBOOL(hAPP(X20215,X20214))
| hBOOL(hAPP(X20215,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20214,X20213))) )
& ( X20214 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20213),esk69_3(X20213,X20214,X20215))),esk70_3(X20213,X20214,X20215))
| ~ hBOOL(hAPP(X20215,X20214))
| hBOOL(hAPP(X20215,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20214,X20213))) )
& ( ~ hBOOL(hAPP(X20215,esk70_3(X20213,X20214,X20215)))
| ~ hBOOL(hAPP(X20215,X20214))
| hBOOL(hAPP(X20215,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20214,X20213))) ) ),
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_8056,plain,
! [X33690,X33691,X33692,X33693,X33694,X33695,X33696] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33692)),X33691),c_List_Olists(X33692,X33690)))
| ~ hBOOL(hAPP(hAPP(c_member(X33692),X33693),hAPP(c_List_Oset(X33692),X33691)))
| hBOOL(hAPP(hAPP(c_member(X33692),X33693),X33690)) )
& ( hBOOL(hAPP(hAPP(c_member(X33696),esk471_3(X33694,X33695,X33696)),hAPP(c_List_Oset(X33696),X33695)))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33696)),X33695),c_List_Olists(X33696,X33694))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X33696),esk471_3(X33694,X33695,X33696)),X33694))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33696)),X33695),c_List_Olists(X33696,X33694))) ) ),
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_8057,plain,
! [X33550,X33551,X33552,X33553] : c_List_Olist_Olist__size(X33553,X33552,hAPP(hAPP(c_List_Olist_OCons(X33553),X33551),X33550)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X33552,X33551)),c_List_Olist_Olist__size(X33553,X33552,X33550))),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_8058,plain,
! [X23373,X23374,X23375,X23376,X23377] :
( ~ class_Rings_Ocomm__semiring__1(X23377)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23377),X23376),X23375))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23374),X23373))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23377),hAPP(hAPP(c_Power_Opower__class_Opower(X23377),X23376),X23374)),hAPP(hAPP(c_Power_Opower__class_Opower(X23377),X23375),X23373))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__power__le])]) ).
fof(i_0_8059,plain,
! [X27438,X27439,X27440,X27441] : c_Map_Orestrict__map(X27441,X27440,X27439,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27441,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X27441),X27438),c_Orderings_Obot__class_Obot(tc_fun(X27441,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27441,tc_Option_Ooption(X27440)),X27439),X27438),c_Option_Ooption_ONone(X27440)),
inference(variable_rename,[status(thm)],[fact_restrict__complement__singleton__eq]) ).
fof(i_0_8060,plain,
! [X32403,X32404,X32405] : c_Random_Oselect__weight(X32405,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X32405)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X32405),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X32404)),X32403)) = c_Random_Oselect__weight(X32405,X32403),
inference(variable_rename,[status(thm)],[fact_select__weight__cons__zero]) ).
fof(i_0_8061,plain,
! [X19950,X19951,X19952,X19953] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19952))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19952))
| X19952 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X19953,X19952) = X19950
| X19953 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19952),X19951)),X19950) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19952),X19950))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19950),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)),X19952))
| X19952 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X19953,X19952) = X19950
| X19953 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19952),X19951)),X19950) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19952))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19950))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19950),X19952))
| X19952 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X19953,X19952) = X19950
| X19953 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19952),X19951)),X19950) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19952),X19950))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19950),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)),X19950))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19950),X19952))
| X19952 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X19953,X19952) = X19950
| X19953 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19952),X19951)),X19950) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5661])])]) ).
fof(i_0_8062,plain,
! [X34200,X34201] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X34201)),c_List_Otranspose__rel(X34201)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X34201)),c_List_Olist_ONil(X34201)),X34200)))
| c_List_Otranspose(X34201,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X34201)),c_List_Olist_ONil(X34201)),X34200)) = c_List_Otranspose(X34201,X34200) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose_Opsimps_I2_J])]) ).
cnf(i_0_8063,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_8064,plain,
! [X25071,X25072,X25073] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25073,tc_HOL_Obool)),X25072),X25071) != c_Orderings_Obot__class_Obot(tc_fun(X25073,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25073,tc_HOL_Obool)),X25072),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25073,tc_HOL_Obool)),X25071))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25073,tc_HOL_Obool)),X25072),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25073,tc_HOL_Obool)),X25071)))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25073,tc_HOL_Obool)),X25072),X25071) = c_Orderings_Obot__class_Obot(tc_fun(X25073,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_disjoint__eq__subset__Compl])]) ).
fof(i_0_8065,plain,
! [X25464,X25465,X25466] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25466),X25465))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25466,tc_HOL_Obool)),X25464),X25465))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25466),X25465)),hAPP(c_Finite__Set_Ocard(X25466),X25464)))
| X25464 = X25465 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__seteq])]) ).
fof(i_0_8066,plain,
! [X31289,X31290,X31291] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X31291,tc_HOL_Obool)),X31290),X31289))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31291,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31291,tc_HOL_Obool),X31289)),X31290)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inter__lower])]) ).
fof(i_0_8067,plain,
! [X30390,X30391,X30392,X30393,X30394] : hAPP(c_Relation_Oconverse(X30394,X30393),hAPP(hAPP(c_Relation_Orel__comp(X30394,X30392,X30393),X30391),X30390)) = hAPP(hAPP(c_Relation_Orel__comp(X30393,X30392,X30394),hAPP(c_Relation_Oconverse(X30392,X30393),X30390)),hAPP(c_Relation_Oconverse(X30394,X30392),X30391)),
inference(variable_rename,[status(thm)],[fact_converse__rel__comp]) ).
fof(i_0_8068,plain,
! [X19979,X19980,X19981,X19982] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19981))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19981))
| X19981 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19982),X19981) = X19980
| X19982 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19981),X19980)),X19979) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19981),X19979))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19979),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)),X19981))
| X19981 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19982),X19981) = X19980
| X19982 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19981),X19980)),X19979) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19981))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19979))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19979),X19981))
| X19981 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19982),X19981) = X19980
| X19982 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19981),X19980)),X19979) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19981),X19979))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19979),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)),X19979))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19979),X19981))
| X19981 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19982),X19981) = X19980
| X19982 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19981),X19980)),X19979) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5663])])]) ).
fof(i_0_8069,plain,
! [X22484,X22485,X22486,X22487] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22487),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22487),X22486),X22485)),X22484))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22487),X22486),X22484))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22487),X22485),X22484))
| ~ class_Orderings_Olinorder(X22487) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22487),X22486),X22484))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22487),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22487),X22486),X22485)),X22484))
| ~ class_Orderings_Olinorder(X22487) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22487),X22485),X22484))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22487),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22487),X22486),X22485)),X22484))
| ~ class_Orderings_Olinorder(X22487) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__le__iff__disj])])]) ).
fof(i_0_8070,plain,
! [X22494,X22495,X22496,X22497] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22497),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22497),X22496),X22495)),X22494))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22497),X22496),X22494))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22497),X22495),X22494))
| ~ class_Orderings_Olinorder(X22497) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22497),X22496),X22494))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22497),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22497),X22496),X22495)),X22494))
| ~ class_Orderings_Olinorder(X22497) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22497),X22495),X22494))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22497),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22497),X22496),X22495)),X22494))
| ~ class_Orderings_Olinorder(X22497) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__less__iff__disj])])]) ).
fof(i_0_8071,plain,
! [X20198,X20199,X20200,X20201,X20202,X20203,X20204,X20205] :
( ( X20198 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X20200,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X20200,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20199),X20198))) )
& ( X20198 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20202),X20198))
| X20199 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20198),X20201)),X20202)
| hBOOL(hAPP(X20200,X20201))
| ~ hBOOL(hAPP(X20200,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20199),X20198))) )
& ( X20203 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X20203 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X20205,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20204),X20203))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk68_3(X20203,X20204,X20205)),X20203))
| X20203 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X20205,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20204),X20203))) )
& ( X20204 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20203),esk67_3(X20203,X20204,X20205))),esk68_3(X20203,X20204,X20205))
| X20203 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X20205,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20204),X20203))) )
& ( ~ hBOOL(hAPP(X20205,esk67_3(X20203,X20204,X20205)))
| X20203 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X20205,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20204),X20203))) )
& ( X20203 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X20205,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X20205,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20204),X20203))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk68_3(X20203,X20204,X20205)),X20203))
| ~ hBOOL(hAPP(X20205,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X20205,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20204),X20203))) )
& ( X20204 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20203),esk67_3(X20203,X20204,X20205))),esk68_3(X20203,X20204,X20205))
| ~ hBOOL(hAPP(X20205,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X20205,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20204),X20203))) )
& ( ~ hBOOL(hAPP(X20205,esk67_3(X20203,X20204,X20205)))
| ~ hBOOL(hAPP(X20205,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X20205,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20204),X20203))) ) ),
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_8072,plain,
! [X25294,X25295,X25296] :
( ~ class_Orderings_Olinorder(X25296)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25296),X25295))
| X25294 = c_Orderings_Obot__class_Obot(tc_fun(X25296,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25296,tc_HOL_Obool)),X25294),X25295))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X25296),c_Big__Operators_Olattice_OSup__fin(X25296,c_Orderings_Oord__class_Omax(X25296),X25294)),c_Big__Operators_Olattice_OSup__fin(X25296,c_Orderings_Oord__class_Omax(X25296),X25295)) = c_Big__Operators_Olattice_OSup__fin(X25296,c_Orderings_Oord__class_Omax(X25296),X25295) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Osubset__idem])]) ).
fof(i_0_8073,plain,
! [X25421,X25422,X25423] :
( ~ class_Orderings_Olinorder(X25423)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25423),X25422))
| X25421 = c_Orderings_Obot__class_Obot(tc_fun(X25423,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25423,tc_HOL_Obool)),X25421),X25422))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X25423),c_Big__Operators_Olattice_OInf__fin(X25423,c_Orderings_Oord__class_Omin(X25423),X25421)),c_Big__Operators_Olattice_OInf__fin(X25423,c_Orderings_Oord__class_Omin(X25423),X25422)) = c_Big__Operators_Olattice_OInf__fin(X25423,c_Orderings_Oord__class_Omin(X25423),X25422) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Osubset__idem])]) ).
cnf(i_0_8074,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_8075,plain,
! [X30822,X30823,X30824,X30825,X30826,X30827] :
( ~ c_Finite__Set_Ofun__left__comm(X30827,X30826,X30825)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30827),X30824))
| hBOOL(hAPP(hAPP(c_member(X30827),X30823),X30824))
| hAPP(hAPP(c_Finite__Set_Ofold(X30827,X30826,X30825),X30822),hAPP(hAPP(c_Set_Oinsert(X30827),X30823),X30824)) = hAPP(hAPP(c_Finite__Set_Ofold(X30827,X30826,X30825),hAPP(hAPP(X30825,X30823),X30822)),X30824) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5665])]) ).
fof(i_0_8076,plain,
! [X31625,X31626,X31627,X31628,X31629] :
( ~ hBOOL(hAPP(hAPP(c_member(X31629),X31628),c_Map_Odom(X31629,X31627,X31626)))
| hAPP(c_Map_Omap__add(X31629,X31627,X31625,X31626),X31628) = hAPP(X31626,X31628) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__add__dom__app__simps_I1_J])]) ).
fof(i_0_8077,plain,
! [X17764,X17765,X17766,X17767,X17768] :
( ~ hBOOL(hAPP(X17768,X17767))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17766),X17767),X17765))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17768,X17766)),X17765),X17764))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17768,X17766)),X17767),X17764)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc_OWhileTrue])]) ).
cnf(i_0_8078,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_8079,plain,
! [X31261,X31262] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X31262,tc_HOL_Obool),tc_HOL_Obool)),X31261),hAPP(c_Set_OPow(X31262),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31262,tc_HOL_Obool),X31261)))),
inference(variable_rename,[status(thm)],[fact_subset__Pow__Union]) ).
fof(i_0_8080,plain,
! [X32172,X32173,X32174,X32175,X32176] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32176)),X32175) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32174)),X32173)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32176)),X32172) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32174)),X32173)
| ~ hBOOL(hAPP(c_List_Odistinct(X32174),X32173))
| c_Map_Omap__of(X32174,X32176,hAPP(hAPP(c_List_Ozip(X32174,X32176),X32173),X32175)) != c_Map_Omap__of(X32174,X32176,hAPP(hAPP(c_List_Ozip(X32174,X32176),X32173),X32172))
| X32175 = X32172 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__zip__inject])]) ).
fof(i_0_8081,plain,
! [X24697,X24698,X24699,X24700] :
( ~ hBOOL(hAPP(hAPP(c_member(X24700),X24699),X24698))
| ~ hBOOL(hAPP(hAPP(c_member(X24700),X24699),X24697))
| hBOOL(hAPP(hAPP(c_member(X24700),X24699),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24700,tc_HOL_Obool)),X24698),X24697))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntI])]) ).
fof(i_0_8082,plain,
! [X31630,X31631,X31632,X31633] : c_Map_Odom(X31633,X31632,c_Map_Omap__add(X31633,X31632,X31631,X31630)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31633,tc_HOL_Obool)),c_Map_Odom(X31633,X31632,X31630)),c_Map_Odom(X31633,X31632,X31631)),
inference(variable_rename,[status(thm)],[fact_dom__map__add]) ).
fof(i_0_8083,plain,
! [X27372,X27373,X27374,X27375] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X27374),X27373))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27375),X27372),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X27373),hAPP(c_Nat_OSuc,X27374))) = c_Groups_Ozero__class_Ozero(X27375)
| ~ class_Groups_Ocomm__monoid__add(X27375) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X27374),X27373))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27375),X27372),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X27373),hAPP(c_Nat_OSuc,X27374))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27375),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27375),X27372),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X27373),X27374))),hAPP(X27372,X27374))
| ~ class_Groups_Ocomm__monoid__add(X27375) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5667])])]) ).
fof(i_0_8084,plain,
! [X22418,X22419,X22420,X22421,X22422,X22423] :
( ( hBOOL(hAPP(X22423,hAPP(c_Product__Type_Ofst(X22419,X22418),hAPP(hAPP(c_Product__Type_OPair(X22419,X22418),X22422),X22420))))
| ~ hBOOL(hAPP(X22421,X22420))
| ~ hBOOL(hAPP(X22423,X22422)) )
& ( hBOOL(hAPP(X22421,hAPP(c_Product__Type_Osnd(X22419,X22418),hAPP(hAPP(c_Product__Type_OPair(X22419,X22418),X22422),X22420))))
| ~ hBOOL(hAPP(X22421,X22420))
| ~ hBOOL(hAPP(X22423,X22422)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conjI__realizer])])]) ).
fof(i_0_8085,plain,
! [X30931,X30932,X30933,X30934,X30935,X30936] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X30936)
| hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30935,tc_fun(X30934,X30936)),X30933),X30932),X30931) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30935,X30936),X30933),hAPP(hAPP(c_COMBC(X30935,X30934,X30936),X30932),X30931)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INFI__apply])]) ).
fof(i_0_8086,plain,
! [X26066,X26067,X26068,X26069,X26070,X26071] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X26071)
| hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26070,tc_fun(X26069,X26071)),X26068),X26067),X26066) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26070,X26071),X26068),hAPP(hAPP(c_COMBC(X26070,X26069,X26071),X26067),X26066)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUPR__apply])]) ).
fof(i_0_8087,plain,
! [X24563,X24564,X24565] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X24565),X24564))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24565),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24565,tc_HOL_Obool)),X24564),X24563))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X24565),X24563))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24565),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24565,tc_HOL_Obool)),X24564),X24563))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24565),X24564))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24565),X24563))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24565),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24565,tc_HOL_Obool)),X24564),X24563))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Un])])]) ).
fof(i_0_8088,plain,
! [X23920,X23921,X23922,X23923] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23923,tc_HOL_Obool)),X23922),X23921),X23920))
| hBOOL(hAPP(X23922,X23920))
| hBOOL(hAPP(X23921,X23920)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5668])]) ).
fof(i_0_8089,plain,
! [X25041,X25042,X25043] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25043,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25043,tc_HOL_Obool)),X25042),X25041)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25043,tc_HOL_Obool)),X25042),X25041)) = X25042,
inference(variable_rename,[status(thm)],[fact_Un__Diff__Int]) ).
fof(i_0_8090,plain,
! [X33678,X33679,X33680] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33680,tc_HOL_Obool)),X33679),X33678))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X33680),tc_HOL_Obool)),c_List_Olists(X33680,X33679)),c_List_Olists(X33680,X33678))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__mono])]) ).
fof(i_0_8091,plain,
! [X21778,X21779,X21780,X21781] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),X21779),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21781),X21778),X21780)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),X21778),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21781),X21779),X21780)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21781),X21780),c_Groups_Ozero__class_Ozero(X21781)))
| ~ class_Fields_Olinordered__field(X21781) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),X21778),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21781),X21779),X21780)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21781),X21779),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21781),X21778),X21780)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21781),X21780),c_Groups_Ozero__class_Ozero(X21781)))
| ~ class_Fields_Olinordered__field(X21781) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__divide__eq])])]) ).
fof(i_0_8092,plain,
! [X21658,X21659,X21660,X21661] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21661),X21659),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21661),X21658),X21660)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21661),X21658),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21661),X21659),X21660)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21661),X21660),c_Groups_Ozero__class_Ozero(X21661)))
| ~ class_Fields_Olinordered__field(X21661) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21661),X21658),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21661),X21659),X21660)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21661),X21659),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21661),X21658),X21660)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21661),X21660),c_Groups_Ozero__class_Ozero(X21661)))
| ~ class_Fields_Olinordered__field(X21661) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__divide__eq])])]) ).
fof(i_0_8093,plain,
! [X29755,X29756] :
( ( ~ c_Wellfounded_OwfP(X29756,X29755)
| c_Wellfounded_Owf(X29756,hAPP(c_Set_OCollect(tc_prod(X29756,X29756)),hAPP(c_Product__Type_Oprod_Oprod__case(X29756,X29756,tc_HOL_Obool),X29755))) )
& ( ~ c_Wellfounded_Owf(X29756,hAPP(c_Set_OCollect(tc_prod(X29756,X29756)),hAPP(c_Product__Type_Oprod_Oprod__case(X29756,X29756,tc_HOL_Obool),X29755)))
| c_Wellfounded_OwfP(X29756,X29755) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__def])]) ).
fof(i_0_8094,plain,
! [X20055,X20056] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20055),X20056)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20055),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)),X20056)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20055),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),X20055),X20056)),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)),X20056)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__neg__iff])])]) ).
fof(i_0_8095,plain,
! [X28607,X28608,X28609,X28610,X28611,X28612] :
( ( hAPP(hAPP(c_Product__Type_OSigma(X28609,X28612),X28608),hAPP(c_COMBK(tc_fun(X28612,tc_HOL_Obool),X28609),X28610)) != hAPP(hAPP(c_Product__Type_OSigma(X28609,X28612),X28607),hAPP(c_COMBK(tc_fun(X28612,tc_HOL_Obool),X28609),X28610))
| X28608 = X28607
| ~ hBOOL(hAPP(hAPP(c_member(X28612),X28611),X28610)) )
& ( X28608 != X28607
| hAPP(hAPP(c_Product__Type_OSigma(X28609,X28612),X28608),hAPP(c_COMBK(tc_fun(X28612,tc_HOL_Obool),X28609),X28610)) = hAPP(hAPP(c_Product__Type_OSigma(X28609,X28612),X28607),hAPP(c_COMBK(tc_fun(X28612,tc_HOL_Obool),X28609),X28610))
| ~ hBOOL(hAPP(hAPP(c_member(X28612),X28611),X28610)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Times__eq__cancel2])])]) ).
fof(i_0_8096,plain,
! [X19948,X19949] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19949))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19949),X19948)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X19949,X19948) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19949),X19948) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__neg__trivial])]) ).
fof(i_0_8097,plain,
! [X29984,X29985] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29985,tc_HOL_Obool)),esk350_2(X29984,X29985)),hAPP(c_Relation_OImage(X29985,X29985,X29984),esk350_2(X29984,X29985))))
| c_Wellfounded_Owf(X29985,X29984) )
& ( esk350_2(X29984,X29985) != c_Orderings_Obot__class_Obot(tc_fun(X29985,tc_HOL_Obool))
| c_Wellfounded_Owf(X29985,X29984) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfI__pf])])])]) ).
fof(i_0_8098,plain,
! [X22083,X22084,X22085,X22086,X22087] :
( ~ hBOOL(hAPP(hAPP(X22087,X22086),X22085))
| hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22084,X22083,tc_HOL_Obool),X22087),hAPP(hAPP(c_Product__Type_OPair(X22084,X22083),X22086),X22085))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_splitI])]) ).
fof(i_0_8099,plain,
! [X22078,X22079,X22080,X22081,X22082] :
( ~ hBOOL(hAPP(hAPP(X22082,X22081),X22080))
| hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22079,X22078,tc_HOL_Obool),X22082),hAPP(hAPP(c_Product__Type_OPair(X22079,X22078),X22081),X22080))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_prod__caseI])]) ).
fof(i_0_8100,plain,
! [X20057,X20058] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20057),X20058)),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)),X20057))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20058),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)),X20057))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20057),X20058)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20058),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_8101,plain,
! [X20482,X20483,X20484] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20484),X20483)),X20482))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20484),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20482),X20483))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20484),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20482),X20483)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20484),X20483)),X20482)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv])]) ).
fof(i_0_8102,plain,
! [X20444,X20445,X20446] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20446),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20445),X20444)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20446),X20444)),X20445)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20446),X20444)),X20445))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20446),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20445),X20444))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__conv])]) ).
fof(i_0_8103,plain,
! [X25491,X25492,X25493] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25493),X25492))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25493,tc_HOL_Obool)),X25492),X25491))
| hAPP(c_Finite__Set_Ocard(X25493),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25493,tc_HOL_Obool)),X25491),X25492)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25493),X25491)),hAPP(c_Finite__Set_Ocard(X25493),X25492)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff__subset])]) ).
fof(i_0_8104,plain,
! [X28034,X28035,X28036,X28037,X28038] :
( ~ c_Finite__Set_Ofolding__idem(X28038,X28037,X28036,X28035)
| hAPP(c_Fun_Ocomp(X28037,X28037,X28037,hAPP(X28036,X28034)),hAPP(X28036,X28034)) = hAPP(X28036,X28034) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Oidem__comp])]) ).
cnf(i_0_8105,plain,
c_Int_Opred(c_Int_OBit1(X1)) = c_Int_OBit0(X1),
inference(split_conjunct,[status(thm)],[i_0_5669]) ).
fof(i_0_8106,plain,
! [X21074,X21075,X21076] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21076)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21076)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21075)),X21074)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21075)),X21074) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21075)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21076)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21075)),X21074)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21076)),X21074)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21076))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21075)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21076)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21075)),X21074)) = 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),X21076),X21075))),X21074)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21076))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5670])])]) ).
cnf(i_0_8107,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_8108,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_8109,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_8110,plain,
! [X24452,X24453,X24454] : hAPP(c_Relation_OField(X24454),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X24454,X24454),tc_HOL_Obool)),X24453),X24452)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24454,tc_HOL_Obool)),hAPP(c_Relation_OField(X24454),X24453)),hAPP(c_Relation_OField(X24454),X24452)),
inference(variable_rename,[status(thm)],[fact_Field__Un]) ).
fof(i_0_8111,plain,
! [X32193,X32194,X32195,X32196,X32197] :
( ( hAPP(hAPP(c_List_Omap(tc_prod(X32197,X32195),X32197),c_Product__Type_Ofst(X32197,X32195)),X32193) = X32196
| hAPP(hAPP(c_List_Ozip(X32197,X32195),X32196),X32194) != X32193
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32197)),X32196) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32195)),X32194) )
& ( hAPP(hAPP(c_List_Omap(tc_prod(X32197,X32195),X32195),c_Product__Type_Osnd(X32197,X32195)),X32193) = X32194
| hAPP(hAPP(c_List_Ozip(X32197,X32195),X32196),X32194) != X32193
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32197)),X32196) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32195)),X32194) )
& ( hAPP(hAPP(c_List_Omap(tc_prod(X32197,X32195),X32197),c_Product__Type_Ofst(X32197,X32195)),X32193) != X32196
| hAPP(hAPP(c_List_Omap(tc_prod(X32197,X32195),X32195),c_Product__Type_Osnd(X32197,X32195)),X32193) != X32194
| hAPP(hAPP(c_List_Ozip(X32197,X32195),X32196),X32194) = X32193
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32197)),X32196) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32195)),X32194) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__eq__conv])])]) ).
fof(i_0_8112,plain,
! [X27087,X27088,X27089,X27090,X27091,X27092,X27093] :
( ( X27088 != X27090
| X27088 = X27090
| hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27093,tc_Option_Ooption(X27092)),X27091),X27090),hAPP(c_Option_Ooption_OSome(X27092),X27089)),X27088) != hAPP(c_Option_Ooption_OSome(X27092),X27087) )
& ( hAPP(X27091,X27088) = hAPP(c_Option_Ooption_OSome(X27092),X27087)
| X27088 = X27090
| hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27093,tc_Option_Ooption(X27092)),X27091),X27090),hAPP(c_Option_Ooption_OSome(X27092),X27089)),X27088) != hAPP(c_Option_Ooption_OSome(X27092),X27087) )
& ( X27088 != X27090
| X27089 = X27087
| hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27093,tc_Option_Ooption(X27092)),X27091),X27090),hAPP(c_Option_Ooption_OSome(X27092),X27089)),X27088) != hAPP(c_Option_Ooption_OSome(X27092),X27087) )
& ( hAPP(X27091,X27088) = hAPP(c_Option_Ooption_OSome(X27092),X27087)
| X27089 = X27087
| hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27093,tc_Option_Ooption(X27092)),X27091),X27090),hAPP(c_Option_Ooption_OSome(X27092),X27089)),X27088) != hAPP(c_Option_Ooption_OSome(X27092),X27087) )
& ( X27088 != X27090
| X27089 != X27087
| hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27093,tc_Option_Ooption(X27092)),X27091),X27090),hAPP(c_Option_Ooption_OSome(X27092),X27089)),X27088) = hAPP(c_Option_Ooption_OSome(X27092),X27087) )
& ( X27088 = X27090
| hAPP(X27091,X27088) != hAPP(c_Option_Ooption_OSome(X27092),X27087)
| hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27093,tc_Option_Ooption(X27092)),X27091),X27090),hAPP(c_Option_Ooption_OSome(X27092),X27089)),X27088) = hAPP(c_Option_Ooption_OSome(X27092),X27087) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__upd__Some__unfold])])]) ).
fof(i_0_8113,plain,
! [X24689,X24690,X24691,X24692] :
( ( hBOOL(hAPP(X24691,X24689))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24692,tc_HOL_Obool)),X24691),X24690),X24689)) )
& ( hBOOL(hAPP(X24690,X24689))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24692,tc_HOL_Obool)),X24691),X24690),X24689)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5674])])]) ).
fof(i_0_8114,plain,
! [X24957,X24958,X24959,X24960] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24960,tc_HOL_Obool)),X24959),X24958),X24957))
| hBOOL(hAPP(X24959,X24957)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1D1])]) ).
fof(i_0_8115,plain,
! [X24961,X24962,X24963,X24964] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24964,tc_HOL_Obool)),X24963),X24962),X24961))
| hBOOL(hAPP(X24962,X24961)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1D2])]) ).
cnf(i_0_8116,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_8117,plain,
! [X32301,X32302,X32303,X32304,X32305,X32306] :
( ( hBOOL(hAPP(hAPP(X32305,X32304),X32302))
| ~ c_List_Olistrelp(X32306,X32305,hAPP(hAPP(c_List_Olist_OCons(X32306),X32304),X32303),hAPP(hAPP(c_List_Olist_OCons(X32306),X32302),X32301)) )
& ( c_List_Olistrelp(X32306,X32305,X32303,X32301)
| ~ c_List_Olistrelp(X32306,X32305,hAPP(hAPP(c_List_Olist_OCons(X32306),X32304),X32303),hAPP(hAPP(c_List_Olist_OCons(X32306),X32302),X32301)) )
& ( ~ hBOOL(hAPP(hAPP(X32305,X32304),X32302))
| ~ c_List_Olistrelp(X32306,X32305,X32303,X32301)
| c_List_Olistrelp(X32306,X32305,hAPP(hAPP(c_List_Olist_OCons(X32306),X32304),X32303),hAPP(hAPP(c_List_Olist_OCons(X32306),X32302),X32301)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp_Oequations_I2_J])])]) ).
fof(i_0_8118,plain,
! [X32295,X32296,X32297,X32298,X32299,X32300] :
( ~ hBOOL(hAPP(hAPP(X32300,X32299),X32298))
| ~ c_List_Olistrelp(X32297,X32300,X32296,X32295)
| c_List_Olistrelp(X32297,X32300,hAPP(hAPP(c_List_Olist_OCons(X32297),X32299),X32296),hAPP(hAPP(c_List_Olist_OCons(X32297),X32298),X32295)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp_OCons])]) ).
cnf(i_0_8119,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_8120,plain,
! [X29084] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X29084),c_Int_OInteg))
| X29084 = hAPP(c_Int_ORep__Integ,esk306_1(X29084)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Rep__Integ__cases])])]) ).
fof(i_0_8121,plain,
! [X31486,X31487,X31488] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X31488,tc_HOL_Obool)),esk417_3(X31486,X31487,X31488)),X31487))
| hBOOL(hAPP(hAPP(c_member(X31488),X31486),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31488,tc_HOL_Obool),X31487))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X31488),X31486),esk417_3(X31486,X31487,X31488)))
| hBOOL(hAPP(hAPP(c_member(X31488),X31486),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31488,tc_HOL_Obool),X31487))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_InterI])])])]) ).
fof(i_0_8122,plain,
! [X33772,X33773,X33774,X33777,X33778,X33779,X33780,X33781] :
( ( X33773 = hAPP(hAPP(c_List_Olist_OCons(X33774),esk478_3(X33772,X33773,X33774)),esk479_3(X33772,X33773,X33774))
| X33773 = c_List_Olist_ONil(X33774)
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33774)),X33773),c_List_Olists(X33774,X33772))) )
& ( hBOOL(hAPP(hAPP(c_member(X33774),esk478_3(X33772,X33773,X33774)),X33772))
| X33773 = c_List_Olist_ONil(X33774)
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33774)),X33773),c_List_Olists(X33774,X33772))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33774)),esk479_3(X33772,X33773,X33774)),c_List_Olists(X33774,X33772)))
| X33773 = c_List_Olist_ONil(X33774)
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33774)),X33773),c_List_Olists(X33774,X33772))) )
& ( X33778 != c_List_Olist_ONil(X33779)
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33779)),X33778),c_List_Olists(X33779,X33777))) )
& ( X33778 != hAPP(hAPP(c_List_Olist_OCons(X33779),X33780),X33781)
| ~ hBOOL(hAPP(hAPP(c_member(X33779),X33780),X33777))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33779)),X33781),c_List_Olists(X33779,X33777)))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33779)),X33778),c_List_Olists(X33779,X33777))) ) ),
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_8123,plain,
! [X25098,X25099,X25100,X25101,X25102] :
( ~ c_Finite__Set_Ofolding__one(X25102,X25101,X25100)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25102),X25099))
| X25099 = c_Orderings_Obot__class_Obot(tc_fun(X25102,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25102),X25098))
| X25098 = c_Orderings_Obot__class_Obot(tc_fun(X25102,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25102,tc_HOL_Obool)),X25099),X25098) != c_Orderings_Obot__class_Obot(tc_fun(X25102,tc_HOL_Obool))
| hAPP(X25100,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25102,tc_HOL_Obool)),X25099),X25098)) = hAPP(hAPP(X25101,hAPP(X25100,X25099)),hAPP(X25100,X25098)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Ounion__disjoint])]) ).
fof(i_0_8124,plain,
! [X20309,X20310,X20311,X20312] :
( ~ class_Divides_Oring__div(X20312)
| c_Divides_Odiv__class_Omod(X20312,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20312),X20311),X20310),X20309) = c_Divides_Odiv__class_Omod(X20312,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20312),c_Divides_Odiv__class_Omod(X20312,X20311,X20309)),c_Divides_Odiv__class_Omod(X20312,X20310,X20309)),X20309) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__eq])]) ).
fof(i_0_8125,plain,
! [X19853,X19854,X19855,X19856] :
( ~ class_Divides_Osemiring__div(X19856)
| c_Divides_Odiv__class_Omod(X19856,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19856),X19855),X19854),X19853) = c_Divides_Odiv__class_Omod(X19856,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19856),c_Divides_Odiv__class_Omod(X19856,X19855,X19853)),c_Divides_Odiv__class_Omod(X19856,X19854,X19853)),X19853) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__eq])]) ).
fof(i_0_8126,plain,
! [X19817,X19818,X19819,X19820] :
( ~ class_Divides_Osemiring__div(X19820)
| c_Divides_Odiv__class_Omod(X19820,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19820),X19819),X19818),X19817) = c_Divides_Odiv__class_Omod(X19820,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19820),c_Divides_Odiv__class_Omod(X19820,X19819,X19817)),c_Divides_Odiv__class_Omod(X19820,X19818,X19817)),X19817) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__eq])]) ).
fof(i_0_8127,plain,
! [X23340,X23341,X23342,X23343] :
( ~ class_Divides_Osemiring__div(X23343)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23343),X23342),X23341))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23343),X23342),X23340))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23343),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23343),X23341),X23340)),X23342) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23343),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23343),X23341),X23342)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23343),X23340),X23342)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__add])]) ).
fof(i_0_8128,plain,
! [X21007,X21008,X21009] :
( ~ class_Rings_Olinordered__semidom(X21009)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21009),c_Groups_Oone__class_Oone(X21009)),X21008))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21009),c_Groups_Oone__class_Oone(X21009)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21009),X21008),hAPP(hAPP(c_Power_Opower__class_Opower(X21009),X21008),X21007)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__gt1__lemma])]) ).
fof(i_0_8129,plain,
! [X19379,X19380] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19380),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19380),X19379),X19379)),c_Groups_Ozero__class_Ozero(X19380)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19380),X19379),c_Groups_Ozero__class_Ozero(X19380)))
| ~ class_Groups_Olinordered__ab__group__add(X19380) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19380),X19379),c_Groups_Ozero__class_Ozero(X19380)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19380),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19380),X19379),X19379)),c_Groups_Ozero__class_Ozero(X19380)))
| ~ class_Groups_Olinordered__ab__group__add(X19380) ) ),
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_8130,plain,
! [X18369,X18370] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18370),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18370),X18369),X18369)),c_Groups_Ozero__class_Ozero(X18370)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18370),X18369),c_Groups_Ozero__class_Ozero(X18370)))
| ~ class_Rings_Olinordered__idom(X18370) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18370),X18369),c_Groups_Ozero__class_Ozero(X18370)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18370),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18370),X18369),X18369)),c_Groups_Ozero__class_Ozero(X18370)))
| ~ class_Rings_Olinordered__idom(X18370) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__less__0__iff])])]) ).
fof(i_0_8131,plain,
! [X18365,X18366] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18366),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18366),X18365),X18365)),c_Groups_Ozero__class_Ozero(X18366)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18366),X18365),c_Groups_Ozero__class_Ozero(X18366)))
| ~ class_Groups_Olinordered__ab__group__add(X18366) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18366),X18365),c_Groups_Ozero__class_Ozero(X18366)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18366),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18366),X18365),X18365)),c_Groups_Ozero__class_Ozero(X18366)))
| ~ class_Groups_Olinordered__ab__group__add(X18366) ) ),
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_8132,plain,
! [X29947,X29948] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk340_2(X29947,X29948)),X29948))
| 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)),X29947),X29948) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29947),esk340_2(X29947,X29948)))
| 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)),X29947),X29948) ) ),
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_8133,plain,
! [X31203,X31204,X31205,X31206] :
( ~ hBOOL(hAPP(hAPP(c_member(X31206),X31205),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31206,tc_HOL_Obool),X31204)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X31206,tc_HOL_Obool)),X31203),X31204))
| hBOOL(hAPP(hAPP(c_member(X31206),X31205),X31203)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_InterE])]) ).
fof(i_0_8134,plain,
! [X31199,X31200,X31201,X31202] :
( ~ hBOOL(hAPP(hAPP(c_member(X31202),X31201),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31202,tc_HOL_Obool),X31200)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X31202,tc_HOL_Obool)),X31199),X31200))
| hBOOL(hAPP(hAPP(c_member(X31202),X31201),X31199)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_InterD])]) ).
fof(i_0_8135,plain,
! [X21088,X21089] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21089))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21089),X21088)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21089),X21088) = 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_8136,plain,
! [X28246,X28247] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X28247,X28246)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X28247,X28246),tc_HOL_Obool))))
| hAPP(c_Finite__Set_Ocard(X28246),c_Orderings_Otop__class_Otop(tc_fun(X28246,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X28247),c_Orderings_Otop__class_Otop(tc_fun(X28247,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD1])]) ).
fof(i_0_8137,plain,
! [X25427,X25428,X25429] :
( ~ class_Orderings_Olinorder(X25429)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25429),X25428))
| X25428 = c_Orderings_Obot__class_Obot(tc_fun(X25429,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25429),X25427))
| X25427 = c_Orderings_Obot__class_Obot(tc_fun(X25429,tc_HOL_Obool))
| c_Big__Operators_Olattice_OInf__fin(X25429,c_Orderings_Oord__class_Omin(X25429),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25429,tc_HOL_Obool)),X25428),X25427)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25429),c_Big__Operators_Olattice_OInf__fin(X25429,c_Orderings_Oord__class_Omin(X25429),X25428)),c_Big__Operators_Olattice_OInf__fin(X25429,c_Orderings_Oord__class_Omin(X25429),X25427)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__idem])]) ).
fof(i_0_8138,plain,
! [X25300,X25301,X25302] :
( ~ class_Orderings_Olinorder(X25302)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25302),X25301))
| X25301 = c_Orderings_Obot__class_Obot(tc_fun(X25302,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25302),X25300))
| X25300 = c_Orderings_Obot__class_Obot(tc_fun(X25302,tc_HOL_Obool))
| c_Big__Operators_Olattice_OSup__fin(X25302,c_Orderings_Oord__class_Omax(X25302),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25302,tc_HOL_Obool)),X25301),X25300)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25302),c_Big__Operators_Olattice_OSup__fin(X25302,c_Orderings_Oord__class_Omax(X25302),X25301)),c_Big__Operators_Olattice_OSup__fin(X25302,c_Orderings_Oord__class_Omax(X25302),X25300)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__idem])]) ).
fof(i_0_8139,plain,
! [X23594,X23595,X23596,X23597] :
( ~ hBOOL(hAPP(hAPP(c_member(X23597),X23596),X23595))
| hBOOL(hAPP(hAPP(c_member(X23597),X23596),X23594))
| hBOOL(hAPP(hAPP(c_member(X23597),X23596),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23597,tc_HOL_Obool)),X23595),X23594))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5677])]) ).
fof(i_0_8140,plain,
! [X20140,X20141,X20142] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20142),X20141))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20140))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20142),X20140)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20141),X20140))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono1])]) ).
fof(i_0_8141,plain,
! [X20104,X20105,X20106] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20106))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20106),X20105))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20104),X20105)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20104),X20106))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__le__mono2])]) ).
fof(i_0_8142,plain,
! [X18974,X18975,X18976] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18976),X18975))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18974))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18974),X18976)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18974),X18975))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2])]) ).
fof(i_0_8143,plain,
! [X19486,X19487,X19488] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19488),X19487))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19486))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19488),X19486)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19487),X19486))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono1])]) ).
fof(i_0_8144,plain,
! [X19483,X19484,X19485] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19485),X19484))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19483))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19483),X19485)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19483),X19484))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono2])]) ).
fof(i_0_8145,plain,
! [X31748,X31749,X31750] :
( ~ c_Fun_Oinj__on(tc_List_Olist(X31750),tc_List_Olist(X31749),hAPP(c_List_Omap(X31750,X31749),X31748),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X31750),tc_HOL_Obool)))
| c_Fun_Oinj__on(X31750,X31749,X31748,c_Orderings_Otop__class_Otop(tc_fun(X31750,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__mapD])]) ).
fof(i_0_8146,plain,
! [X31740,X31741,X31742] :
( ( ~ c_Fun_Oinj__on(tc_List_Olist(X31742),tc_List_Olist(X31741),hAPP(c_List_Omap(X31742,X31741),X31740),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X31742),tc_HOL_Obool)))
| c_Fun_Oinj__on(X31742,X31741,X31740,c_Orderings_Otop__class_Otop(tc_fun(X31742,tc_HOL_Obool))) )
& ( ~ c_Fun_Oinj__on(X31742,X31741,X31740,c_Orderings_Otop__class_Otop(tc_fun(X31742,tc_HOL_Obool)))
| c_Fun_Oinj__on(tc_List_Olist(X31742),tc_List_Olist(X31741),hAPP(c_List_Omap(X31742,X31741),X31740),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X31742),tc_HOL_Obool))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__map])]) ).
fof(i_0_8147,plain,
! [X23069,X23070,X23071,X23072] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23072,tc_HOL_Obool)),X23071),X23070))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23072,tc_HOL_Obool)),X23071),hAPP(hAPP(c_Set_Oinsert(X23072),X23069),X23070))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__insertI2])]) ).
fof(i_0_8148,plain,
! [X31014,X31015,X31016,X31017,X31018] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31018,tc_fun(X31017,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X31018),X31016),X31015)),X31014) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31017,tc_HOL_Obool)),hAPP(X31014,X31016)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31018,tc_fun(X31017,tc_HOL_Obool)),X31015),X31014)),
inference(variable_rename,[status(thm)],[fact_INT__insert]) ).
fof(i_0_8149,plain,
! [X26140,X26141,X26142,X26143,X26144] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26144,tc_fun(X26143,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X26144),X26142),X26141)),X26140) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26143,tc_HOL_Obool)),hAPP(X26140,X26142)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26144,tc_fun(X26143,tc_HOL_Obool)),X26141),X26140)),
inference(variable_rename,[status(thm)],[fact_UN__insert]) ).
fof(i_0_8150,plain,
! [X28839,X28840,X28841,X28842] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X28841),X28839),hAPP(c_Finite__Set_Ofold1(X28841,c_Orderings_Oord__class_Omin(X28841)),X28840)))
| ~ hBOOL(hAPP(hAPP(c_member(X28841),X28842),X28840))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X28841),X28839),X28842))
| X28840 = c_Orderings_Obot__class_Obot(tc_fun(X28841,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28841),X28840))
| ~ class_Orderings_Olinorder(X28841) )
& ( hBOOL(hAPP(hAPP(c_member(X28841),esk285_3(X28839,X28840,X28841)),X28840))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X28841),X28839),hAPP(c_Finite__Set_Ofold1(X28841,c_Orderings_Oord__class_Omin(X28841)),X28840)))
| X28840 = c_Orderings_Obot__class_Obot(tc_fun(X28841,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28841),X28840))
| ~ class_Orderings_Olinorder(X28841) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X28841),X28839),esk285_3(X28839,X28840,X28841)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X28841),X28839),hAPP(c_Finite__Set_Ofold1(X28841,c_Orderings_Oord__class_Omin(X28841)),X28840)))
| X28840 = c_Orderings_Obot__class_Obot(tc_fun(X28841,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28841),X28840))
| ~ class_Orderings_Olinorder(X28841) ) ),
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_8151,plain,
! [X28831,X28832,X28833,X28834] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28833),X28831),hAPP(c_Finite__Set_Ofold1(X28833,c_Orderings_Oord__class_Omin(X28833)),X28832)))
| ~ hBOOL(hAPP(hAPP(c_member(X28833),X28834),X28832))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28833),X28831),X28834))
| X28832 = c_Orderings_Obot__class_Obot(tc_fun(X28833,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28833),X28832))
| ~ class_Orderings_Olinorder(X28833) )
& ( hBOOL(hAPP(hAPP(c_member(X28833),esk284_3(X28831,X28832,X28833)),X28832))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28833),X28831),hAPP(c_Finite__Set_Ofold1(X28833,c_Orderings_Oord__class_Omin(X28833)),X28832)))
| X28832 = c_Orderings_Obot__class_Obot(tc_fun(X28833,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28833),X28832))
| ~ class_Orderings_Olinorder(X28833) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28833),X28831),esk284_3(X28831,X28832,X28833)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28833),X28831),hAPP(c_Finite__Set_Ofold1(X28833,c_Orderings_Oord__class_Omin(X28833)),X28832)))
| X28832 = c_Orderings_Obot__class_Obot(tc_fun(X28833,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28833),X28832))
| ~ class_Orderings_Olinorder(X28833) ) ),
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_8152,plain,
! [X28815,X28816,X28817,X28818] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28817),X28815),hAPP(c_Finite__Set_Ofold1(X28817,c_Lattices_Osemilattice__inf__class_Oinf(X28817)),X28816)))
| ~ hBOOL(hAPP(hAPP(c_member(X28817),X28818),X28816))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28817),X28815),X28818))
| X28816 = c_Orderings_Obot__class_Obot(tc_fun(X28817,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28817),X28816))
| ~ class_Lattices_Osemilattice__inf(X28817) )
& ( hBOOL(hAPP(hAPP(c_member(X28817),esk282_3(X28815,X28816,X28817)),X28816))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28817),X28815),hAPP(c_Finite__Set_Ofold1(X28817,c_Lattices_Osemilattice__inf__class_Oinf(X28817)),X28816)))
| X28816 = c_Orderings_Obot__class_Obot(tc_fun(X28817,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28817),X28816))
| ~ class_Lattices_Osemilattice__inf(X28817) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28817),X28815),esk282_3(X28815,X28816,X28817)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28817),X28815),hAPP(c_Finite__Set_Ofold1(X28817,c_Lattices_Osemilattice__inf__class_Oinf(X28817)),X28816)))
| X28816 = c_Orderings_Obot__class_Obot(tc_fun(X28817,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28817),X28816))
| ~ class_Lattices_Osemilattice__inf(X28817) ) ),
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_8153,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk492_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_8154,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk493_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_8155,plain,
! [X20398,X20399,X20400] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20400),X20399),X20398))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20400),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20400),X20399),X20398)),c_Groups_Ozero__class_Ozero(X20400)))
| ~ class_Groups_Oordered__ab__group__add(X20400) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20400),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20400),X20399),X20398)),c_Groups_Ozero__class_Ozero(X20400)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20400),X20399),X20398))
| ~ class_Groups_Oordered__ab__group__add(X20400) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__diff__le__0])])]) ).
fof(i_0_8156,plain,
! [X20401,X20402,X20403] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20403),X20402),X20401))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20403),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20403),X20402),X20401)),c_Groups_Ozero__class_Ozero(X20403)))
| ~ class_Groups_Oordered__ab__group__add(X20403) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20403),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20403),X20402),X20401)),c_Groups_Ozero__class_Ozero(X20403)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20403),X20402),X20401))
| ~ class_Groups_Oordered__ab__group__add(X20403) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__iff__diff__less__0])])]) ).
fof(i_0_8157,plain,
! [X20143,X20144,X20145] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20145),X20144))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20143),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),X20144),X20143)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20145),X20143))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono1__neg])]) ).
cnf(i_0_8158,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_8159,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_8160,plain,
! [X32564,X32565,X32566] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32566),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32565)),X32564)))
| hBOOL(hAPP(hAPP(c_member(X32565),hAPP(hAPP(c_List_Onth(X32565),X32564),X32566)),hAPP(c_List_Oset(X32565),X32564))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__mem])]) ).
fof(i_0_8161,plain,
! [X19660,X19661] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19661))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19660))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19661),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19661),X19660))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n__less__n__mult__m])]) ).
fof(i_0_8162,plain,
! [X19662,X19663] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19663))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19662))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19663),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19662),X19663))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n__less__m__mult__n])]) ).
fof(i_0_8163,plain,
! [X26301,X26302] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26302),X26301))
| hAPP(c_Finite__Set_Ocard(X26302),X26301) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X26302,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X26302),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26301) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oeq__fold__g])]) ).
fof(i_0_8164,plain,
! [X26299,X26300] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26300),X26299))
| hAPP(c_Finite__Set_Ocard(X26300),X26299) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X26300,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X26300),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26299) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X26300),X26299))
| hAPP(c_Finite__Set_Ocard(X26300),X26299) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5680])]) ).
fof(i_0_8165,plain,
! [X21713,X21714,X21715,X21716] :
( ~ class_Fields_Ofield(X21716)
| X21715 = c_Groups_Ozero__class_Ozero(X21716)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21716),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21716),X21714),X21715)),X21713) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21716),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21716),X21714),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21716),X21715),X21713))),X21715) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__diff__eq__iff])]) ).
fof(i_0_8166,plain,
! [X21692,X21693,X21694,X21695] :
( ~ class_Fields_Ofield(X21695)
| X21694 = c_Groups_Ozero__class_Ozero(X21695)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21695),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21695),X21693),X21694)),X21692) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21695),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21695),X21693),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21695),X21694),X21692))),X21694) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__add__eq__iff])]) ).
fof(i_0_8167,plain,
! [X21696,X21697,X21698,X21699] :
( ~ class_Fields_Ofield__inverse__zero(X21699)
| X21698 = c_Groups_Ozero__class_Ozero(X21699)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21699),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21699),X21697),X21698)),X21696) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21699),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21699),X21697),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21699),X21696),X21698))),X21698) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__frac__num])]) ).
fof(i_0_8168,plain,
! [X32567,X32568,X32569,X32571,X32572,X32573,X32574] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk454_3(X32567,X32568,X32569)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32569)),X32567)))
| ~ hBOOL(hAPP(hAPP(c_member(X32569),X32568),hAPP(c_List_Oset(X32569),X32567))) )
& ( hAPP(hAPP(c_List_Onth(X32569),X32567),esk454_3(X32567,X32568,X32569)) = X32568
| ~ hBOOL(hAPP(hAPP(c_member(X32569),X32568),hAPP(c_List_Oset(X32569),X32567))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32574),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32573)),X32571)))
| hAPP(hAPP(c_List_Onth(X32573),X32571),X32574) != X32572
| hBOOL(hAPP(hAPP(c_member(X32573),X32572),hAPP(c_List_Oset(X32573),X32571))) ) ),
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_8169,plain,
! [X19059,X19060,X19061,X19062] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19062),X19061))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19060),X19059))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19062),X19060)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19061),X19059))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono])]) ).
fof(i_0_8170,plain,
! [X19336,X19337,X19338,X19339] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19339),X19338))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19337),X19336))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19339),X19337)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19338),X19336))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono])]) ).
fof(i_0_8171,plain,
! [X19552,X19553,X19554,X19555] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19555),X19554))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19553),X19552))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19555),X19553)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19554),X19552))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__zless__mono])]) ).
fof(i_0_8172,plain,
! [X20454,X20455,X20456] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20456),X20455))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20454),X20456))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20456),X20454)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20455),X20454))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less__mono])]) ).
fof(i_0_8173,plain,
! [X20331,X20332,X20333] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20333),X20332))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20333),X20331))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20331),X20332)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20331),X20333))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less__mono2])]) ).
fof(i_0_8174,plain,
! [X18339,X18340,X18341,X18342] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18342),X18341))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18340),X18339))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18342),X18340)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18341),X18339))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono])]) ).
fof(i_0_8175,plain,
! [X18742,X18743,X18744,X18745,X18746] :
( ~ class_Rings_Ocomm__semiring__1(X18746)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18746),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18746),X18745),X18744)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18746),X18743),X18742)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18746),X18743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18746),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18746),X18745),X18744)),X18742)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J])]) ).
fof(i_0_8176,plain,
! [X27081,X27082,X27083] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27083,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X27083),X27082)),hAPP(c_SetInterval_Oord__class_OlessThan(X27083),X27081)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27083),X27082),X27081))
| ~ class_Orderings_Olinorder(X27083) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27083),X27082),X27081))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27083,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X27083),X27082)),hAPP(c_SetInterval_Oord__class_OlessThan(X27083),X27081)))
| ~ class_Orderings_Olinorder(X27083) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lessThan__subset__iff])])]) ).
fof(i_0_8177,plain,
! [X26996,X26997,X26998] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26998,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X26998),X26997)),hAPP(c_SetInterval_Oord__class_OatMost(X26998),X26996)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26998),X26997),X26996))
| ~ class_Orderings_Oorder(X26998) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26998),X26997),X26996))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26998,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X26998),X26997)),hAPP(c_SetInterval_Oord__class_OatMost(X26998),X26996)))
| ~ class_Orderings_Oorder(X26998) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atMost__subset__iff])])]) ).
fof(i_0_8178,plain,
! [X27652,X27653,X27654] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27654,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X27654),X27653)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X27654),X27652)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27654),X27652),X27653))
| ~ class_Orderings_Olinorder(X27654) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27654),X27652),X27653))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27654,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X27654),X27653)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X27654),X27652)))
| ~ class_Orderings_Olinorder(X27654) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThan__subset__iff])])]) ).
fof(i_0_8179,plain,
! [X27608,X27609,X27610] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27610,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X27610),X27609)),hAPP(c_SetInterval_Oord__class_OatLeast(X27610),X27608)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27610),X27608),X27609))
| ~ class_Orderings_Oorder(X27610) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27610),X27608),X27609))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27610,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X27610),X27609)),hAPP(c_SetInterval_Oord__class_OatLeast(X27610),X27608)))
| ~ class_Orderings_Oorder(X27610) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeast__subset__iff])])]) ).
fof(i_0_8180,plain,
! [X27084,X27085,X27086] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X27086,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X27086),X27085)),hAPP(c_SetInterval_Oord__class_OlessThan(X27086),X27084)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27086),X27085),X27084))
| ~ class_Orderings_Olinorder(X27086) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27086),X27085),X27084))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X27086,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X27086),X27085)),hAPP(c_SetInterval_Oord__class_OlessThan(X27086),X27084)))
| ~ class_Orderings_Olinorder(X27086) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lessThan__strict__subset__iff])])]) ).
cnf(i_0_8181,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_8182,plain,
! [X21622,X21623,X21624] :
( ~ class_Fields_Olinordered__field(X21624)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21624),X21623),c_Groups_Ozero__class_Ozero(X21624)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21624),c_Groups_Ozero__class_Ozero(X21624)),X21622))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21624),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21624),X21623),X21622)),c_Groups_Ozero__class_Ozero(X21624))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonpos__pos])]) ).
fof(i_0_8183,plain,
! [X21640,X21641,X21642] :
( ~ class_Fields_Olinordered__field(X21642)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21642),c_Groups_Ozero__class_Ozero(X21642)),X21641))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21642),X21640),c_Groups_Ozero__class_Ozero(X21642)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21642),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21642),X21641),X21640)),c_Groups_Ozero__class_Ozero(X21642))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonneg__neg])]) ).
fof(i_0_8184,plain,
! [X19437,X19438,X19439] :
( ~ class_Rings_Oordered__cancel__semiring(X19439)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19439),X19438),c_Groups_Ozero__class_Ozero(X19439)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19439),c_Groups_Ozero__class_Ozero(X19439)),X19437))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19439),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19439),X19438),X19437)),c_Groups_Ozero__class_Ozero(X19439))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonneg])]) ).
fof(i_0_8185,plain,
! [X19398,X19399,X19400] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19400),c_Groups_Ozero__class_Ozero(X19400)),X19399))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19400),X19398),c_Groups_Ozero__class_Ozero(X19400)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19400),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19400),X19399),X19398)),c_Groups_Ozero__class_Ozero(X19400)))
| ~ class_Rings_Oordered__cancel__semiring(X19400) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19400),X19399),c_Groups_Ozero__class_Ozero(X19400)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19400),c_Groups_Ozero__class_Ozero(X19400)),X19398))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19400),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19400),X19399),X19398)),c_Groups_Ozero__class_Ozero(X19400)))
| ~ class_Rings_Oordered__cancel__semiring(X19400) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__neg__le])])]) ).
fof(i_0_8186,plain,
! [X19443,X19444,X19445] :
( ~ class_Rings_Oordered__cancel__semiring(X19445)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19445),c_Groups_Ozero__class_Ozero(X19445)),X19444))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19445),X19443),c_Groups_Ozero__class_Ozero(X19445)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19445),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19445),X19444),X19443)),c_Groups_Ozero__class_Ozero(X19445))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos])]) ).
fof(i_0_8187,plain,
! [X19440,X19441,X19442] :
( ~ class_Rings_Oordered__cancel__semiring(X19442)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19442),c_Groups_Ozero__class_Ozero(X19442)),X19441))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19442),X19440),c_Groups_Ozero__class_Ozero(X19442)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19442),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19442),X19440),X19441)),c_Groups_Ozero__class_Ozero(X19442))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos2])]) ).
fof(i_0_8188,plain,
! [X21542,X21543,X21544] :
( ~ class_Fields_Olinordered__field(X21544)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21544),X21543),c_Groups_Ozero__class_Ozero(X21544)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21544),c_Groups_Ozero__class_Ozero(X21544)),X21542))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21544),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21544),X21543),X21542)),c_Groups_Ozero__class_Ozero(X21544))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__neg__pos])]) ).
fof(i_0_8189,plain,
! [X21545,X21546,X21547] :
( ~ class_Fields_Olinordered__field(X21547)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21547),c_Groups_Ozero__class_Ozero(X21547)),X21546))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21547),X21545),c_Groups_Ozero__class_Ozero(X21547)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21547),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21547),X21546),X21545)),c_Groups_Ozero__class_Ozero(X21547))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__pos__neg])]) ).
fof(i_0_8190,plain,
! [X18930,X18931,X18932] :
( ~ class_Rings_Olinordered__semiring__strict(X18932)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18932),X18931),c_Groups_Ozero__class_Ozero(X18932)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18932),c_Groups_Ozero__class_Ozero(X18932)),X18930))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18932),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18932),X18931),X18930)),c_Groups_Ozero__class_Ozero(X18932))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__pos])]) ).
fof(i_0_8191,plain,
! [X18914,X18915,X18916] :
( ~ class_Rings_Olinordered__semiring__strict(X18916)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18916),c_Groups_Ozero__class_Ozero(X18916)),X18915))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18916),X18914),c_Groups_Ozero__class_Ozero(X18916)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18916),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18916),X18915),X18914)),c_Groups_Ozero__class_Ozero(X18916))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg])]) ).
fof(i_0_8192,plain,
! [X18917,X18918,X18919] :
( ~ class_Rings_Olinordered__semiring__strict(X18919)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18919),c_Groups_Ozero__class_Ozero(X18919)),X18918))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18919),X18917),c_Groups_Ozero__class_Ozero(X18919)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18919),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18919),X18917),X18918)),c_Groups_Ozero__class_Ozero(X18919))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg2])]) ).
fof(i_0_8193,plain,
! [X32286,X32287,X32288] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32288,tc_HOL_Obool)),hAPP(c_List_Oset(X32288),X32287)),hAPP(c_List_Oset(X32288),hAPP(hAPP(c_List_Olist_OCons(X32288),X32286),X32287)))),
inference(variable_rename,[status(thm)],[fact_set__subset__Cons]) ).
fof(i_0_8194,plain,
! [X33966,X33967,X33968,X33969] : c_List_Otranspose(X33969,hAPP(hAPP(c_List_Omap(tc_List_Olist(X33968),tc_List_Olist(X33969)),hAPP(c_List_Omap(X33968,X33969),X33967)),X33966)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X33968),tc_List_Olist(X33969)),hAPP(c_List_Omap(X33968,X33969),X33967)),c_List_Otranspose(X33968,X33966)),
inference(variable_rename,[status(thm)],[fact_transpose__map__map]) ).
cnf(i_0_8195,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_8196,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_8197,plain,
! [X23244,X23245,X23246,X23247] :
( ~ class_Rings_Ocomm__semiring__1(X23247)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23247),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23247),X23246),X23245)),X23244))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23247),X23246),X23244)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__left])]) ).
fof(i_0_8198,plain,
! [X23240,X23241,X23242,X23243] :
( ~ class_Rings_Ocomm__semiring__1(X23243)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23243),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23243),X23242),X23241)),X23240))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23243),X23241),X23240)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__right])]) ).
fof(i_0_8199,plain,
! [X23992,X23993,X23994,X23995] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23995),X23994),X23992))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23995),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23995),X23994),X23993)),X23992))
| ~ class_Lattices_Osemilattice__sup(X23995) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23995),X23993),X23992))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23995),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23995),X23994),X23993)),X23992))
| ~ class_Lattices_Osemilattice__sup(X23995) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5684])])]) ).
fof(i_0_8200,plain,
! [X23961,X23962,X23963,X23964] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23964),X23963),X23961))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23964),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23964),X23963),X23962)),X23961))
| ~ class_Lattices_Osemilattice__sup(X23964) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23964),X23962),X23961))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23964),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23964),X23963),X23962)),X23961))
| ~ class_Lattices_Osemilattice__sup(X23964) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23964),X23963),X23961))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23964),X23962),X23961))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23964),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23964),X23963),X23962)),X23961))
| ~ class_Lattices_Osemilattice__sup(X23964) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__sup__iff])])]) ).
fof(i_0_8201,plain,
! [X22689,X22690,X22691,X22692] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22692),X22691),X22689))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22692),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22692),X22691),X22690)),X22689))
| ~ class_Orderings_Olinorder(X22692) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22692),X22690),X22689))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22692),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22692),X22691),X22690)),X22689))
| ~ class_Orderings_Olinorder(X22692) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22692),X22691),X22689))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22692),X22690),X22689))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22692),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22692),X22691),X22690)),X22689))
| ~ class_Orderings_Olinorder(X22692) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__sup__iff])])]) ).
fof(i_0_8202,plain,
! [X22658,X22659,X22660,X22661] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22661),X22660),X22658))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22661),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22661),X22660),X22659)),X22658))
| ~ class_Orderings_Olinorder(X22661) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22661),X22659),X22658))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22661),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22661),X22660),X22659)),X22658))
| ~ class_Orderings_Olinorder(X22661) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5685])])]) ).
fof(i_0_8203,plain,
! [X22574,X22575,X22576,X22577] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22577),X22576),X22574))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22577),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22577),X22576),X22575)),X22574))
| ~ class_Orderings_Olinorder(X22577) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22577),X22575),X22574))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22577),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22577),X22576),X22575)),X22574))
| ~ class_Orderings_Olinorder(X22577) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22577),X22576),X22574))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22577),X22575),X22574))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22577),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22577),X22576),X22575)),X22574))
| ~ class_Orderings_Olinorder(X22577) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__less__iff__conj])])]) ).
fof(i_0_8204,plain,
! [X32560,X32561,X32562,X32563] :
( ( hAPP(hAPP(c_List_Onth(X32563),X32562),X32561) != hAPP(hAPP(c_List_Onth(X32563),X32562),X32560)
| X32561 = X32560
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32560),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32563)),X32562)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32561),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32563)),X32562)))
| ~ hBOOL(hAPP(c_List_Odistinct(X32563),X32562)) )
& ( X32561 != X32560
| hAPP(hAPP(c_List_Onth(X32563),X32562),X32561) = hAPP(hAPP(c_List_Onth(X32563),X32562),X32560)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32560),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32563)),X32562)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32561),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32563)),X32562)))
| ~ hBOOL(hAPP(c_List_Odistinct(X32563),X32562)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__eq__iff__index__eq])])]) ).
fof(i_0_8205,plain,
! [X32552,X32553,X32554,X32555,X32556,X32557] :
( ( ~ hBOOL(hAPP(c_List_Odistinct(X32553),X32552))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32554),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32553)),X32552)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32555),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32553)),X32552)))
| X32554 = X32555
| hAPP(hAPP(c_List_Onth(X32553),X32552),X32554) != hAPP(hAPP(c_List_Onth(X32553),X32552),X32555) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk452_2(X32556,X32557)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32557)),X32556)))
| hBOOL(hAPP(c_List_Odistinct(X32557),X32556)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk453_2(X32556,X32557)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32557)),X32556)))
| hBOOL(hAPP(c_List_Odistinct(X32557),X32556)) )
& ( esk452_2(X32556,X32557) != esk453_2(X32556,X32557)
| hBOOL(hAPP(c_List_Odistinct(X32557),X32556)) )
& ( hAPP(hAPP(c_List_Onth(X32557),X32556),esk452_2(X32556,X32557)) = hAPP(hAPP(c_List_Onth(X32557),X32556),esk453_2(X32556,X32557))
| hBOOL(hAPP(c_List_Odistinct(X32557),X32556)) ) ),
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_8206,plain,
! [X31963,X31964,X31965,X31966] :
( ( hBOOL(hAPP(c_List_Odistinct(X31965),X31963))
| ~ hBOOL(hAPP(c_List_Odistinct(X31966),hAPP(hAPP(c_List_Omap(X31965,X31966),X31964),X31963))) )
& ( c_Fun_Oinj__on(X31965,X31966,X31964,hAPP(c_List_Oset(X31965),X31963))
| ~ hBOOL(hAPP(c_List_Odistinct(X31966),hAPP(hAPP(c_List_Omap(X31965,X31966),X31964),X31963))) )
& ( ~ hBOOL(hAPP(c_List_Odistinct(X31965),X31963))
| ~ c_Fun_Oinj__on(X31965,X31966,X31964,hAPP(c_List_Oset(X31965),X31963))
| hBOOL(hAPP(c_List_Odistinct(X31966),hAPP(hAPP(c_List_Omap(X31965,X31966),X31964),X31963))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__map])])]) ).
fof(i_0_8207,plain,
! [X25402,X25403] :
( ~ class_Orderings_Olinorder(X25403)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25403),X25402))
| X25402 = c_Orderings_Obot__class_Obot(tc_fun(X25403,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25403),c_Big__Operators_Olattice_OInf__fin(X25403,c_Orderings_Oord__class_Omin(X25403),X25402)),c_Big__Operators_Olattice_OSup__fin(X25403,c_Orderings_Oord__class_Omax(X25403),X25402))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__le__Sup])]) ).
fof(i_0_8208,plain,
! [X26632,X26633,X26634,X26635,X26636] :
( ~ c_Fun_Oinj__on(X26636,X26635,X26634,X26633)
| c_Fun_Oinj__on(X26636,X26635,X26634,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26636,tc_HOL_Obool)),X26633),X26632)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__diff])]) ).
cnf(i_0_8209,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_8210,plain,
! [X30686,X30687,X30688,X30689,X30690,X30691] :
( ~ c_Finite__Set_Ofun__left__comm__idem(X30691,X30690,X30689)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30691),X30688))
| hAPP(hAPP(c_Finite__Set_Ofold(X30691,X30690,X30689),X30687),hAPP(hAPP(c_Set_Oinsert(X30691),X30686),X30688)) = hAPP(hAPP(c_Finite__Set_Ofold(X30691,X30690,X30689),hAPP(hAPP(X30689,X30686),X30687)),X30688) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__insert__idem2])]) ).
fof(i_0_8211,plain,
! [X23747,X23748,X23749] :
( ~ hBOOL(hAPP(hAPP(c_member(X23749),X23748),X23747))
| hAPP(hAPP(c_Set_Oinsert(X23749),X23748),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23749,tc_HOL_Obool)),X23747),hAPP(hAPP(c_Set_Oinsert(X23749),X23748),c_Orderings_Obot__class_Obot(tc_fun(X23749,tc_HOL_Obool))))) = X23747 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__Diff])]) ).
fof(i_0_8212,plain,
! [X28183,X28184] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28184),c_Orderings_Otop__class_Otop(tc_fun(X28184,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28183),c_Orderings_Otop__class_Otop(tc_fun(X28183,tc_HOL_Obool))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28184,X28183)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X28184,X28183),tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Prod__UNIV])]) ).
fof(i_0_8213,plain,
! [X28179,X28180] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X28180),c_Orderings_Otop__class_Otop(tc_fun(X28180,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X28180,X28179)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X28180,X28179),tc_HOL_Obool)))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X28179),c_Orderings_Otop__class_Otop(tc_fun(X28179,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X28180,X28179)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X28180,X28179),tc_HOL_Obool)))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28180),c_Orderings_Otop__class_Otop(tc_fun(X28180,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28179),c_Orderings_Otop__class_Otop(tc_fun(X28179,tc_HOL_Obool))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X28180,X28179)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X28180,X28179),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_8214,plain,
! [X27343,X27344,X27345,X27346] :
( ~ class_Groups_Ocomm__monoid__add(X27346)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X27345),X27344))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27346),X27343),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X27345,X27344)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27346),hAPP(X27343,X27345)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27346),X27343),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X27345),X27344))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__head__Suc])]) ).
fof(i_0_8215,plain,
! [X28428,X28429,X28430,X28431,X28432] :
( ~ hBOOL(hAPP(hAPP(c_member(X28432),hAPP(X28431,X28430)),X28429))
| hBOOL(hAPP(hAPP(c_member(X28428),X28430),hAPP(c_Set_Ovimage(X28428,X28432,X28431),X28429))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimageI2])]) ).
cnf(i_0_8216,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_8217,plain,
! [X34091,X34092,X34093] :
( ( ~ c_List_Olinorder__class_Osorted(X34093,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X34093,X34093,c_COMBI(X34093)),X34092),X34091))
| c_List_Olinorder__class_Osorted(X34093,X34091)
| ~ class_Orderings_Olinorder(X34093) )
& ( ~ c_List_Olinorder__class_Osorted(X34093,X34091)
| c_List_Olinorder__class_Osorted(X34093,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X34093,X34093,c_COMBI(X34093)),X34092),X34091))
| ~ class_Orderings_Olinorder(X34093) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__insort])])]) ).
fof(i_0_8218,plain,
! [X27339,X27340,X27341,X27342] :
( ~ class_Groups_Ocomm__monoid__add(X27342)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X27341),X27340))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27342),X27339),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X27341),X27340)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27342),hAPP(X27339,X27341)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27342),X27339),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X27341)),X27340))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__head__upt__Suc])]) ).
fof(i_0_8219,plain,
! [X22368,X22369,X22370] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22368,tc_HOL_Obool)),X22370),X22369))
| X22370 != X22369 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22368,tc_HOL_Obool)),X22369),X22370))
| X22370 != X22369 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22368,tc_HOL_Obool)),X22370),X22369))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22368,tc_HOL_Obool)),X22369),X22370))
| X22370 = X22369 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__eq__subset])])]) ).
fof(i_0_8220,plain,
! [X22281,X22282,X22283] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22283,tc_HOL_Obool)),X22282),X22281))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22283,tc_HOL_Obool)),X22281),X22282))
| X22282 = X22281 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityI])]) ).
fof(i_0_8221,plain,
! [X34326,X34327,X34328] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34328),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34327)),X34326)))
| hAPP(hAPP(c_List_Onth(X34327),hAPP(c_List_Orev(X34327),X34326)),X34328) = hAPP(hAPP(c_List_Onth(X34327),X34326),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34327)),X34326)),hAPP(c_Nat_OSuc,X34328))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__nth])]) ).
fof(i_0_8222,plain,
! [X30969,X30970,X30971,X30972,X30973] :
( ~ hBOOL(hAPP(hAPP(c_member(X30973),X30972),X30971))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30970,tc_HOL_Obool)),hAPP(X30969,X30972)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30973,tc_fun(X30970,tc_HOL_Obool)),X30971),X30969)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30973,tc_fun(X30970,tc_HOL_Obool)),X30971),X30969) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__absorb])]) ).
fof(i_0_8223,plain,
! [X26103,X26104,X26105,X26106,X26107] :
( ~ hBOOL(hAPP(hAPP(c_member(X26107),X26106),X26105))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26104,tc_HOL_Obool)),hAPP(X26103,X26106)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26107,tc_fun(X26104,tc_HOL_Obool)),X26105),X26103)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26107,tc_fun(X26104,tc_HOL_Obool)),X26105),X26103) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__absorb])]) ).
fof(i_0_8224,plain,
! [X32788,X32789,X32790,X32791,X32792] : hAPP(hAPP(c_List_Olist__update(X32792,hAPP(hAPP(c_List_Olist__update(X32792,X32791),X32790),X32789)),X32790),X32788) = hAPP(hAPP(c_List_Olist__update(X32792,X32791),X32790),X32788),
inference(variable_rename,[status(thm)],[fact_list__update__overwrite]) ).
fof(i_0_8225,plain,
! [X18661,X18662] : 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,X18662)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18661))),
inference(variable_rename,[status(thm)],[fact_negative__zless]) ).
fof(i_0_8226,plain,
! [X23858,X23859,X23860] :
( ~ class_Rings_Oring__1(X23860)
| ~ hBOOL(hAPP(hAPP(c_member(X23860),X23859),c_Int_Oring__1__class_OInts(X23860)))
| ~ hBOOL(hAPP(hAPP(c_member(X23860),X23858),c_Int_Oring__1__class_OInts(X23860)))
| hBOOL(hAPP(hAPP(c_member(X23860),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23860),X23859),X23858)),c_Int_Oring__1__class_OInts(X23860))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__diff])]) ).
fof(i_0_8227,plain,
! [X23855,X23856,X23857] :
( ~ class_Rings_Oring__1(X23857)
| ~ hBOOL(hAPP(hAPP(c_member(X23857),X23856),c_Int_Oring__1__class_OInts(X23857)))
| ~ hBOOL(hAPP(hAPP(c_member(X23857),X23855),c_Int_Oring__1__class_OInts(X23857)))
| hBOOL(hAPP(hAPP(c_member(X23857),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23857),X23856),X23855)),c_Int_Oring__1__class_OInts(X23857))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__mult])]) ).
fof(i_0_8228,plain,
! [X23813,X23814,X23815] :
( ~ class_Rings_Osemiring__1(X23815)
| ~ hBOOL(hAPP(hAPP(c_member(X23815),X23814),c_Nat_Osemiring__1__class_ONats(X23815)))
| ~ hBOOL(hAPP(hAPP(c_member(X23815),X23813),c_Nat_Osemiring__1__class_ONats(X23815)))
| hBOOL(hAPP(hAPP(c_member(X23815),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23815),X23814),X23813)),c_Nat_Osemiring__1__class_ONats(X23815))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__mult])]) ).
fof(i_0_8229,plain,
! [X23852,X23853,X23854] :
( ~ class_Rings_Oring__1(X23854)
| ~ hBOOL(hAPP(hAPP(c_member(X23854),X23853),c_Int_Oring__1__class_OInts(X23854)))
| ~ hBOOL(hAPP(hAPP(c_member(X23854),X23852),c_Int_Oring__1__class_OInts(X23854)))
| hBOOL(hAPP(hAPP(c_member(X23854),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23854),X23853),X23852)),c_Int_Oring__1__class_OInts(X23854))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__add])]) ).
fof(i_0_8230,plain,
! [X23810,X23811,X23812] :
( ~ class_Rings_Osemiring__1(X23812)
| ~ hBOOL(hAPP(hAPP(c_member(X23812),X23811),c_Nat_Osemiring__1__class_ONats(X23812)))
| ~ hBOOL(hAPP(hAPP(c_member(X23812),X23810),c_Nat_Osemiring__1__class_ONats(X23812)))
| hBOOL(hAPP(hAPP(c_member(X23812),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23812),X23811),X23810)),c_Nat_Osemiring__1__class_ONats(X23812))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__add])]) ).
fof(i_0_8231,plain,
! [X19395,X19396,X19397] :
( ~ class_Groups_Oordered__comm__monoid__add(X19397)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19397),X19396),c_Groups_Ozero__class_Ozero(X19397)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19397),X19395),c_Groups_Ozero__class_Ozero(X19397)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19397),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19397),X19396),X19395)),c_Groups_Ozero__class_Ozero(X19397))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos])]) ).
fof(i_0_8232,plain,
! [X19573,X19574,X19575] :
( ~ class_Groups_Oordered__comm__monoid__add(X19575)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19575),X19574),c_Groups_Ozero__class_Ozero(X19575)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19575),X19573),c_Groups_Ozero__class_Ozero(X19575)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19575),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19575),X19574),X19573)),c_Groups_Ozero__class_Ozero(X19575))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos])]) ).
fof(i_0_8233,plain,
! [X19570,X19571,X19572] :
( ~ class_Groups_Oordered__comm__monoid__add(X19572)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19572),X19571),c_Groups_Ozero__class_Ozero(X19572)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19572),X19570),c_Groups_Ozero__class_Ozero(X19572)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19572),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19572),X19571),X19570)),c_Groups_Ozero__class_Ozero(X19572))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg])]) ).
fof(i_0_8234,plain,
! [X18359,X18360,X18361] :
( ~ class_Groups_Oordered__comm__monoid__add(X18361)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18361),X18360),c_Groups_Ozero__class_Ozero(X18361)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18361),X18359),c_Groups_Ozero__class_Ozero(X18361)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18361),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18361),X18360),X18359)),c_Groups_Ozero__class_Ozero(X18361))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__neg])]) ).
fof(i_0_8235,plain,
! [X33661,X33662,X33663] : c_List_Olist_Olist__size(X33663,X33662,X33661) = 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(X33663,tc_Nat_Onat),X33662),X33661))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33663)),X33661)),
inference(variable_rename,[status(thm)],[fact_list__size__conv__listsum]) ).
fof(i_0_8236,plain,
! [X27808,X27809,X27810,X27811] : c_Map_Odom(X27811,X27810,c_Map_Orestrict__map(X27811,X27810,X27809,X27808)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27811,tc_HOL_Obool)),c_Map_Odom(X27811,X27810,X27809)),X27808),
inference(variable_rename,[status(thm)],[fact_dom__restrict]) ).
fof(i_0_8237,plain,
! [X31927,X31928,X31929,X31930] :
( c_Map_Omap__of(X31930,X31929,X31928) != c_Map_Omap__of(X31930,X31929,X31927)
| hAPP(c_Set_Oimage(tc_prod(X31930,X31929),X31930,c_Product__Type_Ofst(X31930,X31929)),hAPP(c_List_Oset(tc_prod(X31930,X31929)),X31928)) = hAPP(c_Set_Oimage(tc_prod(X31930,X31929),X31930,c_Product__Type_Ofst(X31930,X31929)),hAPP(c_List_Oset(tc_prod(X31930,X31929)),X31927)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__eq__dom])]) ).
fof(i_0_8238,plain,
! [X28277,X28278] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28278),c_Orderings_Otop__class_Otop(tc_fun(X28278,tc_HOL_Obool))))
| ~ c_Fun_Oinj__on(X28278,X28278,X28277,c_Orderings_Otop__class_Otop(tc_fun(X28278,tc_HOL_Obool)))
| hAPP(c_Set_Oimage(X28278,X28278,X28277),c_Orderings_Otop__class_Otop(tc_fun(X28278,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X28278,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__inj__surj])]) ).
fof(i_0_8239,plain,
! [X32457,X32458,X32459,X32460] :
( ~ class_Rings_Osemiring__1(X32460)
| hAPP(c_List_Omonoid__add__class_Olistsum(X32460),hAPP(hAPP(c_List_Omap(X32459,X32460),hAPP(c_COMBK(X32460,X32459),X32458)),X32457)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X32460),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X32460),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32459)),X32457))),X32458) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__triv])]) ).
fof(i_0_8240,plain,
! [X21034,X21035,X21036] :
( ~ class_Rings_Oring__1(X21036)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21036),hAPP(c_Groups_Ouminus__class_Ouminus(X21036),X21035)),X21034) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21036),hAPP(hAPP(c_Power_Opower__class_Opower(X21036),hAPP(c_Groups_Ouminus__class_Ouminus(X21036),c_Groups_Oone__class_Oone(X21036))),X21034)),hAPP(hAPP(c_Power_Opower__class_Opower(X21036),X21035),X21034)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus])]) ).
fof(i_0_8241,plain,
! [X28197,X28198,X28199,X28200] : hBOOL(hAPP(hAPP(c_member(X28200),hAPP(X28199,X28198)),hAPP(c_Set_Oimage(X28197,X28200,X28199),c_Orderings_Otop__class_Otop(tc_fun(X28197,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_rangeI]) ).
fof(i_0_8242,plain,
! [X20771,X20772,X20773,X20774] :
( ~ class_Int_Onumber(X20774)
| ~ class_Rings_Oring(X20774)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20774),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20774),X20773),X20772)),hAPP(c_Int_Onumber__class_Onumber__of(X20774),X20771)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20774),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20774),X20773),hAPP(c_Int_Onumber__class_Onumber__of(X20774),X20771))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20774),X20772),hAPP(c_Int_Onumber__class_Onumber__of(X20774),X20771))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__diff__distrib__number__of])]) ).
fof(i_0_8243,plain,
! [X20754,X20755,X20756,X20757] :
( ~ class_Int_Onumber(X20757)
| ~ class_Rings_Osemiring(X20757)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20757),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20757),X20756),X20755)),hAPP(c_Int_Onumber__class_Onumber__of(X20757),X20754)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20757),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20757),X20756),hAPP(c_Int_Onumber__class_Onumber__of(X20757),X20754))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20757),X20755),hAPP(c_Int_Onumber__class_Onumber__of(X20757),X20754))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__distrib__number__of])]) ).
fof(i_0_8244,plain,
! [X31582,X31583,X31584,X31585,X31586,X31587] :
( ( hAPP(X31584,X31583) = c_Option_Ooption_ONone(X31586)
| hAPP(X31584,X31583) = hAPP(c_Option_Ooption_OSome(X31586),X31582)
| hAPP(c_Map_Omap__add(X31587,X31586,X31585,X31584),X31583) != hAPP(c_Option_Ooption_OSome(X31586),X31582) )
& ( hAPP(X31585,X31583) = hAPP(c_Option_Ooption_OSome(X31586),X31582)
| hAPP(X31584,X31583) = hAPP(c_Option_Ooption_OSome(X31586),X31582)
| hAPP(c_Map_Omap__add(X31587,X31586,X31585,X31584),X31583) != hAPP(c_Option_Ooption_OSome(X31586),X31582) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__add__SomeD])])]) ).
fof(i_0_8245,plain,
! [X31576,X31577,X31578,X31579,X31580,X31581] :
( ( hAPP(X31578,X31577) = c_Option_Ooption_ONone(X31580)
| hAPP(X31578,X31577) = hAPP(c_Option_Ooption_OSome(X31580),X31576)
| hAPP(c_Map_Omap__add(X31581,X31580,X31579,X31578),X31577) != hAPP(c_Option_Ooption_OSome(X31580),X31576) )
& ( hAPP(X31579,X31577) = hAPP(c_Option_Ooption_OSome(X31580),X31576)
| hAPP(X31578,X31577) = hAPP(c_Option_Ooption_OSome(X31580),X31576)
| hAPP(c_Map_Omap__add(X31581,X31580,X31579,X31578),X31577) != hAPP(c_Option_Ooption_OSome(X31580),X31576) )
& ( hAPP(X31578,X31577) != hAPP(c_Option_Ooption_OSome(X31580),X31576)
| hAPP(c_Map_Omap__add(X31581,X31580,X31579,X31578),X31577) = hAPP(c_Option_Ooption_OSome(X31580),X31576) )
& ( hAPP(X31578,X31577) != c_Option_Ooption_ONone(X31580)
| hAPP(X31579,X31577) != hAPP(c_Option_Ooption_OSome(X31580),X31576)
| hAPP(c_Map_Omap__add(X31581,X31580,X31579,X31578),X31577) = hAPP(c_Option_Ooption_OSome(X31580),X31576) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__add__Some__iff])])]) ).
fof(i_0_8246,plain,
! [X25374,X25375,X25376] :
( ~ class_Orderings_Olinorder(X25376)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25376),X25375))
| X25375 = c_Orderings_Obot__class_Obot(tc_fun(X25376,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25376),X25374))
| X25374 = c_Orderings_Obot__class_Obot(tc_fun(X25376,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25376,tc_HOL_Obool)),X25375),X25374) != c_Orderings_Obot__class_Obot(tc_fun(X25376,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMin(X25376,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25376,tc_HOL_Obool)),X25375),X25374)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25376),c_Big__Operators_Olinorder__class_OMin(X25376,X25375)),c_Big__Operators_Olinorder__class_OMin(X25376,X25374)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Ounion__disjoint])]) ).
fof(i_0_8247,plain,
! [X25383,X25384,X25385] :
( ~ class_Orderings_Olinorder(X25385)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25385),X25384))
| X25384 = c_Orderings_Obot__class_Obot(tc_fun(X25385,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25385),X25383))
| X25383 = c_Orderings_Obot__class_Obot(tc_fun(X25385,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25385,tc_HOL_Obool)),X25384),X25383) != c_Orderings_Obot__class_Obot(tc_fun(X25385,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMax(X25385,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25385,tc_HOL_Obool)),X25384),X25383)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25385),c_Big__Operators_Olinorder__class_OMax(X25385,X25384)),c_Big__Operators_Olinorder__class_OMax(X25385,X25383)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Ounion__disjoint])]) ).
fof(i_0_8248,plain,
! [X25368,X25369,X25370] :
( ~ class_Lattices_Olattice(X25370)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25370),X25369))
| X25369 = c_Orderings_Obot__class_Obot(tc_fun(X25370,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25370),X25368))
| X25368 = c_Orderings_Obot__class_Obot(tc_fun(X25370,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25370,tc_HOL_Obool)),X25369),X25368) != c_Orderings_Obot__class_Obot(tc_fun(X25370,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OInf__fin(X25370,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25370,tc_HOL_Obool)),X25369),X25368)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25370),c_Big__Operators_Olattice__class_OInf__fin(X25370,X25369)),c_Big__Operators_Olattice__class_OInf__fin(X25370,X25368)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__disjoint])]) ).
fof(i_0_8249,plain,
! [X25012,X25013,X25014] :
( ~ class_Lattices_Olattice(X25014)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25014),X25013))
| X25013 = c_Orderings_Obot__class_Obot(tc_fun(X25014,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25014),X25012))
| X25012 = c_Orderings_Obot__class_Obot(tc_fun(X25014,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25014,tc_HOL_Obool)),X25013),X25012) != c_Orderings_Obot__class_Obot(tc_fun(X25014,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OSup__fin(X25014,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25014,tc_HOL_Obool)),X25013),X25012)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25014),c_Big__Operators_Olattice__class_OSup__fin(X25014,X25013)),c_Big__Operators_Olattice__class_OSup__fin(X25014,X25012)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__disjoint])]) ).
fof(i_0_8250,plain,
! [X23220,X23221,X23222,X23223] :
( ~ class_Rings_Ocomm__semiring__1(X23223)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23223),X23222),X23221))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23223),hAPP(hAPP(c_Power_Opower__class_Opower(X23223),X23222),X23220)),hAPP(hAPP(c_Power_Opower__class_Opower(X23223),X23221),X23220))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__power__same])]) ).
fof(i_0_8251,plain,
! [X19238,X19239,X19240,X19241] :
( ~ class_Groups_Oordered__ab__semigroup__add(X19241)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19241),X19240),X19239))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19241),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19241),X19240),X19238)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19241),X19239),X19238))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__mono])]) ).
fof(i_0_8252,plain,
! [X19234,X19235,X19236,X19237] :
( ~ class_Groups_Oordered__ab__semigroup__add(X19237)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19237),X19236),X19235))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19237),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19237),X19234),X19236)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19237),X19234),X19235))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__mono])]) ).
fof(i_0_8253,plain,
! [X18282,X18283,X18284,X18285] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X18285)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18285),X18284),X18283))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18285),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18285),X18284),X18282)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18285),X18283),X18282))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono])]) ).
fof(i_0_8254,plain,
! [X18286,X18287,X18288,X18289] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X18289)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18289),X18288),X18287))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18289),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18289),X18286),X18288)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18289),X18286),X18287))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono])]) ).
fof(i_0_8255,plain,
! [X28836,X28837,X28838] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X28838)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28838),X28837))
| X28837 = c_Orderings_Obot__class_Obot(tc_fun(X28838,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28838),X28836))
| X28836 = c_Orderings_Obot__class_Obot(tc_fun(X28838,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ofold1(X28838,c_Groups_Otimes__class_Otimes(X28838)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28838,tc_HOL_Obool)),X28837),X28836)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X28838),hAPP(c_Finite__Set_Ofold1(X28838,c_Groups_Otimes__class_Otimes(X28838)),X28837)),hAPP(c_Finite__Set_Ofold1(X28838,c_Groups_Otimes__class_Otimes(X28838)),X28836)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__Un2])]) ).
fof(i_0_8256,plain,
! [X34313,X34314,X34315] : hAPP(c_List_Orev(X34315),hAPP(hAPP(c_List_Odrop(X34315),X34314),X34313)) = hAPP(hAPP(c_List_Otake(X34315),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34315)),X34313)),X34314)),hAPP(c_List_Orev(X34315),X34313)),
inference(variable_rename,[status(thm)],[fact_rev__drop]) ).
fof(i_0_8257,plain,
! [X34316,X34317,X34318] : hAPP(c_List_Orev(X34318),hAPP(hAPP(c_List_Otake(X34318),X34317),X34316)) = hAPP(hAPP(c_List_Odrop(X34318),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34318)),X34316)),X34317)),hAPP(c_List_Orev(X34318),X34316)),
inference(variable_rename,[status(thm)],[fact_rev__take]) ).
fof(i_0_8258,plain,
! [X26556,X26557,X26558] :
( ~ class_Orderings_Olinorder(X26558)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26558),X26557),X26556))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26558,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X26558),X26557),c_Orderings_Obot__class_Obot(tc_fun(X26558,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(X26558,X26557,X26556)) = c_SetInterval_Oord__class_OatLeastAtMost(X26558,X26557,X26556) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I5_J])]) ).
fof(i_0_8259,plain,
! [X23418,X23419] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23419,tc_HOL_Obool)),X23418),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X23419,tc_HOL_Obool)),X23418)))
| X23418 = c_Orderings_Obot__class_Obot(tc_fun(X23419,tc_HOL_Obool)) )
& ( X23418 != c_Orderings_Obot__class_Obot(tc_fun(X23419,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23419,tc_HOL_Obool)),X23418),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X23419,tc_HOL_Obool)),X23418))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__Compl__self__eq])]) ).
fof(i_0_8260,plain,
! [X27099,X27100,X27101,X27102,X27103,X27104,X27105] :
( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27105,tc_Option_Ooption(X27104)),X27103),X27102),hAPP(c_Option_Ooption_OSome(X27104),X27101)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27105,tc_Option_Ooption(X27104)),X27100),X27102),hAPP(c_Option_Ooption_OSome(X27104),X27099))
| X27101 = X27099 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__upd__eqD1])]) ).
fof(i_0_8261,plain,
! [X21137,X21138,X21139] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21139),c_Int_OPls))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21139)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21138)),X21137)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21139),c_Int_OPls))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21139)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21138)),X21137)) = 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),X21139),X21138))),X21137) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5688])]) ).
fof(i_0_8262,plain,
! [X22070,X22071] : c_Divides_Opdivmod(X22071,X22070) = 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),X22071)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X22070))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X22071),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X22070))),
inference(variable_rename,[status(thm)],[fact_pdivmod__def]) ).
fof(i_0_8263,plain,
! [X31286,X31287,X31288] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X31288,tc_HOL_Obool)),X31287),X31286))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31288,tc_HOL_Obool)),X31287),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31288,tc_HOL_Obool),X31286))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Union__upper])]) ).
fof(i_0_8264,plain,
! [X30648,X30649,X30650,X30651] : hAPP(c_Finite__Set_Ofold__image(X30651,X30650,X30649),X30648) = c_Finite__Set_Ofold(X30650,X30651,hAPP(hAPP(c_COMBB(X30651,tc_fun(X30651,X30651),X30650),X30649),X30648)),
inference(variable_rename,[status(thm)],[fact_fold__image__def]) ).
fof(i_0_8265,plain,
! [X22723,X22724] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X22724)),X22723) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X22724),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),X22724)),X22723),
inference(variable_rename,[status(thm)],[fact_max__Suc1]) ).
fof(i_0_8266,plain,
! [X31295,X31296] : hAPP(c_Relation_OField(X31296),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X31296,X31296),tc_HOL_Obool),X31295)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X31296,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(X31296,X31296),tc_HOL_Obool),tc_fun(X31296,tc_HOL_Obool),c_Relation_OField(X31296)),X31295)),
inference(variable_rename,[status(thm)],[fact_Field__Union]) ).
fof(i_0_8267,plain,
! [X23478,X23479] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23478),X23479)),X23479))
| X23478 = 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)),X23479)) )
& ( X23478 != 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),X23478),X23479)),X23479))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23479)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel2])])]) ).
fof(i_0_8268,plain,
! [X23476,X23477] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23477),X23476)),X23477))
| X23476 = 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)),X23477)) )
& ( X23476 != 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),X23477),X23476)),X23477))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23477)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel1])])]) ).
fof(i_0_8269,plain,
! [X24180,X24181,X24182] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24182,tc_HOL_Obool)),X24181),X24180))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24182,tc_HOL_Obool)),X24181),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24182,tc_HOL_Obool)),X24180),X24181)) = X24180 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__partition])]) ).
fof(i_0_8270,plain,
! [X31708,X31709,X31710] :
( ~ c_Fun_Oinj__on(X31710,X31709,X31708,c_Orderings_Otop__class_Otop(tc_fun(X31710,tc_HOL_Obool)))
| c_Fun_Oinj__on(tc_List_Olist(X31710),tc_List_Olist(X31709),hAPP(c_List_Omap(X31710,X31709),X31708),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X31710),tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__mapI])]) ).
fof(i_0_8271,plain,
! [X25055,X25056,X25057] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25057,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25057,tc_HOL_Obool)),X25056),X25055)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25057,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25057,tc_HOL_Obool)),X25056)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25057,tc_HOL_Obool)),X25055)),
inference(variable_rename,[status(thm)],[fact_Compl__Int]) ).
fof(i_0_8272,plain,
! [X25058,X25059,X25060] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25060,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25060,tc_HOL_Obool)),X25059),X25058)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25060,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25060,tc_HOL_Obool)),X25059)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25060,tc_HOL_Obool)),X25058)),
inference(variable_rename,[status(thm)],[fact_Compl__Un]) ).
fof(i_0_8273,plain,
! [X28003,X28004,X28005,X28006,X28007] :
( ( hBOOL(hAPP(hAPP(X28006,X28004),X28003))
| ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X28007,X28006,X28005),X28004),X28003)) )
& ( hBOOL(hAPP(X28005,X28003))
| ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X28007,X28006,X28005),X28004),X28003)) )
& ( ~ hBOOL(hAPP(hAPP(X28006,X28004),X28003))
| ~ hBOOL(hAPP(X28005,X28003))
| hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X28007,X28006,X28005),X28004),X28003)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_peek__and__def])])]) ).
fof(i_0_8274,plain,
! [X28406,X28407,X28408,X28409,X28410] :
( ( ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(X28410,X28409,X28408),X28407),X28406))
| hBOOL(hAPP(X28407,hAPP(X28408,X28406))) )
& ( ~ hBOOL(hAPP(X28407,hAPP(X28408,X28406)))
| hBOOL(hAPP(hAPP(c_Set_Ovimage(X28410,X28409,X28408),X28407),X28406)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__code])]) ).
fof(i_0_8275,plain,
! [X31302,X31303,X31304,X31306] :
( ( hBOOL(hAPP(hAPP(c_member(X31304),esk403_3(X31302,X31303,X31304)),X31303))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X31304),c_Complete__Lattice_OInf__class_OInf(X31304,X31303)),X31302))
| ~ class_Complete__Lattice_Ocomplete__lattice(X31304)
| ~ class_Orderings_Olinorder(X31304) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X31304),esk403_3(X31302,X31303,X31304)),X31302))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X31304),c_Complete__Lattice_OInf__class_OInf(X31304,X31303)),X31302))
| ~ class_Complete__Lattice_Ocomplete__lattice(X31304)
| ~ class_Orderings_Olinorder(X31304) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X31304),X31306),X31303))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X31304),X31306),X31302))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X31304),c_Complete__Lattice_OInf__class_OInf(X31304,X31303)),X31302))
| ~ class_Complete__Lattice_Ocomplete__lattice(X31304)
| ~ class_Orderings_Olinorder(X31304) ) ),
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_8276,plain,
! [X20805,X20806,X20807,X20808] :
( ~ class_Int_Onumber__ring(X20808)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20808),hAPP(c_Int_Onumber__class_Onumber__of(X20808),X20807)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20808),hAPP(c_Int_Onumber__class_Onumber__of(X20808),X20806)),X20805)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20808),hAPP(c_Int_Onumber__class_Onumber__of(X20808),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20807),X20806))),X20805) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__number__of__left])]) ).
fof(i_0_8277,plain,
! [X20848,X20849,X20850,X20851] :
( ~ class_Int_Onumber__ring(X20851)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20851),hAPP(c_Int_Onumber__class_Onumber__of(X20851),X20850)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20851),hAPP(c_Int_Onumber__class_Onumber__of(X20851),X20849)),X20848)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20851),hAPP(c_Int_Onumber__class_Onumber__of(X20851),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20850),X20849))),X20848) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__diff1])]) ).
fof(i_0_8278,plain,
! [X20787,X20788,X20789,X20790] :
( ~ class_Int_Onumber__ring(X20790)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20790),hAPP(c_Int_Onumber__class_Onumber__of(X20790),X20789)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20790),hAPP(c_Int_Onumber__class_Onumber__of(X20790),X20788)),X20787)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20790),hAPP(c_Int_Onumber__class_Onumber__of(X20790),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20789),X20788))),X20787) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__left])]) ).
fof(i_0_8279,plain,
! [X31948,X31949,X31950] : hAPP(c_Option_Omap(X31950,X31949),X31948) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(X31949),X31950,c_Option_Ooption_ONone(X31949),hAPP(hAPP(c_COMBB(X31949,tc_Option_Ooption(X31949),X31950),c_Option_Ooption_OSome(X31949)),X31948)),
inference(variable_rename,[status(thm)],[fact_Option_Omap__def]) ).
fof(i_0_8280,plain,
! [X26883,X26884,X26885] :
( ~ class_Orderings_Olinorder(X26885)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26885),X26884),X26883))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26885,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X26885),X26884),c_Orderings_Obot__class_Obot(tc_fun(X26885,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(X26885,X26884,X26883)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26885,X26884),X26883) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I3_J])]) ).
fof(i_0_8281,plain,
! [X32516,X32517,X32518,X32519,X32520] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32520),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32519)),X32518)))
| hAPP(hAPP(c_List_Onth(X32517),hAPP(hAPP(c_List_Omap(X32519,X32517),X32516),X32518)),X32520) = hAPP(X32516,hAPP(hAPP(c_List_Onth(X32519),X32518),X32520)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__map])]) ).
fof(i_0_8282,plain,
! [X23369,X23370,X23371,X23372] :
( ~ class_Rings_Ocomm__semiring__1(X23372)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23371),X23370))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23372),hAPP(hAPP(c_Power_Opower__class_Opower(X23372),X23369),X23371)),hAPP(hAPP(c_Power_Opower__class_Opower(X23372),X23369),X23370))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__power__dvd])]) ).
fof(i_0_8283,plain,
! [X22165,X22166] :
( ( X22165 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nitpick_Onat__gcd(X22166,X22165) = X22166
| ~ 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),X22166),X22165))) )
& ( X22165 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nitpick_Onat__gcd(X22166,X22165) = c_Nitpick_Onat__gcd(X22165,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X22166,X22165))
| ~ 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),X22166),X22165))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__gcd_Opsimps])])]) ).
fof(i_0_8284,plain,
! [X31195,X31196,X31197,X31198] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X31198,tc_HOL_Obool)),X31197),X31196))
| ~ hBOOL(hAPP(hAPP(c_member(X31198),X31195),X31197))
| hBOOL(hAPP(hAPP(c_member(X31198),X31195),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31198,tc_HOL_Obool),X31196))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UnionI])]) ).
fof(i_0_8285,plain,
! [X18923,X18924,X18925] :
( ~ class_Rings_Olinordered__semiring__strict(X18925)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18925),c_Groups_Ozero__class_Ozero(X18925)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18925),X18924),X18923)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18925),c_Groups_Ozero__class_Ozero(X18925)),X18923))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18925),c_Groups_Ozero__class_Ozero(X18925)),X18924)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos2])]) ).
fof(i_0_8286,plain,
! [X18920,X18921,X18922] :
( ~ class_Rings_Olinordered__semiring__strict(X18922)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18922),c_Groups_Ozero__class_Ozero(X18922)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18922),X18921),X18920)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18922),c_Groups_Ozero__class_Ozero(X18922)),X18921))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18922),c_Groups_Ozero__class_Ozero(X18922)),X18920)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos])]) ).
fof(i_0_8287,plain,
! [X25506,X25507,X25508] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25508),X25507))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25508),X25506))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25508,tc_HOL_Obool)),X25507),X25506) != c_Orderings_Obot__class_Obot(tc_fun(X25508,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(X25508),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25508,tc_HOL_Obool)),X25507),X25506)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25508),X25507)),hAPP(c_Finite__Set_Ocard(X25508),X25506)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Un__disjoint])]) ).
fof(i_0_8288,plain,
! [X22554,X22555] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X22555)),X22554) = 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),X22555)),X22554),
inference(variable_rename,[status(thm)],[fact_min__Suc1]) ).
fof(i_0_8289,plain,
! [X32029,X32030,X32031] :
( ~ class_Orderings_Olinorder(X32031)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32031),X32030))
| c_List_Olinorder__class_Osorted__list__of__set(X32031,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X32031,tc_HOL_Obool)),X32030),hAPP(hAPP(c_Set_Oinsert(X32031),X32029),c_Orderings_Obot__class_Obot(tc_fun(X32031,tc_HOL_Obool))))) = c_List_Oremove1(X32031,X32029,c_List_Olinorder__class_Osorted__list__of__set(X32031,X32030)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__remove])]) ).
fof(i_0_8290,plain,
! [X28181,X28182] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X28182,X28181)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X28182,X28181),tc_HOL_Obool))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X28181),c_Orderings_Otop__class_Otop(tc_fun(X28181,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD2])]) ).
fof(i_0_8291,plain,
! [X26407,X26408,X26409] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26409,tc_HOL_Obool)),X26408),hAPP(c_Set_OPow(X26409),X26407)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26409,tc_HOL_Obool)),X26408),X26407)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26409,tc_HOL_Obool)),X26408),X26407))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X26409,tc_HOL_Obool)),X26408),hAPP(c_Set_OPow(X26409),X26407))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pow__iff])]) ).
fof(i_0_8292,plain,
! [X26404,X26405,X26406] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26406,tc_HOL_Obool)),X26405),hAPP(c_Set_OPow(X26406),X26404)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26406,tc_HOL_Obool)),X26405),X26404)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_PowD])]) ).
fof(i_0_8293,plain,
! [X20702,X20703] :
( ( ~ 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),X20703)),X20702)))
| X20703 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X20702 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X20703 = 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),X20703)),X20702))) )
& ( X20702 != 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),X20703)),X20702))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__zpower__abs__iff])])]) ).
fof(i_0_8294,plain,
! [X26521,X26522,X26523,X26524] :
( ~ class_Orderings_Olinorder(X26524)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26524),X26523),X26522))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26524),X26522),X26521))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26524,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26524,X26523,X26522)),c_SetInterval_Oord__class_OgreaterThanAtMost(X26524,X26522,X26521)) = c_SetInterval_Oord__class_OatLeastAtMost(X26524,X26523,X26521) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I22_J])]) ).
fof(i_0_8295,plain,
! [X25838,X25839,X25840,X25841] :
( ~ class_Orderings_Olinorder(X25841)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25841),X25840),X25839))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25841),X25839),X25838))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25841,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25841,X25840,X25839)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25841,X25839,X25838)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X25841,X25840,X25838) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I20_J])]) ).
fof(i_0_8296,plain,
! [X25863,X25864,X25865,X25866] :
( ~ class_Orderings_Olinorder(X25866)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25866),X25865),X25864))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25866),X25864),X25863))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25866,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25866,X25865,X25864)),c_SetInterval_Oord__class_OgreaterThanLessThan(X25866,X25864,X25863)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X25866,X25865,X25863) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I16_J])]) ).
fof(i_0_8297,plain,
! [X26421,X26422,X26423,X26424] :
( ~ class_Orderings_Olinorder(X26424)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26424),X26423),X26422))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26424),X26422),X26421))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26424,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X26424,X26423,X26422)),c_SetInterval_Oord__class_OatLeastAtMost(X26424,X26422,X26421)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X26424,X26423,X26421) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I19_J])]) ).
fof(i_0_8298,plain,
! [X24017,X24018,X24019] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24019,tc_HOL_Obool)),X24018),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24019,tc_HOL_Obool)),X24018),X24017))),
inference(variable_rename,[status(thm)],[fact_Un__upper1]) ).
fof(i_0_8299,plain,
! [X24014,X24015,X24016] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24016,tc_HOL_Obool)),X24015),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24016,tc_HOL_Obool)),X24014),X24015))),
inference(variable_rename,[status(thm)],[fact_Un__upper2]) ).
fof(i_0_8300,plain,
! [X30162,X30163,X30164] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30164,X30164)),X30163),X30162))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30164,X30164)),X30163),c_Transitive__Closure_Ortrancl(X30164,X30162))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__into__rtrancl])]) ).
fof(i_0_8301,plain,
! [X25749,X25750,X25751,X25752] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25752),X25751))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25750),X25749))
| hAPP(c_Finite__Set_Ocard(tc_sum(X25752,X25750)),c_Sum__Type_OPlus(X25752,X25750,X25751,X25749)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25752),X25751)),hAPP(c_Finite__Set_Ocard(X25750),X25749)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Plus])]) ).
fof(i_0_8302,plain,
! [X25556,X25557,X25558,X25559] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25559),X25558))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25557),X25556))
| hAPP(c_Finite__Set_Ocard(tc_sum(X25559,X25557)),c_Sum__Type_OPlus(X25559,X25557,X25558,X25556)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25559),X25558)),hAPP(c_Finite__Set_Ocard(X25557),X25556)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X25559),X25558))
| hAPP(c_Finite__Set_Ocard(tc_sum(X25559,X25557)),c_Sum__Type_OPlus(X25559,X25557,X25558,X25556)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X25557),X25556))
| hAPP(c_Finite__Set_Ocard(tc_sum(X25559,X25557)),c_Sum__Type_OPlus(X25559,X25557,X25558,X25556)) = 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_8303,plain,
! [X23983,X23984,X23985,X23986] :
( ~ class_Lattices_Osemilattice__sup(X23986)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23986),X23985),X23984))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23986),X23983),X23984))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23986),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23986),X23985),X23983)),X23984)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__least])]) ).
fof(i_0_8304,plain,
! [X23979,X23980,X23981,X23982] :
( ~ class_Lattices_Osemilattice__sup(X23982)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23982),X23981),X23980))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23982),X23979),X23980))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23982),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23982),X23981),X23979)),X23980)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__supI])]) ).
fof(i_0_8305,plain,
! [X22671,X22672,X22673,X22674] :
( ~ class_Orderings_Olinorder(X22674)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22674),X22673),X22672))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22674),X22671),X22672))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22674),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22674),X22673),X22671)),X22672)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__supI])]) ).
fof(i_0_8306,plain,
! [X22667,X22668,X22669,X22670] :
( ~ class_Orderings_Olinorder(X22670)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22670),X22669),X22668))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22670),X22667),X22668))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22670),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22670),X22669),X22667)),X22668)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__least])]) ).
fof(i_0_8307,plain,
! [X24948,X24949,X24950,X24951] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24951,tc_HOL_Obool)),X24950),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24951,tc_HOL_Obool)),X24949),X24948)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24951,tc_HOL_Obool)),X24949),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24951,tc_HOL_Obool)),X24950),X24948)),
inference(variable_rename,[status(thm)],[fact_Int__left__commute]) ).
fof(i_0_8308,plain,
! [X24060,X24061,X24062,X24063] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24063,tc_HOL_Obool)),X24062),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24063,tc_HOL_Obool)),X24061),X24060)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24063,tc_HOL_Obool)),X24061),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24063,tc_HOL_Obool)),X24062),X24060)),
inference(variable_rename,[status(thm)],[fact_Un__left__commute]) ).
fof(i_0_8309,plain,
! [X24140,X24141,X24142] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24142,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24142,tc_HOL_Obool)),X24141),X24140)),X24140) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24142,tc_HOL_Obool)),X24141),X24140),
inference(variable_rename,[status(thm)],[fact_Un__Diff__cancel2]) ).
fof(i_0_8310,plain,
! [X22433,X22434,X22435] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22435,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22435,tc_HOL_Obool)),X22434),X22433)),X22433) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22435,tc_HOL_Obool)),X22434),X22433),
inference(variable_rename,[status(thm)],[fact_Diff__idemp]) ).
cnf(i_0_8311,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_8312,plain,
! [X24297,X24298,X24299,X24300,X24301] :
( ~ hBOOL(hAPP(hAPP(c_member(X24301),X24300),X24299))
| hBOOL(hAPP(hAPP(c_member(X24298),hAPP(X24297,X24300)),hAPP(c_Set_Oimage(X24301,X24298,X24297),X24299))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_imageI])]) ).
fof(i_0_8313,plain,
! [X23207,X23208,X23209,X23210] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X23210,X23209,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X23210)),X23208),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X23210),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X23210,X23209,X23207)
| c_Hoare__Mirabelle_Ohoare__derivs(X23210,X23209,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X23210)),X23208),X23207)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hoare__derivs_Oinsert])]) ).
fof(i_0_8314,plain,
! [X23553,X23554] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23554),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23553)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X23554))),X23553)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X23554))),X23553))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23554),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23553))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__int__iff])]) ).
fof(i_0_8315,plain,
! [X30782,X30783,X30784,X30785,X30786] :
( ~ c_Finite__Set_Ofun__left__comm(X30786,X30785,X30784)
| c_Finite__Set_Ofun__left__comm(X30783,X30785,hAPP(hAPP(c_COMBB(X30786,tc_fun(X30785,X30785),X30783),X30784),X30782)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__left__comm__apply])]) ).
fof(i_0_8316,plain,
! [X29102,X29103,X29104,X29105,X29106] :
( ~ c_Finite__Set_Ofun__left__comm__idem(X29106,X29105,X29104)
| c_Finite__Set_Ofun__left__comm__idem(X29103,X29105,hAPP(hAPP(c_COMBB(X29106,tc_fun(X29105,X29105),X29103),X29104),X29102)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__left__comm__idem__apply])]) ).
fof(i_0_8317,plain,
! [X25008,X25009,X25010,X25011] :
( ~ hBOOL(hAPP(hAPP(c_member(X25011),X25010),X25009))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25011,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X25011),X25010),X25008)),X25009) = hAPP(hAPP(c_Set_Oinsert(X25011),X25010),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25011,tc_HOL_Obool)),X25008),X25009)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__insert__left__if1])]) ).
fof(i_0_8318,plain,
! [X24992,X24993,X24994,X24995] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X24995),X24994),X24993))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24995,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X24995),X24994),X24992)),X24993) = hAPP(hAPP(c_Set_Oinsert(X24995),X24994),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24995,tc_HOL_Obool)),X24992),X24993)) )
& ( hBOOL(hAPP(hAPP(c_member(X24995),X24994),X24993))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24995,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X24995),X24994),X24992)),X24993) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24995,tc_HOL_Obool)),X24992),X24993) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5690])]) ).
fof(i_0_8319,plain,
! [X28210,X28211,X28212,X28213,X28214] :
( ( hAPP(c_Set_Oimage(X28214,X28213,X28212),X28211) != hAPP(c_Set_Oimage(X28214,X28213,X28212),X28210)
| X28211 = X28210
| ~ c_Fun_Oinj__on(X28214,X28213,X28212,c_Orderings_Otop__class_Otop(tc_fun(X28214,tc_HOL_Obool))) )
& ( X28211 != X28210
| hAPP(c_Set_Oimage(X28214,X28213,X28212),X28211) = hAPP(c_Set_Oimage(X28214,X28213,X28212),X28210)
| ~ c_Fun_Oinj__on(X28214,X28213,X28212,c_Orderings_Otop__class_Otop(tc_fun(X28214,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_8320,plain,
! [X28366,X28367,X28368,X28369,X28370,X28371,X28372] :
( hAPP(c_Fun_Ocomp(X28372,X28371,X28370,X28369),X28368) != X28367
| hAPP(X28369,hAPP(X28368,X28366)) = hAPP(X28367,X28366) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__eq__dest__lhs])]) ).
fof(i_0_8321,plain,
! [X18653] : 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,X18653)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[fact_negative__zless__0]) ).
fof(i_0_8322,plain,
! [X33409,X33410,X33411] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33411),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33410)),X33409)))
| hAPP(hAPP(c_List_Olist_OCons(X33410),hAPP(hAPP(c_List_Onth(X33410),X33409),X33411)),hAPP(hAPP(c_List_Odrop(X33410),hAPP(c_Nat_OSuc,X33411)),X33409)) = hAPP(hAPP(c_List_Odrop(X33410),X33411),X33409) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__drop_H])]) ).
fof(i_0_8323,plain,
! [X28480,X28481,X28482,X28483] : hAPP(c_Set_Oimage(X28483,X28482,X28481),hAPP(c_Set_Ovimage(X28483,X28482,X28481),X28480)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28482,tc_HOL_Obool)),X28480),hAPP(c_Set_Oimage(X28483,X28482,X28481),c_Orderings_Otop__class_Otop(tc_fun(X28483,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_image__vimage__eq]) ).
fof(i_0_8324,plain,
! [X19674,X19675] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19675),c_Groups_Oone__class_Oone(tc_Int_Oint))),X19674))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19675),X19674)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19675),X19674))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19675),c_Groups_Oone__class_Oone(tc_Int_Oint))),X19674)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add1__zle__eq])]) ).
fof(i_0_8325,plain,
! [X26886,X26887,X26888,X26889] :
( ~ class_Orderings_Olinorder(X26889)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26889),X26888),X26887))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26889),X26887),X26886))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26889,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26889,X26888,X26887)),c_SetInterval_Oord__class_OgreaterThanLessThan(X26889,X26887,X26886)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26889,X26888),X26886) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I18_J])]) ).
fof(i_0_8326,plain,
! [X24544] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X24544))
| 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)),X24544))) )
& ( ~ 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)),X24544)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X24544)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I1_J])]) ).
fof(i_0_8327,plain,
! [X25467,X25468,X25469] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25469),X25468))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25469,tc_HOL_Obool)),X25467),X25468))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25469),X25467)),hAPP(c_Finite__Set_Ocard(X25469),X25468))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__mono])]) ).
fof(i_0_8328,plain,
! [X25474,X25475,X25476] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25476),X25475))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25476,tc_HOL_Obool)),X25474),X25475))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25476),X25474)),hAPP(c_Finite__Set_Ocard(X25476),X25475))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__card__mono])]) ).
fof(i_0_8329,plain,
! [X27837,X27838,X27839,X27840,X27841] :
( hAPP(X27841,X27840) != c_Option_Ooption_ONone(X27839)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27838,tc_HOL_Obool)),c_Map_Odom(X27838,X27839,X27841)),hAPP(hAPP(c_Set_Oinsert(X27838),X27840),X27837)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27838,tc_HOL_Obool)),c_Map_Odom(X27838,X27839,X27841)),X27837) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dom__minus])]) ).
fof(i_0_8330,plain,
! [X24161,X24162,X24163,X24164] :
( ~ hBOOL(hAPP(hAPP(c_member(X24164),X24163),X24162))
| hBOOL(hAPP(hAPP(c_member(X24164),X24163),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24164,tc_HOL_Obool)),X24162),X24161))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UnI1])]) ).
fof(i_0_8331,plain,
! [X23928,X23929,X23930,X23931] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X23931),X23930),X23929))
| hBOOL(hAPP(hAPP(c_member(X23931),X23930),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23931,tc_HOL_Obool)),X23928),X23929))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X23931),X23930),X23928))
| hBOOL(hAPP(hAPP(c_member(X23931),X23930),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23931,tc_HOL_Obool)),X23928),X23929))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5691])])]) ).
fof(i_0_8332,plain,
! [X24157,X24158,X24159,X24160] :
( ~ hBOOL(hAPP(hAPP(c_member(X24160),X24159),X24158))
| hBOOL(hAPP(hAPP(c_member(X24160),X24159),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24160,tc_HOL_Obool)),X24157),X24158))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UnI2])]) ).
fof(i_0_8333,plain,
! [X28275,X28276] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28276),c_Orderings_Otop__class_Otop(tc_fun(X28276,tc_HOL_Obool))))
| hAPP(c_Set_Oimage(X28276,X28276,X28275),c_Orderings_Otop__class_Otop(tc_fun(X28276,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X28276,tc_HOL_Obool))
| c_Fun_Oinj__on(X28276,X28276,X28275,c_Orderings_Otop__class_Otop(tc_fun(X28276,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__surj__inj])]) ).
fof(i_0_8334,plain,
! [X20739,X20740,X20741] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20741),X20740),X20739))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20741),hAPP(c_Groups_Oabs__class_Oabs(X20741),X20740)),X20739))
| ~ class_Groups_Oordered__ab__group__add__abs(X20741) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20741),hAPP(c_Groups_Ouminus__class_Ouminus(X20741),X20740)),X20739))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20741),hAPP(c_Groups_Oabs__class_Oabs(X20741),X20740)),X20739))
| ~ class_Groups_Oordered__ab__group__add__abs(X20741) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20741),X20740),X20739))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20741),hAPP(c_Groups_Ouminus__class_Ouminus(X20741),X20740)),X20739))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20741),hAPP(c_Groups_Oabs__class_Oabs(X20741),X20740)),X20739))
| ~ class_Groups_Oordered__ab__group__add__abs(X20741) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__iff])])]) ).
fof(i_0_8335,plain,
! [X20736,X20737,X20738] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20738)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20738),X20737),X20736))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20738),hAPP(c_Groups_Ouminus__class_Ouminus(X20738),X20737)),X20736))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20738),hAPP(c_Groups_Oabs__class_Oabs(X20738),X20737)),X20736)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__leI])]) ).
fof(i_0_8336,plain,
! [X20744,X20745,X20746] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20746),X20745),X20744))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20746),hAPP(c_Groups_Oabs__class_Oabs(X20746),X20745)),X20744))
| ~ class_Rings_Olinordered__idom(X20746) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20746),hAPP(c_Groups_Ouminus__class_Ouminus(X20746),X20745)),X20744))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20746),hAPP(c_Groups_Oabs__class_Oabs(X20746),X20745)),X20744))
| ~ class_Rings_Olinordered__idom(X20746) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20746),X20745),X20744))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20746),hAPP(c_Groups_Ouminus__class_Ouminus(X20746),X20745)),X20744))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20746),hAPP(c_Groups_Oabs__class_Oabs(X20746),X20745)),X20744))
| ~ class_Rings_Olinordered__idom(X20746) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__less__iff])])]) ).
fof(i_0_8337,plain,
! [X31615,X31616,X31617,X31618,X31619] :
( hBOOL(hAPP(hAPP(c_member(X31619),X31618),c_Map_Odom(X31619,X31617,X31616)))
| hAPP(c_Map_Omap__add(X31619,X31617,X31616,X31615),X31618) = hAPP(X31615,X31618) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5692])]) ).
fof(i_0_8338,plain,
! [X31620,X31621,X31622,X31623,X31624] :
( hBOOL(hAPP(hAPP(c_member(X31624),X31623),c_Map_Odom(X31624,X31622,X31621)))
| hAPP(c_Map_Omap__add(X31624,X31622,X31620,X31621),X31623) = hAPP(X31620,X31623) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5693])]) ).
fof(i_0_8339,plain,
! [X33667,X33668,X33669] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33669)),X33668),c_Wellfounded_Oacc(tc_List_Olist(X33669),c_List_Olistrel1(X33669,X33667))))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33669)),X33668),c_List_Olists(X33669,c_Wellfounded_Oacc(X33669,X33667)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__accI])]) ).
fof(i_0_8340,plain,
! [X18897,X18898] :
( ~ class_Rings_Olinordered__ring(X18898)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18898),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18898),X18897),X18897)),c_Groups_Ozero__class_Ozero(X18898))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5694])]) ).
fof(i_0_8341,plain,
! [X28488,X28489,X28490,X28491] :
( ~ c_Fun_Oinj__on(X28491,X28490,X28489,c_Orderings_Otop__class_Otop(tc_fun(X28491,tc_HOL_Obool)))
| hAPP(c_Set_Ovimage(X28491,X28490,X28489),hAPP(c_Set_Oimage(X28491,X28490,X28489),X28488)) = X28488 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__vimage__image__eq])]) ).
fof(i_0_8342,plain,
! [X26876,X26877,X26878,X26879] :
( ~ class_Orderings_Olinorder(X26879)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26879),X26878),X26877))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26879),X26877),X26876))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26879,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X26879,X26878,X26877)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26879,X26877),X26876)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X26879,X26878,X26876) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I15_J])]) ).
fof(i_0_8343,plain,
! [X20167,X20168,X20169,X20170] :
( ~ class_Divides_Osemiring__div(X20170)
| X20169 = c_Groups_Ozero__class_Ozero(X20170)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20170),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20170),X20168),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20170),X20169),X20167))),X20169) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20170),X20167),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20170),X20168),X20169)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self2])]) ).
fof(i_0_8344,plain,
! [X20171,X20172,X20173,X20174] :
( ~ class_Divides_Osemiring__div(X20174)
| X20173 = c_Groups_Ozero__class_Ozero(X20174)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20174),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20174),X20172),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20174),X20171),X20173))),X20173) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20174),X20171),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20174),X20172),X20173)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self1])]) ).
fof(i_0_8345,plain,
! [X21704,X21705,X21706,X21707] :
( ~ class_Fields_Ofield__inverse__zero(X21707)
| X21706 = c_Groups_Ozero__class_Ozero(X21707)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21707),X21705),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21707),X21704),X21706)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21707),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21707),X21704),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21707),X21705),X21706))),X21706) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__num__frac])]) ).
fof(i_0_8346,plain,
! [X29441,X29442,X29443,X29444] :
( ~ class_Groups_Ocomm__monoid__add(X29444)
| ~ c_Fun_Oinj__on(X29443,X29444,X29442,X29441)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29443,X29444),X29442),X29441) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29444,X29444),c_Fun_Oid(X29444)),hAPP(c_Set_Oimage(X29443,X29444,X29442),X29441)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__reindex__id])]) ).
fof(i_0_8347,plain,
! [X29445,X29446,X29447,X29448] :
( ~ class_Groups_Ocomm__monoid__mult(X29448)
| ~ c_Fun_Oinj__on(X29447,X29448,X29446,X29445)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X29447,X29448),X29446),X29445) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X29448,X29448),c_Fun_Oid(X29448)),hAPP(c_Set_Oimage(X29447,X29448,X29446),X29445)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__reindex__id])]) ).
fof(i_0_8348,plain,
! [X29574,X29575] :
( ( ~ c_Wellfounded_Owf(X29575,X29574)
| c_Wellfounded_Owf(X29575,hAPP(hAPP(c_Relation_Orel__comp(X29575,X29575,X29575),X29574),X29574)) )
& ( ~ c_Wellfounded_Owf(X29575,hAPP(hAPP(c_Relation_Orel__comp(X29575,X29575,X29575),X29574),X29574))
| c_Wellfounded_Owf(X29575,X29574) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__comp__self])]) ).
fof(i_0_8349,plain,
! [X23782,X23783,X23784] :
( X23784 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X23783,X23783),tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X23783,X23783),tc_HOL_Obool)),X23784),X23782)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__by__empty])]) ).
fof(i_0_8350,plain,
! [X33163,X33164,X33165] :
( ( hBOOL(hAPP(c_List_Odistinct(X33165),X33164))
| ~ hBOOL(hAPP(c_List_Odistinct(X33165),hAPP(hAPP(c_List_Oappend(X33165),X33164),X33163))) )
& ( hBOOL(hAPP(c_List_Odistinct(X33165),X33163))
| ~ hBOOL(hAPP(c_List_Odistinct(X33165),hAPP(hAPP(c_List_Oappend(X33165),X33164),X33163))) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X33165,tc_HOL_Obool)),hAPP(c_List_Oset(X33165),X33164)),hAPP(c_List_Oset(X33165),X33163)) = c_Orderings_Obot__class_Obot(tc_fun(X33165,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_List_Odistinct(X33165),hAPP(hAPP(c_List_Oappend(X33165),X33164),X33163))) )
& ( ~ hBOOL(hAPP(c_List_Odistinct(X33165),X33164))
| ~ hBOOL(hAPP(c_List_Odistinct(X33165),X33163))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X33165,tc_HOL_Obool)),hAPP(c_List_Oset(X33165),X33164)),hAPP(c_List_Oset(X33165),X33163)) != c_Orderings_Obot__class_Obot(tc_fun(X33165,tc_HOL_Obool))
| hBOOL(hAPP(c_List_Odistinct(X33165),hAPP(hAPP(c_List_Oappend(X33165),X33164),X33163))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__append])])]) ).
fof(i_0_8351,plain,
! [X33630,X33631,X33632] :
( ~ class_Orderings_Olinorder(X33632)
| c_Big__Operators_Olattice_OInf__fin(X33632,c_Orderings_Oord__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__max_OInf__fin__set__fold])]) ).
fof(i_0_8352,plain,
! [X33633,X33634,X33635] :
( ~ class_Orderings_Olinorder(X33635)
| c_Big__Operators_Olattice_OSup__fin(X33635,c_Orderings_Oord__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_min__max_OSup__fin__set__fold])]) ).
fof(i_0_8353,plain,
! [X27380,X27381,X27382,X27383] :
( ~ class_Groups_Ocomm__monoid__add(X27383)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X27382),X27381))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27383),X27380),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X27382,X27381)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27383),hAPP(X27380,X27382)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27383),X27380),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X27382,X27381))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__head])]) ).
fof(i_0_8354,plain,
! [X30504,X30505,X30506] : hAPP(hAPP(c_Nat_Ocompow(X30506,X30506),hAPP(c_Nat_OSuc,X30505)),X30504) = hAPP(c_Fun_Ocomp(X30506,X30506,X30506,X30504),hAPP(hAPP(c_Nat_Ocompow(X30506,X30506),X30505),X30504)),
inference(variable_rename,[status(thm)],[fact_funpow_Osimps_I2_J]) ).
fof(i_0_8355,plain,
! [X33649,X33650,X33651,X33652,X33653] :
( ~ hBOOL(hAPP(hAPP(c_member(X33653),X33652),hAPP(c_List_Oset(X33653),X33651)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33650),hAPP(X33649,X33652)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33650),c_List_Olist_Olist__size(X33653,X33649,X33651))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__size__estimation_H])]) ).
fof(i_0_8356,plain,
! [X33644,X33645,X33646,X33647,X33648] :
( ~ hBOOL(hAPP(hAPP(c_member(X33648),X33647),hAPP(c_List_Oset(X33648),X33646)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33645),hAPP(X33644,X33647)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33645),c_List_Olist_Olist__size(X33648,X33644,X33646))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__size__estimation])]) ).
fof(i_0_8357,plain,
! [X32521,X32522] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32522),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X32521)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X32521),X32522)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X32521))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_elem__le__listsum__nat])]) ).
fof(i_0_8358,plain,
! [X33083,X33084,X33085,X33086] : c_Map_Omap__of(X33086,X33085,hAPP(hAPP(c_List_Oappend(tc_prod(X33086,X33085)),X33084),X33083)) = c_Map_Omap__add(X33086,X33085,c_Map_Omap__of(X33086,X33085,X33083),c_Map_Omap__of(X33086,X33085,X33084)),
inference(variable_rename,[status(thm)],[fact_map__of__append]) ).
fof(i_0_8359,plain,
! [X20237,X20238] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20238))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20238),X20237))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20237),X20238) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20237),X20238)),X20238)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__div__geq])]) ).
fof(i_0_8360,plain,
! [X33701,X33702,X33703] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33703)),X33702),c_List_Olists(X33703,c_Wellfounded_Oacc(X33703,X33701))))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33703)),X33702),c_Wellfounded_Oacc(tc_List_Olist(X33703),c_List_Olistrel1(X33703,X33701)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__accD])]) ).
cnf(i_0_8361,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_8362,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_8363,plain,
! [X23394,X23395,X23396] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23396),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23395),X23394)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23396),X23394))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23394),X23395))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23396),X23395)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__diffD])]) ).
fof(i_0_8364,plain,
! [X23397,X23398,X23399] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23399),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23398),X23397)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23399),X23398))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23397),X23398))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23399),X23397)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__diffD1])]) ).
fof(i_0_8365,plain,
! [X21904,X21905] :
( ~ class_Rings_Osemiring__1(X21905)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X21905),X21904) = c_Nat_Osemiring__1__class_Oof__nat__aux(X21905,hAPP(hAPP(c_COMBC(X21905,X21905,X21905),c_Groups_Oplus__class_Oplus(X21905)),c_Groups_Oone__class_Oone(X21905)),X21904,c_Groups_Ozero__class_Ozero(X21905)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__1__class_Oof__nat__code])]) ).
fof(i_0_8366,plain,
! [X32269,X32270,X32271,X32272] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32272)),X32271)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32272)),X32270)))
| X32271 != hAPP(hAPP(c_List_Olist_OCons(X32272),X32269),X32270) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_impossible__Cons])]) ).
fof(i_0_8367,plain,
! [X26371,X26372,X26373] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26373,tc_HOL_Obool)),X26372),X26371))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X26373,tc_HOL_Obool)),X26372),hAPP(c_Set_OPow(X26373),X26371))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_PowI])]) ).
fof(i_0_8368,plain,
! [X21065,X21066,X21067,X21068,X21069] : hAPP(hAPP(c_Power_Opower_Opower(X21069,X21068,X21067),X21066),hAPP(c_Nat_OSuc,X21065)) = hAPP(hAPP(X21067,X21066),hAPP(hAPP(c_Power_Opower_Opower(X21069,X21068,X21067),X21066),X21065)),
inference(variable_rename,[status(thm)],[fact_power_Opower_Opower__Suc]) ).
fof(i_0_8369,plain,
! [X31599,X31600,X31601,X31602,X31603] :
( ( hAPP(X31600,X31599) = c_Option_Ooption_ONone(X31602)
| hAPP(c_Map_Omap__add(X31603,X31602,X31601,X31600),X31599) != c_Option_Ooption_ONone(X31602) )
& ( hAPP(X31601,X31599) = c_Option_Ooption_ONone(X31602)
| hAPP(c_Map_Omap__add(X31603,X31602,X31601,X31600),X31599) != c_Option_Ooption_ONone(X31602) )
& ( hAPP(X31600,X31599) != c_Option_Ooption_ONone(X31602)
| hAPP(X31601,X31599) != c_Option_Ooption_ONone(X31602)
| hAPP(c_Map_Omap__add(X31603,X31602,X31601,X31600),X31599) = c_Option_Ooption_ONone(X31602) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__add__None])])]) ).
fof(i_0_8370,plain,
! [X25306,X25307,X25308] :
( ~ class_Orderings_Olinorder(X25308)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25308,tc_HOL_Obool)),X25307),X25306))
| X25307 = c_Orderings_Obot__class_Obot(tc_fun(X25308,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25308),X25306))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25308),c_Big__Operators_Olinorder__class_OMin(X25308,X25306)),c_Big__Operators_Olinorder__class_OMin(X25308,X25307))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__antimono])]) ).
fof(i_0_8371,plain,
! [X25303,X25304,X25305] :
( ~ class_Orderings_Olinorder(X25305)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25305,tc_HOL_Obool)),X25304),X25303))
| X25304 = c_Orderings_Obot__class_Obot(tc_fun(X25305,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25305),X25303))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25305),c_Big__Operators_Olinorder__class_OMax(X25305,X25304)),c_Big__Operators_Olinorder__class_OMax(X25305,X25303))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__mono])]) ).
fof(i_0_8372,plain,
! [X20430,X20431] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20431),X20430))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20431),X20430)),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),X20431),X20430)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20431),X20430)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__bin__lemma])]) ).
fof(i_0_8373,plain,
! [X23721,X23722,X23723] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X23723),X23722),hAPP(hAPP(c_Set_Oinsert(X23723),X23721),c_Orderings_Obot__class_Obot(tc_fun(X23723,tc_HOL_Obool)))))
| X23722 = X23721 )
& ( X23722 != X23721
| hBOOL(hAPP(hAPP(c_member(X23723),X23722),hAPP(hAPP(c_Set_Oinsert(X23723),X23721),c_Orderings_Obot__class_Obot(tc_fun(X23723,tc_HOL_Obool))))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singleton__iff])]) ).
fof(i_0_8374,plain,
! [X23718,X23719,X23720] :
( ~ hBOOL(hAPP(hAPP(c_member(X23720),X23719),hAPP(hAPP(c_Set_Oinsert(X23720),X23718),c_Orderings_Obot__class_Obot(tc_fun(X23720,tc_HOL_Obool)))))
| X23719 = X23718 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singletonE])]) ).
fof(i_0_8375,plain,
! [X28192,X28193,X28194,X28195,X28196] :
( X28196 != hAPP(X28195,X28194)
| hBOOL(hAPP(hAPP(c_member(X28193),X28196),hAPP(c_Set_Oimage(X28192,X28193,X28195),c_Orderings_Otop__class_Otop(tc_fun(X28192,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range__eqI])]) ).
fof(i_0_8376,plain,
! [X28768,X28769,X28770,X28771] :
( ( X28771 != c_Orderings_Obot__class_Obot(tc_fun(X28770,tc_HOL_Obool))
| hAPP(c_Set_Oimage(tc_prod(X28770,X28769),X28769,c_Product__Type_Osnd(X28770,X28769)),hAPP(hAPP(c_Product__Type_OSigma(X28770,X28769),X28771),hAPP(c_COMBK(tc_fun(X28769,tc_HOL_Obool),X28770),X28768))) = c_Orderings_Obot__class_Obot(tc_fun(X28769,tc_HOL_Obool)) )
& ( X28771 = c_Orderings_Obot__class_Obot(tc_fun(X28770,tc_HOL_Obool))
| hAPP(c_Set_Oimage(tc_prod(X28770,X28769),X28769,c_Product__Type_Osnd(X28770,X28769)),hAPP(hAPP(c_Product__Type_OSigma(X28770,X28769),X28771),hAPP(c_COMBK(tc_fun(X28769,tc_HOL_Obool),X28770),X28768))) = X28768 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snd__image__times])]) ).
fof(i_0_8377,plain,
! [X28764,X28765,X28766,X28767] :
( ( X28767 != c_Orderings_Obot__class_Obot(tc_fun(X28766,tc_HOL_Obool))
| hAPP(c_Set_Oimage(tc_prod(X28765,X28766),X28765,c_Product__Type_Ofst(X28765,X28766)),hAPP(hAPP(c_Product__Type_OSigma(X28765,X28766),X28764),hAPP(c_COMBK(tc_fun(X28766,tc_HOL_Obool),X28765),X28767))) = c_Orderings_Obot__class_Obot(tc_fun(X28765,tc_HOL_Obool)) )
& ( X28767 = c_Orderings_Obot__class_Obot(tc_fun(X28766,tc_HOL_Obool))
| hAPP(c_Set_Oimage(tc_prod(X28765,X28766),X28765,c_Product__Type_Ofst(X28765,X28766)),hAPP(hAPP(c_Product__Type_OSigma(X28765,X28766),X28764),hAPP(c_COMBK(tc_fun(X28766,tc_HOL_Obool),X28765),X28767))) = X28764 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fst__image__times])]) ).
fof(i_0_8378,plain,
! [X23086,X23087,X23088,X23089,X23090] :
( ( X23089 = X23086
| X23089 = X23087
| hAPP(hAPP(c_Set_Oinsert(X23090),X23089),hAPP(hAPP(c_Set_Oinsert(X23090),X23088),c_Orderings_Obot__class_Obot(tc_fun(X23090,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X23090),X23087),hAPP(hAPP(c_Set_Oinsert(X23090),X23086),c_Orderings_Obot__class_Obot(tc_fun(X23090,tc_HOL_Obool)))) )
& ( X23088 = X23087
| X23089 = X23087
| hAPP(hAPP(c_Set_Oinsert(X23090),X23089),hAPP(hAPP(c_Set_Oinsert(X23090),X23088),c_Orderings_Obot__class_Obot(tc_fun(X23090,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X23090),X23087),hAPP(hAPP(c_Set_Oinsert(X23090),X23086),c_Orderings_Obot__class_Obot(tc_fun(X23090,tc_HOL_Obool)))) )
& ( X23089 = X23086
| X23088 = X23086
| hAPP(hAPP(c_Set_Oinsert(X23090),X23089),hAPP(hAPP(c_Set_Oinsert(X23090),X23088),c_Orderings_Obot__class_Obot(tc_fun(X23090,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X23090),X23087),hAPP(hAPP(c_Set_Oinsert(X23090),X23086),c_Orderings_Obot__class_Obot(tc_fun(X23090,tc_HOL_Obool)))) )
& ( X23088 = X23087
| X23088 = X23086
| hAPP(hAPP(c_Set_Oinsert(X23090),X23089),hAPP(hAPP(c_Set_Oinsert(X23090),X23088),c_Orderings_Obot__class_Obot(tc_fun(X23090,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X23090),X23087),hAPP(hAPP(c_Set_Oinsert(X23090),X23086),c_Orderings_Obot__class_Obot(tc_fun(X23090,tc_HOL_Obool)))) )
& ( X23089 != X23087
| X23088 != X23086
| hAPP(hAPP(c_Set_Oinsert(X23090),X23089),hAPP(hAPP(c_Set_Oinsert(X23090),X23088),c_Orderings_Obot__class_Obot(tc_fun(X23090,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(X23090),X23087),hAPP(hAPP(c_Set_Oinsert(X23090),X23086),c_Orderings_Obot__class_Obot(tc_fun(X23090,tc_HOL_Obool)))) )
& ( X23089 != X23086
| X23088 != X23087
| hAPP(hAPP(c_Set_Oinsert(X23090),X23089),hAPP(hAPP(c_Set_Oinsert(X23090),X23088),c_Orderings_Obot__class_Obot(tc_fun(X23090,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(X23090),X23087),hAPP(hAPP(c_Set_Oinsert(X23090),X23086),c_Orderings_Obot__class_Obot(tc_fun(X23090,tc_HOL_Obool)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_doubleton__eq__iff])])]) ).
fof(i_0_8379,plain,
! [X25670,X25671,X25672,X25673,X25674] :
( ~ class_Rings_Ocomm__semiring__1(X25674)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25673),X25672))
| ~ hBOOL(hAPP(hAPP(c_member(X25673),X25671),X25672))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X25674),hAPP(X25670,X25671)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25673,X25674),X25670),X25672))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__setprod])]) ).
fof(i_0_8380,plain,
! [X32843,X32844,X32845,X32846,X32847] :
( ( X32847 != X32844
| hAPP(hAPP(c_List_Onth(X32846),hAPP(hAPP(c_List_Olist__update(X32846,X32845),X32847),X32843)),X32844) = X32843
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32847),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32846)),X32845))) )
& ( X32847 = X32844
| hAPP(hAPP(c_List_Onth(X32846),hAPP(hAPP(c_List_Olist__update(X32846,X32845),X32847),X32843)),X32844) = hAPP(hAPP(c_List_Onth(X32846),X32845),X32844)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32847),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32846)),X32845))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__list__update])])]) ).
fof(i_0_8381,plain,
! [X23490,X23491,X23492,X23493] :
( ~ class_Orderings_Oorder(X23493)
| ~ c_Orderings_Oorder_Omono(tc_Nat_Onat,X23493,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23492)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23491),X23490))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23493),hAPP(X23492,X23491)),hAPP(X23492,X23490))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_OmonoD])]) ).
fof(i_0_8382,plain,
! [X19346,X19347,X19348] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19348),X19346))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19348),X19347)),X19346)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19347),X19346))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19348),X19347)),X19346)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5697])])]) ).
fof(i_0_8383,plain,
! [X19343,X19344,X19345] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19345),X19344)),X19343))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19345),X19343)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD1])]) ).
fof(i_0_8384,plain,
! [X19340,X19341,X19342] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19342),X19341)),X19340))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19341),X19340)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD2])]) ).
fof(i_0_8385,plain,
! [X18332,X18333,X18334] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18334),X18333)),X18332))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18334),X18332)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__lessD1])]) ).
fof(i_0_8386,plain,
! [X20529,X20530] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20530))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20530),hAPP(c_Nat_OSuc,X20529))),X20530)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__less])]) ).
fof(i_0_8387,plain,
! [X17937,X17938,X17939,X17940] :
( ( ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X17940),X17939,hAPP(c_Nat_OSuc,X17938),X17937)
| c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X17940)),X17939,X17938,X17937) )
& ( ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X17940)),X17939,X17938,X17937)
| c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X17940),X17939,hAPP(c_Nat_OSuc,X17938),X17937) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln_Oequations_I9_J])]) ).
fof(i_0_8388,plain,
! [X17925,X17926,X17927,X17928] :
( ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X17928)),X17927,X17926,X17925)
| c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X17928),X17927,hAPP(c_Nat_OSuc,X17926),X17925) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln_OBody])]) ).
fof(i_0_8389,plain,
! [X27133,X27134,X27135,X27136,X27137] :
( hAPP(X27137,X27136) != c_Option_Ooption_ONone(X27135)
| c_Map_Oran(X27134,X27135,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27134,tc_Option_Ooption(X27135)),X27137),X27136),hAPP(c_Option_Ooption_OSome(X27135),X27133))) = hAPP(hAPP(c_Set_Oinsert(X27135),X27133),c_Map_Oran(X27134,X27135,X27137)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ran__map__upd])]) ).
fof(i_0_8390,plain,
! [X26846,X26847,X26848,X26849] :
( ~ class_Orderings_Olinorder(X26849)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26849),X26848),X26847))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26849),X26847),X26846))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26849,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26849,X26848),X26847)),c_SetInterval_Oord__class_OatLeastAtMost(X26849,X26847,X26846)) = c_SetInterval_Oord__class_OatLeastAtMost(X26849,X26848,X26846) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I21_J])]) ).
fof(i_0_8391,plain,
! [X26850,X26851,X26852] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26852),X26851))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26852),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26851),X26850)) = 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,X26852),X26851)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26851),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26851),X26850))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__add__Un])]) ).
fof(i_0_8392,plain,
! [X23295,X23296,X23297] : hAPP(hAPP(c_Set_Oinsert(X23297),X23296),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23297,tc_HOL_Obool)),X23295),hAPP(hAPP(c_Set_Oinsert(X23297),X23296),c_Orderings_Obot__class_Obot(tc_fun(X23297,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(X23297),X23296),X23295),
inference(variable_rename,[status(thm)],[fact_insert__Diff__single]) ).
cnf(i_0_8393,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_8394,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_8395,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_8396,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_8397,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_8398,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_8399,plain,
! [X25461,X25462,X25463] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25463),X25462))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25463),X25462)),hAPP(c_Finite__Set_Ocard(X25463),hAPP(hAPP(c_Set_Oinsert(X25463),X25461),X25462)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__insert__le])]) ).
fof(i_0_8400,plain,
! [X18523,X18524,X18525] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18525)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18524)),X18523)) = 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),X18525),X18524))),X18523),
inference(variable_rename,[status(thm)],[fact_zadd__int__left]) ).
fof(i_0_8401,plain,
! [X31297,X31298,X31299,X31301] :
( ( hBOOL(hAPP(hAPP(c_member(X31299),esk402_3(X31297,X31298,X31299)),X31297))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X31299),X31298),c_Complete__Lattice_OSup__class_OSup(X31299,X31297)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X31299)
| ~ class_Orderings_Olinorder(X31299) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X31299),X31298),esk402_3(X31297,X31298,X31299)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X31299),X31298),c_Complete__Lattice_OSup__class_OSup(X31299,X31297)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X31299)
| ~ class_Orderings_Olinorder(X31299) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X31299),X31301),X31297))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X31299),X31298),X31301))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X31299),X31298),c_Complete__Lattice_OSup__class_OSup(X31299,X31297)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X31299)
| ~ class_Orderings_Olinorder(X31299) ) ),
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_8402,plain,
! [X24545] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X24545))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X24545)))
| ~ c_Nat__Transfer_Onat__set(X24545) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X24545)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X24545))
| ~ c_Nat__Transfer_Onat__set(X24545) ) ),
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_8403,plain,
hAPP(c_Relation_OImage(X1,X1,c_Relation_OId(X1)),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_5703]) ).
fof(i_0_8404,plain,
! [X23547,X23548] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X23548)),hAPP(c_Int_Onat,X23547)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23548),X23547))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23547))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23548)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23548),X23547))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X23548)),hAPP(c_Int_Onat,X23547)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23547))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23548)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__relations_I4_J])])]) ).
fof(i_0_8405,plain,
! [X19152,X19153] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X19153)),hAPP(c_Int_Onat,X19152)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19153),X19152))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19152))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19153)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19153),X19152))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X19153)),hAPP(c_Int_Onat,X19152)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19152))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19153)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__relations_I3_J])])]) ).
fof(i_0_8406,plain,
! [X19687,X19688] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X19688)),hAPP(c_Int_Onat,X19687)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19688),X19687))
| ~ 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__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19688)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19688),X19687))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X19688)),hAPP(c_Int_Onat,X19687)))
| ~ 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__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19688)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__relations_I2_J])])]) ).
fof(i_0_8407,plain,
! [X25789,X25790,X25791] :
( ~ class_Orderings_Olinorder(X25791)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25791),X25790),X25789))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25791,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X25791,X25790,X25789)),hAPP(hAPP(c_Set_Oinsert(X25791),X25789),c_Orderings_Obot__class_Obot(tc_fun(X25791,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(X25791,X25790,X25789) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I4_J])]) ).
fof(i_0_8408,plain,
! [X23736,X23737,X23738,X23739] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X23739),X23738),X23737))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23739,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X23739),X23738),X23736)),X23737) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23739,tc_HOL_Obool)),X23736),X23737) )
& ( hBOOL(hAPP(hAPP(c_member(X23739),X23738),X23737))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23739,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X23739),X23738),X23736)),X23737) = hAPP(hAPP(c_Set_Oinsert(X23739),X23738),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23739,tc_HOL_Obool)),X23736),X23737)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5704])]) ).
fof(i_0_8409,plain,
! [X17444,X17445,X17446,X17447,X17448,X17449] :
( ~ hBOOL(hAPP(X17449,X17448))
| ~ c_Natural_Oevaln(X17447,X17448,X17446,X17445)
| c_Natural_Oevaln(c_Com_Ocom_OCond(X17449,X17447,X17444),X17448,X17446,X17445) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln_OIfTrue])]) ).
fof(i_0_8410,plain,
! [X30070,X30071,X30072] :
( ( hBOOL(hAPP(hAPP(c_member(X30072),esk362_3(X30070,X30071,X30072)),X30071))
| ~ hBOOL(hAPP(hAPP(c_member(X30072),X30070),X30071))
| c_Big__Operators_Olinorder__class_OMin(X30072,X30071) = X30070
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30072),X30071))
| ~ class_Orderings_Olinorder(X30072) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30072),X30070),esk362_3(X30070,X30071,X30072)))
| ~ hBOOL(hAPP(hAPP(c_member(X30072),X30070),X30071))
| c_Big__Operators_Olinorder__class_OMin(X30072,X30071) = X30070
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30072),X30071))
| ~ class_Orderings_Olinorder(X30072) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__eqI])])])]) ).
fof(i_0_8411,plain,
! [X33072,X33073,X33074,X33075,X33076] : hAPP(hAPP(c_List_Omap(X33076,X33075),X33074),hAPP(hAPP(c_List_Oappend(X33076),X33073),X33072)) = hAPP(hAPP(c_List_Oappend(X33075),hAPP(hAPP(c_List_Omap(X33076,X33075),X33074),X33073)),hAPP(hAPP(c_List_Omap(X33076,X33075),X33074),X33072)),
inference(variable_rename,[status(thm)],[fact_map__append]) ).
fof(i_0_8412,plain,
! [X31444,X31445] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X31445,tc_HOL_Obool)),esk408_2(X31444,X31445)),X31444))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X31445),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31445,tc_HOL_Obool),X31444)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X31445,tc_HOL_Obool)),X31444)) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31445),esk408_2(X31444,X31445)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X31445),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31445,tc_HOL_Obool),X31444)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X31445,tc_HOL_Obool)),X31444)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Union])])])]) ).
fof(i_0_8413,plain,
! [X23384,X23385,X23386,X23387] :
( ~ class_Divides_Osemiring__div(X23387)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23387),X23386),X23385))
| hAPP(hAPP(c_Power_Opower__class_Opower(X23387),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23387),X23385),X23386)),X23384) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23387),hAPP(hAPP(c_Power_Opower__class_Opower(X23387),X23385),X23384)),hAPP(hAPP(c_Power_Opower__class_Opower(X23387),X23386),X23384)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__power])]) ).
fof(i_0_8414,plain,
! [X20148,X20149] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20149))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X20148))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20149),X20148)),X20149)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__div__less__self])]) ).
fof(i_0_8415,plain,
! [X20432,X20433] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20433))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20432))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20432),X20433)),X20432)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less])]) ).
fof(i_0_8416,plain,
! [X20114,X20115] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X20115))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20114))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20114),X20115)),X20114)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__less__dividend])]) ).
cnf(i_0_8417,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_8418,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_8419,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_8420,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_8421,plain,
! [X24790,X24791,X24792,X24793] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24793,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X24793),X24792),X24791)),hAPP(hAPP(c_Set_Oinsert(X24793),X24792),X24790)) = hAPP(hAPP(c_Set_Oinsert(X24793),X24792),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24793,tc_HOL_Obool)),X24791),X24790)),
inference(variable_rename,[status(thm)],[fact_insert__inter__insert]) ).
fof(i_0_8422,plain,
! [X20133,X20134] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20134),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)),X20133))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20134),X20133)),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_8423,plain,
! [X20127,X20128] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20128))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20127),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),X20128),X20127)),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_8424,plain,
! [X20059,X20060] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20060),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)),X20059))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20060),X20059)),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_8425,plain,
! [X19354,X19355,X19356,X19357,X19358] :
( ~ c_Natural_Oevaln(X19358,X19357,X19356,X19355)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19356),X19354))
| c_Natural_Oevaln(X19358,X19357,X19354,X19355) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln__nonstrict])]) ).
fof(i_0_8426,plain,
! [X23236,X23237,X23238,X23239] :
( ~ class_Divides_Osemiring__div(X23239)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23239),X23238),c_Divides_Odiv__class_Omod(X23239,X23237,X23236)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23239),X23238),X23236))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23239),X23238),X23237)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mod__imp__dvd])]) ).
fof(i_0_8427,plain,
! [X23224,X23225,X23226,X23227] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23227),X23226),c_Divides_Odiv__class_Omod(X23227,X23224,X23225)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23227),X23226),X23224))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23227),X23226),X23225))
| ~ class_Divides_Osemiring__div(X23227) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23227),X23226),X23224))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23227),X23226),c_Divides_Odiv__class_Omod(X23227,X23224,X23225)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23227),X23226),X23225))
| ~ class_Divides_Osemiring__div(X23227) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mod__iff])])]) ).
fof(i_0_8428,plain,
! [X20181,X20182,X20183] :
( ~ class_Divides_Osemiring__div(X20183)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20183),c_Divides_Odiv__class_Omod(X20183,X20182,X20181)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20183),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20183),X20182),X20181)),X20181)) = X20182 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__div__class_Omod__div__equality_H])]) ).
fof(i_0_8429,plain,
! [X21517,X21518,X21519] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21519),X21518),c_Groups_Ozero__class_Ozero(X21519)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21519),c_Groups_Ozero__class_Ozero(X21519)),X21518))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21519),c_Groups_Ozero__class_Ozero(X21519)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21519),X21518),X21517)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21519) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21519),X21517),c_Groups_Ozero__class_Ozero(X21519)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21519),c_Groups_Ozero__class_Ozero(X21519)),X21518))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21519),c_Groups_Ozero__class_Ozero(X21519)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21519),X21518),X21517)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21519) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21519),X21518),c_Groups_Ozero__class_Ozero(X21519)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21519),c_Groups_Ozero__class_Ozero(X21519)),X21517))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21519),c_Groups_Ozero__class_Ozero(X21519)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21519),X21518),X21517)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21519) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21519),X21517),c_Groups_Ozero__class_Ozero(X21519)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21519),c_Groups_Ozero__class_Ozero(X21519)),X21517))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21519),c_Groups_Ozero__class_Ozero(X21519)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21519),X21518),X21517)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21519) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21519),c_Groups_Ozero__class_Ozero(X21519)),X21518))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21519),c_Groups_Ozero__class_Ozero(X21519)),X21517))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21519),c_Groups_Ozero__class_Ozero(X21519)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21519),X21518),X21517)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21519) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21519),X21518),c_Groups_Ozero__class_Ozero(X21519)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21519),X21517),c_Groups_Ozero__class_Ozero(X21519)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21519),c_Groups_Ozero__class_Ozero(X21519)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21519),X21518),X21517)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21519) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__divide__iff])])]) ).
fof(i_0_8430,plain,
! [X19452,X19453,X19454] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19454),X19453),c_Groups_Ozero__class_Ozero(X19454)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19454),c_Groups_Ozero__class_Ozero(X19454)),X19453))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19454),c_Groups_Ozero__class_Ozero(X19454)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19454),X19453),X19452)))
| ~ class_Rings_Olinordered__ring__strict(X19454) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19454),X19452),c_Groups_Ozero__class_Ozero(X19454)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19454),c_Groups_Ozero__class_Ozero(X19454)),X19453))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19454),c_Groups_Ozero__class_Ozero(X19454)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19454),X19453),X19452)))
| ~ class_Rings_Olinordered__ring__strict(X19454) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19454),X19453),c_Groups_Ozero__class_Ozero(X19454)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19454),c_Groups_Ozero__class_Ozero(X19454)),X19452))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19454),c_Groups_Ozero__class_Ozero(X19454)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19454),X19453),X19452)))
| ~ class_Rings_Olinordered__ring__strict(X19454) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19454),X19452),c_Groups_Ozero__class_Ozero(X19454)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19454),c_Groups_Ozero__class_Ozero(X19454)),X19452))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19454),c_Groups_Ozero__class_Ozero(X19454)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19454),X19453),X19452)))
| ~ class_Rings_Olinordered__ring__strict(X19454) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19454),c_Groups_Ozero__class_Ozero(X19454)),X19453))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19454),c_Groups_Ozero__class_Ozero(X19454)),X19452))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19454),c_Groups_Ozero__class_Ozero(X19454)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19454),X19453),X19452)))
| ~ class_Rings_Olinordered__ring__strict(X19454) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19454),X19453),c_Groups_Ozero__class_Ozero(X19454)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19454),X19452),c_Groups_Ozero__class_Ozero(X19454)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19454),c_Groups_Ozero__class_Ozero(X19454)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19454),X19453),X19452)))
| ~ class_Rings_Olinordered__ring__strict(X19454) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__mult__iff])])]) ).
fof(i_0_8431,plain,
! [X21554,X21555,X21556] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21556),X21555),c_Groups_Ozero__class_Ozero(X21556)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21556),c_Groups_Ozero__class_Ozero(X21556)),X21555))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21556),c_Groups_Ozero__class_Ozero(X21556)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21556),X21555),X21554)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21556) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21556),X21554),c_Groups_Ozero__class_Ozero(X21556)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21556),c_Groups_Ozero__class_Ozero(X21556)),X21555))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21556),c_Groups_Ozero__class_Ozero(X21556)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21556),X21555),X21554)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21556) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21556),X21555),c_Groups_Ozero__class_Ozero(X21556)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21556),c_Groups_Ozero__class_Ozero(X21556)),X21554))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21556),c_Groups_Ozero__class_Ozero(X21556)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21556),X21555),X21554)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21556) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21556),X21554),c_Groups_Ozero__class_Ozero(X21556)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21556),c_Groups_Ozero__class_Ozero(X21556)),X21554))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21556),c_Groups_Ozero__class_Ozero(X21556)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21556),X21555),X21554)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21556) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21556),c_Groups_Ozero__class_Ozero(X21556)),X21555))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21556),c_Groups_Ozero__class_Ozero(X21556)),X21554))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21556),c_Groups_Ozero__class_Ozero(X21556)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21556),X21555),X21554)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21556) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21556),X21555),c_Groups_Ozero__class_Ozero(X21556)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21556),X21554),c_Groups_Ozero__class_Ozero(X21556)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21556),c_Groups_Ozero__class_Ozero(X21556)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21556),X21555),X21554)))
| ~ class_Fields_Olinordered__field__inverse__zero(X21556) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__divide__iff])])]) ).
cnf(i_0_8432,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_8433,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_8434,plain,
! [X19351,X19352,X19353] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19353),X19352))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19351),X19353)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19351),X19352))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__left__mono])]) ).
fof(i_0_8435,plain,
! [X20359,X20360,X20361] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20361),X20360))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20361),X20359)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20360),X20359))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__le__mono])]) ).
fof(i_0_8436,plain,
! [X20356,X20357,X20358] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20358),X20357))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20356),X20357)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20356),X20358))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__le__mono2])]) ).
fof(i_0_8437,plain,
! [X20009,X20010,X20011] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20011),X20010))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20011),X20009)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20010),X20009))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__le__mono])]) ).
fof(i_0_8438,plain,
! [X19053,X19054,X19055] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19055),X19054))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19055),X19053)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19054),X19053))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono1])]) ).
fof(i_0_8439,plain,
! [X19056,X19057,X19058] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19058),X19057))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19056),X19058)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19056),X19057))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono2])]) ).
fof(i_0_8440,plain,
! [X19333,X19334,X19335] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19335),X19334))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19335),X19333)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19334),X19333))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono1])]) ).
cnf(i_0_8441,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_8442,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_8443,plain,
! [X18591,X18592,X18593] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18593),X18592))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18593),X18591)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18592),X18591))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__strict__right__mono])]) ).
fof(i_0_8444,plain,
! [X18343,X18344,X18345] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18345),X18344))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18345),X18343)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18344),X18343))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono1])]) ).
fof(i_0_8445,plain,
! [X33624,X33625,X33626] :
( ~ class_Orderings_Olinorder(X33626)
| c_Big__Operators_Olinorder__class_OMin(X33626,hAPP(c_List_Oset(X33626),hAPP(hAPP(c_List_Olist_OCons(X33626),X33625),X33624))) = hAPP(c_List_Ofoldl(X33626,X33626,c_Orderings_Oord__class_Omin(X33626),X33625),X33624) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__fin__set__fold])]) ).
fof(i_0_8446,plain,
! [X33627,X33628,X33629] :
( ~ class_Orderings_Olinorder(X33629)
| c_Big__Operators_Olinorder__class_OMax(X33629,hAPP(c_List_Oset(X33629),hAPP(hAPP(c_List_Olist_OCons(X33629),X33628),X33627))) = hAPP(c_List_Ofoldl(X33629,X33629,c_Orderings_Oord__class_Omax(X33629),X33628),X33627) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__fin__set__fold])]) ).
fof(i_0_8447,plain,
! [X33621,X33622,X33623] :
( ~ class_Lattices_Olattice(X33623)
| c_Big__Operators_Olattice__class_OInf__fin(X33623,hAPP(c_List_Oset(X33623),hAPP(hAPP(c_List_Olist_OCons(X33623),X33622),X33621))) = hAPP(c_List_Ofoldl(X33623,X33623,c_Lattices_Osemilattice__inf__class_Oinf(X33623),X33622),X33621) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin__set__fold])]) ).
fof(i_0_8448,plain,
! [X33618,X33619,X33620] :
( ~ class_Lattices_Olattice(X33620)
| c_Big__Operators_Olattice__class_OSup__fin(X33620,hAPP(c_List_Oset(X33620),hAPP(hAPP(c_List_Olist_OCons(X33620),X33619),X33618))) = hAPP(c_List_Ofoldl(X33620,X33620,c_Lattices_Osemilattice__sup__class_Osup(X33620),X33619),X33618) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin__set__fold])]) ).
fof(i_0_8449,plain,
! [X20550,X20551,X20552] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20552),X20551))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20551),X20552))),X20550) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20551)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20552),X20550)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq2])]) ).
fof(i_0_8450,plain,
! [X20184,X20185,X20186] :
( ~ class_Divides_Osemiring__div(X20186)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20186),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20186),X20185),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20186),X20184),X20185))),c_Divides_Odiv__class_Omod(X20186,X20184,X20185)) = X20184 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__equality2])]) ).
cnf(i_0_8451,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_8452,plain,
! [X32743,X32744,X32745,X32746,X32747] : hAPP(hAPP(c_List_Olist__update(X32747,hAPP(hAPP(c_List_Olist_OCons(X32747),X32746),X32745)),hAPP(c_Nat_OSuc,X32744)),X32743) = hAPP(hAPP(c_List_Olist_OCons(X32747),X32746),hAPP(hAPP(c_List_Olist__update(X32747,X32745),X32744),X32743)),
inference(variable_rename,[status(thm)],[fact_list__update__code_I3_J]) ).
fof(i_0_8453,plain,
! [X18255,X18256,X18257,X18258,X18259,X18260] :
( ( X18258 = X18256
| c_Nitpick_Opair__box_OPairBox(X18260,X18259,X18258,X18257) != c_Nitpick_Opair__box_OPairBox(X18260,X18259,X18256,X18255) )
& ( X18257 = X18255
| c_Nitpick_Opair__box_OPairBox(X18260,X18259,X18258,X18257) != c_Nitpick_Opair__box_OPairBox(X18260,X18259,X18256,X18255) )
& ( X18258 != X18256
| X18257 != X18255
| c_Nitpick_Opair__box_OPairBox(X18260,X18259,X18258,X18257) = c_Nitpick_Opair__box_OPairBox(X18260,X18259,X18256,X18255) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__box_Oinject])])]) ).
fof(i_0_8454,plain,
! [X18502,X18503,X18504,X18505,X18506] :
( c_Sum__Type_OSumr(X18506,X18505,X18504,X18503) != c_Sum__Type_OSumr(X18506,X18505,X18504,X18502)
| X18503 = X18502 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sumr__inject])]) ).
fof(i_0_8455,plain,
! [X18507,X18508,X18509,X18510,X18511] :
( c_Sum__Type_OSuml(X18511,X18510,X18509,X18508) != c_Sum__Type_OSuml(X18511,X18510,X18509,X18507)
| X18508 = X18507 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suml__inject])]) ).
fof(i_0_8456,plain,
! [X28383,X28384,X28385,X28386,X28387,X28388] :
( hAPP(X28388,X28387) != X28386
| ~ hBOOL(hAPP(hAPP(c_member(X28385),X28386),X28384))
| hBOOL(hAPP(hAPP(c_member(X28383),X28387),hAPP(c_Set_Ovimage(X28383,X28385,X28388),X28384))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimageI])]) ).
fof(i_0_8457,plain,
! [X24240,X24241,X24242,X24243,X24244,X24245] :
( X24245 != hAPP(X24244,X24243)
| ~ hBOOL(hAPP(hAPP(c_member(X24242),X24243),X24241))
| hBOOL(hAPP(hAPP(c_member(X24240),X24245),hAPP(c_Set_Oimage(X24242,X24240,X24244),X24241))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__eqI])]) ).
fof(i_0_8458,plain,
! [X24291,X24292,X24293,X24294,X24295,X24296] :
( ~ hBOOL(hAPP(hAPP(c_member(X24296),X24295),X24294))
| X24293 != hAPP(X24292,X24295)
| hBOOL(hAPP(hAPP(c_member(X24291),X24293),hAPP(c_Set_Oimage(X24296,X24291,X24292),X24294))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__image__eqI])]) ).
fof(i_0_8459,plain,
! [X17438,X17439,X17440,X17441,X17442,X17443] :
( hBOOL(hAPP(X17443,X17442))
| ~ c_Natural_Oevaln(X17441,X17442,X17440,X17439)
| c_Natural_Oevaln(c_Com_Ocom_OCond(X17443,X17438,X17441),X17442,X17440,X17439) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5710])]) ).
fof(i_0_8460,plain,
! [X26610,X26611,X26612,X26613,X26614,X26615] :
( ( hAPP(X26613,X26611) != hAPP(X26613,X26610)
| X26611 = X26610
| ~ hBOOL(hAPP(hAPP(c_member(X26615),X26610),X26612))
| ~ hBOOL(hAPP(hAPP(c_member(X26615),X26611),X26612))
| ~ c_Fun_Oinj__on(X26615,X26614,X26613,X26612) )
& ( X26611 != X26610
| hAPP(X26613,X26611) = hAPP(X26613,X26610)
| ~ hBOOL(hAPP(hAPP(c_member(X26615),X26610),X26612))
| ~ hBOOL(hAPP(hAPP(c_member(X26615),X26611),X26612))
| ~ c_Fun_Oinj__on(X26615,X26614,X26613,X26612) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff])])]) ).
fof(i_0_8461,plain,
! [X26616,X26617,X26618,X26619,X26620,X26621] :
( ~ c_Fun_Oinj__on(X26621,X26620,X26619,X26618)
| hAPP(X26619,X26617) != hAPP(X26619,X26616)
| ~ hBOOL(hAPP(hAPP(c_member(X26621),X26617),X26618))
| ~ hBOOL(hAPP(hAPP(c_member(X26621),X26616),X26618))
| X26617 = X26616 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__onD])]) ).
fof(i_0_8462,plain,
! [X26604,X26605,X26606,X26607,X26608,X26609] :
( ~ c_Fun_Oinj__on(X26609,X26608,X26607,X26606)
| X26605 = X26604
| ~ hBOOL(hAPP(hAPP(c_member(X26609),X26605),X26606))
| ~ hBOOL(hAPP(hAPP(c_member(X26609),X26604),X26606))
| hAPP(X26607,X26605) != hAPP(X26607,X26604) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__contraD])]) ).
fof(i_0_8463,plain,
! [X20610,X20611] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20610),X20611))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20610),X20611) = 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)),X20611)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20610),X20611))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20610),X20611) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20610),X20611)),X20611))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20611)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5711])])]) ).
fof(i_0_8464,plain,
! [X20612,X20613] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20613))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20612),X20613))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20612),X20613) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20612),X20613)),X20613)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5712])]) ).
fof(i_0_8465,plain,
! [X20122,X20123] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20122),X20123))
| ~ 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),X20123),X20122)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20123)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20122))
| ~ 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),X20123),X20122)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20123)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20122),X20123))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20122))
| 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),X20123),X20122)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20123)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonneg1__imp__zdiv__pos__iff])])]) ).
fof(i_0_8466,plain,
! [X27583,X27584,X27585,X27586,X27587] :
( ~ c_Finite__Set_Ofolding__one__idem(X27587,X27586,X27585)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27587),X27584))
| X27583 = c_Orderings_Obot__class_Obot(tc_fun(X27587,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27587,tc_HOL_Obool)),X27583),X27584))
| hAPP(hAPP(X27586,hAPP(X27585,X27583)),hAPP(X27585,X27584)) = hAPP(X27585,X27584) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Osubset__idem])]) ).
fof(i_0_8467,plain,
! [X30425,X30426,X30427] :
( hAPP(hAPP(c_Relation_Orel__comp(X30427,X30427,X30427),hAPP(c_Relation_Oconverse(X30427,X30427),X30426)),X30426) != X30426
| hAPP(c_Relation_ODomain(X30427,X30427),X30426) != X30425
| c_Equiv__Relations_Oequiv(X30427,X30425,X30426) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comp__equivI])]) ).
fof(i_0_8468,plain,
! [X18136,X18137,X18138] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(X18138,X18137,X18136)) = 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),X18137)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X18136))),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_8469,plain,
! [X19114,X19115,X19116,X19117,X19118] :
( ~ class_Orderings_Oord(X19118)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19117,X19118)),X19116),X19115))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19118),hAPP(X19116,X19114)),hAPP(X19115,X19114))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funD])]) ).
fof(i_0_8470,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__funE])]) ).
fof(i_0_8471,plain,
! [X31751,X31752,X31753,X31754,X31755] :
( hAPP(hAPP(c_List_Omap(X31755,X31754),X31753),X31752) != hAPP(hAPP(c_List_Omap(X31755,X31754),X31753),X31751)
| ~ c_Fun_Oinj__on(X31755,X31754,X31753,c_Orderings_Otop__class_Otop(tc_fun(X31755,tc_HOL_Obool)))
| X31752 = X31751 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__injective])]) ).
fof(i_0_8472,plain,
! [X31743,X31744,X31745,X31746,X31747] :
( ( hAPP(hAPP(c_List_Omap(X31747,X31746),X31745),X31744) != hAPP(hAPP(c_List_Omap(X31747,X31746),X31745),X31743)
| X31744 = X31743
| ~ c_Fun_Oinj__on(X31747,X31746,X31745,c_Orderings_Otop__class_Otop(tc_fun(X31747,tc_HOL_Obool))) )
& ( X31744 != X31743
| hAPP(hAPP(c_List_Omap(X31747,X31746),X31745),X31744) = hAPP(hAPP(c_List_Omap(X31747,X31746),X31745),X31743)
| ~ c_Fun_Oinj__on(X31747,X31746,X31745,c_Orderings_Otop__class_Otop(tc_fun(X31747,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_8473,plain,
! [X32835,X32836,X32837,X32838] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32838),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32837)),X32836)))
| hAPP(hAPP(c_List_Onth(X32837),hAPP(hAPP(c_List_Olist__update(X32837,X32836),X32838),X32835)),X32838) = X32835 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__list__update__eq])]) ).
fof(i_0_8474,plain,
! [X27305,X27306,X27307] :
( ~ class_Groups_Ocomm__monoid__add(X27307)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27307),X27306),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X27305))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27307),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27307),X27306),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X27305))),hAPP(X27306,hAPP(c_Nat_OSuc,X27305))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__atMost__Suc])]) ).
fof(i_0_8475,plain,
! [X26828,X26829,X26830,X26831] :
( ~ class_Orderings_Olinorder(X26831)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26831),X26830),X26829))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26831),X26829),X26828))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26831,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26831,X26830),X26829)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26831,X26829),X26828)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26831,X26830),X26828) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I17_J])]) ).
fof(i_0_8476,plain,
! [X33829,X33830] : c_List_Obutlast(X33830,X33829) = hAPP(hAPP(c_List_Otake(X33830),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33830)),X33829)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X33829),
inference(variable_rename,[status(thm)],[fact_butlast__conv__take]) ).
fof(i_0_8477,plain,
! [X28809,X28810,X28811] :
( ~ class_Lattices_Osemilattice__inf(X28811)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28811),X28810))
| ~ hBOOL(hAPP(hAPP(c_member(X28811),X28809),X28810))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28811),hAPP(c_Finite__Set_Ofold1(X28811,c_Lattices_Osemilattice__inf__class_Oinf(X28811)),X28810)),X28809)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__belowI])]) ).
fof(i_0_8478,plain,
! [X28820,X28821,X28822] :
( ~ class_Orderings_Olinorder(X28822)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28822),X28821))
| ~ hBOOL(hAPP(hAPP(c_member(X28822),X28820),X28821))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28822),hAPP(c_Finite__Set_Ofold1(X28822,c_Orderings_Oord__class_Omin(X28822)),X28821)),X28820)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofold1__belowI])]) ).
fof(i_0_8479,plain,
! [X19700] : ~ 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,X19700))))),
inference(variable_rename,[status(thm)],[i_0_5713]) ).
fof(i_0_8480,plain,
! [X34159,X34160,X34161,X34162] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X34161),X34162),hAPP(c_List_Oset(X34161),X34159)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X34161),X34160),X34162))
| ~ c_List_Olinorder__class_Osorted(X34161,hAPP(hAPP(c_List_Olist_OCons(X34161),X34160),X34159))
| ~ class_Orderings_Olinorder(X34161) )
& ( c_List_Olinorder__class_Osorted(X34161,X34159)
| ~ c_List_Olinorder__class_Osorted(X34161,hAPP(hAPP(c_List_Olist_OCons(X34161),X34160),X34159))
| ~ class_Orderings_Olinorder(X34161) )
& ( hBOOL(hAPP(hAPP(c_member(X34161),esk488_3(X34159,X34160,X34161)),hAPP(c_List_Oset(X34161),X34159)))
| ~ c_List_Olinorder__class_Osorted(X34161,X34159)
| c_List_Olinorder__class_Osorted(X34161,hAPP(hAPP(c_List_Olist_OCons(X34161),X34160),X34159))
| ~ class_Orderings_Olinorder(X34161) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X34161),X34160),esk488_3(X34159,X34160,X34161)))
| ~ c_List_Olinorder__class_Osorted(X34161,X34159)
| c_List_Olinorder__class_Osorted(X34161,hAPP(hAPP(c_List_Olist_OCons(X34161),X34160),X34159))
| ~ class_Orderings_Olinorder(X34161) ) ),
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_8481,plain,
! [X34066,X34067,X34068,X34069] :
( ( c_List_Olinorder__class_Osorted(X34068,X34066)
| ~ c_List_Olinorder__class_Osorted(X34068,hAPP(hAPP(c_List_Olist_OCons(X34068),X34067),X34066))
| ~ class_Orderings_Olinorder(X34068) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X34068),X34069),hAPP(c_List_Oset(X34068),X34066)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X34068),X34067),X34069))
| ~ c_List_Olinorder__class_Osorted(X34068,hAPP(hAPP(c_List_Olist_OCons(X34068),X34067),X34066))
| ~ class_Orderings_Olinorder(X34068) )
& ( hBOOL(hAPP(hAPP(c_member(X34068),esk487_3(X34066,X34067,X34068)),hAPP(c_List_Oset(X34068),X34066)))
| ~ c_List_Olinorder__class_Osorted(X34068,X34066)
| c_List_Olinorder__class_Osorted(X34068,hAPP(hAPP(c_List_Olist_OCons(X34068),X34067),X34066))
| ~ class_Orderings_Olinorder(X34068) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X34068),X34067),esk487_3(X34066,X34067,X34068)))
| ~ c_List_Olinorder__class_Osorted(X34068,X34066)
| c_List_Olinorder__class_Osorted(X34068,hAPP(hAPP(c_List_Olist_OCons(X34068),X34067),X34066))
| ~ class_Orderings_Olinorder(X34068) ) ),
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_8482,plain,
! [X17428,X17429,X17430] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(X17430,X17429)),X17428),hAPP(hAPP(hAPP(c_Natural_Oupdate,X17428),X17430),hAPP(X17429,X17428)))),
inference(variable_rename,[status(thm)],[fact_evalc_Oequations_I2_J]) ).
fof(i_0_8483,plain,
! [X17421,X17422,X17423] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(X17423,X17422)),X17421),hAPP(hAPP(hAPP(c_Natural_Oupdate,X17421),X17423),hAPP(X17422,X17421)))),
inference(variable_rename,[status(thm)],[fact_evalc_OAssign]) ).
fof(i_0_8484,plain,
! [X20616,X20617] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20617))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20616))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20616),X20617)),X20616) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20616),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20617),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_8485,plain,
! [X21643,X21644,X21645] :
( ~ class_Fields_Olinordered__field(X21645)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21645),c_Groups_Ozero__class_Ozero(X21645)),X21644))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21645),c_Groups_Ozero__class_Ozero(X21645)),X21643))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21645),c_Groups_Ozero__class_Ozero(X21645)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21645),X21644),X21643))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonneg__pos])]) ).
fof(i_0_8486,plain,
! [X19401,X19402,X19403] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19403),c_Groups_Ozero__class_Ozero(X19403)),X19402))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19403),c_Groups_Ozero__class_Ozero(X19403)),X19401))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19403),c_Groups_Ozero__class_Ozero(X19403)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19403),X19402),X19401)))
| ~ class_Rings_Oordered__ring(X19403) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19403),X19402),c_Groups_Ozero__class_Ozero(X19403)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19403),X19401),c_Groups_Ozero__class_Ozero(X19403)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19403),c_Groups_Ozero__class_Ozero(X19403)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19403),X19402),X19401)))
| ~ class_Rings_Oordered__ring(X19403) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__pos__le])])]) ).
fof(i_0_8487,plain,
! [X19446,X19447,X19448] :
( ~ class_Rings_Oordered__cancel__semiring(X19448)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19448),c_Groups_Ozero__class_Ozero(X19448)),X19447))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19448),c_Groups_Ozero__class_Ozero(X19448)),X19446))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19448),c_Groups_Ozero__class_Ozero(X19448)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19448),X19447),X19446))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonneg])]) ).
fof(i_0_8488,plain,
! [X19381,X19382,X19383] :
( ~ class_Groups_Oordered__comm__monoid__add(X19383)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19383),c_Groups_Ozero__class_Ozero(X19383)),X19382))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19383),c_Groups_Ozero__class_Ozero(X19383)),X19381))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19383),c_Groups_Ozero__class_Ozero(X19383)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19383),X19382),X19381))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg])]) ).
fof(i_0_8489,plain,
! [X18673,X18674,X18675] :
( ~ class_Rings_Olinordered__semidom(X18675)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18675),c_Groups_Oone__class_Oone(X18675)),X18674))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18675),c_Groups_Oone__class_Oone(X18675)),X18673))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18675),c_Groups_Oone__class_Oone(X18675)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18675),X18674),X18673))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__1__mult])]) ).
fof(i_0_8490,plain,
! [X21548,X21549,X21550] :
( ~ class_Fields_Olinordered__field(X21550)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21550),c_Groups_Ozero__class_Ozero(X21550)),X21549))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21550),c_Groups_Ozero__class_Ozero(X21550)),X21548))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21550),c_Groups_Ozero__class_Ozero(X21550)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21550),X21549),X21548))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__pos__pos])]) ).
fof(i_0_8491,plain,
! [X18911,X18912,X18913] :
( ~ class_Rings_Olinordered__semiring__strict(X18913)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18913),c_Groups_Ozero__class_Ozero(X18913)),X18912))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18913),c_Groups_Ozero__class_Ozero(X18913)),X18911))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18913),c_Groups_Ozero__class_Ozero(X18913)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18913),X18912),X18911))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__pos])]) ).
fof(i_0_8492,plain,
! [X19587,X19588,X19589] :
( ~ class_Groups_Oordered__comm__monoid__add(X19589)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19589),c_Groups_Ozero__class_Ozero(X19589)),X19588))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19589),c_Groups_Ozero__class_Ozero(X19589)),X19587))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19589),c_Groups_Ozero__class_Ozero(X19589)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19589),X19588),X19587))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg])]) ).
fof(i_0_8493,plain,
! [X19584,X19585,X19586] :
( ~ class_Groups_Oordered__comm__monoid__add(X19586)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19586),c_Groups_Ozero__class_Ozero(X19586)),X19585))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19586),c_Groups_Ozero__class_Ozero(X19586)),X19584))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19586),c_Groups_Ozero__class_Ozero(X19586)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19586),X19585),X19584))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos])]) ).
fof(i_0_8494,plain,
! [X18362,X18363,X18364] :
( ~ class_Groups_Oordered__comm__monoid__add(X18364)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18364),c_Groups_Ozero__class_Ozero(X18364)),X18363))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18364),c_Groups_Ozero__class_Ozero(X18364)),X18362))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18364),c_Groups_Ozero__class_Ozero(X18364)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18364),X18363),X18362))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__pos])]) ).
fof(i_0_8495,plain,
! [X26482,X26483,X26484,X26485] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26485),X26484))
| hAPP(c_Finite__Set_Ocard(X26483),hAPP(c_Set_Oimage(X26485,X26483,X26482),X26484)) != hAPP(c_Finite__Set_Ocard(X26485),X26484)
| c_Fun_Oinj__on(X26485,X26483,X26482,X26484) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__card__imp__inj__on])]) ).
fof(i_0_8496,plain,
! [X26486,X26487,X26488,X26489] :
( ( ~ c_Fun_Oinj__on(X26489,X26487,X26486,X26488)
| hAPP(c_Finite__Set_Ocard(X26487),hAPP(c_Set_Oimage(X26489,X26487,X26486),X26488)) = hAPP(c_Finite__Set_Ocard(X26489),X26488)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26489),X26488)) )
& ( hAPP(c_Finite__Set_Ocard(X26487),hAPP(c_Set_Oimage(X26489,X26487,X26486),X26488)) != hAPP(c_Finite__Set_Ocard(X26489),X26488)
| c_Fun_Oinj__on(X26489,X26487,X26486,X26488)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26489),X26488)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff__eq__card])])]) ).
fof(i_0_8497,plain,
! [X24183,X24184,X24185] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24185,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24185,tc_HOL_Obool)),X24184),X24183)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24185,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24185,tc_HOL_Obool)),X24184)),X24183),
inference(variable_rename,[status(thm)],[fact_Compl__Diff__eq]) ).
cnf(i_0_8498,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_8499,plain,
! [X21040,X21041,X21042,X21043] :
( ~ class_Rings_Olinordered__semidom(X21043)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21043),X21042),X21041) != hAPP(hAPP(c_Power_Opower__class_Opower(X21043),X21040),X21041)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21043),c_Groups_Ozero__class_Ozero(X21043)),X21042))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21043),c_Groups_Ozero__class_Ozero(X21043)),X21040))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21041))
| X21042 = X21040 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__imp__eq__base])]) ).
cnf(i_0_8500,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_8501,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_8502,plain,
! [X28631,X28632,X28633,X28634] : hAPP(c_Finite__Set_Ocard(tc_prod(X28634,X28633)),hAPP(hAPP(c_Product__Type_OSigma(X28634,X28633),X28632),hAPP(c_COMBK(tc_fun(X28633,tc_HOL_Obool),X28634),X28631))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X28634),X28632)),hAPP(c_Finite__Set_Ocard(X28633),X28631)),
inference(variable_rename,[status(thm)],[fact_card__cartesian__product]) ).
fof(i_0_8503,plain,
! [X25004,X25005,X25006,X25007] :
( ~ hBOOL(hAPP(hAPP(c_member(X25007),X25006),X25005))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25007,tc_HOL_Obool)),X25005),hAPP(hAPP(c_Set_Oinsert(X25007),X25006),X25004)) = hAPP(hAPP(c_Set_Oinsert(X25007),X25006),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25007,tc_HOL_Obool)),X25005),X25004)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__insert__right__if1])]) ).
fof(i_0_8504,plain,
! [X24988,X24989,X24990,X24991] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X24991),X24990),X24989))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24991,tc_HOL_Obool)),X24989),hAPP(hAPP(c_Set_Oinsert(X24991),X24990),X24988)) = hAPP(hAPP(c_Set_Oinsert(X24991),X24990),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24991,tc_HOL_Obool)),X24989),X24988)) )
& ( hBOOL(hAPP(hAPP(c_member(X24991),X24990),X24989))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24991,tc_HOL_Obool)),X24989),hAPP(hAPP(c_Set_Oinsert(X24991),X24990),X24988)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24991,tc_HOL_Obool)),X24989),X24988) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5717])]) ).
fof(i_0_8505,plain,
! [X32544,X32545,X32546,X32547,X32548,X32549,X32550] :
( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32544)),X32546) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32544)),X32545)
| X32546 != X32545 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32547),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32544)),X32546)))
| hAPP(hAPP(c_List_Onth(X32544),X32546),X32547) = hAPP(hAPP(c_List_Onth(X32544),X32545),X32547)
| X32546 != X32545 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk451_3(X32548,X32549,X32550)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32548)),X32550)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32548)),X32550) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32548)),X32549)
| X32550 = X32549 )
& ( hAPP(hAPP(c_List_Onth(X32548),X32550),esk451_3(X32548,X32549,X32550)) != hAPP(hAPP(c_List_Onth(X32548),X32549),esk451_3(X32548,X32549,X32550))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32548)),X32550) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32548)),X32549)
| X32550 = X32549 ) ),
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_8506,plain,
! [X30642,X30643,X30644,X30645,X30646,X30647] :
( ~ c_Finite__Set_Ofolding(X30647,X30646,X30645,X30644)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30647),X30643))
| hAPP(hAPP(X30644,X30643),X30642) = hAPP(hAPP(c_Finite__Set_Ofold(X30647,X30646,X30645),X30642),X30643) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Oeq__fold])]) ).
fof(i_0_8507,plain,
! [X23110,X23111,X23112,X23113] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X23113,X23112,X23111)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X23113),tc_HOL_Obool)),X23110),X23111))
| c_Hoare__Mirabelle_Ohoare__derivs(X23113,X23112,X23110) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_weaken])]) ).
fof(i_0_8508,plain,
! [X26087,X26088,X26089,X26090,X26091] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X26091)
| ~ hBOOL(hAPP(hAPP(c_member(X26090),X26089),X26088))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26091),hAPP(X26087,X26089)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26090,X26091),X26088),X26087))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__SUPI])]) ).
fof(i_0_8509,plain,
! [X19841,X19842,X19843,X19844] :
( ~ class_Divides_Osemiring__div(X19844)
| c_Divides_Odiv__class_Omod(X19844,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19844),c_Divides_Odiv__class_Omod(X19844,X19843,X19842)),X19841),X19842) = c_Divides_Odiv__class_Omod(X19844,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19844),X19843),X19841),X19842) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__simps_I4_J])]) ).
fof(i_0_8510,plain,
! [X19809,X19810,X19811,X19812] :
( ~ class_Divides_Osemiring__div(X19812)
| c_Divides_Odiv__class_Omod(X19812,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19812),c_Divides_Odiv__class_Omod(X19812,X19811,X19810)),X19809),X19810) = c_Divides_Odiv__class_Omod(X19812,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19812),X19811),X19809),X19810) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__simps_I1_J])]) ).
fof(i_0_8511,plain,
! [X20313,X20314,X20315,X20316] :
( ~ class_Divides_Oring__div(X20316)
| c_Divides_Odiv__class_Omod(X20316,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20316),X20315),X20314),X20313) = c_Divides_Odiv__class_Omod(X20316,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20316),c_Divides_Odiv__class_Omod(X20316,X20315,X20313)),X20314),X20313) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__left__eq])]) ).
fof(i_0_8512,plain,
! [X19857,X19858,X19859,X19860] :
( ~ class_Divides_Osemiring__div(X19860)
| c_Divides_Odiv__class_Omod(X19860,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19860),X19859),X19858),X19857) = c_Divides_Odiv__class_Omod(X19860,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19860),c_Divides_Odiv__class_Omod(X19860,X19859,X19857)),X19858),X19857) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__left__eq])]) ).
fof(i_0_8513,plain,
! [X19821,X19822,X19823,X19824] :
( ~ class_Divides_Osemiring__div(X19824)
| c_Divides_Odiv__class_Omod(X19824,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19824),X19823),X19822),X19821) = c_Divides_Odiv__class_Omod(X19824,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19824),c_Divides_Odiv__class_Omod(X19824,X19823,X19821)),X19822),X19821) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__left__eq])]) ).
fof(i_0_8514,plain,
! [X22387,X22388,X22389] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22389,tc_HOL_Obool)),X22388),X22387))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22389,tc_HOL_Obool)),X22388),X22387))
| X22388 = X22387 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22389,tc_HOL_Obool)),X22388),X22387))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22389,tc_HOL_Obool)),X22388),X22387)) )
& ( X22388 != X22387
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22389,tc_HOL_Obool)),X22388),X22387)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__iff__psubset__eq])])]) ).
fof(i_0_8515,plain,
! [X22384,X22385,X22386] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22386,tc_HOL_Obool)),X22385),X22384))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22386,tc_HOL_Obool)),X22385),X22384)) )
& ( X22385 != X22384
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22386,tc_HOL_Obool)),X22385),X22384)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22386,tc_HOL_Obool)),X22385),X22384))
| X22385 = X22384
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22386,tc_HOL_Obool)),X22385),X22384)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__eq])])]) ).
fof(i_0_8516,plain,
! [X24560,X24561,X24562] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24562),X24561))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24562),X24560))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24562),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24562,tc_HOL_Obool)),X24561),X24560))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UnI])]) ).
fof(i_0_8517,plain,
! [X26391,X26392,X26393] : hAPP(c_Set_OPow(X26393),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26393,tc_HOL_Obool)),X26392),X26391)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X26393,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X26393),X26392)),hAPP(c_Set_OPow(X26393),X26391)),
inference(variable_rename,[status(thm)],[fact_Pow__Int__eq]) ).
fof(i_0_8518,plain,
! [X27332,X27333,X27334,X27335] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27334),X27333))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27334,X27335),X27332),X27333) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X27335,X27334,c_Groups_Oplus__class_Oplus(X27335)),X27332),c_Groups_Ozero__class_Ozero(X27335)),X27333)
| ~ class_Groups_Ocomm__monoid__add(X27335) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X27334),X27333))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27334,X27335),X27332),X27333) = c_Groups_Ozero__class_Ozero(X27335)
| ~ class_Groups_Ocomm__monoid__add(X27335) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5718])])]) ).
fof(i_0_8519,plain,
! [X27328,X27329,X27330,X27331] :
( ~ class_Groups_Ocomm__monoid__add(X27331)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27330),X27329))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27330,X27331),X27328),X27329) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X27331,X27330,c_Groups_Oplus__class_Oplus(X27331)),X27328),c_Groups_Ozero__class_Ozero(X27331)),X27329) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oeq__fold])]) ).
fof(i_0_8520,plain,
! [X26274,X26275,X26276,X26277] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26276),X26275))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26276,X26277),X26274),X26275) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X26277,X26276,c_Groups_Otimes__class_Otimes(X26277)),X26274),c_Groups_Oone__class_Oone(X26277)),X26275)
| ~ class_Groups_Ocomm__monoid__mult(X26277) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X26276),X26275))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26276,X26277),X26274),X26275) = c_Groups_Oone__class_Oone(X26277)
| ~ class_Groups_Ocomm__monoid__mult(X26277) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5719])])]) ).
fof(i_0_8521,plain,
! [X26278,X26279,X26280,X26281] :
( ~ class_Groups_Ocomm__monoid__mult(X26281)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26280),X26279))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26280,X26281),X26278),X26279) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X26281,X26280,c_Groups_Otimes__class_Otimes(X26281)),X26278),c_Groups_Oone__class_Oone(X26281)),X26279) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oeq__fold])]) ).
fof(i_0_8522,plain,
! [X22390,X22391,X22392] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22392,tc_HOL_Obool)),X22391),X22390))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22392,tc_HOL_Obool)),X22391),X22390)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__imp__subset])]) ).
fof(i_0_8523,plain,
! [X22259,X22260] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22260))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22259),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X22260,X22259) = 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),X22260),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22259)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__neg])]) ).
fof(i_0_8524,plain,
! [X33166,X33167,X33168,X33169] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33169),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33168)),X33167)))
| hAPP(hAPP(c_List_Onth(X33168),hAPP(hAPP(c_List_Oappend(X33168),X33167),X33166)),X33169) = hAPP(hAPP(c_List_Onth(X33168),X33167),X33169) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33169),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33168)),X33167)))
| hAPP(hAPP(c_List_Onth(X33168),hAPP(hAPP(c_List_Oappend(X33168),X33167),X33166)),X33169) = hAPP(hAPP(c_List_Onth(X33168),X33166),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33169),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33168)),X33167))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5720])]) ).
fof(i_0_8525,plain,
! [X23665,X23666,X23667] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X23667),X23666),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X23667,tc_HOL_Obool)),X23665)))
| ~ hBOOL(hAPP(hAPP(c_member(X23667),X23666),X23665)) )
& ( hBOOL(hAPP(hAPP(c_member(X23667),X23666),X23665))
| hBOOL(hAPP(hAPP(c_member(X23667),X23666),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X23667,tc_HOL_Obool)),X23665))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5721])]) ).
fof(i_0_8526,plain,
! [X23662,X23663,X23664] :
( ~ hBOOL(hAPP(hAPP(c_member(X23664),X23663),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X23664,tc_HOL_Obool)),X23662)))
| ~ hBOOL(hAPP(hAPP(c_member(X23664),X23663),X23662)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5722])]) ).
fof(i_0_8527,plain,
! [X23659,X23660,X23661] :
( ~ hBOOL(hAPP(hAPP(c_member(X23661),X23660),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X23661,tc_HOL_Obool)),X23659)))
| ~ hBOOL(hAPP(hAPP(c_member(X23661),X23660),X23659)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5723])]) ).
fof(i_0_8528,plain,
! [X26670,X26671,X26672,X26674,X26675,X26676] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk198_2(X26670,X26671)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X26671)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26672),X26671))
| ~ hBOOL(hAPP(X26670,X26672)) )
& ( hBOOL(hAPP(X26670,esk198_2(X26670,X26671)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26672),X26671))
| ~ hBOOL(hAPP(X26670,X26672)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk199_2(X26674,X26675)),X26675))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X26676),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X26675)))
| ~ hBOOL(hAPP(X26674,X26676)) )
& ( hBOOL(hAPP(X26674,esk199_2(X26674,X26675)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X26676),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X26675)))
| ~ hBOOL(hAPP(X26674,X26676)) ) ),
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_8529,plain,
! [X27232,X27233,X27234,X27235] : hAPP(c_Map_Orestrict__map(X27235,X27234,hAPP(c_COMBK(tc_Option_Ooption(X27234),X27235),c_Option_Ooption_ONone(X27234)),X27233),X27232) = c_Option_Ooption_ONone(X27234),
inference(variable_rename,[status(thm)],[fact_restrict__map__empty]) ).
fof(i_0_8530,plain,
! [X33416,X33417,X33418,X33419] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X33419) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Odrop(X33418),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X33419)),hAPP(hAPP(c_List_Olist_OCons(X33418),X33417),X33416)) = hAPP(hAPP(c_List_Olist_OCons(X33418),X33417),X33416) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X33419) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Odrop(X33418),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X33419)),hAPP(hAPP(c_List_Olist_OCons(X33418),X33417),X33416)) = hAPP(hAPP(c_List_Odrop(X33418),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X33419)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X33416) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_drop__Cons__number__of])]) ).
fof(i_0_8531,plain,
! [X29925,X29926] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk334_2(X29925,X29926)),c_Int_OInteg))
| hBOOL(hAPP(X29926,X29925)) )
& ( ~ hBOOL(hAPP(X29926,hAPP(c_Int_OAbs__Integ,esk334_2(X29925,X29926))))
| hBOOL(hAPP(X29926,X29925)) ) ),
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_8532,plain,
! [X23549,X23550] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23550),X23549)),X23550))
| hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X23549) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| X23550 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X23549) != 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),X23550),X23549)),X23550))
| X23550 = 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_8533,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_8534,plain,
! [X29610,X29611,X29612] :
( ~ c_Wellfounded_Owf(X29612,X29611)
| c_Wellfounded_Owf(X29612,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X29612,X29612),tc_HOL_Obool)),X29611),X29610)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__Int1])]) ).
fof(i_0_8535,plain,
! [X29613,X29614,X29615] :
( ~ c_Wellfounded_Owf(X29615,X29614)
| c_Wellfounded_Owf(X29615,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X29615,X29615),tc_HOL_Obool)),X29613),X29614)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__Int2])]) ).
fof(i_0_8536,plain,
! [X22406,X22407] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22407))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22406),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22407),X22406) = 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),X22407),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22406)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__neg])]) ).
fof(i_0_8537,plain,
! [X33548,X33549] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X33549)
| X33548 = c_List_Olist_ONil(X33549)
| hAPP(c_Finite__Set_Ofold1(X33549,c_Groups_Otimes__class_Otimes(X33549)),hAPP(c_List_Oset(X33549),X33548)) = hAPP(c_List_Ofoldl(X33549,X33549,c_Groups_Otimes__class_Otimes(X33549),hAPP(c_List_Ohd(X33549),X33548)),hAPP(c_List_Otl(X33549),X33548)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__set])]) ).
fof(i_0_8538,plain,
! [X33354,X33355,X33356,X33357,X33358] : hAPP(hAPP(c_List_Odrop(tc_prod(X33358,X33357)),X33356),hAPP(hAPP(c_List_Ozip(X33358,X33357),X33355),X33354)) = hAPP(hAPP(c_List_Ozip(X33358,X33357),hAPP(hAPP(c_List_Odrop(X33358),X33356),X33355)),hAPP(hAPP(c_List_Odrop(X33357),X33356),X33354)),
inference(variable_rename,[status(thm)],[fact_drop__zip]) ).
fof(i_0_8539,plain,
! [X32644,X32645,X32646,X32647,X32648] : hAPP(hAPP(c_List_Otake(tc_prod(X32648,X32647)),X32646),hAPP(hAPP(c_List_Ozip(X32648,X32647),X32645),X32644)) = hAPP(hAPP(c_List_Ozip(X32648,X32647),hAPP(hAPP(c_List_Otake(X32648),X32646),X32645)),hAPP(hAPP(c_List_Otake(X32647),X32646),X32644)),
inference(variable_rename,[status(thm)],[fact_take__zip]) ).
fof(i_0_8540,plain,
! [X26880,X26881,X26882] :
( ~ class_Orderings_Olinorder(X26882)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26882),X26881),X26880))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26882,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26882,X26881),X26880)),hAPP(hAPP(c_Set_Oinsert(X26882),X26880),c_Orderings_Obot__class_Obot(tc_fun(X26882,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(X26882,X26881,X26880) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I6_J])]) ).
fof(i_0_8541,plain,
! [X22267,X22268] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22268),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22267),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X22268,X22267) = 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),X22268),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22267)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__neg__neg])]) ).
fof(i_0_8542,plain,
! [X30569,X30570,X30571,X30572,X30573] :
( ~ c_Relation_Osingle__valued(X30573,X30572,X30571)
| ~ c_Relation_Osingle__valued(X30572,X30570,X30569)
| c_Relation_Osingle__valued(X30573,X30570,hAPP(hAPP(c_Relation_Orel__comp(X30573,X30572,X30570),X30571),X30569)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__rel__comp])]) ).
fof(i_0_8543,plain,
! [X34311,X34312] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X34312),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X34312))),c_List_Otranspose(X34312,X34311)))),
inference(variable_rename,[status(thm)],[fact_sorted__transpose]) ).
fof(i_0_8544,plain,
! [X26857,X26858,X26859,X26860,X26861] :
( ~ class_Orderings_Olinorder(X26861)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26861,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26861,X26860),X26859)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26861,X26858),X26857)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26861,hAPP(hAPP(c_Orderings_Oord__class_Omax(X26861),X26860),X26858)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X26861),X26859),X26857)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastLessThan])]) ).
fof(i_0_8545,plain,
! [X26511,X26512,X26513,X26514,X26515] :
( ~ class_Orderings_Olinorder(X26515)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26515,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26515,X26514,X26513)),c_SetInterval_Oord__class_OatLeastAtMost(X26515,X26512,X26511)) = c_SetInterval_Oord__class_OatLeastAtMost(X26515,hAPP(hAPP(c_Orderings_Oord__class_Omax(X26515),X26514),X26512),hAPP(hAPP(c_Orderings_Oord__class_Omin(X26515),X26513),X26511)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMost])]) ).
fof(i_0_8546,plain,
! [X25852,X25853,X25854,X25855,X25856] :
( ~ class_Orderings_Olinorder(X25856)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25856,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25856,X25855,X25854)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25856,X25853,X25852)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X25856,hAPP(hAPP(c_Orderings_Oord__class_Omax(X25856),X25855),X25853),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25856),X25854),X25852)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__greaterThanAtMost])]) ).
fof(i_0_8547,plain,
! [X25729,X25730,X25731,X25732,X25733] :
( ~ class_Orderings_Olinorder(X25733)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25733,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X25733,X25732,X25731)),c_SetInterval_Oord__class_OgreaterThanLessThan(X25733,X25730,X25729)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X25733,hAPP(hAPP(c_Orderings_Oord__class_Omax(X25733),X25732),X25730),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25733),X25731),X25729)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__greaterThanLessThan])]) ).
fof(i_0_8548,plain,
! [X23651,X23652,X23653,X23654] :
( ~ hBOOL(hAPP(hAPP(c_member(X23654),X23653),X23652))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23654,tc_HOL_Obool)),X23652),X23651))
| hBOOL(hAPP(hAPP(c_member(X23654),X23653),X23651)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__rev__mp])]) ).
fof(i_0_8549,plain,
! [X23655,X23656,X23657,X23658] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23658,tc_HOL_Obool)),X23657),X23656))
| ~ hBOOL(hAPP(hAPP(c_member(X23658),X23655),X23657))
| hBOOL(hAPP(hAPP(c_member(X23658),X23655),X23656)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__mp])]) ).
fof(i_0_8550,plain,
! [X23647,X23648,X23649,X23650] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23650,tc_HOL_Obool)),X23649),X23648))
| ~ hBOOL(hAPP(hAPP(c_member(X23650),X23647),X23649))
| hBOOL(hAPP(hAPP(c_member(X23650),X23647),X23648)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mono])]) ).
fof(i_0_8551,plain,
! [X23590,X23591,X23592,X23593] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23593,tc_HOL_Obool)),X23592),X23591))
| ~ hBOOL(hAPP(hAPP(c_member(X23593),X23590),X23592))
| hBOOL(hAPP(hAPP(c_member(X23593),X23590),X23591)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subsetD])]) ).
fof(i_0_8552,plain,
! [X23701,X23702,X23703,X23704] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23704,tc_HOL_Obool)),X23703),X23702))
| ~ hBOOL(hAPP(hAPP(c_member(X23704),X23701),X23703))
| hBOOL(hAPP(hAPP(c_member(X23704),X23701),X23702)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubsetD])]) ).
fof(i_0_8553,plain,
! [X33035,X33036,X33037,X33038] : hAPP(hAPP(c_List_Onth(X33038),hAPP(hAPP(c_List_Oappend(X33038),X33037),hAPP(hAPP(c_List_Olist_OCons(X33038),X33036),X33035))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33038)),X33037)) = X33036,
inference(variable_rename,[status(thm)],[fact_nth__append__length]) ).
fof(i_0_8554,plain,
! [X22702,X22703,X22704] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22704),hAPP(c_Int_Onumber__class_Onumber__of(X22704),X22703)),hAPP(c_Int_Onumber__class_Onumber__of(X22704),X22702)))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22704),hAPP(c_Int_Onumber__class_Onumber__of(X22704),X22703)),hAPP(c_Int_Onumber__class_Onumber__of(X22704),X22702)) = hAPP(c_Int_Onumber__class_Onumber__of(X22704),X22702)
| ~ class_Int_Onumber(X22704)
| ~ class_Orderings_Oord(X22704) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22704),hAPP(c_Int_Onumber__class_Onumber__of(X22704),X22703)),hAPP(c_Int_Onumber__class_Onumber__of(X22704),X22702)))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22704),hAPP(c_Int_Onumber__class_Onumber__of(X22704),X22703)),hAPP(c_Int_Onumber__class_Onumber__of(X22704),X22702)) = hAPP(c_Int_Onumber__class_Onumber__of(X22704),X22703)
| ~ class_Int_Onumber(X22704)
| ~ class_Orderings_Oord(X22704) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5725])])]) ).
fof(i_0_8555,plain,
! [X22549,X22550,X22551] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22551),hAPP(c_Int_Onumber__class_Onumber__of(X22551),X22550)),hAPP(c_Int_Onumber__class_Onumber__of(X22551),X22549)))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22551),hAPP(c_Int_Onumber__class_Onumber__of(X22551),X22550)),hAPP(c_Int_Onumber__class_Onumber__of(X22551),X22549)) = hAPP(c_Int_Onumber__class_Onumber__of(X22551),X22550)
| ~ class_Int_Onumber(X22551)
| ~ class_Orderings_Oord(X22551) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22551),hAPP(c_Int_Onumber__class_Onumber__of(X22551),X22550)),hAPP(c_Int_Onumber__class_Onumber__of(X22551),X22549)))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22551),hAPP(c_Int_Onumber__class_Onumber__of(X22551),X22550)),hAPP(c_Int_Onumber__class_Onumber__of(X22551),X22549)) = hAPP(c_Int_Onumber__class_Onumber__of(X22551),X22549)
| ~ class_Int_Onumber(X22551)
| ~ class_Orderings_Oord(X22551) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5726])])]) ).
fof(i_0_8556,plain,
! [X22290,X22291] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22291),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22290),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22291),X22290) = 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),X22291),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22290)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__neg__neg])]) ).
fof(i_0_8557,plain,
! [X26583,X26584] : 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)),X26584),X26583),
inference(variable_rename,[status(thm)],[fact_inj__on__add__nat]) ).
fof(i_0_8558,plain,
! [X20118,X20119] :
( ( ~ 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),X20118),X20119)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20118))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20119)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20118))
| 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),X20118),X20119)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20119)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__nonneg__iff])])]) ).
fof(i_0_8559,plain,
! [X21475,X21476,X21477,X21478,X21479] :
( ~ class_Fields_Ofield__inverse__zero(X21479)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21479),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21479),X21478),X21477)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21479),X21476),X21475)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21479),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21479),X21478),X21476)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21479),X21477),X21475)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times__divide__times__eq])]) ).
fof(i_0_8560,plain,
! [X18747,X18748,X18749,X18750,X18751] :
( ~ class_Rings_Ocomm__semiring__1(X18751)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18751),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18751),X18750),X18749)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18751),X18748),X18747)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18751),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18751),X18750),X18748)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18751),X18749),X18747)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J])]) ).
fof(i_0_8561,plain,
! [X18203,X18204,X18205,X18206,X18207] :
( ~ class_Rings_Ocomm__semiring__1(X18207)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18207),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18207),X18206),X18205)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18207),X18204),X18203)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18207),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18207),X18206),X18204)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18207),X18205),X18203)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])]) ).
fof(i_0_8562,plain,
! [X18737,X18738,X18739,X18740,X18741] :
( ~ class_Rings_Ocomm__semiring__1(X18741)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18741),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18741),X18740),X18739)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18741),X18738),X18737)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18741),X18740),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18741),X18739),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18741),X18738),X18737))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J])]) ).
fof(i_0_8563,plain,
! [X34121,X34122,X34123,X34124,X34125] :
( ~ class_Orderings_Olinorder(X34125)
| ~ c_List_Olinorder__class_Osorted(X34125,hAPP(hAPP(c_List_Omap(X34124,X34125),X34123),X34122))
| c_List_Olinorder__class_Osorted(X34125,hAPP(hAPP(c_List_Omap(X34124,X34125),X34123),c_List_Oremove1(X34124,X34121,X34122))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__map__remove1])]) ).
fof(i_0_8564,plain,
! [X31343,X31344,X31345] : hAPP(c_Relation_ODomain(X31345,X31344),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X31345,X31344),tc_HOL_Obool),X31343)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X31345,X31344),tc_HOL_Obool),tc_fun(X31345,tc_HOL_Obool)),X31343),c_Relation_ODomain(X31345,X31344)),
inference(variable_rename,[status(thm)],[fact_Domain__Union]) ).
fof(i_0_8565,plain,
! [X31340,X31341,X31342] : hAPP(c_Relation_ORange(X31342,X31341),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X31342,X31341),tc_HOL_Obool),X31340)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X31342,X31341),tc_HOL_Obool),tc_fun(X31341,tc_HOL_Obool)),X31340),c_Relation_ORange(X31342,X31341)),
inference(variable_rename,[status(thm)],[fact_Range__Union]) ).
fof(i_0_8566,plain,
! [X26678,X26679,X26681,X26682,X26683,X26685] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk200_2(X26678,X26679)),X26679))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X26681),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X26679)))
| hBOOL(hAPP(X26678,X26681)) )
& ( ~ hBOOL(hAPP(X26678,esk200_2(X26678,X26679)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X26681),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X26679)))
| hBOOL(hAPP(X26678,X26681)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk201_2(X26682,X26683)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X26683)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26685),X26683))
| hBOOL(hAPP(X26682,X26685)) )
& ( ~ hBOOL(hAPP(X26682,esk201_2(X26682,X26683)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26685),X26683))
| hBOOL(hAPP(X26682,X26685)) ) ),
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_8567,plain,
! [X23868,X23869,X23870] :
( ~ class_Rings_Oring__1(X23870)
| ~ hBOOL(hAPP(hAPP(c_member(X23870),X23869),c_Int_Oring__1__class_OInts(X23870)))
| hBOOL(hAPP(hAPP(c_member(X23870),hAPP(hAPP(c_Power_Opower__class_Opower(X23870),X23869),X23868)),c_Int_Oring__1__class_OInts(X23870))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__power])]) ).
fof(i_0_8568,plain,
! [X29152,X29153] : hAPP(c_Set_OCollect(X29153),hAPP(hAPP(c_COMBC(X29153,tc_fun(X29153,tc_HOL_Obool),tc_HOL_Obool),c_member(X29153)),X29152)) = X29152,
inference(variable_rename,[status(thm)],[fact_Collect__mem__eq]) ).
fof(i_0_8569,plain,
! [X20910,X20911] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X20911))
| 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),X20911),X20910))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__one__le__power])]) ).
fof(i_0_8570,plain,
! [X23499,X23500,X23501] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23501),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23500,X23499)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23501),X23499))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23501),X23500)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__zmod__imp__zdvd])]) ).
fof(i_0_8571,plain,
! [X20869,X20870,X20871] :
( ~ class_Rings_Olinordered__semidom(X20871)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20871),c_Groups_Oone__class_Oone(X20871)),X20870))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20869))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20871),c_Groups_Oone__class_Oone(X20871)),hAPP(hAPP(c_Power_Opower__class_Opower(X20871),X20870),X20869))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__power])]) ).
fof(i_0_8572,plain,
! [X21619,X21620,X21621] :
( ~ class_Fields_Olinordered__field(X21621)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21621),X21620),c_Groups_Ozero__class_Ozero(X21621)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21621),X21619),c_Groups_Ozero__class_Ozero(X21621)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21621),c_Groups_Ozero__class_Ozero(X21621)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21621),X21620),X21619))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonpos__neg])]) ).
fof(i_0_8573,plain,
! [X19434,X19435,X19436] :
( ~ class_Rings_Oordered__ring(X19436)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19436),X19435),c_Groups_Ozero__class_Ozero(X19436)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19436),X19434),c_Groups_Ozero__class_Ozero(X19436)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19436),c_Groups_Ozero__class_Ozero(X19436)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19436),X19435),X19434))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonpos])]) ).
fof(i_0_8574,plain,
! [X21539,X21540,X21541] :
( ~ class_Fields_Olinordered__field(X21541)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21541),X21540),c_Groups_Ozero__class_Ozero(X21541)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21541),X21539),c_Groups_Ozero__class_Ozero(X21541)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21541),c_Groups_Ozero__class_Ozero(X21541)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21541),X21540),X21539))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__neg__neg])]) ).
fof(i_0_8575,plain,
! [X18933,X18934,X18935] :
( ~ class_Rings_Olinordered__ring__strict(X18935)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18935),X18934),c_Groups_Ozero__class_Ozero(X18935)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18935),X18933),c_Groups_Ozero__class_Ozero(X18935)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18935),c_Groups_Ozero__class_Ozero(X18935)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18935),X18934),X18933))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__neg])]) ).
fof(i_0_8576,plain,
! [X27302,X27303,X27304] :
( ~ class_Groups_Ocomm__monoid__add(X27304)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27304),X27303),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X27302))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27304),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27304),X27303),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X27302))),hAPP(X27303,X27302)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__lessThan__Suc])]) ).
fof(i_0_8577,plain,
! [X18357,X18358] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18358),X18357)),X18358)),
inference(variable_rename,[status(thm)],[i_0_5727]) ).
fof(i_0_8578,plain,
! [X18355,X18356] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18356),X18355)),X18355)),
inference(variable_rename,[status(thm)],[i_0_5728]) ).
fof(i_0_8579,plain,
! [X32228,X32229,X32230,X32231] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32231)),X32230) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32229)),X32228)
| ~ hBOOL(hAPP(c_List_Odistinct(X32231),X32230))
| c_Map_Odom(X32231,X32229,c_Map_Omap__of(X32231,X32229,hAPP(hAPP(c_List_Ozip(X32231,X32229),X32230),X32228))) = hAPP(c_List_Oset(X32231),X32230) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dom__map__of__zip])]) ).
fof(i_0_8580,plain,
! [X21970,X21971] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21971))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21970))
| c_Divides_OposDivAlg(X21971,X21970) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21971),X21970)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21971,X21970)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg__div__mod])]) ).
fof(i_0_8581,plain,
! [X20120,X20121] :
( ( ~ 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),X20120),X20121)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20121),X20120))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20121)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20121),X20120))
| 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),X20120),X20121)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20121)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__pos__iff])])]) ).
fof(i_0_8582,plain,
! [X29668,X29669] : c_List_Olex(X29669,X29668) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(X29669),tc_List_Olist(X29669)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(X29669,X29668)),
inference(variable_rename,[status(thm)],[fact_lex__def]) ).
fof(i_0_8583,plain,
! [X33125,X33126,X33127,X33128] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X33128),X33127),hAPP(c_List_Oset(X33128),X33126)))
| c_List_Oremove1(X33128,X33127,hAPP(hAPP(c_List_Oappend(X33128),X33126),X33125)) = hAPP(hAPP(c_List_Oappend(X33128),c_List_Oremove1(X33128,X33127,X33126)),X33125) )
& ( hBOOL(hAPP(hAPP(c_member(X33128),X33127),hAPP(c_List_Oset(X33128),X33126)))
| c_List_Oremove1(X33128,X33127,hAPP(hAPP(c_List_Oappend(X33128),X33126),X33125)) = hAPP(hAPP(c_List_Oappend(X33128),X33126),c_List_Oremove1(X33128,X33127,X33125)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5729])]) ).
cnf(i_0_8584,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_8585,plain,
! [X22654,X22655,X22656,X22657] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22657),X22656),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22657),X22655),X22654)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22657),X22656),X22655))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22657),X22656),X22654))
| ~ class_Orderings_Olinorder(X22657) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22657),X22656),X22655))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22657),X22656),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22657),X22655),X22654)))
| ~ class_Orderings_Olinorder(X22657) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22657),X22656),X22654))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22657),X22656),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22657),X22655),X22654)))
| ~ class_Orderings_Olinorder(X22657) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__max__iff__disj])])]) ).
fof(i_0_8586,plain,
! [X22578,X22579,X22580,X22581] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22581),X22580),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22581),X22579),X22578)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22581),X22580),X22579))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22581),X22580),X22578))
| ~ 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),X22579),X22578)))
| ~ class_Orderings_Olinorder(X22581) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22581),X22580),X22578))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22581),X22580),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22581),X22579),X22578)))
| ~ class_Orderings_Olinorder(X22581) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__max__iff__disj])])]) ).
fof(i_0_8587,plain,
! [X28189,X28190,X28191] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X28191,X28190,c_Orderings_Obot__class_Obot(tc_fun(X28191,tc_HOL_Obool))),X28189)),
inference(variable_rename,[status(thm)],[i_0_5731]) ).
fof(i_0_8588,plain,
! [X20131,X20132] :
( ( ~ 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),X20131),X20132)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20131),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20132),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20131),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),X20131),X20132)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20132),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_8589,plain,
! [X32667,X32668] :
( X32668 = c_List_Olist_ONil(X32667)
| c_Random_Oselect__weight(X32667,hAPP(hAPP(c_List_Omap(X32667,tc_prod(tc_Code__Numeral_Ocode__numeral,X32667)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X32667),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X32668)) = c_Random_Oselect(X32667,X32668) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_select__weigth__select])]) ).
fof(i_0_8590,plain,
! [X31192,X31193,X31194] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X31193,tc_HOL_Obool)),X31194),X31192))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31193),X31194))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X31193),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31193,tc_HOL_Obool),X31192))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Inter])])]) ).
fof(i_0_8591,plain,
! [X20828,X20829,X20830] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20830),c_Groups_Ozero__class_Ozero(X20830)),X20828))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20830),c_Groups_Ozero__class_Ozero(X20830)),X20829))
| hAPP(c_Groups_Oabs__class_Oabs(X20830),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20830),X20829),X20828)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20830),hAPP(c_Groups_Oabs__class_Oabs(X20830),X20829)),hAPP(c_Groups_Oabs__class_Oabs(X20830),X20828))
| ~ class_Rings_Oordered__ring__abs(X20830) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20830),X20828),c_Groups_Ozero__class_Ozero(X20830)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20830),c_Groups_Ozero__class_Ozero(X20830)),X20829))
| hAPP(c_Groups_Oabs__class_Oabs(X20830),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20830),X20829),X20828)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20830),hAPP(c_Groups_Oabs__class_Oabs(X20830),X20829)),hAPP(c_Groups_Oabs__class_Oabs(X20830),X20828))
| ~ class_Rings_Oordered__ring__abs(X20830) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20830),c_Groups_Ozero__class_Ozero(X20830)),X20828))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20830),X20829),c_Groups_Ozero__class_Ozero(X20830)))
| hAPP(c_Groups_Oabs__class_Oabs(X20830),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20830),X20829),X20828)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20830),hAPP(c_Groups_Oabs__class_Oabs(X20830),X20829)),hAPP(c_Groups_Oabs__class_Oabs(X20830),X20828))
| ~ class_Rings_Oordered__ring__abs(X20830) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20830),X20828),c_Groups_Ozero__class_Ozero(X20830)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20830),X20829),c_Groups_Ozero__class_Ozero(X20830)))
| hAPP(c_Groups_Oabs__class_Oabs(X20830),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20830),X20829),X20828)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20830),hAPP(c_Groups_Oabs__class_Oabs(X20830),X20829)),hAPP(c_Groups_Oabs__class_Oabs(X20830),X20828))
| ~ class_Rings_Oordered__ring__abs(X20830) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__eq__mult])])]) ).
cnf(i_0_8592,plain,
( X1 = X2
| c_Int_OBit1(X1) != c_Int_OBit1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5732]) ).
fof(i_0_8593,plain,
! [X33787,X33788,X33789] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33789),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33788)),X33787)))
| c_List_Obutlast(X33788,hAPP(hAPP(c_List_Otake(X33788),X33789),X33787)) = hAPP(hAPP(c_List_Otake(X33788),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33789),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X33787) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast__take])]) ).
fof(i_0_8594,plain,
! [X27106,X27107] :
( ~ class_Orderings_Oorder(X27107)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27107,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X27107),X27106),c_Orderings_Obot__class_Obot(tc_fun(X27107,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(X27107),X27106)) = hAPP(hAPP(c_Set_Oinsert(X27107),X27106),c_Orderings_Obot__class_Obot(tc_fun(X27107,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__Diff__lessThan])]) ).
fof(i_0_8595,plain,
! [X24794,X24795,X24796,X24797,X24798,X24799,X24800,X24801] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24796,tc_HOL_Obool)),X24795),X24794) != c_Orderings_Obot__class_Obot(tc_fun(X24796,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X24796),X24797),X24795))
| ~ hBOOL(hAPP(hAPP(c_member(X24796),X24798),X24794))
| X24797 != X24798 )
& ( hBOOL(hAPP(hAPP(c_member(X24801),esk130_3(X24799,X24800,X24801)),X24800))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24801,tc_HOL_Obool)),X24800),X24799) = c_Orderings_Obot__class_Obot(tc_fun(X24801,tc_HOL_Obool)) )
& ( hBOOL(hAPP(hAPP(c_member(X24801),esk131_3(X24799,X24800,X24801)),X24799))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24801,tc_HOL_Obool)),X24800),X24799) = c_Orderings_Obot__class_Obot(tc_fun(X24801,tc_HOL_Obool)) )
& ( esk130_3(X24799,X24800,X24801) = esk131_3(X24799,X24800,X24801)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24801,tc_HOL_Obool)),X24800),X24799) = c_Orderings_Obot__class_Obot(tc_fun(X24801,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_8596,plain,
! [X34174,X34175,X34176] :
( ~ class_Orderings_Olinorder(X34176)
| ~ hBOOL(hAPP(hAPP(c_member(X34176),X34175),hAPP(c_List_Oset(X34176),X34174)))
| ~ c_List_Olinorder__class_Osorted(X34176,X34174)
| hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X34176,X34176,c_COMBI(X34176)),X34175),c_List_Oremove1(X34176,X34175,X34174)) = X34174 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__remove1])]) ).
fof(i_0_8597,plain,
! [X21901,X21902] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21902),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)),X21901))
| c_Divides_OnegDivAlg(X21902,X21901) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21902),X21901)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21902,X21901)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negDivAlg__div__mod])]) ).
fof(i_0_8598,plain,
! [X25318,X25319,X25320] :
( ~ class_Lattices_Olattice(X25320)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25320),X25319))
| X25318 = c_Orderings_Obot__class_Obot(tc_fun(X25320,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25320,tc_HOL_Obool)),X25318),X25319))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25320),c_Big__Operators_Olattice__class_OInf__fin(X25320,X25318)),c_Big__Operators_Olattice__class_OInf__fin(X25320,X25319)) = c_Big__Operators_Olattice__class_OInf__fin(X25320,X25319) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Osubset__idem])]) ).
fof(i_0_8599,plain,
! [X25111,X25112,X25113] :
( ~ class_Lattices_Olattice(X25113)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25113),X25112))
| X25111 = c_Orderings_Obot__class_Obot(tc_fun(X25113,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25113,tc_HOL_Obool)),X25111),X25112))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25113),c_Big__Operators_Olattice__class_OSup__fin(X25113,X25111)),c_Big__Operators_Olattice__class_OSup__fin(X25113,X25112)) = c_Big__Operators_Olattice__class_OSup__fin(X25113,X25112) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Osubset__idem])]) ).
fof(i_0_8600,plain,
! [X25324,X25325,X25326] :
( ~ class_Orderings_Olinorder(X25326)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25326),X25325))
| X25324 = c_Orderings_Obot__class_Obot(tc_fun(X25326,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25326,tc_HOL_Obool)),X25324),X25325))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X25326),c_Big__Operators_Olinorder__class_OMax(X25326,X25324)),c_Big__Operators_Olinorder__class_OMax(X25326,X25325)) = c_Big__Operators_Olinorder__class_OMax(X25326,X25325) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Osubset__idem])]) ).
fof(i_0_8601,plain,
! [X25321,X25322,X25323] :
( ~ class_Orderings_Olinorder(X25323)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25323),X25322))
| X25321 = c_Orderings_Obot__class_Obot(tc_fun(X25323,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25323,tc_HOL_Obool)),X25321),X25322))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X25323),c_Big__Operators_Olinorder__class_OMin(X25323,X25321)),c_Big__Operators_Olinorder__class_OMin(X25323,X25322)) = c_Big__Operators_Olinorder__class_OMin(X25323,X25322) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Osubset__idem])]) ).
fof(i_0_8602,plain,
! [X20693,X20694,X20695] : 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,X20695,X20694)),X20693),X20694) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20695),X20693),X20694),
inference(variable_rename,[status(thm)],[fact_zpower__zmod]) ).
fof(i_0_8603,plain,
! [X20387,X20388,X20389] : 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,X20389,X20388)),X20387),X20388) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20389),X20387),X20388),
inference(variable_rename,[status(thm)],[fact_zdiff__zmod__left]) ).
fof(i_0_8604,plain,
! [X31281,X31282,X31283,X31284] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31283),X31282),c_Complete__Lattice_OInf__class_OInf(X31283,X31281)))
| ~ hBOOL(hAPP(hAPP(c_member(X31283),X31284),X31281))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31283),X31282),X31284))
| ~ class_Complete__Lattice_Ocomplete__lattice(X31283) )
& ( hBOOL(hAPP(hAPP(c_member(X31283),esk401_3(X31281,X31282,X31283)),X31281))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31283),X31282),c_Complete__Lattice_OInf__class_OInf(X31283,X31281)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X31283) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31283),X31282),esk401_3(X31281,X31282,X31283)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31283),X31282),c_Complete__Lattice_OInf__class_OInf(X31283,X31281)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X31283) ) ),
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_8605,plain,
! [X32868,X32869,X32870,X32871] :
( ( X32871 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Otake(X32870),X32871),hAPP(hAPP(c_List_Olist_OCons(X32870),X32869),X32868)) = c_List_Olist_ONil(X32870) )
& ( X32871 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Otake(X32870),X32871),hAPP(hAPP(c_List_Olist_OCons(X32870),X32869),X32868)) = hAPP(hAPP(c_List_Olist_OCons(X32870),X32869),hAPP(hAPP(c_List_Otake(X32870),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X32871),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X32868)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__Cons_H])]) ).
fof(i_0_8606,plain,
! [X24685,X24686,X24687,X24688] :
( ~ hBOOL(hAPP(X24688,X24687))
| ~ hBOOL(hAPP(X24686,X24687))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24685,tc_HOL_Obool)),X24688),X24686),X24687)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1I])]) ).
fof(i_0_8607,plain,
! [X28365] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X28365)),c_Int_OInteg)),
inference(variable_rename,[status(thm)],[fact_Rep__Integ]) ).
fof(i_0_8608,plain,
! [X27564,X27565,X27566,X27567,X27568] :
( ~ c_Finite__Set_Ofolding__one__idem(X27568,X27567,X27566)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27568),X27565))
| X27565 = c_Orderings_Obot__class_Obot(tc_fun(X27568,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27568),X27564))
| X27564 = c_Orderings_Obot__class_Obot(tc_fun(X27568,tc_HOL_Obool))
| hAPP(X27566,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27568,tc_HOL_Obool)),X27565),X27564)) = hAPP(hAPP(X27567,hAPP(X27566,X27565)),hAPP(X27566,X27564)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Ounion__idem])]) ).
fof(i_0_8609,plain,
! [X19387,X19388,X19389,X19390] :
( ~ class_Groups_Oordered__comm__monoid__add(X19390)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19390),c_Groups_Ozero__class_Ozero(X19390)),X19389))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19390),X19388),X19387))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19390),X19388),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19390),X19389),X19387))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing])]) ).
fof(i_0_8610,plain,
! [X19391,X19392,X19393,X19394] :
( ~ class_Groups_Oordered__comm__monoid__add(X19394)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19394),c_Groups_Ozero__class_Ozero(X19394)),X19393))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19394),X19392),X19391))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19394),X19392),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19394),X19391),X19393))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing2])]) ).
fof(i_0_8611,plain,
! [X18410,X18411,X18412,X18413] :
( ~ class_Rings_Olinordered__semidom(X18413)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18413),c_Groups_Ozero__class_Ozero(X18413)),X18412))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18413),X18411),X18410))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18413),X18411),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18413),X18412),X18410))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__add__strict])]) ).
fof(i_0_8612,plain,
! [X19580,X19581,X19582,X19583] :
( ~ class_Groups_Oordered__comm__monoid__add(X19583)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19583),c_Groups_Ozero__class_Ozero(X19583)),X19582))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19583),X19581),X19580))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19583),X19581),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19583),X19582),X19580))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing])]) ).
fof(i_0_8613,plain,
! [X19576,X19577,X19578,X19579] :
( ~ class_Groups_Oordered__comm__monoid__add(X19579)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19579),c_Groups_Ozero__class_Ozero(X19579)),X19578))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19579),X19577),X19576))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19579),X19577),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19579),X19578),X19576))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2])]) ).
fof(i_0_8614,plain,
! [X20156,X20157] : X20157 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20156),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20157),X20156))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20157,X20156)),
inference(variable_rename,[status(thm)],[fact_zmod__zdiv__equality]) ).
fof(i_0_8615,plain,
! [X24751,X24752,X24753,X24754] :
( ~ class_Lattices_Osemilattice__inf(X24754)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24754),X24753),X24752))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24754),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24754),X24753),X24751)),X24752)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI1])]) ).
fof(i_0_8616,plain,
! [X24755,X24756,X24757,X24758] :
( ~ class_Lattices_Osemilattice__inf(X24758)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24758),X24757),X24756))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24758),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24758),X24755),X24757)),X24756)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI2])]) ).
fof(i_0_8617,plain,
! [X22453,X22454,X22455,X22456] :
( ~ class_Orderings_Olinorder(X22456)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22456),X22455),X22454))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22456),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22456),X22455),X22453)),X22454)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infI1])]) ).
fof(i_0_8618,plain,
! [X22457,X22458,X22459,X22460] :
( ~ class_Orderings_Olinorder(X22460)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22460),X22459),X22458))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22460),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22460),X22457),X22459)),X22458)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infI2])]) ).
fof(i_0_8619,plain,
! [X24786,X24787,X24788,X24789] :
( ~ class_Lattices_Osemilattice__inf(X24789)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24789),X24788),X24787))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24789),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24789),X24788),X24786)),X24787)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__infI1])]) ).
fof(i_0_8620,plain,
! [X24782,X24783,X24784,X24785] :
( ~ class_Lattices_Osemilattice__inf(X24785)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24785),X24784),X24783))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24785),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24785),X24782),X24784)),X24783)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__infI2])]) ).
fof(i_0_8621,plain,
! [X22502,X22503,X22504,X22505] :
( ~ class_Orderings_Olinorder(X22505)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22505),X22504),X22503))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22505),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22505),X22504),X22502)),X22503)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oless__infI1])]) ).
fof(i_0_8622,plain,
! [X22506,X22507,X22508,X22509] :
( ~ class_Orderings_Olinorder(X22509)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22509),X22508),X22507))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22509),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22509),X22506),X22508)),X22507)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oless__infI2])]) ).
fof(i_0_8623,plain,
! [X32877,X32878] : hAPP(c_Relation_OImage(tc_List_Olist(X32878),tc_List_Olist(X32878),c_List_Olistrel(X32878,X32877)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X32878)),c_List_Olist_ONil(X32878)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X32878),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X32878)),c_List_Olist_ONil(X32878)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X32878),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_listrel__Nil]) ).
fof(i_0_8624,plain,
! [X27469,X27470,X27471,X27472] :
( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27471,tc_Nat_Onat),X27469),X27470) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(X27471),X27472),X27470))
| hAPP(X27469,X27472) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27471),X27470)) )
& ( hBOOL(hAPP(hAPP(c_member(X27471),esk245_3(X27469,X27470,X27471)),X27470))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27471,tc_Nat_Onat),X27469),X27470) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27471),X27470)) )
& ( hAPP(X27469,esk245_3(X27469,X27470,X27471)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27471,tc_Nat_Onat),X27469),X27470) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27471),X27470)) ) ),
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_8625,plain,
! [X25632,X25633,X25634,X25635] :
( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25634,tc_Nat_Onat),X25632),X25633) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(X25634),X25635),X25633))
| hAPP(X25632,X25635) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25634),X25633)) )
& ( hBOOL(hAPP(hAPP(c_member(X25634),esk152_3(X25632,X25633,X25634)),X25633))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25634,tc_Nat_Onat),X25632),X25633) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25634),X25633)) )
& ( hAPP(X25632,esk152_3(X25632,X25633,X25634)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25634,tc_Nat_Onat),X25632),X25633) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25634),X25633)) ) ),
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_8626,plain,
! [X27289,X27290,X27291,X27292,X27293] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X27293),X27292),X27291))
| hAPP(c_Map_Orestrict__map(X27293,X27290,X27289,X27291),X27292) = hAPP(X27289,X27292) )
& ( hBOOL(hAPP(hAPP(c_member(X27293),X27292),X27291))
| hAPP(c_Map_Orestrict__map(X27293,X27290,X27289,X27291),X27292) = c_Option_Ooption_ONone(X27290) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5733])]) ).
fof(i_0_8627,plain,
! [X27151,X27152,X27153,X27154,X27155] :
( ~ hBOOL(hAPP(hAPP(c_member(X27155),X27154),X27153))
| hAPP(c_Map_Orestrict__map(X27155,X27152,X27151,X27153),X27154) = hAPP(X27151,X27154) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_restrict__in])]) ).
fof(i_0_8628,plain,
! [X20540,X20541,X20542,X20543,X20544,X20545,X20546] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20541),X20540))
| hBOOL(hAPP(X20542,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X20542,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20541),X20540))) )
& ( X20541 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20540),X20543)
| hBOOL(hAPP(X20542,X20543))
| ~ hBOOL(hAPP(X20542,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20541),X20540))) )
& ( X20545 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20544),esk74_3(X20544,X20545,X20546))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20545),X20544))
| hBOOL(hAPP(X20546,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20545),X20544))) )
& ( ~ hBOOL(hAPP(X20546,esk74_3(X20544,X20545,X20546)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20545),X20544))
| hBOOL(hAPP(X20546,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20545),X20544))) )
& ( X20545 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20544),esk74_3(X20544,X20545,X20546))
| ~ hBOOL(hAPP(X20546,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X20546,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20545),X20544))) )
& ( ~ hBOOL(hAPP(X20546,esk74_3(X20544,X20545,X20546)))
| ~ hBOOL(hAPP(X20546,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X20546,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20545),X20544))) ) ),
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_8629,plain,
! [X20532,X20533,X20534,X20535,X20536,X20537,X20538] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20533),X20532))
| hBOOL(hAPP(X20534,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X20534,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20533),X20532))) )
& ( X20533 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20532),X20535)
| hBOOL(hAPP(X20534,X20535))
| ~ hBOOL(hAPP(X20534,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20533),X20532))) )
& ( X20537 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20536),esk73_3(X20536,X20537,X20538))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20537),X20536))
| hBOOL(hAPP(X20538,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20537),X20536))) )
& ( ~ hBOOL(hAPP(X20538,esk73_3(X20536,X20537,X20538)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20537),X20536))
| hBOOL(hAPP(X20538,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20537),X20536))) )
& ( X20537 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20536),esk73_3(X20536,X20537,X20538))
| ~ hBOOL(hAPP(X20538,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X20538,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20537),X20536))) )
& ( ~ hBOOL(hAPP(X20538,esk73_3(X20536,X20537,X20538)))
| ~ hBOOL(hAPP(X20538,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X20538,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20537),X20536))) ) ),
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_8630,plain,
! [X23349,X23350,X23351,X23352] :
( ~ class_Divides_Osemiring__div(X23352)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23352),X23351),X23350))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23352),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23352),X23350),X23351)),X23349) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23352),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23352),X23350),X23349)),X23351) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__div__mult])]) ).
fof(i_0_8631,plain,
! [X28222,X28223] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28223),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28223,tc_HOL_Obool)),X28222)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X28223),c_Orderings_Otop__class_Otop(tc_fun(X28223,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28223),X28222)) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28223),c_Orderings_Otop__class_Otop(tc_fun(X28223,tc_HOL_Obool))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X28223),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28223,tc_HOL_Obool)),X28222)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28223),X28222)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__compl])])]) ).
fof(i_0_8632,plain,
! [X21164,X21165] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21165),X21164))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X21164))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21165)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21164))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21165),X21164))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21165)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21164))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21165),X21164))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21165),X21164))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21165)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21164))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X21164))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21165),X21164))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21165)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21164))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__nat__number__of])])]) ).
fof(i_0_8633,plain,
! [X24153,X24154,X24155,X24156] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24156,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X24156),X24155),X24154)),X24153) = hAPP(hAPP(c_Set_Oinsert(X24156),X24155),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24156,tc_HOL_Obool)),X24154),X24153)),
inference(variable_rename,[status(thm)],[fact_Un__insert__left]) ).
cnf(i_0_8634,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_8635,plain,
! [X29090,X29091,X29092,X29093] :
( ~ c_Finite__Set_Ofun__left__comm__idem(X29093,X29092,X29091)
| hAPP(c_Fun_Ocomp(X29092,X29092,X29092,hAPP(X29091,X29090)),hAPP(X29091,X29090)) = hAPP(X29091,X29090) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__comp__idem])]) ).
fof(i_0_8636,plain,
! [X31661,X31662,X31663] : hBOOL(hAPP(c_Finite__Set_Ofinite(X31663),c_Map_Odom(X31663,X31662,c_Map_Omap__of(X31663,X31662,X31661)))),
inference(variable_rename,[status(thm)],[fact_finite__dom__map__of]) ).
fof(i_0_8637,plain,
! [X18148,X18149] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(X18149,X18148)) = 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),X18149)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X18148))),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_8638,plain,
! [X22229,X22230,X22231,X22232] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22232,X22231),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22230),X22229)))
| X22231 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X22232,X22231) = X22229 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__mod])]) ).
fof(i_0_8639,plain,
! [X22200,X22201,X22202] : hAPP(c_Product__Type_Osnd(X22202,X22201),X22200) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22202,X22201,X22201),hAPP(c_COMBK(tc_fun(X22201,X22201),X22202),c_COMBI(X22201))),X22200),
inference(variable_rename,[status(thm)],[fact_snd__def]) ).
fof(i_0_8640,plain,
! [X23879,X23880] :
( ~ class_Int_Oring__char__0(X23880)
| ~ hBOOL(hAPP(hAPP(c_member(X23880),X23879),c_Int_Oring__1__class_OInts(X23880)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23880),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23880),c_Groups_Oone__class_Oone(X23880)),X23879)),X23879) != c_Groups_Ozero__class_Ozero(X23880) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__odd__nonzero])]) ).
fof(i_0_8641,plain,
! [X24701,X24702,X24703] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24703),X24702))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24703),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24703,tc_HOL_Obool)),X24702),X24701))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24703),X24701))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24703),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24703,tc_HOL_Obool)),X24702),X24701))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Int])])]) ).
fof(i_0_8642,plain,
! [X24533,X24534,X24535] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24535),X24534))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24535),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24535,tc_HOL_Obool)),X24534),X24533))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Diff])]) ).
fof(i_0_8643,plain,
! [X34055,X34056,X34057,X34058] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X34058),X34057),X34056))
| ~ c_List_Olinorder__class_Osorted(X34058,hAPP(hAPP(c_List_Olist_OCons(X34058),X34057),hAPP(hAPP(c_List_Olist_OCons(X34058),X34056),X34055)))
| ~ class_Orderings_Olinorder(X34058) )
& ( c_List_Olinorder__class_Osorted(X34058,hAPP(hAPP(c_List_Olist_OCons(X34058),X34056),X34055))
| ~ c_List_Olinorder__class_Osorted(X34058,hAPP(hAPP(c_List_Olist_OCons(X34058),X34057),hAPP(hAPP(c_List_Olist_OCons(X34058),X34056),X34055)))
| ~ class_Orderings_Olinorder(X34058) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X34058),X34057),X34056))
| ~ c_List_Olinorder__class_Osorted(X34058,hAPP(hAPP(c_List_Olist_OCons(X34058),X34056),X34055))
| c_List_Olinorder__class_Osorted(X34058,hAPP(hAPP(c_List_Olist_OCons(X34058),X34057),hAPP(hAPP(c_List_Olist_OCons(X34058),X34056),X34055)))
| ~ class_Orderings_Olinorder(X34058) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__many__eq])])]) ).
fof(i_0_8644,plain,
! [X34051,X34052,X34053,X34054] :
( ~ class_Orderings_Olinorder(X34054)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X34054),X34053),X34052))
| ~ c_List_Olinorder__class_Osorted(X34054,hAPP(hAPP(c_List_Olist_OCons(X34054),X34052),X34051))
| c_List_Olinorder__class_Osorted(X34054,hAPP(hAPP(c_List_Olist_OCons(X34054),X34053),hAPP(hAPP(c_List_Olist_OCons(X34054),X34052),X34051))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__many])]) ).
fof(i_0_8645,plain,
! [X22014,X22015,X22016,X22017] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22017,X22016),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X22015),X22014)))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X22017,X22016) = X22014 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__eq])]) ).
fof(i_0_8646,plain,
! [X19902,X19903] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19903))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19903,X19902)),X19903)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__le__nonneg__dividend])]) ).
fof(i_0_8647,plain,
! [X20146,X20147] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20147))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20146,X20147)),X20147)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__le__divisor])]) ).
fof(i_0_8648,plain,
! [X19928,X19929] :
( ( 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,X19928,X19929)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19929)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19928,X19929)),X19929))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19929)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__conj])])]) ).
fof(i_0_8649,plain,
! [X19908,X19909] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19909))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19908,X19909)),X19909)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__bound])]) ).
fof(i_0_8650,plain,
! [X20053,X20054] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20054))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20053,X20054)),X20054)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__less__divisor])]) ).
fof(i_0_8651,plain,
! [X32166,X32167] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X32167),hAPP(c_List_Oset(X32167),X32166))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32167)),X32166))),
inference(variable_rename,[status(thm)],[fact_card__length]) ).
fof(i_0_8652,plain,
! [X23445,X23446,X23447] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23447),hAPP(c_Int_Onumber__class_Onumber__of(X23447),X23446)),hAPP(c_Int_Onumber__class_Onumber__of(X23447),X23445)))
| c_Divides_Odiv__class_Omod(X23447,hAPP(c_Int_Onumber__class_Onumber__of(X23447),X23445),hAPP(c_Int_Onumber__class_Onumber__of(X23447),X23446)) = c_Groups_Ozero__class_Ozero(X23447)
| ~ class_Divides_Osemiring__div(X23447)
| ~ class_Int_Onumber(X23447) )
& ( c_Divides_Odiv__class_Omod(X23447,hAPP(c_Int_Onumber__class_Onumber__of(X23447),X23445),hAPP(c_Int_Onumber__class_Onumber__of(X23447),X23446)) != c_Groups_Ozero__class_Ozero(X23447)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23447),hAPP(c_Int_Onumber__class_Onumber__of(X23447),X23446)),hAPP(c_Int_Onumber__class_Onumber__of(X23447),X23445)))
| ~ class_Divides_Osemiring__div(X23447)
| ~ class_Int_Onumber(X23447) ) ),
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_8653,plain,
! [X26378,X26379,X26380,X26381,X26382] :
( hAPP(c_Set_Oimage(X26382,X26381,X26380),X26379) != X26378
| hAPP(c_Set_Oimage(tc_fun(X26382,tc_HOL_Obool),tc_fun(X26381,tc_HOL_Obool),c_Set_Oimage(X26382,X26381,X26380)),hAPP(c_Set_OPow(X26382),X26379)) = hAPP(c_Set_OPow(X26381),X26378) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__Pow__surj])]) ).
fof(i_0_8654,plain,
! [X32333,X32334,X32335] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X32335),X32334),hAPP(c_List_Oset(X32335),X32333)))
| ~ hBOOL(hAPP(c_List_Odistinct(X32335),hAPP(hAPP(c_List_Olist_OCons(X32335),X32334),X32333))) )
& ( hBOOL(hAPP(c_List_Odistinct(X32335),X32333))
| ~ hBOOL(hAPP(c_List_Odistinct(X32335),hAPP(hAPP(c_List_Olist_OCons(X32335),X32334),X32333))) )
& ( hBOOL(hAPP(hAPP(c_member(X32335),X32334),hAPP(c_List_Oset(X32335),X32333)))
| ~ hBOOL(hAPP(c_List_Odistinct(X32335),X32333))
| hBOOL(hAPP(c_List_Odistinct(X32335),hAPP(hAPP(c_List_Olist_OCons(X32335),X32334),X32333))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5735])])]) ).
fof(i_0_8655,plain,
! [X28457,X28458,X28459,X28460] :
( hAPP(c_Set_Oimage(X28460,X28459,X28458),c_Orderings_Otop__class_Otop(tc_fun(X28460,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X28459,tc_HOL_Obool))
| hAPP(c_Set_Oimage(X28460,X28459,X28458),hAPP(c_Set_Ovimage(X28460,X28459,X28458),X28457)) = X28457 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__image__vimage__eq])]) ).
cnf(i_0_8656,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_8657,plain,
! [X23506,X23507,X23508] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23508),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23507),X23506)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23508),X23506))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23508),X23507)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__zdiffD])]) ).
fof(i_0_8658,plain,
! [X22233,X22234,X22235,X22236] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22236,X22235),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22234),X22233)))
| X22235 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22236),X22235) = X22234 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__div])]) ).
fof(i_0_8659,plain,
! [X29956,X29957,X29958] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29958),c_Map_Odom(X29958,X29957,X29956)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29958),c_Orderings_Otop__class_Otop(tc_fun(X29958,tc_HOL_Obool))))
| hAPP(X29956,esk344_3(X29956,X29957,X29958)) = c_Option_Ooption_ONone(X29957) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5736])])]) ).
fof(i_0_8660,plain,
! [X20733,X20734,X20735] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20735)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20735),hAPP(c_Groups_Oabs__class_Oabs(X20735),X20734)),X20733))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20735),hAPP(c_Groups_Ouminus__class_Ouminus(X20735),X20734)),X20733)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__D2])]) ).
fof(i_0_8661,plain,
! [X19271,X19272,X19273] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19273),hAPP(c_Groups_Ouminus__class_Ouminus(X19273),X19272)),X19271))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19273),hAPP(c_Groups_Ouminus__class_Ouminus(X19273),X19271)),X19272))
| ~ class_Groups_Oordered__ab__group__add(X19273) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19273),hAPP(c_Groups_Ouminus__class_Ouminus(X19273),X19271)),X19272))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19273),hAPP(c_Groups_Ouminus__class_Ouminus(X19273),X19272)),X19271))
| ~ class_Groups_Oordered__ab__group__add(X19273) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__iff])])]) ).
fof(i_0_8662,plain,
! [X18798,X18799,X18800] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18800),hAPP(c_Groups_Ouminus__class_Ouminus(X18800),X18799)),X18798))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18800),hAPP(c_Groups_Ouminus__class_Ouminus(X18800),X18798)),X18799))
| ~ class_Groups_Oordered__ab__group__add(X18800) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18800),hAPP(c_Groups_Ouminus__class_Ouminus(X18800),X18798)),X18799))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18800),hAPP(c_Groups_Ouminus__class_Ouminus(X18800),X18799)),X18798))
| ~ class_Groups_Oordered__ab__group__add(X18800) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__less__iff])])]) ).
fof(i_0_8663,plain,
! [X19922,X19923] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19922,X19923)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19923),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19923),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19922,X19923)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19923),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_8664,plain,
! [X19924,X19925] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19925),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,X19924,X19925)),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_8665,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_8666,plain,
! [X29139,X29140,X29141,X29142] : hAPP(c_Set_Ovimage(X29142,X29141,X29140),hAPP(c_Set_OCollect(X29141),X29139)) = hAPP(c_Set_OCollect(X29142),hAPP(hAPP(c_COMBB(X29141,tc_HOL_Obool,X29142),X29139),X29140)),
inference(variable_rename,[status(thm)],[fact_vimage__Collect__eq]) ).
fof(i_0_8667,plain,
! [X22018,X22019,X22020,X22021] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22021,X22020),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X22019),X22018)))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X22021),X22020) = X22019 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__eq])]) ).
fof(i_0_8668,plain,
! [X26440,X26441,X26442,X26443] :
( ~ c_Fun_Oinj__on(X26443,X26442,X26441,X26440)
| hAPP(c_Finite__Set_Ocard(X26442),hAPP(c_Set_Oimage(X26443,X26442,X26441),X26440)) = hAPP(c_Finite__Set_Ocard(X26443),X26440) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image])]) ).
fof(i_0_8669,plain,
! [X33326,X33327,X33328,X33329] : hAPP(hAPP(c_List_Otake(X33329),X33328),hAPP(hAPP(c_List_Odrop(X33329),X33327),X33326)) = hAPP(hAPP(c_List_Odrop(X33329),X33327),hAPP(hAPP(c_List_Otake(X33329),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33328),X33327)),X33326)),
inference(variable_rename,[status(thm)],[fact_take__drop]) ).
fof(i_0_8670,plain,
! [X34024,X34025,X34026,X34027,X34028] :
( ~ class_Orderings_Olinorder(X34028)
| ~ c_List_Olinorder__class_Osorted(X34028,hAPP(hAPP(c_List_Omap(X34027,X34028),X34026),X34025))
| c_List_Olinorder__class_Osorted(X34028,hAPP(hAPP(c_List_Omap(X34027,X34028),X34026),hAPP(c_List_Ofilter(X34027,X34024),X34025))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__filter])]) ).
fof(i_0_8671,plain,
! [X20629,X20630,X20631] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20631,X20630) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20629,X20630)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20629),X20631))
| X20631 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20629),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20630),esk76_3(X20629,X20630,X20631))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mod__eq__lemma])])]) ).
fof(i_0_8672,plain,
! [X34389,X34390,X34391,X34392,X34393,X34394,X34395] :
( ( c_List_OtakeWhile(X34391,X34390,X34389) != X34389
| ~ hBOOL(hAPP(hAPP(c_member(X34391),X34392),hAPP(c_List_Oset(X34391),X34389)))
| hBOOL(hAPP(X34390,X34392)) )
& ( hBOOL(hAPP(hAPP(c_member(X34395),esk496_3(X34393,X34394,X34395)),hAPP(c_List_Oset(X34395),X34393)))
| c_List_OtakeWhile(X34395,X34394,X34393) = X34393 )
& ( ~ hBOOL(hAPP(X34394,esk496_3(X34393,X34394,X34395)))
| c_List_OtakeWhile(X34395,X34394,X34393) = X34393 ) ),
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_takeWhile__eq__all__conv])])])])])]) ).
fof(i_0_8673,plain,
! [X19377,X19378] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19378),c_Groups_Ozero__class_Ozero(X19378)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19378),X19377),X19377)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19378),c_Groups_Ozero__class_Ozero(X19378)),X19377))
| ~ class_Groups_Olinordered__ab__group__add(X19378) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19378),c_Groups_Ozero__class_Ozero(X19378)),X19377))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19378),c_Groups_Ozero__class_Ozero(X19378)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19378),X19377),X19377)))
| ~ class_Groups_Olinordered__ab__group__add(X19378) ) ),
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_8674,plain,
! [X18367,X18368] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18368),c_Groups_Ozero__class_Ozero(X18368)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18368),X18367),X18367)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18368),c_Groups_Ozero__class_Ozero(X18368)),X18367))
| ~ class_Groups_Olinordered__ab__group__add(X18368) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18368),c_Groups_Ozero__class_Ozero(X18368)),X18367))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18368),c_Groups_Ozero__class_Ozero(X18368)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18368),X18367),X18367)))
| ~ class_Groups_Olinordered__ab__group__add(X18368) ) ),
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_8675,plain,
! [X18382,X18383] :
( ( ~ 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),X18383),X18382)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18383))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18382)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18383))
| 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),X18383),X18382))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18382))
| 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),X18383),X18382))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__gr__0])])]) ).
fof(i_0_8676,plain,
! [X23107,X23108,X23109] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X23109),tc_HOL_Obool)),X23108),X23107))
| c_Hoare__Mirabelle_Ohoare__derivs(X23109,X23107,X23108) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_asm])]) ).
fof(i_0_8677,plain,
! [X20303,X20304,X20305,X20306,X20307,X20308] :
( ~ class_Divides_Oring__div(X20308)
| c_Divides_Odiv__class_Omod(X20308,X20307,X20306) != c_Divides_Odiv__class_Omod(X20308,X20305,X20306)
| c_Divides_Odiv__class_Omod(X20308,X20304,X20306) != c_Divides_Odiv__class_Omod(X20308,X20303,X20306)
| c_Divides_Odiv__class_Omod(X20308,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20308),X20307),X20304),X20306) = c_Divides_Odiv__class_Omod(X20308,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20308),X20305),X20303),X20306) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__cong])]) ).
fof(i_0_8678,plain,
! [X19835,X19836,X19837,X19838,X19839,X19840] :
( ~ class_Divides_Osemiring__div(X19840)
| c_Divides_Odiv__class_Omod(X19840,X19839,X19838) != c_Divides_Odiv__class_Omod(X19840,X19837,X19838)
| c_Divides_Odiv__class_Omod(X19840,X19836,X19838) != c_Divides_Odiv__class_Omod(X19840,X19835,X19838)
| c_Divides_Odiv__class_Omod(X19840,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19840),X19839),X19836),X19838) = c_Divides_Odiv__class_Omod(X19840,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19840),X19837),X19835),X19838) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__cong])]) ).
fof(i_0_8679,plain,
! [X19803,X19804,X19805,X19806,X19807,X19808] :
( ~ class_Divides_Osemiring__div(X19808)
| c_Divides_Odiv__class_Omod(X19808,X19807,X19806) != c_Divides_Odiv__class_Omod(X19808,X19805,X19806)
| c_Divides_Odiv__class_Omod(X19808,X19804,X19806) != c_Divides_Odiv__class_Omod(X19808,X19803,X19806)
| c_Divides_Odiv__class_Omod(X19808,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19808),X19807),X19804),X19806) = c_Divides_Odiv__class_Omod(X19808,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19808),X19805),X19803),X19806) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__cong])]) ).
fof(i_0_8680,plain,
! [X23232,X23233,X23234,X23235] :
( ~ class_Divides_Osemiring__div(X23235)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23235),X23234),X23233))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23235),X23234),X23232))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23235),X23234),c_Divides_Odiv__class_Omod(X23235,X23233,X23232))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mod])]) ).
fof(i_0_8681,plain,
! [X21810,X21811,X21812,X21813] :
( ~ class_Fields_Ofield(X21813)
| X21812 = c_Groups_Ozero__class_Ozero(X21813)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21811),X21810))
| hAPP(hAPP(c_Power_Opower__class_Opower(X21813),X21812),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21810),X21811)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21813),hAPP(hAPP(c_Power_Opower__class_Opower(X21813),X21812),X21810)),hAPP(hAPP(c_Power_Opower__class_Opower(X21813),X21812),X21811)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__diff])]) ).
fof(i_0_8682,plain,
! [X23750,X23751,X23752] :
( hBOOL(hAPP(hAPP(c_member(X23752),X23751),X23750))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23752,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X23752),X23751),X23750)),hAPP(hAPP(c_Set_Oinsert(X23752),X23751),c_Orderings_Obot__class_Obot(tc_fun(X23752,tc_HOL_Obool)))) = X23750 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5738])]) ).
fof(i_0_8683,plain,
! [X27313,X27314,X27315,X27316,X27317] :
( ~ class_Groups_Ocomm__monoid__add(X27317)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27316),X27315))
| hBOOL(hAPP(hAPP(c_member(X27316),X27314),X27315))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27316,X27317),X27313),hAPP(hAPP(c_Set_Oinsert(X27316),X27314),X27315)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27317),hAPP(X27313,X27314)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27316,X27317),X27313),X27315)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5739])]) ).
fof(i_0_8684,plain,
! [X27308,X27309,X27310,X27311,X27312] :
( ~ class_Groups_Ocomm__monoid__add(X27312)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27311),X27310))
| hBOOL(hAPP(hAPP(c_member(X27311),X27309),X27310))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27311,X27312),X27308),hAPP(hAPP(c_Set_Oinsert(X27311),X27309),X27310)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27312),hAPP(X27308,X27309)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27311,X27312),X27308),X27310)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5740])]) ).
fof(i_0_8685,plain,
! [X25710,X25711,X25712,X25713,X25714] :
( ~ class_Groups_Ocomm__monoid__mult(X25714)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25713),X25712))
| hBOOL(hAPP(hAPP(c_member(X25713),X25711),X25712))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25713,X25714),X25710),hAPP(hAPP(c_Set_Oinsert(X25713),X25711),X25712)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25714),hAPP(X25710,X25711)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25713,X25714),X25710),X25712)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5741])]) ).
fof(i_0_8686,plain,
! [X25705,X25706,X25707,X25708,X25709] :
( ~ class_Groups_Ocomm__monoid__mult(X25709)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25708),X25707))
| hBOOL(hAPP(hAPP(c_member(X25708),X25706),X25707))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25708,X25709),X25705),hAPP(hAPP(c_Set_Oinsert(X25708),X25706),X25707)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25709),hAPP(X25705,X25706)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25708,X25709),X25705),X25707)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5742])]) ).
fof(i_0_8687,plain,
! [X22221,X22222,X22223] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22223),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22222)),X22221))
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22223,X22222),hAPP(c_Divides_OnegateSnd,X22221))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__neg])]) ).
fof(i_0_8688,plain,
! [X17957,X17958,X17959,X17960] :
( ~ c_Natural_Oevaln(X17960,X17959,X17958,X17957)
| c_Natural_Oevaln(X17960,X17959,hAPP(c_Nat_OSuc,X17958),X17957) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln__Suc])]) ).
fof(i_0_8689,plain,
! [X23732,X23733,X23734,X23735] :
( ~ hBOOL(hAPP(hAPP(c_member(X23735),X23734),X23733))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23735,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X23735),X23734),X23732)),X23733) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23735,tc_HOL_Obool)),X23732),X23733) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__Diff1])]) ).
fof(i_0_8690,plain,
! [X28249,X28250,X28251] : c_Map_Odom(X28251,X28250,hAPP(hAPP(c_COMBB(X28250,tc_Option_Ooption(X28250),X28251),c_Option_Ooption_OSome(X28250)),X28249)) = c_Orderings_Otop__class_Otop(tc_fun(X28251,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_dom__const]) ).
fof(i_0_8691,plain,
! [X20367,X20368,X20369] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20369),X20368))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20369),X20367))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20368),X20369)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20367),X20369)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20368),X20367) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat_Odiff__diff__eq])]) ).
fof(i_0_8692,plain,
! [X34400,X34401,X34402] : c_List_OtakeWhile(X34402,X34401,X34400) = hAPP(hAPP(c_List_Otake(X34402),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34402)),c_List_OtakeWhile(X34402,X34401,X34400))),X34400),
inference(variable_rename,[status(thm)],[fact_takeWhile__eq__take]) ).
fof(i_0_8693,plain,
! [X26799,X26800,X26801,X26803,X26804,X26805] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk234_2(X26799,X26800)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26800)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26801),X26800))
| ~ hBOOL(hAPP(X26799,X26801)) )
& ( hBOOL(hAPP(X26799,esk234_2(X26799,X26800)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26801),X26800))
| ~ hBOOL(hAPP(X26799,X26801)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk235_2(X26803,X26804)),X26804))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X26805),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26804)))
| ~ hBOOL(hAPP(X26803,X26805)) )
& ( hBOOL(hAPP(X26803,esk235_2(X26803,X26804)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X26805),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26804)))
| ~ hBOOL(hAPP(X26803,X26805)) ) ),
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_8694,plain,
! [X20328,X20329,X20330] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20330)),X20329)),hAPP(c_Nat_OSuc,X20328)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20330),X20329)),X20328),
inference(variable_rename,[status(thm)],[fact_Suc__diff__diff]) ).
fof(i_0_8695,plain,
! [X20996,X20997,X20998,X20999] :
( ~ class_Rings_Olinordered__semidom(X20999)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20999),X20998),hAPP(c_Nat_OSuc,X20997)) != hAPP(hAPP(c_Power_Opower__class_Opower(X20999),X20996),hAPP(c_Nat_OSuc,X20997))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20999),c_Groups_Ozero__class_Ozero(X20999)),X20998))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20999),c_Groups_Ozero__class_Ozero(X20999)),X20996))
| X20998 = X20996 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inject__base])]) ).
cnf(i_0_8696,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_8697,plain,
! [X19678,X19679] :
( ( X19679 = 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),X19679)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19678)))) )
& ( X19678 = 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),X19679)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19678)))) )
& ( X19679 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X19678 != 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),X19679)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19678)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__zle__neg])])]) ).
fof(i_0_8698,plain,
! [X29648] :
( ~ class_Orderings_Owellorder(X29648)
| c_Wellfounded_Owf(X29648,hAPP(c_Set_OCollect(tc_prod(X29648,X29648)),hAPP(c_Product__Type_Oprod_Oprod__case(X29648,X29648,tc_HOL_Obool),c_Orderings_Oord__class_Oless(X29648)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf])]) ).
fof(i_0_8699,plain,
! [X33863,X33864,X33865,X33866,X33867,X33868,X33869] :
( ( hAPP(c_List_Ofilter(X33865,X33864),X33863) != c_List_Olist_ONil(X33865)
| ~ hBOOL(hAPP(hAPP(c_member(X33865),X33866),hAPP(c_List_Oset(X33865),X33863)))
| ~ hBOOL(hAPP(X33864,X33866)) )
& ( hBOOL(hAPP(hAPP(c_member(X33869),esk482_3(X33867,X33868,X33869)),hAPP(c_List_Oset(X33869),X33867)))
| hAPP(c_List_Ofilter(X33869,X33868),X33867) = c_List_Olist_ONil(X33869) )
& ( hBOOL(hAPP(X33868,esk482_3(X33867,X33868,X33869)))
| hAPP(c_List_Ofilter(X33869,X33868),X33867) = c_List_Olist_ONil(X33869) ) ),
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_8700,plain,
! [X23282,X23283,X23284,X23285] :
( ~ class_Rings_Ocomm__ring__1(X23285)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23285),X23284),X23283))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23285),X23284),X23282))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23285),X23284),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X23285),X23283),X23282))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__diff])]) ).
fof(i_0_8701,plain,
! [X23133,X23134,X23135,X23136] :
( ~ class_Rings_Ocomm__semiring__1(X23136)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23136),X23135),X23134))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23136),X23135),X23133))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23136),X23135),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23136),X23134),X23133))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__add])]) ).
fof(i_0_8702,plain,
! [X24769,X24770,X24771,X24772] :
( ~ class_Lattices_Osemilattice__inf(X24772)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24772),X24771),X24770))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24772),X24771),X24769))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24772),X24771),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24772),X24770),X24769))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__greatest])]) ).
fof(i_0_8703,plain,
! [X24765,X24766,X24767,X24768] :
( ~ class_Lattices_Osemilattice__inf(X24768)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24768),X24767),X24766))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24768),X24767),X24765))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24768),X24767),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24768),X24766),X24765))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI])]) ).
fof(i_0_8704,plain,
! [X24747,X24748,X24749,X24750] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24750),X24749),X24748))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24750),X24749),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24750),X24748),X24747)))
| ~ class_Lattices_Osemilattice__inf(X24750) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24750),X24749),X24747))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24750),X24749),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24750),X24748),X24747)))
| ~ class_Lattices_Osemilattice__inf(X24750) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24750),X24749),X24748))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24750),X24749),X24747))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24750),X24749),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24750),X24748),X24747)))
| ~ class_Lattices_Osemilattice__inf(X24750) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__inf__iff])])]) ).
fof(i_0_8705,plain,
! [X22471,X22472,X22473,X22474] :
( ~ class_Orderings_Olinorder(X22474)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22474),X22473),X22472))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22474),X22473),X22471))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22474),X22473),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22474),X22472),X22471))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__greatest])]) ).
fof(i_0_8706,plain,
! [X22467,X22468,X22469,X22470] :
( ~ class_Orderings_Olinorder(X22470)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22470),X22469),X22468))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22470),X22469),X22467))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22470),X22469),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22470),X22468),X22467))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infI])]) ).
fof(i_0_8707,plain,
! [X22449,X22450,X22451,X22452] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22452),X22451),X22450))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22452),X22451),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22452),X22450),X22449)))
| ~ class_Orderings_Olinorder(X22452) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22452),X22451),X22449))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22452),X22451),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22452),X22450),X22449)))
| ~ class_Orderings_Olinorder(X22452) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22452),X22451),X22450))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22452),X22451),X22449))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22452),X22451),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22452),X22450),X22449)))
| ~ class_Orderings_Olinorder(X22452) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__inf__iff])])]) ).
fof(i_0_8708,plain,
! [X22498,X22499,X22500,X22501] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22501),X22500),X22499))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22501),X22500),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22501),X22499),X22498)))
| ~ class_Orderings_Olinorder(X22501) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22501),X22500),X22498))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22501),X22500),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22501),X22499),X22498)))
| ~ class_Orderings_Olinorder(X22501) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22501),X22500),X22499))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22501),X22500),X22498))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22501),X22500),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22501),X22499),X22498)))
| ~ class_Orderings_Olinorder(X22501) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__less__iff__conj])])]) ).
fof(i_0_8709,plain,
! [X18972,X18973] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18973)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18972)))),
inference(variable_rename,[status(thm)],[i_0_5745]) ).
fof(i_0_8710,plain,
! [X19708,X19709,X19710] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19710))
| X19710 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19709),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19710),X19708))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19709))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19708),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_8711,plain,
! [X33871,X33872,X33873,X33874,X33875,X33876,X33877] :
( ( hAPP(c_List_Ofilter(X33873,X33872),X33871) != X33871
| ~ hBOOL(hAPP(hAPP(c_member(X33873),X33874),hAPP(c_List_Oset(X33873),X33871)))
| hBOOL(hAPP(X33872,X33874)) )
& ( hBOOL(hAPP(hAPP(c_member(X33877),esk483_3(X33875,X33876,X33877)),hAPP(c_List_Oset(X33877),X33875)))
| hAPP(c_List_Ofilter(X33877,X33876),X33875) = X33875 )
& ( ~ hBOOL(hAPP(X33876,esk483_3(X33875,X33876,X33877)))
| hAPP(c_List_Ofilter(X33877,X33876),X33875) = X33875 ) ),
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_8712,plain,
! [X19904,X19905] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19905))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19904))
| 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,X19905,X19904))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I2_J])]) ).
fof(i_0_8713,plain,
! [X17498,X17499,X17500,X17501,X17502] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17502),X17501),X17500))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17499),X17500),X17498))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X17502,X17499)),X17501),X17498)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc_OSemi])]) ).
fof(i_0_8714,plain,
! [X33059,X33060,X33061,X33062] : hAPP(hAPP(c_List_Onth(X33062),hAPP(hAPP(c_List_Oappend(X33062),X33061),X33060)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33062)),X33061)),X33059)) = hAPP(hAPP(c_List_Onth(X33062),X33060),X33059),
inference(variable_rename,[status(thm)],[fact_nth__append__length__plus]) ).
cnf(i_0_8715,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_8716,plain,
! [X32902,X32903,X32904,X32905,X32906,X32907] : hAPP(c_List_Olist_Olist__case(X32907,X32906,X32905,X32904),hAPP(hAPP(c_List_Olist_OCons(X32906),X32903),X32902)) = hAPP(hAPP(X32904,X32903),X32902),
inference(variable_rename,[status(thm)],[fact_list_Osimps_I5_J]) ).
fof(i_0_8717,plain,
! [X24024,X24025,X24026,X24027] :
( ~ hBOOL(hAPP(X24027,X24026))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24025,tc_HOL_Obool)),X24027),X24024),X24026)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup1I1])]) ).
fof(i_0_8718,plain,
! [X23916,X23917,X23918,X23919] :
( ( ~ hBOOL(hAPP(X23919,X23918))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23916,tc_HOL_Obool)),X23917),X23919),X23918)) )
& ( ~ hBOOL(hAPP(X23917,X23918))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23916,tc_HOL_Obool)),X23917),X23919),X23918)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5747])])]) ).
fof(i_0_8719,plain,
! [X24020,X24021,X24022,X24023] :
( ~ hBOOL(hAPP(X24023,X24022))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24021,tc_HOL_Obool)),X24020),X24023),X24022)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup1I2])]) ).
fof(i_0_8720,plain,
! [X21027,X21028,X21029] :
( ~ class_Rings_Olinordered__idom(X21029)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21029),c_Groups_Ozero__class_Ozero(X21029)),hAPP(hAPP(c_Power_Opower__class_Opower(X21029),hAPP(c_Groups_Oabs__class_Oabs(X21029),X21028)),X21027))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power__abs])]) ).
fof(i_0_8721,plain,
! [X20553,X20554,X20555] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20555),X20554))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20553),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20554),X20555))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20553),X20555)),hAPP(c_Nat_OSuc,X20554)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq1])]) ).
fof(i_0_8722,plain,
! [X23062,X23063] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23063,tc_HOL_Obool)),X23062),c_Orderings_Obot__class_Obot(tc_fun(X23063,tc_HOL_Obool))))
| X23062 = c_Orderings_Obot__class_Obot(tc_fun(X23063,tc_HOL_Obool)) )
& ( X23062 != c_Orderings_Obot__class_Obot(tc_fun(X23063,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23063,tc_HOL_Obool)),X23062),c_Orderings_Obot__class_Obot(tc_fun(X23063,tc_HOL_Obool)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__empty])]) ).
fof(i_0_8723,plain,
! [X29852,X29853] :
( ~ c_Wellfounded_OwfP(X29853,X29852)
| c_Wellfounded_Oacyclic(X29853,hAPP(c_Set_OCollect(tc_prod(X29853,X29853)),hAPP(c_Product__Type_Oprod_Oprod__case(X29853,X29853,tc_HOL_Obool),X29852))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__acyclicP])]) ).
fof(i_0_8724,plain,
! [X23551,X23552] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23552)),X23551))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23552),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X23551)))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23552),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X23551))))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23552)),X23551)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__dvd__iff])]) ).
cnf(i_0_8725,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_8726,plain,
! [X29503,X29504,X29505,X29506] : hAPP(hAPP(c_Relation_Orel__comp(X29506,X29505,X29504),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29506,X29505),tc_HOL_Obool))),X29503) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29506,X29504),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_rel__comp__empty1]) ).
fof(i_0_8727,plain,
! [X20233,X20234] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X20233,X20234) != 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),X20233)),X20234) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20233),X20234))
| X20234 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X20233,X20234) = 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),X20233)),X20234) = 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),X20233),X20234))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| X20234 = 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_8728,plain,
! [X33935,X33936,X33937,X33938,X33939,X33940,X33941] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X33939),X33940),hAPP(c_List_Oset(X33939),X33936)))
| hBOOL(hAPP(X33938,X33940))
| c_List_Opartition(X33939,X33938,X33937) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33939),tc_List_Olist(X33939)),X33936),X33935) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X33939),X33941),hAPP(c_List_Oset(X33939),X33935)))
| ~ hBOOL(hAPP(X33938,X33941))
| c_List_Opartition(X33939,X33938,X33937) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33939),tc_List_Olist(X33939)),X33936),X33935) ) ),
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_8729,plain,
! [X19772,X19773,X19774] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19774),hAPP(c_Groups_Ouminus__class_Ouminus(X19774),X19773)),hAPP(c_Groups_Ouminus__class_Ouminus(X19774),X19772)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19774),X19772),X19773))
| ~ class_Lattices_Oboolean__algebra(X19774) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19774),X19772),X19773))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19774),hAPP(c_Groups_Ouminus__class_Ouminus(X19774),X19773)),hAPP(c_Groups_Ouminus__class_Ouminus(X19774),X19772)))
| ~ class_Lattices_Oboolean__algebra(X19774) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__le__compl__iff])])]) ).
fof(i_0_8730,plain,
! [X19268,X19269,X19270] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19270),hAPP(c_Groups_Ouminus__class_Ouminus(X19270),X19269)),hAPP(c_Groups_Ouminus__class_Ouminus(X19270),X19268)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19270),X19268),X19269))
| ~ class_Groups_Oordered__ab__group__add(X19270) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19270),X19268),X19269))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19270),hAPP(c_Groups_Ouminus__class_Ouminus(X19270),X19269)),hAPP(c_Groups_Ouminus__class_Ouminus(X19270),X19268)))
| ~ class_Groups_Oordered__ab__group__add(X19270) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__iff__le])])]) ).
fof(i_0_8731,plain,
! [X18801,X18802,X18803] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18803),hAPP(c_Groups_Ouminus__class_Ouminus(X18803),X18802)),hAPP(c_Groups_Ouminus__class_Ouminus(X18803),X18801)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18803),X18801),X18802))
| ~ class_Groups_Oordered__ab__group__add(X18803) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18803),X18801),X18802))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18803),hAPP(c_Groups_Ouminus__class_Ouminus(X18803),X18802)),hAPP(c_Groups_Ouminus__class_Ouminus(X18803),X18801)))
| ~ class_Groups_Oordered__ab__group__add(X18803) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__iff__less])])]) ).
fof(i_0_8732,plain,
! [X26791,X26792,X26794,X26795,X26796,X26798] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk232_2(X26791,X26792)),X26792))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X26794),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26792)))
| hBOOL(hAPP(X26791,X26794)) )
& ( ~ hBOOL(hAPP(X26791,esk232_2(X26791,X26792)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X26794),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26792)))
| hBOOL(hAPP(X26791,X26794)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk233_2(X26795,X26796)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26796)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26798),X26796))
| hBOOL(hAPP(X26795,X26798)) )
& ( ~ hBOOL(hAPP(X26795,esk233_2(X26795,X26796)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26798),X26796))
| hBOOL(hAPP(X26795,X26798)) ) ),
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_8733,plain,
! [X21012,X21013,X21014] :
( ~ class_Rings_Olinordered__semidom(X21014)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21014),c_Groups_Oone__class_Oone(X21014)),X21013))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21014),c_Groups_Oone__class_Oone(X21014)),hAPP(hAPP(c_Power_Opower__class_Opower(X21014),X21013),hAPP(c_Nat_OSuc,X21012)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__gt1])]) ).
fof(i_0_8734,plain,
! [X19705,X19706,X19707] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19707))
| X19707 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19707),X19705))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19706),X19707))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X19705)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__quotient__aux1])]) ).
cnf(i_0_8735,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_8736,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_8737,plain,
! [X21166,X21167] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21167)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21166)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21167),X21166))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21167),c_Int_OPls)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21167),X21166))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21167)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21166))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21167),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),X21167)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21166))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5751])])]) ).
fof(i_0_8738,plain,
! [X20775,X20776,X20777] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20777),hAPP(c_Int_Onumber__class_Onumber__of(X20777),X20776)),hAPP(c_Int_Onumber__class_Onumber__of(X20777),X20775)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20776),X20775))
| ~ class_Int_Onumber__ring(X20777)
| ~ class_Rings_Olinordered__idom(X20777) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20776),X20775))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20777),hAPP(c_Int_Onumber__class_Onumber__of(X20777),X20776)),hAPP(c_Int_Onumber__class_Onumber__of(X20777),X20775)))
| ~ class_Int_Onumber__ring(X20777)
| ~ class_Rings_Olinordered__idom(X20777) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__number__of])])]) ).
fof(i_0_8739,plain,
! [X20784,X20785,X20786] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20786),hAPP(c_Int_Onumber__class_Onumber__of(X20786),X20785)),hAPP(c_Int_Onumber__class_Onumber__of(X20786),X20784)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20785),X20784))
| ~ class_Int_Onumber__ring(X20786)
| ~ class_Rings_Olinordered__idom(X20786) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20785),X20784))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20786),hAPP(c_Int_Onumber__class_Onumber__of(X20786),X20785)),hAPP(c_Int_Onumber__class_Onumber__of(X20786),X20784)))
| ~ class_Int_Onumber__ring(X20786)
| ~ class_Rings_Olinordered__idom(X20786) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of])])]) ).
fof(i_0_8740,plain,
! [X23509,X23510] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23510))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23509))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23510),X23509))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23509),X23510))
| X23510 = X23509 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__antisym__nonneg])]) ).
fof(i_0_8741,plain,
! [X23141,X23142,X23143] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23143),X23141))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23142),X23141))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23141),X23142))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23143),X23142))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23142),X23143)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23141),X23143))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23142),X23141))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23141),X23142))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23143),X23142))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23142),X23143)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5752])])]) ).
fof(i_0_8742,plain,
! [X32683,X32684,X32685,X32686] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32686)),X32685)),X32684))
| hAPP(hAPP(c_List_Olist__update(X32686,X32685),X32684),X32683) = X32685 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__beyond])]) ).
fof(i_0_8743,plain,
! [X19041] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19041),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19041),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19041),X19041)))),
inference(variable_rename,[status(thm)],[fact_le__cube]) ).
fof(i_0_8744,plain,
! [X33805,X33806,X33807] :
( ~ hBOOL(hAPP(hAPP(c_member(X33807),X33806),hAPP(c_List_Oset(X33807),c_List_Obutlast(X33807,X33805))))
| hBOOL(hAPP(hAPP(c_member(X33807),X33806),hAPP(c_List_Oset(X33807),X33805))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__butlastD])]) ).
fof(i_0_8745,plain,
! [X24344,X24345,X24346,X24347,X24348] :
( ~ hBOOL(hAPP(hAPP(c_member(X24348),X24347),X24346))
| hAPP(hAPP(c_Set_Oinsert(X24345),hAPP(X24344,X24347)),hAPP(c_Set_Oimage(X24348,X24345,X24344),X24346)) = hAPP(c_Set_Oimage(X24348,X24345,X24344),X24346) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__image])]) ).
cnf(i_0_8746,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_8747,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_8748,plain,
! [X22226,X22227,X22228] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22228,X22228),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22227),X22226)))
| X22228 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X22227 = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__quotient])]) ).
fof(i_0_8749,plain,
! [X22206,X22207,X22208] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22208,X22208),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22207),X22206)))
| X22208 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X22206 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__remainder])]) ).
fof(i_0_8750,plain,
! [X30742,X30743,X30744,X30745,X30746] :
( ~ c_Finite__Set_Ofolding__one(X30746,X30745,X30744)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30746),X30743))
| hBOOL(hAPP(hAPP(c_member(X30746),X30742),X30743))
| hAPP(X30744,hAPP(hAPP(c_Set_Oinsert(X30746),X30742),X30743)) = hAPP(hAPP(c_Finite__Set_Ofold(X30746,X30746,X30745),X30742),X30743) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5755])]) ).
fof(i_0_8751,plain,
! [X30473,X30474,X30475] :
( ~ c_Wellfounded_Owf(X30475,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30475,X30475),tc_HOL_Obool),X30474),X30473))
| c_Wellfounded_Owf(X30475,X30473) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__exp])]) ).
fof(i_0_8752,plain,
! [X19141,X19142,X19143] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19143),hAPP(c_Int_Oring__1__class_Oof__int(X19143),X19142)),hAPP(c_Int_Oring__1__class_Oof__int(X19143),X19141)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19142),X19141))
| ~ class_Rings_Olinordered__idom(X19143) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19142),X19141))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19143),hAPP(c_Int_Oring__1__class_Oof__int(X19143),X19142)),hAPP(c_Int_Oring__1__class_Oof__int(X19143),X19141)))
| ~ class_Rings_Olinordered__idom(X19143) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__le__iff])])]) ).
fof(i_0_8753,plain,
! [X19134,X19135,X19136] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19136),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X19136),X19135)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X19136),X19134)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19135),X19134))
| ~ class_Rings_Olinordered__semidom(X19136) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19135),X19134))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19136),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X19136),X19135)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X19136),X19134)))
| ~ class_Rings_Olinordered__semidom(X19136) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__le__iff])])]) ).
fof(i_0_8754,plain,
! [X18985,X18986,X18987] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18987),hAPP(c_Int_Oring__1__class_Oof__int(X18987),X18986)),hAPP(c_Int_Oring__1__class_Oof__int(X18987),X18985)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18986),X18985))
| ~ class_Rings_Olinordered__idom(X18987) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18986),X18985))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18987),hAPP(c_Int_Oring__1__class_Oof__int(X18987),X18986)),hAPP(c_Int_Oring__1__class_Oof__int(X18987),X18985)))
| ~ class_Rings_Olinordered__idom(X18987) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__less__iff])])]) ).
fof(i_0_8755,plain,
! [X18536,X18537,X18538] :
( ~ class_Rings_Olinordered__semidom(X18538)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18538),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18538),X18537)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18538),X18536)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18537),X18536)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__less__imp__less])]) ).
fof(i_0_8756,plain,
! [X18530,X18531,X18532] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18532),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18532),X18531)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18532),X18530)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18531),X18530))
| ~ class_Rings_Olinordered__semidom(X18532) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18531),X18530))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18532),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18532),X18531)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18532),X18530)))
| ~ class_Rings_Olinordered__semidom(X18532) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__less__iff])])]) ).
fof(i_0_8757,plain,
! [X29928] :
( X29928 = hAPP(c_Int_OAbs__Integ,esk335_1(X29928))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk335_1(X29928)),c_Int_OInteg)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5756])])]) ).
cnf(i_0_8758,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_8759,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_8760,plain,
! [X21607,X21608,X21609,X21610] :
( ~ class_Fields_Ofield(X21610)
| X21609 = c_Groups_Ozero__class_Ozero(X21610)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21610),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21610),X21608),X21609)),X21607) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21610),hAPP(hAPP(c_Power_Opower__class_Opower(X21610),X21608),X21607)),hAPP(hAPP(c_Power_Opower__class_Opower(X21610),X21609),X21607)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__power__divide])]) ).
fof(i_0_8761,plain,
! [X19676,X19677] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19677),X19676))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19677),c_Groups_Oone__class_Oone(tc_Int_Oint))),X19676)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__imp__add1__zle])]) ).
fof(i_0_8762,plain,
! [X25330,X25331,X25332] :
( ~ class_Orderings_Olinorder(X25332)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25332),X25331))
| X25331 = c_Orderings_Obot__class_Obot(tc_fun(X25332,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25332),X25330))
| X25330 = c_Orderings_Obot__class_Obot(tc_fun(X25332,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMin(X25332,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25332,tc_HOL_Obool)),X25331),X25330)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25332),c_Big__Operators_Olinorder__class_OMin(X25332,X25331)),c_Big__Operators_Olinorder__class_OMin(X25332,X25330)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__Un])]) ).
fof(i_0_8763,plain,
! [X25333,X25334,X25335] :
( ~ class_Orderings_Olinorder(X25335)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25335),X25334))
| X25334 = c_Orderings_Obot__class_Obot(tc_fun(X25335,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25335),X25333))
| X25333 = c_Orderings_Obot__class_Obot(tc_fun(X25335,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMax(X25335,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25335,tc_HOL_Obool)),X25334),X25333)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25335),c_Big__Operators_Olinorder__class_OMax(X25335,X25334)),c_Big__Operators_Olinorder__class_OMax(X25335,X25333)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__Un])]) ).
fof(i_0_8764,plain,
! [X25327,X25328,X25329] :
( ~ class_Lattices_Olattice(X25329)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25329),X25328))
| X25328 = c_Orderings_Obot__class_Obot(tc_fun(X25329,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25329),X25327))
| X25327 = c_Orderings_Obot__class_Obot(tc_fun(X25329,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OInf__fin(X25329,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25329,tc_HOL_Obool)),X25328),X25327)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25329),c_Big__Operators_Olattice__class_OInf__fin(X25329,X25328)),c_Big__Operators_Olattice__class_OInf__fin(X25329,X25327)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__idem])]) ).
fof(i_0_8765,plain,
! [X25114,X25115,X25116] :
( ~ class_Lattices_Olattice(X25116)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25116),X25115))
| X25115 = c_Orderings_Obot__class_Obot(tc_fun(X25116,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25116),X25114))
| X25114 = c_Orderings_Obot__class_Obot(tc_fun(X25116,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OSup__fin(X25116,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25116,tc_HOL_Obool)),X25115),X25114)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25116),c_Big__Operators_Olattice__class_OSup__fin(X25116,X25115)),c_Big__Operators_Olattice__class_OSup__fin(X25116,X25114)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__idem])]) ).
fof(i_0_8766,plain,
! [X28230,X28231] :
( ( hAPP(c_Code__Numeral_Oof__nat,X28231) != hAPP(c_Code__Numeral_Oof__nat,X28230)
| X28231 = X28230
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X28230),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X28231),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) )
& ( X28231 != X28230
| hAPP(c_Code__Numeral_Oof__nat,X28231) = hAPP(c_Code__Numeral_Oof__nat,X28230)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X28230),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X28231),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_8767,plain,
! [X19359,X19360] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X19360)),hAPP(c_Int_Onat,X19359)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19360),X19359))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19360)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19360),X19359))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X19360)),hAPP(c_Int_Onat,X19359)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19360)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X19360)),hAPP(c_Int_Onat,X19359)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19360),X19359))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19359)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19360),X19359))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X19360)),hAPP(c_Int_Onat,X19359)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19359)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__eq__zle])])]) ).
fof(i_0_8768,plain,
! [X19689,X19690] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X19690)),hAPP(c_Int_Onat,X19689)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19690),X19689))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19690)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19690),X19689))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X19690)),hAPP(c_Int_Onat,X19689)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19690)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__eq__zless])])]) ).
fof(i_0_8769,plain,
! [X18993,X18994] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X18993)),hAPP(c_Int_Onat,X18994)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18993),X18994))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18994)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18993),X18994))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X18993)),hAPP(c_Int_Onat,X18994)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18994)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mono__iff])])]) ).
cnf(i_0_8770,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_8771,plain,
! [X30469,X30470,X30471,X30472] : hAPP(X30472,hAPP(hAPP(hAPP(c_Nat_Ocompow(X30471,X30471),X30470),X30472),X30469)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(X30471,X30471),X30470),X30472),hAPP(X30472,X30469)),
inference(variable_rename,[status(thm)],[fact_funpow__swap1]) ).
fof(i_0_8772,plain,
! [X33879,X33880,X33881,X33882,X33883,X33884] :
( ~ class_Orderings_Olinorder(X33884)
| hBOOL(hAPP(X33883,X33882))
| hAPP(c_List_Ofilter(X33881,X33883),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X33881,X33884,X33880),X33882),X33879)) = hAPP(c_List_Ofilter(X33881,X33883),X33879) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5760])]) ).
fof(i_0_8773,plain,
! [X18841,X18842,X18843,X18844] :
( ~ class_Rings_Ocomm__semiring__1(X18844)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18844),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18844),X18843),X18842)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18844),X18841),X18842)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18844),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18844),X18843),X18841)),X18842) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J])]) ).
fof(i_0_8774,plain,
! [X24838,X24839,X24840,X24841] :
( ~ class_Lattices_Odistrib__lattice(X24841)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24841),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24841),X24840),X24839)),X24838) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24841),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24841),X24840),X24838)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24841),X24839),X24838)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__distrib2])]) ).
fof(i_0_8775,plain,
! [X24842,X24843,X24844,X24845] :
( ~ class_Lattices_Odistrib__lattice(X24845)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24845),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24845),X24844),X24843)),X24842) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24845),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24845),X24844),X24842)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24845),X24843),X24842)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__inf__distrib2])]) ).
fof(i_0_8776,plain,
! [X22594,X22595,X22596,X22597] :
( ~ class_Orderings_Olinorder(X22597)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22597),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22597),X22596),X22595)),X22594) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22597),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22597),X22596),X22594)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22597),X22595),X22594)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__inf__distrib2])]) ).
fof(i_0_8777,plain,
! [X22590,X22591,X22592,X22593] :
( ~ class_Orderings_Olinorder(X22593)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22593),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22593),X22592),X22591)),X22590) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22593),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22593),X22592),X22590)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22593),X22591),X22590)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__distrib2])]) ).
fof(i_0_8778,plain,
! [X21484,X21485,X21486,X21487] :
( ~ class_Rings_Odivision__ring(X21487)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21487),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21487),X21486),X21485)),X21484) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21487),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21487),X21486),X21484)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21487),X21485),X21484)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__divide__distrib])]) ).
fof(i_0_8779,plain,
! [X21471,X21472,X21473,X21474] :
( ~ class_Rings_Odivision__ring(X21474)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21474),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21474),X21473),X21472)),X21471) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21474),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21474),X21473),X21471)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21474),X21472),X21471)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__divide__distrib])]) ).
fof(i_0_8780,plain,
! [X21499,X21500,X21501,X21502] :
( ~ class_Fields_Ofield__inverse__zero(X21502)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21502),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21502),X21501),X21500)),X21499) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21502),hAPP(hAPP(c_Power_Opower__class_Opower(X21502),X21501),X21499)),hAPP(hAPP(c_Power_Opower__class_Opower(X21502),X21500),X21499)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__divide])]) ).
fof(i_0_8781,plain,
! [X20933,X20934,X20935,X20936] :
( ~ class_Groups_Ocomm__monoid__mult(X20936)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20936),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20936),X20935),X20934)),X20933) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20936),hAPP(hAPP(c_Power_Opower__class_Opower(X20936),X20935),X20933)),hAPP(hAPP(c_Power_Opower__class_Opower(X20936),X20934),X20933)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult__distrib])]) ).
fof(i_0_8782,plain,
! [X20677,X20678,X20679,X20680] :
( ~ class_Rings_Ocomm__semiring__1(X20680)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20680),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20680),X20679),X20678)),X20677) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20680),hAPP(hAPP(c_Power_Opower__class_Opower(X20680),X20679),X20677)),hAPP(hAPP(c_Power_Opower__class_Opower(X20680),X20678),X20677)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J])]) ).
fof(i_0_8783,plain,
! [X22612,X22613,X22614,X22615] :
( ~ class_Groups_Oordered__ab__group__add(X22615)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22615),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22615),X22614),X22613)),X22612) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22615),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22615),X22614),X22612)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22615),X22613),X22612)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__diff__distrib__left])]) ).
fof(i_0_8784,plain,
! [X22490,X22491,X22492,X22493] :
( ~ class_Groups_Oordered__ab__group__add(X22493)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22493),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22493),X22492),X22491)),X22490) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22493),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22493),X22492),X22490)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22493),X22491),X22490)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__diff__distrib__left])]) ).
fof(i_0_8785,plain,
! [X18863,X18864,X18865,X18866] :
( ~ class_Rings_Ocomm__semiring(X18866)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18866),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18866),X18865),X18864)),X18863) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18866),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18866),X18865),X18863)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18866),X18864),X18863)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__class_Odistrib])]) ).
fof(i_0_8786,plain,
! [X18845,X18846,X18847,X18848] :
( ~ class_Rings_Ocomm__semiring__1(X18848)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18848),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18848),X18847),X18846)),X18845) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18848),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18848),X18847),X18845)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18848),X18846),X18845)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J])]) ).
fof(i_0_8787,plain,
! [X22618,X22619,X22620,X22621] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X22621)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22621),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22621),X22620),X22619)),X22618) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22621),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22621),X22620),X22618)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22621),X22619),X22618)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__add__distrib__left])]) ).
fof(i_0_8788,plain,
! [X22540,X22541,X22542,X22543] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X22543)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22543),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22543),X22542),X22541)),X22540) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22543),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22543),X22542),X22540)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22543),X22541),X22540)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__add__distrib__left])]) ).
fof(i_0_8789,plain,
! [X32123,X32124,X32125,X32126,X32127] :
( ~ class_Orderings_Olinorder(X32127)
| hAPP(c_List_Oset(X32126),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32126,X32127,X32125),X32124),X32123)) = hAPP(hAPP(c_Set_Oinsert(X32126),X32124),hAPP(c_List_Oset(X32126),X32123)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__insort])]) ).
fof(i_0_8790,plain,
! [X20051,X20052] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20052))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20051))
| 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),X20052),X20051))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I1_J])]) ).
fof(i_0_8791,plain,
! [X19556,X19557] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19557))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19556))
| 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),X19557),X19556))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J])]) ).
fof(i_0_8792,plain,
! [X19520,X19521] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19521))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19520))
| 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),X19521),X19520))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J])]) ).
fof(i_0_8793,plain,
! [X19495,X19496] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19496))
| ~ 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),X19496),X19495))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19495))
| ~ 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),X19496),X19495))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19496))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19495))
| 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),X19496),X19495))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__0__less__mult__iff])])]) ).
fof(i_0_8794,plain,
! [X23448,X23449,X23450,X23451,X23452] :
( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23452),X23449),X23451) != hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23452),X23448),X23450)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23452),X23449),X23450) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23452),X23451),X23448)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23452),X23450),X23448))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23452),X23451),X23449))
| X23450 = c_Groups_Ozero__class_Ozero(X23452)
| X23451 = c_Groups_Ozero__class_Ozero(X23452)
| ~ class_Divides_Osemiring__div(X23452) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23452),X23449),X23450) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23452),X23451),X23448)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23452),X23449),X23451) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23452),X23448),X23450)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23452),X23450),X23448))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23452),X23451),X23449))
| X23450 = c_Groups_Ozero__class_Ozero(X23452)
| X23451 = c_Groups_Ozero__class_Ozero(X23452)
| ~ class_Divides_Osemiring__div(X23452) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__div__div__eq__mult])])]) ).
fof(i_0_8795,plain,
! [X30766,X30767,X30768] :
( ~ class_Orderings_Olinorder(X30768)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30768),X30767))
| hBOOL(hAPP(hAPP(c_member(X30768),X30766),X30767))
| c_Big__Operators_Olattice_OInf__fin(X30768,c_Orderings_Oord__class_Omin(X30768),hAPP(hAPP(c_Set_Oinsert(X30768),X30766),X30767)) = hAPP(hAPP(c_Finite__Set_Ofold(X30768,X30768,c_Orderings_Oord__class_Omin(X30768)),X30766),X30767) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5761])]) ).
fof(i_0_8796,plain,
! [X30639,X30640,X30641] :
( ~ class_Orderings_Olinorder(X30641)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30641),X30640))
| hBOOL(hAPP(hAPP(c_member(X30641),X30639),X30640))
| c_Big__Operators_Olattice_OSup__fin(X30641,c_Orderings_Oord__class_Omax(X30641),hAPP(hAPP(c_Set_Oinsert(X30641),X30639),X30640)) = hAPP(hAPP(c_Finite__Set_Ofold(X30641,X30641,c_Orderings_Oord__class_Omax(X30641)),X30639),X30640) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5762])]) ).
fof(i_0_8797,plain,
! [X27643,X27644] :
( ~ class_Orderings_Olinorder(X27644)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27644,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X27644),X27643),c_Orderings_Obot__class_Obot(tc_fun(X27644,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(X27644),X27643)) = hAPP(c_SetInterval_Oord__class_OatLeast(X27644),X27643) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I1_J])]) ).
fof(i_0_8798,plain,
! [X30368,X30369,X30370] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X30370,X30369)),hAPP(c_Relation_Oconverse(X30369,X30370),X30368)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X30369,X30370)),X30368)) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X30369,X30370)),X30368))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X30370,X30369)),hAPP(c_Relation_Oconverse(X30369,X30370),X30368))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__converse])]) ).
fof(i_0_8799,plain,
! [X28311] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28311),c_Orderings_Otop__class_Otop(tc_fun(X28311,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(X28311),c_Orderings_Otop__class_Otop(tc_fun(X28311,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__card__ge__0])]) ).
fof(i_0_8800,plain,
! [X32005,X32006,X32007] :
( ~ hBOOL(hAPP(c_List_Odistinct(X32007),X32006))
| hAPP(c_List_Oset(X32007),c_List_Oremove1(X32007,X32005,X32006)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X32007,tc_HOL_Obool)),hAPP(c_List_Oset(X32007),X32006)),hAPP(hAPP(c_Set_Oinsert(X32007),X32005),c_Orderings_Obot__class_Obot(tc_fun(X32007,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__remove1__eq])]) ).
fof(i_0_8801,plain,
! [X31330,X31331,X31332] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31332,tc_HOL_Obool)),X31331),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31332,tc_HOL_Obool),X31330)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X31332,tc_HOL_Obool),tc_fun(X31332,tc_HOL_Obool)),X31330),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31332,tc_HOL_Obool)),X31331)),
inference(variable_rename,[status(thm)],[fact_Int__Union]) ).
fof(i_0_8802,plain,
! [X31251,X31252,X31253] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31253,tc_HOL_Obool)),X31252),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31253,tc_HOL_Obool),X31251)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X31253,tc_HOL_Obool),tc_fun(X31253,tc_HOL_Obool)),X31251),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31253,tc_HOL_Obool)),X31252)),
inference(variable_rename,[status(thm)],[fact_Un__Inter]) ).
fof(i_0_8803,plain,
! [X32141,X32142,X32143,X32144,X32145] :
( ~ class_Orderings_Olinorder(X32145)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32144)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32144,X32145,X32143),X32142),X32141)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32144)),X32141)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__insort])]) ).
fof(i_0_8804,plain,
! [X23558,X23559] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23559))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23559),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23558)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X23559)),X23558)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23559))
| X23558 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X23559)),X23558)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23559))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23559))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X23559)),X23558)) )
& ( X23558 != 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)),X23559))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X23559)),X23558)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23559))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23559),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23558)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X23559)),X23558)) )
& ( X23558 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23559),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23558)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X23559)),X23558)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5763])])]) ).
fof(i_0_8805,plain,
! [X19020,X19021] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X19021)),X19020))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19021),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19020)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19021)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19021),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19020)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X19021)),X19020))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19021)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__iff])])]) ).
cnf(i_0_8806,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_8807,plain,
! [X23322,X23323] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23323,tc_HOL_Obool)),X23322),c_Orderings_Obot__class_Obot(tc_fun(X23323,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[i_0_5764]) ).
fof(i_0_8808,plain,
! [X27259,X27260,X27261,X27262,X27263] :
( hBOOL(hAPP(hAPP(c_member(X27263),X27262),X27261))
| hAPP(c_Map_Orestrict__map(X27263,X27260,X27259,X27261),X27262) = c_Option_Ooption_ONone(X27260) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5765])]) ).
fof(i_0_8809,plain,
! [X32163,X32164,X32165] :
( ~ class_Orderings_Olinorder(X32165)
| c_List_Oremove1(X32165,X32164,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32165,X32165,c_COMBI(X32165)),X32164),X32163)) = X32163 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remove1__insort])]) ).
fof(i_0_8810,plain,
! [X29904,X29905,X29906,X29907,X29908,X29909,X29910] :
( ( ~ hBOOL(hAPP(c_Predicate_OPowp(X29906,X29905),X29904))
| ~ hBOOL(hAPP(hAPP(c_member(X29906),X29907),X29904))
| hBOOL(hAPP(X29905,X29907)) )
& ( hBOOL(hAPP(hAPP(c_member(X29910),esk332_3(X29908,X29909,X29910)),X29908))
| hBOOL(hAPP(c_Predicate_OPowp(X29910,X29909),X29908)) )
& ( ~ hBOOL(hAPP(X29909,esk332_3(X29908,X29909,X29910)))
| hBOOL(hAPP(c_Predicate_OPowp(X29910,X29909),X29908)) ) ),
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_8811,plain,
! [X27294,X27295,X27296,X27297] : hAPP(c_Map_Orestrict__map(X27297,X27296,X27295,c_Orderings_Obot__class_Obot(tc_fun(X27297,tc_HOL_Obool))),X27294) = c_Option_Ooption_ONone(X27296),
inference(variable_rename,[status(thm)],[fact_restrict__map__to__empty]) ).
fof(i_0_8812,plain,
! [X23461,X23462,X23463,X23464] : hAPP(c_Product__Type_Oprod_Oprod__case(X23464,X23463,X23462),c_Product__Type_Ocurry(X23464,X23463,X23462,X23461)) = X23461,
inference(variable_rename,[status(thm)],[fact_split__curry]) ).
fof(i_0_8813,plain,
! [X21100,X21101,X21102] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(X21102),X21101) != hAPP(c_Int_Onumber__class_Onumber__of(X21102),X21100)
| c_Int_Oiszero(X21102,hAPP(c_Int_Onumber__class_Onumber__of(X21102),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21101),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21100))))
| ~ class_Int_Onumber__ring(X21102) )
& ( ~ c_Int_Oiszero(X21102,hAPP(c_Int_Onumber__class_Onumber__of(X21102),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21101),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21100))))
| hAPP(c_Int_Onumber__class_Onumber__of(X21102),X21101) = hAPP(c_Int_Onumber__class_Onumber__of(X21102),X21100)
| ~ class_Int_Onumber__ring(X21102) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of__eq])])]) ).
fof(i_0_8814,plain,
! [X33312,X33313,X33314,X33315] :
( ( X33314 = hAPP(hAPP(c_List_Otake(X33315),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33315)),X33314)),X33312)
| hAPP(hAPP(c_List_Oappend(X33315),X33314),X33313) != X33312 )
& ( X33313 = hAPP(hAPP(c_List_Odrop(X33315),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33315)),X33314)),X33312)
| hAPP(hAPP(c_List_Oappend(X33315),X33314),X33313) != X33312 )
& ( X33314 != hAPP(hAPP(c_List_Otake(X33315),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33315)),X33314)),X33312)
| X33313 != hAPP(hAPP(c_List_Odrop(X33315),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33315)),X33314)),X33312)
| hAPP(hAPP(c_List_Oappend(X33315),X33314),X33313) = X33312 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__eq__conv__conj])])]) ).
fof(i_0_8815,plain,
! [X30751,X30752,X30753] :
( ~ class_Groups_Oab__semigroup__mult(X30753)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30753),X30752))
| hBOOL(hAPP(hAPP(c_member(X30753),X30751),X30752))
| hAPP(c_Finite__Set_Ofold1(X30753,c_Groups_Otimes__class_Otimes(X30753)),hAPP(hAPP(c_Set_Oinsert(X30753),X30751),X30752)) = hAPP(hAPP(c_Finite__Set_Ofold(X30753,X30753,c_Groups_Otimes__class_Otimes(X30753)),X30751),X30752) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5766])]) ).
cnf(i_0_8816,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_8817,plain,
! [X20235,X20236] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X20235,X20236) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20235),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20236)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20235),X20236))
| X20236 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X20235,X20236) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20235),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20236)) = 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),X20235),X20236))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| X20236 = 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_8818,plain,
! [X29204,X29205] : hAPP(c_Set_OCollect(X29205),hAPP(hAPP(c_COMBC(X29205,X29205,tc_HOL_Obool),c_fequal),X29204)) = hAPP(hAPP(c_Set_Oinsert(X29205),X29204),c_Orderings_Obot__class_Obot(tc_fun(X29205,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_singleton__conv]) ).
cnf(i_0_8819,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_8820,plain,
! [X24173,X24174,X24175] : hAPP(hAPP(c_Set_Oinsert(X24175),X24174),X24173) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24175,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X24175),X24174),c_Orderings_Obot__class_Obot(tc_fun(X24175,tc_HOL_Obool)))),X24173),
inference(variable_rename,[status(thm)],[fact_insert__is__Un]) ).
fof(i_0_8821,plain,
! [X17424,X17425,X17426,X17427] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(X17427,X17426)),X17425),X17424))
| X17424 = hAPP(hAPP(hAPP(c_Natural_Oupdate,X17425),X17427),hAPP(X17426,X17425)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc__elim__cases_I2_J])]) ).
cnf(i_0_8822,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_8823,plain,
! [X20334,X20335,X20336] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20336),X20335))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20336),X20334)),X20335)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__diff__less])]) ).
fof(i_0_8824,plain,
! [X24778,X24779,X24780,X24781] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24781),X24780),X24779))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24781),X24780),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24781),X24779),X24778)))
| ~ class_Lattices_Osemilattice__inf(X24781) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24781),X24780),X24778))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24781),X24780),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24781),X24779),X24778)))
| ~ class_Lattices_Osemilattice__inf(X24781) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5769])])]) ).
fof(i_0_8825,plain,
! [X22480,X22481,X22482,X22483] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22483),X22482),X22481))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22483),X22482),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22483),X22481),X22480)))
| ~ class_Orderings_Olinorder(X22483) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22483),X22482),X22480))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22483),X22482),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22483),X22481),X22480)))
| ~ class_Orderings_Olinorder(X22483) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5770])])]) ).
fof(i_0_8826,plain,
! [X32225,X32226,X32227] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X32227),X32226),hAPP(c_List_Oset(X32227),X32225)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32227)),c_List_Oremove1(X32227,X32226,X32225)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32227)),X32225)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
& ( hBOOL(hAPP(hAPP(c_member(X32227),X32226),hAPP(c_List_Oset(X32227),X32225)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32227)),c_List_Oremove1(X32227,X32226,X32225)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32227)),X32225) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5771])]) ).
fof(i_0_8827,plain,
! [X20460,X20461,X20462] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20462),X20461))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20461),X20462)),X20460) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20461),X20460)),X20462) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__assoc2])]) ).
fof(i_0_8828,plain,
! [X20457,X20458,X20459] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20459),X20458))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20458),X20457)),X20459) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20458),X20459)),X20457) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__assoc2])]) ).
fof(i_0_8829,plain,
! [X24723,X24724,X24725] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24725,tc_HOL_Obool)),X24724),X24723))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24725,tc_HOL_Obool)),X24724),X24723) = X24724 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__absorb2])]) ).
fof(i_0_8830,plain,
! [X24720,X24721,X24722] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24722,tc_HOL_Obool)),X24721),X24720))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24722,tc_HOL_Obool)),X24720),X24721) = X24721 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__absorb1])]) ).
fof(i_0_8831,plain,
! [X24011,X24012,X24013] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24013,tc_HOL_Obool)),X24012),X24011))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24013,tc_HOL_Obool)),X24012),X24011) = X24011 )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24013,tc_HOL_Obool)),X24012),X24011) != X24011
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24013,tc_HOL_Obool)),X24012),X24011)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__Un__eq])]) ).
fof(i_0_8832,plain,
! [X24008,X24009,X24010] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24010,tc_HOL_Obool)),X24009),X24008))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24010,tc_HOL_Obool)),X24009),X24008) = X24008 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__absorb1])]) ).
fof(i_0_8833,plain,
! [X24005,X24006,X24007] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24007,tc_HOL_Obool)),X24006),X24005))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24007,tc_HOL_Obool)),X24005),X24006) = X24005 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__absorb2])]) ).
fof(i_0_8834,plain,
! [X23496,X23497,X23498] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23498),X23497))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23498),X23496))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23498),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23497,X23496))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__zmod])]) ).
fof(i_0_8835,plain,
! [X25000,X25001,X25002,X25003] :
( hBOOL(hAPP(hAPP(c_member(X25003),X25002),X25001))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25003,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X25003),X25002),X25000)),X25001) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25003,tc_HOL_Obool)),X25000),X25001) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5772])]) ).
fof(i_0_8836,plain,
! [X29137,X29138] : hAPP(c_Set_OCollect(X29138),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29138),c_fNot),X29137)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X29138,tc_HOL_Obool)),hAPP(c_Set_OCollect(X29138),X29137)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(i_0_8837,plain,
! [X18484,X18485,X18486,X18487,X18488] : hAPP(c_Sum__Type_OSumr(X18488,X18487,X18486,X18485),hAPP(c_Sum__Type_OInr(X18488,X18486),X18484)) = hAPP(X18485,X18484),
inference(variable_rename,[status(thm)],[fact_Sumr_Osimps]) ).
fof(i_0_8838,plain,
! [X18479,X18480,X18481,X18482,X18483] : hAPP(c_Sum__Type_OSuml(X18483,X18482,X18481,X18480),hAPP(c_Sum__Type_OInl(X18483,X18481),X18479)) = hAPP(X18480,X18479),
inference(variable_rename,[status(thm)],[fact_Suml_Osimps]) ).
fof(i_0_8839,plain,
! [X33323,X33324,X33325] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33325)),X33324)),X33323))
| hAPP(hAPP(c_List_Odrop(X33325),X33323),X33324) = c_List_Olist_ONil(X33325) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_drop__all])]) ).
fof(i_0_8840,plain,
! [X33320,X33321,X33322] :
( ( hAPP(hAPP(c_List_Odrop(X33322),X33321),X33320) != c_List_Olist_ONil(X33322)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33322)),X33320)),X33321)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33322)),X33320)),X33321))
| hAPP(hAPP(c_List_Odrop(X33322),X33321),X33320) = c_List_Olist_ONil(X33322) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_drop__eq__Nil])]) ).
fof(i_0_8841,plain,
! [X23626,X23627,X23628,X23629] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X23629),X23628),hAPP(hAPP(c_Set_Oinsert(X23629),X23627),X23626)))
| X23628 = X23627
| hBOOL(hAPP(hAPP(c_member(X23629),X23628),X23626)) )
& ( X23628 != X23627
| hBOOL(hAPP(hAPP(c_member(X23629),X23628),hAPP(hAPP(c_Set_Oinsert(X23629),X23627),X23626))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X23629),X23628),X23626))
| hBOOL(hAPP(hAPP(c_member(X23629),X23628),hAPP(hAPP(c_Set_Oinsert(X23629),X23627),X23626))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__iff])])]) ).
fof(i_0_8842,plain,
! [X23586,X23587,X23588,X23589] :
( ~ hBOOL(hAPP(hAPP(c_member(X23589),X23588),hAPP(hAPP(c_Set_Oinsert(X23589),X23587),X23586)))
| X23588 = X23587
| hBOOL(hAPP(hAPP(c_member(X23589),X23588),X23586)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insertE])]) ).
cnf(i_0_8843,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_8844,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_8845,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_8846,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_8847,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_8848,plain,
! [X32634,X32635,X32636] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32636)),X32635)),X32634))
| hAPP(hAPP(c_List_Otake(X32636),X32634),X32635) = X32635 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__all])]) ).
cnf(i_0_8849,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_8850,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_8851,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_8852,plain,
! [X26832,X26833,X26834,X26835] :
( ~ class_Orderings_Olinorder(X26835)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26835),X26834),X26833))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26835,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26835,X26834),X26832)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26835,X26834),X26833)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26835,X26833),X26832) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__diff])]) ).
fof(i_0_8853,plain,
! [X22060,X22061,X22062,X22063,X22064,X22065,X22066] :
( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X22062,X22061),X22060))
| ~ hBOOL(hAPP(hAPP(X22061,X22063),X22060))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X22062,X22061),X22063)) )
& ( hBOOL(hAPP(hAPP(X22065,esk86_3(X22064,X22065,X22066)),X22064))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X22066,X22065),X22064)) )
& ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X22066,X22065),esk86_3(X22064,X22065,X22066)))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X22066,X22065),X22064)) ) ),
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])])])])])]) ).
fof(i_0_8854,plain,
! [X22052,X22053,X22054,X22055,X22056,X22057,X22058] :
( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X22054,X22053),X22052))
| ~ hBOOL(hAPP(hAPP(X22053,X22055),X22052))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X22054,X22053),X22055)) )
& ( hBOOL(hAPP(hAPP(X22057,esk85_3(X22056,X22057,X22058)),X22056))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X22058,X22057),X22056)) )
& ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X22058,X22057),esk85_3(X22056,X22057,X22058)))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X22058,X22057),X22056)) ) ),
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])])])])])]) ).
cnf(i_0_8855,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_8856,plain,
! [X28641,X28642,X28643,X28644] :
( ( hAPP(hAPP(c_Product__Type_OSigma(X28644,X28643),X28642),hAPP(c_COMBK(tc_fun(X28643,tc_HOL_Obool),X28644),X28641)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28644,X28643),tc_HOL_Obool))
| X28642 = c_Orderings_Obot__class_Obot(tc_fun(X28644,tc_HOL_Obool))
| X28641 = c_Orderings_Obot__class_Obot(tc_fun(X28643,tc_HOL_Obool)) )
& ( X28642 != c_Orderings_Obot__class_Obot(tc_fun(X28644,tc_HOL_Obool))
| hAPP(hAPP(c_Product__Type_OSigma(X28644,X28643),X28642),hAPP(c_COMBK(tc_fun(X28643,tc_HOL_Obool),X28644),X28641)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28644,X28643),tc_HOL_Obool)) )
& ( X28641 != c_Orderings_Obot__class_Obot(tc_fun(X28643,tc_HOL_Obool))
| hAPP(hAPP(c_Product__Type_OSigma(X28644,X28643),X28642),hAPP(c_COMBK(tc_fun(X28643,tc_HOL_Obool),X28644),X28641)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28644,X28643),tc_HOL_Obool)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Times__empty])])]) ).
cnf(i_0_8857,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_8858,plain,
! [X27640,X27641,X27642] :
( ~ class_Orderings_Olinorder(X27642)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27642),X27641),X27640))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27642,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X27642,X27641,X27640)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X27642),X27640)) = hAPP(c_SetInterval_Oord__class_OatLeast(X27642),X27641) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I13_J])]) ).
fof(i_0_8859,plain,
! [X27662,X27663,X27664] :
( ~ class_Orderings_Olinorder(X27664)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27664),X27663),X27662))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27664,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X27664,X27663,X27662)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X27664),X27662)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X27664),X27663) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I11_J])]) ).
fof(i_0_8860,plain,
! [X27637,X27638,X27639] :
( ~ class_Orderings_Olinorder(X27639)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27639),X27638),X27637))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27639,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X27639,X27638,X27637)),hAPP(c_SetInterval_Oord__class_OatLeast(X27639),X27637)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X27639),X27638) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I12_J])]) ).
fof(i_0_8861,plain,
! [X33614,X33615] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X33615)
| c_Complete__Lattice_OSup__class_OSup(X33615,hAPP(c_List_Oset(X33615),X33614)) = hAPP(c_List_Ofoldl(X33615,X33615,c_Lattices_Osemilattice__sup__class_Osup(X33615),c_Orderings_Obot__class_Obot(X33615)),X33614) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__set__fold])]) ).
fof(i_0_8862,plain,
! [X33616,X33617] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X33617)
| c_Complete__Lattice_OInf__class_OInf(X33617,hAPP(c_List_Oset(X33617),X33616)) = hAPP(c_List_Ofoldl(X33617,X33617,c_Lattices_Osemilattice__inf__class_Oinf(X33617),c_Orderings_Otop__class_Otop(X33617)),X33616) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__set__fold])]) ).
cnf(i_0_8863,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_8864,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_8865,plain,
! [X26554,X26555] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X26555,X26554)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26554),X26555)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[fact_card__atLeastAtMost__int]) ).
fof(i_0_8866,plain,
! [X24536,X24537,X24538,X24539] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24539),X24538))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24537),hAPP(c_Set_Oimage(X24539,X24537,X24536),X24538))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageI])]) ).
cnf(i_0_8867,plain,
( c_List_Oconcat(X2,X1) = c_List_Olist_ONil(X2)
| esk492_2(X1,X2) != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5619]) ).
cnf(i_0_8868,plain,
( c_List_Olist_ONil(X2) = c_List_Oconcat(X2,X1)
| esk493_2(X1,X2) != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5620]) ).
fof(i_0_8869,plain,
! [X25154,X25155] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25155),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25154)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25155),X25154)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25155),X25154))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25155),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25154))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_OatMost__iff])]) ).
fof(i_0_8870,plain,
! [X25129,X25130] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25130),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25129)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25129),X25130)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25129),X25130))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25130),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25129))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_OatLeast__iff])]) ).
fof(i_0_8871,plain,
! [X31409,X31410,X31411] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31411)
| c_Complete__Lattice_OSup__class_OSup(X31411,hAPP(hAPP(c_Set_Oinsert(X31411),X31410),hAPP(hAPP(c_Set_Oinsert(X31411),X31409),c_Orderings_Obot__class_Obot(tc_fun(X31411,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X31411),X31410),X31409) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__binary])]) ).
fof(i_0_8872,plain,
! [X31412,X31413,X31414] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31414)
| c_Complete__Lattice_OInf__class_OInf(X31414,hAPP(hAPP(c_Set_Oinsert(X31414),X31413),hAPP(hAPP(c_Set_Oinsert(X31414),X31412),c_Orderings_Obot__class_Obot(tc_fun(X31414,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X31414),X31413),X31412) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__binary])]) ).
fof(i_0_8873,plain,
! [X23356,X23357,X23358,X23359] :
( ~ class_Divides_Osemiring__div(X23359)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23359),X23358),X23357))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23359),X23356),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23359),X23357),X23358)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23359),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23359),X23356),X23357)),X23358) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__swap])]) ).
fof(i_0_8874,plain,
! [X25165,X25166,X25167,X25168] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25168),X25167),c_SetInterval_Oord_OatMost(X25168,X25166,X25165)))
| hBOOL(hAPP(hAPP(X25166,X25167),X25165)) )
& ( ~ hBOOL(hAPP(hAPP(X25166,X25167),X25165))
| hBOOL(hAPP(hAPP(c_member(X25168),X25167),c_SetInterval_Oord_OatMost(X25168,X25166,X25165))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatMost__iff])]) ).
fof(i_0_8875,plain,
! [X25141,X25142,X25143,X25144] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25144),X25143),c_SetInterval_Oord_OlessThan(X25144,X25142,X25141)))
| hBOOL(hAPP(hAPP(X25142,X25143),X25141)) )
& ( ~ hBOOL(hAPP(hAPP(X25142,X25143),X25141))
| hBOOL(hAPP(hAPP(c_member(X25144),X25143),c_SetInterval_Oord_OlessThan(X25144,X25142,X25141))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OlessThan__iff])]) ).
fof(i_0_8876,plain,
! [X25137,X25138,X25139,X25140] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25140),X25139),c_SetInterval_Oord_OatLeast(X25140,X25138,X25137)))
| hBOOL(hAPP(hAPP(X25138,X25137),X25139)) )
& ( ~ hBOOL(hAPP(hAPP(X25138,X25137),X25139))
| hBOOL(hAPP(hAPP(c_member(X25140),X25139),c_SetInterval_Oord_OatLeast(X25140,X25138,X25137))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeast__iff])]) ).
fof(i_0_8877,plain,
! [X25145,X25146,X25147,X25148] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25148),X25147),c_SetInterval_Oord_OgreaterThan(X25148,X25146,X25145)))
| hBOOL(hAPP(hAPP(X25146,X25145),X25147)) )
& ( ~ hBOOL(hAPP(hAPP(X25146,X25145),X25147))
| hBOOL(hAPP(hAPP(c_member(X25148),X25147),c_SetInterval_Oord_OgreaterThan(X25148,X25146,X25145))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThan__iff])]) ).
fof(i_0_8878,plain,
! [X33845,X33846,X33847,X33848,X33849] :
( c_List_Opartition(X33849,X33848,X33847) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33849),tc_List_Olist(X33849)),X33846),X33845)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X33849,tc_HOL_Obool)),hAPP(c_List_Oset(X33849),X33846)),hAPP(c_List_Oset(X33849),X33845)) = hAPP(c_List_Oset(X33849),X33847) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_partition__set])]) ).
fof(i_0_8879,plain,
! [X32581,X32582,X32583,X32584] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X32584) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Onth(X32583),hAPP(hAPP(c_List_Olist_OCons(X32583),X32582),X32581)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X32584)) = X32582 )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X32584) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Onth(X32583),hAPP(hAPP(c_List_Olist_OCons(X32583),X32582),X32581)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X32584)) = hAPP(hAPP(c_List_Onth(X32583),X32581),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X32584)),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_8880,plain,
! [X30235,X30236] : hAPP(hAPP(c_Relation_Orel__comp(X30236,X30236,X30236),X30235),c_Transitive__Closure_Ortrancl(X30236,X30235)) = hAPP(hAPP(c_Relation_Orel__comp(X30236,X30236,X30236),c_Transitive__Closure_Ortrancl(X30236,X30235)),X30235),
inference(variable_rename,[status(thm)],[fact_r__comp__rtrancl__eq]) ).
cnf(i_0_8881,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_8882,plain,
! [X34465,X34466,X34467,X34468,X34469,X34470] : hAPP(hAPP(hAPP(c_COMBS(X34470,X34469,X34468),X34467),X34466),X34465) = hAPP(hAPP(X34467,X34465),hAPP(X34466,X34465)),
inference(variable_rename,[status(thm)],[help_c__COMBS__1]) ).
cnf(i_0_8883,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_8884,plain,
! [X20841,X20842] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20842)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20842),hAPP(c_Groups_Ouminus__class_Ouminus(X20842),hAPP(c_Groups_Oabs__class_Oabs(X20842),X20841))),c_Groups_Ozero__class_Ozero(X20842))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__le__zero])]) ).
fof(i_0_8885,plain,
! [X24149,X24150,X24151,X24152] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24152,tc_HOL_Obool)),X24151),hAPP(hAPP(c_Set_Oinsert(X24152),X24150),X24149)) = hAPP(hAPP(c_Set_Oinsert(X24152),X24150),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24152,tc_HOL_Obool)),X24151),X24149)),
inference(variable_rename,[status(thm)],[fact_Un__insert__right]) ).
fof(i_0_8886,plain,
! [X18958,X18959,X18960] :
( ( X18959 = c_Groups_Ozero__class_Ozero(X18960)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18960),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18960),X18959),X18959)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18960),X18958),X18958)) != c_Groups_Ozero__class_Ozero(X18960)
| ~ class_Rings_Olinordered__ring__strict(X18960) )
& ( X18958 = c_Groups_Ozero__class_Ozero(X18960)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18960),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18960),X18959),X18959)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18960),X18958),X18958)) != c_Groups_Ozero__class_Ozero(X18960)
| ~ class_Rings_Olinordered__ring__strict(X18960) )
& ( X18959 != c_Groups_Ozero__class_Ozero(X18960)
| X18958 != c_Groups_Ozero__class_Ozero(X18960)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18960),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18960),X18959),X18959)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18960),X18958),X18958)) = c_Groups_Ozero__class_Ozero(X18960)
| ~ class_Rings_Olinordered__ring__strict(X18960) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__eq__zero__iff])])]) ).
fof(i_0_8887,plain,
! [X31604,X31605,X31606,X31607,X31608,X31609] :
( hAPP(X31609,X31608) != hAPP(c_Option_Ooption_OSome(X31607),X31606)
| hAPP(c_Map_Omap__add(X31605,X31607,X31604,X31609),X31608) = hAPP(c_Option_Ooption_OSome(X31607),X31606) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__add__find__right])]) ).
fof(i_0_8888,plain,
! [X30661,X30662,X30663] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30663),X30662))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X30663,tc_HOL_Obool)),X30662),X30661) = hAPP(hAPP(c_Finite__Set_Ofold(X30663,tc_fun(X30663,tc_HOL_Obool),c_Set_Oinsert(X30663)),X30661),X30662) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_union__fold__insert])]) ).
fof(i_0_8889,plain,
! [X21134,X21135] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(X21135),X21134) != c_Groups_Ozero__class_Ozero(X21135)
| c_Int_Oiszero(X21135,hAPP(c_Int_Onumber__class_Onumber__of(X21135),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21134),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
| ~ class_Int_Onumber__ring(X21135) )
& ( ~ c_Int_Oiszero(X21135,hAPP(c_Int_Onumber__class_Onumber__of(X21135),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21134),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
| hAPP(c_Int_Onumber__class_Onumber__of(X21135),X21134) = c_Groups_Ozero__class_Ozero(X21135)
| ~ class_Int_Onumber__ring(X21135) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I3_J])])]) ).
fof(i_0_8890,plain,
! [X21132,X21133] :
( ( c_Groups_Ozero__class_Ozero(X21133) != hAPP(c_Int_Onumber__class_Onumber__of(X21133),X21132)
| c_Int_Oiszero(X21133,hAPP(c_Int_Onumber__class_Onumber__of(X21133),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21132))))
| ~ class_Int_Onumber__ring(X21133) )
& ( ~ c_Int_Oiszero(X21133,hAPP(c_Int_Onumber__class_Onumber__of(X21133),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21132))))
| c_Groups_Ozero__class_Ozero(X21133) = hAPP(c_Int_Onumber__class_Onumber__of(X21133),X21132)
| ~ class_Int_Onumber__ring(X21133) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I1_J])])]) ).
fof(i_0_8891,plain,
! [X29563,X29564,X29565,X29566] :
( ~ c_Wellfounded_Owf(X29566,X29565)
| ~ c_Wellfounded_Owf(X29564,X29563)
| c_Wellfounded_Owf(tc_prod(X29566,X29564),c_Wellfounded_Olex__prod(X29566,X29564,X29565,X29563)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__lex__prod])]) ).
cnf(i_0_8892,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_8893,plain,
! [X25214,X25215] :
( ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25215,X25214) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25215),X25214)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25215),X25214))
| c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25215,X25214) = 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_8894,plain,
! [X25212,X25213] :
( ( 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),X25213,X25212)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25213),X25212)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25213),X25212))
| 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),X25213,X25212) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5782])]) ).
fof(i_0_8895,plain,
! [X32037,X32038,X32039,X32040] :
( ~ hBOOL(hAPP(c_List_Odistinct(X32040),X32039))
| hBOOL(hAPP(c_List_Odistinct(tc_prod(X32040,X32038)),hAPP(hAPP(c_List_Ozip(X32040,X32038),X32039),X32037))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__zipI1])]) ).
fof(i_0_8896,plain,
! [X32041,X32042,X32043,X32044] :
( ~ hBOOL(hAPP(c_List_Odistinct(X32044),X32043))
| hBOOL(hAPP(c_List_Odistinct(tc_prod(X32042,X32044)),hAPP(hAPP(c_List_Ozip(X32042,X32044),X32041),X32043))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__zipI2])]) ).
fof(i_0_8897,plain,
! [X30760,X30761,X30762] :
( ~ class_Orderings_Olinorder(X30762)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30762),X30761))
| hBOOL(hAPP(hAPP(c_member(X30762),X30760),X30761))
| c_Big__Operators_Olinorder__class_OMin(X30762,hAPP(hAPP(c_Set_Oinsert(X30762),X30760),X30761)) = hAPP(hAPP(c_Finite__Set_Ofold(X30762,X30762,c_Orderings_Oord__class_Omin(X30762)),X30760),X30761) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5783])]) ).
fof(i_0_8898,plain,
! [X30763,X30764,X30765] :
( ~ class_Orderings_Olinorder(X30765)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30765),X30764))
| hBOOL(hAPP(hAPP(c_member(X30765),X30763),X30764))
| c_Big__Operators_Olinorder__class_OMax(X30765,hAPP(hAPP(c_Set_Oinsert(X30765),X30763),X30764)) = hAPP(hAPP(c_Finite__Set_Ofold(X30765,X30765,c_Orderings_Oord__class_Omax(X30765)),X30763),X30764) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5784])]) ).
fof(i_0_8899,plain,
! [X30757,X30758,X30759] :
( ~ class_Lattices_Olattice(X30759)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30759),X30758))
| hBOOL(hAPP(hAPP(c_member(X30759),X30757),X30758))
| c_Big__Operators_Olattice__class_OInf__fin(X30759,hAPP(hAPP(c_Set_Oinsert(X30759),X30757),X30758)) = hAPP(hAPP(c_Finite__Set_Ofold(X30759,X30759,c_Lattices_Osemilattice__inf__class_Oinf(X30759)),X30757),X30758) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5785])]) ).
fof(i_0_8900,plain,
! [X30754,X30755,X30756] :
( ~ class_Lattices_Olattice(X30756)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30756),X30755))
| hBOOL(hAPP(hAPP(c_member(X30756),X30754),X30755))
| c_Big__Operators_Olattice__class_OSup__fin(X30756,hAPP(hAPP(c_Set_Oinsert(X30756),X30754),X30755)) = hAPP(hAPP(c_Finite__Set_Ofold(X30756,X30756,c_Lattices_Osemilattice__sup__class_Osup(X30756)),X30754),X30755) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5786])]) ).
fof(i_0_8901,plain,
! [X31336,X31337,X31338,X31339] : hAPP(c_Set_Ovimage(X31339,X31338,X31337),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31338,tc_HOL_Obool),X31336)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X31338,tc_HOL_Obool),tc_fun(X31339,tc_HOL_Obool)),X31336),c_Set_Ovimage(X31339,X31338,X31337)),
inference(variable_rename,[status(thm)],[fact_vimage__Union]) ).
fof(i_0_8902,plain,
! [X31314,X31315,X31316,X31317] : hAPP(c_Set_Oimage(X31317,X31316,X31315),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31317,tc_HOL_Obool),X31314)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X31317,tc_HOL_Obool),tc_fun(X31316,tc_HOL_Obool)),X31314),c_Set_Oimage(X31317,X31316,X31315)),
inference(variable_rename,[status(thm)],[fact_image__Union]) ).
fof(i_0_8903,plain,
! [X26397,X26398] : hBOOL(hAPP(hAPP(c_member(tc_fun(X26398,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X26398,tc_HOL_Obool))),hAPP(c_Set_OPow(X26398),X26397))),
inference(variable_rename,[status(thm)],[fact_Pow__bottom]) ).
fof(i_0_8904,plain,
! [X32432,X32433,X32434] :
( ~ class_Groups_Omonoid__add(X32434)
| hAPP(c_List_Omonoid__add__class_Olistsum(X32434),hAPP(hAPP(c_List_Omap(X32433,X32434),hAPP(c_COMBK(X32434,X32433),c_Groups_Ozero__class_Ozero(X32434))),X32432)) = c_Groups_Ozero__class_Ozero(X32434) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__0])]) ).
fof(i_0_8905,plain,
! [X24945,X24946,X24947] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24947,tc_HOL_Obool)),X24946),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24947,tc_HOL_Obool)),X24946),X24945)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24947,tc_HOL_Obool)),X24946),X24945),
inference(variable_rename,[status(thm)],[fact_Int__left__absorb]) ).
fof(i_0_8906,plain,
! [X24064,X24065,X24066] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24066,tc_HOL_Obool)),X24065),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24066,tc_HOL_Obool)),X24065),X24064)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24066,tc_HOL_Obool)),X24065),X24064),
inference(variable_rename,[status(thm)],[fact_Un__left__absorb]) ).
fof(i_0_8907,plain,
! [X24143,X24144,X24145] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24145,tc_HOL_Obool)),X24144),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24145,tc_HOL_Obool)),X24143),X24144)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24145,tc_HOL_Obool)),X24144),X24143),
inference(variable_rename,[status(thm)],[fact_Un__Diff__cancel]) ).
fof(i_0_8908,plain,
! [X33424,X33425] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33425)),X33424)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| hAPP(c_List_Orotate1(X33425),X33424) = X33424 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate1__length01])]) ).
fof(i_0_8909,plain,
! [X26245,X26246,X26247,X26248,X26249] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X26249,X26248,X26247),X26246),X26245),c_Orderings_Obot__class_Obot(tc_fun(X26248,tc_HOL_Obool))) = X26245,
inference(variable_rename,[status(thm)],[fact_fold__image__empty]) ).
fof(i_0_8910,plain,
! [X23076,X23077,X23078] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23078),X23077))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23078),X23076))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23078),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23077),X23076))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__diff__nat])]) ).
fof(i_0_8911,plain,
! [X20614,X20615] :
( ( X20615 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20615),X20614) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X20615 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20615),X20614) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20614),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20615),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X20614)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__if])]) ).
fof(i_0_8912,plain,
! [X23543,X23544] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X23544)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X23543)))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X23543),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X23544)) = 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),X23543),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X23544)) != 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),X23544)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X23543))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__iff__zmod__eq__0__number__of])]) ).
fof(i_0_8913,plain,
! [X17125,X17126,X17127,X17128,X17129,X17130] : c_Hoare__Mirabelle_Otriple_Otriple__case(X17130,X17129,X17128,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17130),X17127),X17126),X17125)) = hAPP(hAPP(hAPP(X17128,X17127),X17126),X17125),
inference(variable_rename,[status(thm)],[fact_triple_Osimps_I2_J]) ).
fof(i_0_8914,plain,
! [X17119,X17120,X17121,X17122,X17123,X17124] : c_Hoare__Mirabelle_Otriple_Otriple__rec(X17124,X17123,X17122,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17124),X17121),X17120),X17119)) = hAPP(hAPP(hAPP(X17122,X17121),X17120),X17119),
inference(variable_rename,[status(thm)],[fact_triple_Orecs]) ).
fof(i_0_8915,plain,
! [X29742,X29743,X29744,X29745,X29747,X29748,X29749,X29750,X29751] :
( ( ~ hBOOL(hAPP(c_Predicate_ORangeP(X29745,X29744,X29743),X29742))
| hBOOL(hAPP(hAPP(X29743,esk324_2(X29742,X29743)),X29742)) )
& ( ~ hBOOL(hAPP(hAPP(X29748,X29749),X29747))
| hBOOL(hAPP(c_Predicate_ORangeP(X29751,X29750,X29748),X29747)) ) ),
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_8916,plain,
! [X21072,X21073] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21073)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21072)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21073) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21072) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21072)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21073) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21073)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21073) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21072) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21072)))
| X21073 = X21072
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21073)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21073) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21072) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21073)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21073)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21073) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21072) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21072)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21072)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21073)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21073) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21072) )
& ( X21073 != X21072
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21072)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21073)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21073) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21072) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21072)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21073) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21073)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21073) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21072) )
& ( X21073 != X21072
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21073) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21073)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21073) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21072) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21073)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21072)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21073) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21072) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21072)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21072)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21072)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21073) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21072) )
& ( X21073 != X21072
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21072)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21072)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21073) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21072) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21072)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21073) != 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),X21072)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21073) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21072) )
& ( X21073 != X21072
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21073) != 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),X21072)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21073) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21072) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5787])])]) ).
fof(i_0_8917,plain,
! [X19375,X19376] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19376),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19376),X19375)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19376))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19375))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__distrib__neg])]) ).
fof(i_0_8918,plain,
! [X18394,X18395,X18396,X18397] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(X18397,X18396)),c_Nitpick_Opair__box_OPairBox(X18397,X18396,X18395,X18394)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_pair__box_Osize_I2_J]) ).
fof(i_0_8919,plain,
! [X33831,X33832,X33833,X33834] :
( ( X33834 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33833)),X33832)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_List_Obutlast(X33833,hAPP(hAPP(c_List_Olist__update(X33833,X33832),X33834),X33831)) = c_List_Obutlast(X33833,X33832) )
& ( X33834 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33833)),X33832)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_List_Obutlast(X33833,hAPP(hAPP(c_List_Olist__update(X33833,X33832),X33834),X33831)) = hAPP(hAPP(c_List_Olist__update(X33833,c_List_Obutlast(X33833,X33832)),X33834),X33831) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast__list__update])]) ).
fof(i_0_8920,plain,
! [X24314,X24315,X24316,X24317,X24318] : hAPP(c_Set_Oimage(X24318,X24317,X24316),hAPP(hAPP(c_Set_Oinsert(X24318),X24315),X24314)) = hAPP(hAPP(c_Set_Oinsert(X24317),hAPP(X24316,X24315)),hAPP(c_Set_Oimage(X24318,X24317,X24316),X24314)),
inference(variable_rename,[status(thm)],[fact_image__insert]) ).
cnf(i_0_8921,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_8922,plain,
! [X24557,X24558,X24559] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24559,tc_HOL_Obool)),X24558),X24557))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24559),X24557))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24559),X24558)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__subset])]) ).
fof(i_0_8923,plain,
! [X24554,X24555,X24556] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24556),X24555))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24556,tc_HOL_Obool)),X24554),X24555))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24556),X24554)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__finite__subset])]) ).
fof(i_0_8924,plain,
! [X19473,X19474] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19474),hAPP(c_Groups_Ouminus__class_Ouminus(X19474),X19473)),c_Groups_Ozero__class_Ozero(X19474)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19474),c_Groups_Ozero__class_Ozero(X19474)),X19473))
| ~ class_Groups_Oordered__ab__group__add(X19474) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19474),c_Groups_Ozero__class_Ozero(X19474)),X19473))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19474),hAPP(c_Groups_Ouminus__class_Ouminus(X19474),X19473)),c_Groups_Ozero__class_Ozero(X19474)))
| ~ class_Groups_Oordered__ab__group__add(X19474) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__0__iff__le])])]) ).
fof(i_0_8925,plain,
! [X18879,X18880] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18880),hAPP(c_Groups_Ouminus__class_Ouminus(X18880),X18879)),c_Groups_Ozero__class_Ozero(X18880)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18880),c_Groups_Ozero__class_Ozero(X18880)),X18879))
| ~ class_Groups_Oordered__ab__group__add(X18880) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18880),c_Groups_Ozero__class_Ozero(X18880)),X18879))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18880),hAPP(c_Groups_Ouminus__class_Ouminus(X18880),X18879)),c_Groups_Ozero__class_Ozero(X18880)))
| ~ class_Groups_Oordered__ab__group__add(X18880) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__0__iff__less])])]) ).
fof(i_0_8926,plain,
! [X34300,X34301,X34302,X34303] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34303)),X34302) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34301)),X34300)
| hAPP(hAPP(c_List_Ozip(X34303,X34301),hAPP(c_List_Orev(X34303),X34302)),hAPP(c_List_Orev(X34301),X34300)) = hAPP(c_List_Orev(tc_prod(X34303,X34301)),hAPP(hAPP(c_List_Ozip(X34303,X34301),X34302),X34300)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__rev])]) ).
fof(i_0_8927,plain,
! [X20907,X20908] :
( ( ~ 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),X20908),X20907)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20908))
| X20907 = 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)),X20908))
| 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),X20908),X20907))) )
& ( X20907 != 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),X20908),X20907))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__zero__less__power__iff])])]) ).
fof(i_0_8928,plain,
! [X27625,X27626,X27627,X27628] :
( ~ class_Orderings_Olinorder(X27628)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27628,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X27628,X27627,X27626)),hAPP(c_SetInterval_Oord__class_OatLeast(X27628),X27625)) = c_SetInterval_Oord__class_OatLeastAtMost(X27628,hAPP(hAPP(c_Orderings_Oord__class_Omax(X27628),X27627),X27625),X27626) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostL2])]) ).
fof(i_0_8929,plain,
! [X27033,X27034,X27035,X27036] :
( ~ class_Orderings_Olinorder(X27036)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27036,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X27036,X27035,X27034)),hAPP(c_SetInterval_Oord__class_OatMost(X27036),X27033)) = c_SetInterval_Oord__class_OatLeastAtMost(X27036,X27035,hAPP(hAPP(c_Orderings_Oord__class_Omin(X27036),X27034),X27033)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostL1])]) ).
fof(i_0_8930,plain,
! [X32754,X32755,X32756,X32757] : hAPP(hAPP(c_List_Olist__update(X32757,hAPP(hAPP(c_List_Olist_OCons(X32757),X32756),X32755)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32754) = hAPP(hAPP(c_List_Olist_OCons(X32757),X32754),X32755),
inference(variable_rename,[status(thm)],[fact_list__update__code_I2_J]) ).
fof(i_0_8931,plain,
! [X34459,X34460,X34461,X34462,X34463,X34464] : hAPP(hAPP(hAPP(c_COMBC(X34464,X34463,X34462),X34461),X34460),X34459) = hAPP(hAPP(X34461,X34459),X34460),
inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).
fof(i_0_8932,plain,
! [X34453,X34454,X34455,X34456,X34457,X34458] : hAPP(hAPP(hAPP(c_COMBB(X34458,X34457,X34456),X34455),X34454),X34453) = hAPP(X34455,hAPP(X34454,X34453)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
fof(i_0_8933,plain,
! [X18161,X18162,X18163,X18164,X18165] : hAPP(c_Option_Ooption_Ooption__case(X18165,X18164,X18163,X18162),hAPP(c_Option_Ooption_OSome(X18164),X18161)) = hAPP(X18162,X18161),
inference(variable_rename,[status(thm)],[fact_option_Osimps_I5_J]) ).
fof(i_0_8934,plain,
! [X20700,X20701] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20701),hAPP(c_Int_Onumber__class_Onumber__of(X20701),X20700)),c_Groups_Ozero__class_Ozero(X20701)))
| hAPP(c_Groups_Oabs__class_Oabs(X20701),hAPP(c_Int_Onumber__class_Onumber__of(X20701),X20700)) = hAPP(c_Groups_Ouminus__class_Ouminus(X20701),hAPP(c_Int_Onumber__class_Onumber__of(X20701),X20700))
| ~ class_Int_Onumber__ring(X20701)
| ~ class_Rings_Olinordered__idom(X20701) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20701),hAPP(c_Int_Onumber__class_Onumber__of(X20701),X20700)),c_Groups_Ozero__class_Ozero(X20701)))
| hAPP(c_Groups_Oabs__class_Oabs(X20701),hAPP(c_Int_Onumber__class_Onumber__of(X20701),X20700)) = hAPP(c_Int_Onumber__class_Onumber__of(X20701),X20700)
| ~ class_Int_Onumber__ring(X20701)
| ~ class_Rings_Olinordered__idom(X20701) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5788])])]) ).
fof(i_0_8935,plain,
! [X28411,X28412,X28413,X28414] : hAPP(c_Set_Ovimage(X28414,X28413,X28412),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28413,tc_HOL_Obool)),X28411)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28414,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X28414,X28413,X28412),X28411)),
inference(variable_rename,[status(thm)],[fact_vimage__Compl]) ).
fof(i_0_8936,plain,
! [X20071,X20072,X20073] : 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),X20073),X20072)),X20071),X20072) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20071,X20072),
inference(variable_rename,[status(thm)],[fact_mod__mult__self3]) ).
fof(i_0_8937,plain,
! [X20040,X20041] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20041))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20040))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X20041)),hAPP(c_Int_Onat,X20040)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20041),X20040)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__functions_I1_J])]) ).
fof(i_0_8938,plain,
! [X19363,X19364] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19364))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19363))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X19364)),hAPP(c_Int_Onat,X19363)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19364),X19363)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J])]) ).
fof(i_0_8939,plain,
! [X19695,X19696] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19696))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19695))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X19696)),hAPP(c_Int_Onat,X19695)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19696),X19695)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J])]) ).
fof(i_0_8940,plain,
! [X19697,X19698] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19698))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19697))
| hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19698),X19697)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X19698)),hAPP(c_Int_Onat,X19697)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__distrib])]) ).
fof(i_0_8941,plain,
! [X32119,X32120,X32121,X32122] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(X32122,X32121))),hAPP(hAPP(c_List_Ozip(X32122,X32121),X32120),X32119)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32122)),X32120)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32121)),X32119)),
inference(variable_rename,[status(thm)],[fact_length__zip]) ).
fof(i_0_8942,plain,
! [X31359,X31360,X31361,X31362] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X31362,tc_HOL_Obool),hAPP(c_Set_Oimage(X31361,tc_fun(X31362,tc_HOL_Obool),X31360),X31359)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X31361,tc_fun(X31362,tc_HOL_Obool)),X31359),X31360),
inference(variable_rename,[status(thm)],[fact_Union__image__eq]) ).
fof(i_0_8943,plain,
! [X31243,X31244,X31245,X31246] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X31246,tc_HOL_Obool),hAPP(c_Set_Oimage(X31245,tc_fun(X31246,tc_HOL_Obool),X31244),X31243)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31245,tc_fun(X31246,tc_HOL_Obool)),X31243),X31244),
inference(variable_rename,[status(thm)],[fact_Inter__image__eq]) ).
fof(i_0_8944,plain,
! [X31247,X31248,X31249,X31250] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31250,tc_fun(X31249,tc_HOL_Obool)),X31248),X31247) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X31249,tc_HOL_Obool),hAPP(c_Set_Oimage(X31250,tc_fun(X31249,tc_HOL_Obool),X31247),X31248)),
inference(variable_rename,[status(thm)],[fact_INTER__eq__Inter__image]) ).
fof(i_0_8945,plain,
! [X31355,X31356,X31357,X31358] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X31358,tc_fun(X31357,tc_HOL_Obool)),X31356),X31355) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X31357,tc_HOL_Obool),hAPP(c_Set_Oimage(X31358,tc_fun(X31357,tc_HOL_Obool),X31355),X31356)),
inference(variable_rename,[status(thm)],[fact_UNION__eq__Union__image]) ).
fof(i_0_8946,plain,
! [X18208,X18209,X18210,X18211] :
( ~ class_Rings_Osemiring__1(X18211)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X18211,X18210,hAPP(c_Nat_OSuc,X18209),X18208) = c_Nat_Osemiring__1__class_Oof__nat__aux(X18211,X18210,X18209,hAPP(X18210,X18208)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I2_J])]) ).
fof(i_0_8947,plain,
! [X20226,X20227] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20227))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20226))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X20227),hAPP(c_Int_Onat,X20226)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X20227,X20226)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__functions_I2_J])]) ).
fof(i_0_8948,plain,
! [X20224,X20225] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20225))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20224))
| hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X20225,X20224)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X20225),hAPP(c_Int_Onat,X20224)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mod__distrib])]) ).
fof(i_0_8949,plain,
! [X20592,X20593] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X20593,X20592) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20593),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20593),X20592)),X20592)),
inference(variable_rename,[status(thm)],[fact_zmod__zdiv__equality_H]) ).
fof(i_0_8950,plain,
! [X20495,X20496] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20496,X20495) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20496),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20496),X20495)),X20495)),
inference(variable_rename,[status(thm)],[fact_Divides_Omod__div__equality_H]) ).
fof(i_0_8951,plain,
! [X20968,X20969,X20970] :
( ~ class_Rings_Olinordered__semidom(X20970)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20970),c_Groups_Oone__class_Oone(X20970)),X20969))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20970),c_Groups_Oone__class_Oone(X20970)),hAPP(hAPP(c_Power_Opower__class_Opower(X20970),X20969),X20968))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__power])]) ).
fof(i_0_8952,plain,
! [X20955,X20956,X20957] :
( ~ class_Rings_Olinordered__semidom(X20957)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20957),c_Groups_Ozero__class_Ozero(X20957)),X20956))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20957),c_Groups_Ozero__class_Ozero(X20957)),hAPP(hAPP(c_Power_Opower__class_Opower(X20957),X20956),X20955))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power])]) ).
fof(i_0_8953,plain,
! [X20962,X20963,X20964] :
( ~ class_Rings_Olinordered__semidom(X20964)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20964),c_Groups_Ozero__class_Ozero(X20964)),X20963))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20964),c_Groups_Ozero__class_Ozero(X20964)),hAPP(hAPP(c_Power_Opower__class_Opower(X20964),X20963),X20962))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power])]) ).
fof(i_0_8954,plain,
! [X24376,X24377,X24378,X24379,X24380] :
( ~ hBOOL(hAPP(hAPP(c_member(X24380),X24379),X24378))
| hAPP(c_Set_Oimage(X24380,X24377,hAPP(c_COMBK(X24377,X24380),X24376)),X24378) = hAPP(hAPP(c_Set_Oinsert(X24377),X24376),c_Orderings_Obot__class_Obot(tc_fun(X24377,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__constant])]) ).
fof(i_0_8955,plain,
! [X18995,X18996] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18995))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X18996)),hAPP(c_Int_Onat,X18995))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18996),X18995))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X18996)),hAPP(c_Int_Onat,X18995))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18995))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18996),X18995))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X18996)),hAPP(c_Int_Onat,X18995))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__nat__conj])])]) ).
fof(i_0_8956,plain,
! [X28710,X28711] : hAPP(hAPP(c_Product__Type_OSigma(X28711,X28710),c_Orderings_Otop__class_Otop(tc_fun(X28711,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X28710,tc_HOL_Obool),X28711),c_Orderings_Otop__class_Otop(tc_fun(X28710,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X28711,X28710),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_UNIV__Times__UNIV]) ).
fof(i_0_8957,plain,
! [X18978,X18979] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18979),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18978),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18979),X18978))
| X18979 = X18978 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18979),X18978))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18979),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18978),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
& ( X18979 != X18978
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18979),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18978),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_8958,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_8959,plain,
! [X19475,X19476] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19476),hAPP(c_Groups_Ouminus__class_Ouminus(X19476),X19475)),X19475))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19476),c_Groups_Ozero__class_Ozero(X19476)),X19475))
| ~ class_Groups_Olinordered__ab__group__add(X19476) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19476),c_Groups_Ozero__class_Ozero(X19476)),X19475))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19476),hAPP(c_Groups_Ouminus__class_Ouminus(X19476),X19475)),X19475))
| ~ class_Groups_Olinordered__ab__group__add(X19476) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__self__iff])])]) ).
fof(i_0_8960,plain,
! [X18881,X18882] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18882),hAPP(c_Groups_Ouminus__class_Ouminus(X18882),X18881)),X18881))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18882),c_Groups_Ozero__class_Ozero(X18882)),X18881))
| ~ class_Groups_Olinordered__ab__group__add(X18882) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18882),c_Groups_Ozero__class_Ozero(X18882)),X18881))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18882),hAPP(c_Groups_Ouminus__class_Ouminus(X18882),X18881)),X18881))
| ~ class_Groups_Olinordered__ab__group__add(X18882) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__nonneg])])]) ).
fof(i_0_8961,plain,
! [X30465,X30466,X30467,X30468] : hAPP(hAPP(c_Nat_Ocompow(X30468,X30468),X30467),hAPP(hAPP(c_Nat_Ocompow(X30468,X30468),X30466),X30465)) = hAPP(hAPP(c_Nat_Ocompow(X30468,X30468),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30466),X30467)),X30465),
inference(variable_rename,[status(thm)],[fact_funpow__mult]) ).
fof(i_0_8962,plain,
! [X23529,X23530] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23530),X23529))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23530)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23529))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23530)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23529)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23530),X23529)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__int])]) ).
fof(i_0_8963,plain,
! [X23527,X23528] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23528)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23527)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23528),X23527)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23528),X23527))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23528)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23527))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I4_J])]) ).
fof(i_0_8964,plain,
! [X20892,X20893] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20893)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20892)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20893),X20892)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20893),X20892))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20893)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20892))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__number__of__int__code])]) ).
fof(i_0_8965,plain,
! [X19139,X19140] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19140)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19139)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19140),X19139)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19140),X19139))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19140)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19139))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I3_J])]) ).
fof(i_0_8966,plain,
! [X19137,X19138] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19138)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19137)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19138),X19137)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19138),X19137))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19138)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19137))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__int])]) ).
fof(i_0_8967,plain,
! [X20894,X20895] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20895)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20894)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20895),X20894)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20895),X20894))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20895)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20894))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of__int__code])]) ).
fof(i_0_8968,plain,
! [X18554,X18555] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18555)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18554)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18555),X18554)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18555),X18554))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18555)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18554))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I2_J])]) ).
fof(i_0_8969,plain,
! [X18519,X18520] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18520)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18519)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18520),X18519)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18520),X18519))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18520)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18519))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__int])]) ).
fof(i_0_8970,plain,
! [X20434,X20435] :
( ( ~ 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),X20435),X20434)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20434),X20435)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20434),X20435))
| 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),X20435),X20434))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__diff])]) ).
fof(i_0_8971,plain,
! [X19672,X19673] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19673),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19672),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19673),X19672)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19673),X19672))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19673),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19672),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_8972,plain,
! [X20548,X20549] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20549),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20548),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20549),X20548)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20549),X20548))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20549),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20548),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_8973,plain,
! [X20853,X20854,X20855] :
( ~ class_Int_Onumber__ring(X20855)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20855),hAPP(c_Groups_Ouminus__class_Ouminus(X20855),hAPP(c_Int_Onumber__class_Onumber__of(X20855),X20854))),X20853) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20855),hAPP(c_Int_Onumber__class_Onumber__of(X20855),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20854))),X20853) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__number__of__mult])]) ).
fof(i_0_8974,plain,
! [X18670,X18671,X18672] :
( ~ class_Rings_Ocomm__semiring__1(X18672)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18672),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18672),X18671),X18670)),X18670) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18672),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18672),X18671),c_Groups_Oone__class_Oone(X18672))),X18670) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J])]) ).
fof(i_0_8975,plain,
! [X32839,X32840,X32841,X32842] :
( ( hAPP(hAPP(c_List_Olist__update(X32841,X32840),X32842),X32839) != X32840
| hAPP(hAPP(c_List_Onth(X32841),X32840),X32842) = X32839
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32842),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32841)),X32840))) )
& ( hAPP(hAPP(c_List_Onth(X32841),X32840),X32842) != X32839
| hAPP(hAPP(c_List_Olist__update(X32841,X32840),X32842),X32839) = X32840
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32842),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32841)),X32840))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__same__conv])])]) ).
fof(i_0_8976,plain,
! [X21052,X21053] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21053)))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21053),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21052)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21052)))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21053),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21052)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21053)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21053))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21052)))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21053),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21052)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21053),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21052)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21053))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5790])])]) ).
fof(i_0_8977,plain,
! [X25430,X25431,X25432] :
( ~ class_Orderings_Olinorder(X25432)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25432),X25431))
| hBOOL(hAPP(hAPP(c_member(X25432),X25430),X25431))
| X25431 = c_Orderings_Obot__class_Obot(tc_fun(X25432,tc_HOL_Obool))
| c_Big__Operators_Olattice_OInf__fin(X25432,c_Orderings_Oord__class_Omin(X25432),hAPP(hAPP(c_Set_Oinsert(X25432),X25430),X25431)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25432),X25430),c_Big__Operators_Olattice_OInf__fin(X25432,c_Orderings_Oord__class_Omin(X25432),X25431)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5791])]) ).
fof(i_0_8978,plain,
! [X25338,X25339,X25340] :
( ~ class_Orderings_Olinorder(X25340)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25340),X25339))
| hBOOL(hAPP(hAPP(c_member(X25340),X25338),X25339))
| X25339 = c_Orderings_Obot__class_Obot(tc_fun(X25340,tc_HOL_Obool))
| c_Big__Operators_Olattice_OSup__fin(X25340,c_Orderings_Oord__class_Omax(X25340),hAPP(hAPP(c_Set_Oinsert(X25340),X25338),X25339)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25340),X25338),c_Big__Operators_Olattice_OSup__fin(X25340,c_Orderings_Oord__class_Omax(X25340),X25339)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5792])]) ).
fof(i_0_8979,plain,
! [X17278,X17279,X17280,X17281,X17282] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OAss(X17282,X17281),X17280,X17279,X17278)
| X17278 = hAPP(hAPP(hAPP(c_Natural_Oupdate,X17280),X17282),hAPP(X17281,X17280)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln__elim__cases_I2_J])]) ).
fof(i_0_8980,plain,
! [X19033,X19034] : 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),X19034))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19033))),
inference(variable_rename,[status(thm)],[fact_negative__zle]) ).
fof(i_0_8981,plain,
! [X20653,X20654] : 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),X20654)),X20653))),
inference(variable_rename,[status(thm)],[fact_zero__le__zpower__abs]) ).
fof(i_0_8982,plain,
! [X22546,X22547,X22548] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22548),X22547)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22546),X22547)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X22548),X22546)),X22547),
inference(variable_rename,[status(thm)],[fact_min__diff]) ).
fof(i_0_8983,plain,
! [X20375,X20376,X20377] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20377),X20376)),X20375) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20377),X20375)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20376),X20375)),
inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib]) ).
cnf(i_0_8984,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_8985,plain,
! [X18869,X18870,X18871] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18871),X18870)),X18869) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18871),X18869)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18870),X18869)),
inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib]) ).
fof(i_0_8986,plain,
! [X20384,X20385,X20386] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20386),X20385)),X20384) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20386),X20384)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20385),X20384)),
inference(variable_rename,[status(thm)],[fact_diff__mult__distrib]) ).
fof(i_0_8987,plain,
! [X19280,X19281,X19282] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19282),X19281)),X19280) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19282),X19280)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19281),X19280)),
inference(variable_rename,[status(thm)],[fact_add__mult__distrib]) ).
fof(i_0_8988,plain,
! [X32530,X32531,X32532,X32533] : hAPP(hAPP(c_List_Onth(X32533),hAPP(hAPP(c_List_Olist_OCons(X32533),X32532),X32531)),X32530) = c_Nat_Onat_Onat__case(X32533,X32532,hAPP(c_List_Onth(X32533),X32531),X32530),
inference(variable_rename,[status(thm)],[fact_nth_Osimps]) ).
fof(i_0_8989,plain,
! [X25637,X25638,X25639,X25640] :
( ( X25638 = c_Orderings_Obot__class_Obot(tc_fun(X25640,tc_HOL_Obool))
| c_Sum__Type_OPlus(X25640,X25639,X25638,X25637) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X25640,X25639),tc_HOL_Obool)) )
& ( X25637 = c_Orderings_Obot__class_Obot(tc_fun(X25639,tc_HOL_Obool))
| c_Sum__Type_OPlus(X25640,X25639,X25638,X25637) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X25640,X25639),tc_HOL_Obool)) )
& ( X25638 != c_Orderings_Obot__class_Obot(tc_fun(X25640,tc_HOL_Obool))
| X25637 != c_Orderings_Obot__class_Obot(tc_fun(X25639,tc_HOL_Obool))
| c_Sum__Type_OPlus(X25640,X25639,X25638,X25637) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X25640,X25639),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_8990,plain,
! [X23164,X23165,X23166] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23166),X23164))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23165),X23164))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23164),X23165))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23166),X23165)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23164),X23166))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23165),X23164))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23164),X23165))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23166),X23165)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5794])])]) ).
fof(i_0_8991,plain,
! [X23146,X23147,X23148] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23148),X23146))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23147),X23146))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23148),X23147))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23147),X23148)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23146),X23148))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23147),X23146))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23148),X23147))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23147),X23148)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5795])])]) ).
fof(i_0_8992,plain,
! [X25221,X25222,X25223] :
( ( X25223 = X25222
| c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25223,X25222) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X25221),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) )
& ( X25222 = X25221
| c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25223,X25222) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X25221),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) )
& ( X25223 != X25222
| X25222 != X25221
| c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25223,X25222) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X25221),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_8993,plain,
! [X31258,X31259,X31260] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X31260,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X31260,tc_HOL_Obool)),X31259),X31258)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31260,tc_HOL_Obool)),X31259),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31260,tc_HOL_Obool),X31258)),
inference(variable_rename,[status(thm)],[fact_Union__insert]) ).
fof(i_0_8994,plain,
! [X31351,X31352,X31353] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X31353,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X31353,tc_HOL_Obool)),X31352),X31351)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31353,tc_HOL_Obool)),X31352),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31353,tc_HOL_Obool),X31351)),
inference(variable_rename,[status(thm)],[fact_Inter__insert]) ).
fof(i_0_8995,plain,
! [X23533,X23534,X23535] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X23535,X23534) != c_Divides_Odiv__class_Omod(tc_Int_Oint,X23533,X23534)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23534),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23535),X23533))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23534),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23535),X23533)))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X23535,X23534) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X23533,X23534) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__eq__dvd__iff])]) ).
fof(i_0_8996,plain,
! [X29572,X29573] :
( hAPP(hAPP(c_Relation_Orel__comp(X29573,X29573,X29573),X29572),X29572) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29573,X29573),tc_HOL_Obool))
| c_Wellfounded_Owf(X29573,X29572) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__no__loop])]) ).
fof(i_0_8997,plain,
! [X20608,X20609] :
( ( X20609 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20609),X20608) = X20608 )
& ( X20609 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20609),X20608) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20609),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X20608)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__if])]) ).
fof(i_0_8998,plain,
! [X27058,X27059,X27060,X27061,X27062] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27062,tc_Option_Ooption(X27061)),X27060),X27059),hAPP(c_Option_Ooption_OSome(X27061),X27058)) != hAPP(c_COMBK(tc_Option_Ooption(X27061),X27062),c_Option_Ooption_ONone(X27061)),
inference(variable_rename,[status(thm)],[fact_map__upd__nonempty]) ).
fof(i_0_8999,plain,
! [X27298,X27299,X27300,X27301] :
( ~ class_Rings_Osemiring__1(X27301)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27300,X27301),hAPP(c_COMBK(X27301,X27300),X27299)),X27298) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27301),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27301),hAPP(c_Finite__Set_Ocard(X27300),X27298))),X27299) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__constant])]) ).
fof(i_0_9000,plain,
! [X19367,X19368] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19368),hAPP(c_Int_Oring__1__class_Oof__int(X19368),X19367)),c_Groups_Ozero__class_Ozero(X19368)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19367),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ class_Rings_Olinordered__idom(X19368) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19367),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19368),hAPP(c_Int_Oring__1__class_Oof__int(X19368),X19367)),c_Groups_Ozero__class_Ozero(X19368)))
| ~ class_Rings_Olinordered__idom(X19368) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__le__0__iff])])]) ).
fof(i_0_9001,plain,
! [X18648,X18649] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18649),hAPP(c_Int_Oring__1__class_Oof__int(X18649),X18648)),c_Groups_Ozero__class_Ozero(X18649)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18648),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ class_Rings_Olinordered__idom(X18649) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18648),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18649),hAPP(c_Int_Oring__1__class_Oof__int(X18649),X18648)),c_Groups_Ozero__class_Ozero(X18649)))
| ~ class_Rings_Olinordered__idom(X18649) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__less__0__iff])])]) ).
fof(i_0_9002,plain,
! [X19813,X19814,X19815,X19816] :
( ~ class_Divides_Osemiring__div(X19816)
| c_Divides_Odiv__class_Omod(X19816,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19816),X19815),c_Divides_Odiv__class_Omod(X19816,X19814,X19813)),X19813) = c_Divides_Odiv__class_Omod(X19816,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19816),X19815),X19814),X19813) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__simps_I2_J])]) ).
fof(i_0_9003,plain,
! [X20317,X20318,X20319,X20320] :
( ~ class_Divides_Oring__div(X20320)
| c_Divides_Odiv__class_Omod(X20320,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20320),X20319),X20318),X20317) = c_Divides_Odiv__class_Omod(X20320,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20320),X20319),c_Divides_Odiv__class_Omod(X20320,X20318,X20317)),X20317) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__right__eq])]) ).
fof(i_0_9004,plain,
! [X19861,X19862,X19863,X19864] :
( ~ class_Divides_Osemiring__div(X19864)
| c_Divides_Odiv__class_Omod(X19864,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19864),X19863),X19862),X19861) = c_Divides_Odiv__class_Omod(X19864,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19864),X19863),c_Divides_Odiv__class_Omod(X19864,X19862,X19861)),X19861) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__right__eq])]) ).
fof(i_0_9005,plain,
! [X19825,X19826,X19827,X19828] :
( ~ class_Divides_Osemiring__div(X19828)
| c_Divides_Odiv__class_Omod(X19828,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19828),X19827),X19826),X19825) = c_Divides_Odiv__class_Omod(X19828,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19828),X19827),c_Divides_Odiv__class_Omod(X19828,X19826,X19825)),X19825) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__right__eq])]) ).
fof(i_0_9006,plain,
! [X22932,X22933,X22934,X22935] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22935,tc_HOL_Obool)),X22934),X22933))
| ~ hBOOL(hAPP(X22934,X22932))
| hBOOL(hAPP(X22933,X22932)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate1D])]) ).
fof(i_0_9007,plain,
! [X22928,X22929,X22930,X22931] :
( ~ hBOOL(hAPP(X22931,X22930))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22929,tc_HOL_Obool)),X22931),X22928))
| hBOOL(hAPP(X22928,X22930)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate1D])]) ).
fof(i_0_9008,plain,
! [X20393,X20394] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20394))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20394),X20393))
| hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20393),X20394)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X20393)),hAPP(c_Int_Onat,X20394)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__distrib])]) ).
fof(i_0_9009,plain,
! [X27615,X27616,X27617] :
( ~ class_Orderings_Olinorder(X27617)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27617),X27616),X27615))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27617,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X27617,X27616),X27615)),hAPP(c_SetInterval_Oord__class_OatLeast(X27617),X27615)) = hAPP(c_SetInterval_Oord__class_OatLeast(X27617),X27616) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I14_J])]) ).
fof(i_0_9010,plain,
! [X21170,X21171] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21171),hAPP(c_Int_Onumber__class_Onumber__of(X21171),X21170)),c_Groups_Ozero__class_Ozero(X21171)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21170),c_Int_OPls))
| ~ class_Int_Onumber__ring(X21171)
| ~ class_Rings_Olinordered__idom(X21171) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21170),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21171),hAPP(c_Int_Onumber__class_Onumber__of(X21171),X21170)),c_Groups_Ozero__class_Ozero(X21171)))
| ~ class_Int_Onumber__ring(X21171)
| ~ class_Rings_Olinordered__idom(X21171) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I3_J])])]) ).
fof(i_0_9011,plain,
! [X21172,X21173] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21173),hAPP(c_Int_Onumber__class_Onumber__of(X21173),X21172)),c_Groups_Ozero__class_Ozero(X21173)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21172),c_Int_OPls))
| ~ class_Int_Onumber__ring(X21173)
| ~ class_Rings_Olinordered__idom(X21173) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21172),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21173),hAPP(c_Int_Onumber__class_Onumber__of(X21173),X21172)),c_Groups_Ozero__class_Ozero(X21173)))
| ~ class_Int_Onumber__ring(X21173)
| ~ class_Rings_Olinordered__idom(X21173) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I3_J])])]) ).
fof(i_0_9012,plain,
! [X27794,X27795,X27796,X27797] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X27797),X27796),c_Map_Odom(X27797,X27795,X27794)))
| hAPP(X27794,X27796) != c_Option_Ooption_ONone(X27795) )
& ( hAPP(X27794,X27796) = c_Option_Ooption_ONone(X27795)
| hBOOL(hAPP(hAPP(c_member(X27797),X27796),c_Map_Odom(X27797,X27795,X27794))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_domIff])]) ).
fof(i_0_9013,plain,
! [X32177,X32178,X32179,X32180] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32180)),X32179) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32178)),X32177)
| hAPP(hAPP(c_List_Omap(tc_prod(X32180,X32178),X32180),c_Product__Type_Ofst(X32180,X32178)),hAPP(hAPP(c_List_Ozip(X32180,X32178),X32179),X32177)) = X32179 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__fst__zip])]) ).
fof(i_0_9014,plain,
! [X32181,X32182,X32183,X32184] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32184)),X32183) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32182)),X32181)
| hAPP(hAPP(c_List_Omap(tc_prod(X32184,X32182),X32182),c_Product__Type_Osnd(X32184,X32182)),hAPP(hAPP(c_List_Ozip(X32184,X32182),X32183),X32181)) = X32181 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__snd__zip])]) ).
fof(i_0_9015,plain,
! [X20178,X20179,X20180] :
( ~ class_Divides_Osemiring__div(X20180)
| X20179 = c_Groups_Ozero__class_Ozero(X20180)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20180),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20180),X20179),X20178)),X20179) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20180),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20180),X20178),X20179)),c_Groups_Oone__class_Oone(X20180)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__add__self1])]) ).
fof(i_0_9016,plain,
! [X20175,X20176,X20177] :
( ~ class_Divides_Osemiring__div(X20177)
| X20176 = c_Groups_Ozero__class_Ozero(X20177)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20177),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20177),X20175),X20176)),X20176) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20177),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20177),X20175),X20176)),c_Groups_Oone__class_Oone(X20177)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__add__self2])]) ).
fof(i_0_9017,plain,
! [X19845,X19846,X19847,X19848] :
( ~ class_Divides_Osemiring__div(X19848)
| c_Divides_Odiv__class_Omod(X19848,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19848),X19847),X19846),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19848),X19845),X19846)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19848),c_Divides_Odiv__class_Omod(X19848,X19847,X19845)),X19846) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__mult2])]) ).
fof(i_0_9018,plain,
! [X20856,X20857] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20857),X20856))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X20857))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X20856))),
inference(variable_rename,[status(thm)],[fact_nat__abs__mult__distrib]) ).
fof(i_0_9019,plain,
! [X20111,X20112,X20113] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20113))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20113),X20112)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20113),X20111)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20112),X20111) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__div__cancel1])]) ).
fof(i_0_9020,plain,
! [X20150,X20151,X20152] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20152))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20151),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20150),X20152)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20151),X20150)),X20152) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__zmult2__eq])]) ).
fof(i_0_9021,plain,
! [X21080,X21081] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21081)))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21081)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21080)) = 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),X21080)) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21081)))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21081)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21080)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21081)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21080))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5796])]) ).
fof(i_0_9022,plain,
! [X21050,X21051] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21051)))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21051)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21050)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21051)))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21051)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21050)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21051)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21050))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5797])]) ).
fof(i_0_9023,plain,
! [X31941,X31942,X31943] : c_Map_Odom(X31943,X31942,c_Map_Omap__of(X31943,X31942,X31941)) = hAPP(c_Set_Oimage(tc_prod(X31943,X31942),X31943,c_Product__Type_Ofst(X31943,X31942)),hAPP(c_List_Oset(tc_prod(X31943,X31942)),X31941)),
inference(variable_rename,[status(thm)],[fact_dom__map__of__conv__image__fst]) ).
fof(i_0_9024,plain,
! [X22343,X22344,X22345,X22346,X22347] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22347,X22346,X22345),X22344),X22343) = hAPP(hAPP(X22344,hAPP(c_Product__Type_Ofst(X22347,X22346),X22343)),hAPP(c_Product__Type_Osnd(X22347,X22346),X22343)),
inference(variable_rename,[status(thm)],[fact_split__def]) ).
fof(i_0_9025,plain,
! [X22338,X22339,X22340,X22341,X22342] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22342,X22341,X22340),X22339),X22338) = hAPP(hAPP(X22339,hAPP(c_Product__Type_Ofst(X22342,X22341),X22338)),hAPP(c_Product__Type_Osnd(X22342,X22341),X22338)),
inference(variable_rename,[status(thm)],[fact_split__beta]) ).
fof(i_0_9026,plain,
! [X22323,X22324,X22325,X22326,X22327] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22327,X22326,X22325),X22324),X22323) = hAPP(hAPP(X22324,hAPP(c_Product__Type_Ofst(X22327,X22326),X22323)),hAPP(c_Product__Type_Osnd(X22327,X22326),X22323)),
inference(variable_rename,[status(thm)],[fact_prod__case__beta]) ).
fof(i_0_9027,plain,
! [X33018,X33019,X33020,X33021,X33022] :
( ( X33021 = X33019
| hAPP(hAPP(c_List_Oappend(X33022),X33021),hAPP(hAPP(c_List_Olist_OCons(X33022),X33020),c_List_Olist_ONil(X33022))) != hAPP(hAPP(c_List_Oappend(X33022),X33019),hAPP(hAPP(c_List_Olist_OCons(X33022),X33018),c_List_Olist_ONil(X33022))) )
& ( X33020 = X33018
| hAPP(hAPP(c_List_Oappend(X33022),X33021),hAPP(hAPP(c_List_Olist_OCons(X33022),X33020),c_List_Olist_ONil(X33022))) != hAPP(hAPP(c_List_Oappend(X33022),X33019),hAPP(hAPP(c_List_Olist_OCons(X33022),X33018),c_List_Olist_ONil(X33022))) )
& ( X33021 != X33019
| X33020 != X33018
| hAPP(hAPP(c_List_Oappend(X33022),X33021),hAPP(hAPP(c_List_Olist_OCons(X33022),X33020),c_List_Olist_ONil(X33022))) = hAPP(hAPP(c_List_Oappend(X33022),X33019),hAPP(hAPP(c_List_Olist_OCons(X33022),X33018),c_List_Olist_ONil(X33022))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append1__eq__conv])])]) ).
fof(i_0_9028,plain,
! [X23280,X23281] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23281),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23280),X23281)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23281),X23280)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23281),X23280))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23281),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23280),X23281))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__reduce])]) ).
fof(i_0_9029,plain,
! [X33442,X33443,X33444] :
( X33444 = c_List_Olist_ONil(X33443)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33442),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33443)),X33444)))
| hAPP(c_List_Ohd(X33443),hAPP(hAPP(c_List_Odrop(X33443),X33442),X33444)) = hAPP(hAPP(c_List_Onth(X33443),X33444),X33442) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__drop__conv__nth])]) ).
fof(i_0_9030,plain,
! [X20663,X20664,X20665] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20665)
| hAPP(c_Groups_Oabs__class_Oabs(X20665),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20665),hAPP(c_Groups_Oabs__class_Oabs(X20665),X20664)),hAPP(c_Groups_Oabs__class_Oabs(X20665),X20663))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20665),hAPP(c_Groups_Oabs__class_Oabs(X20665),X20664)),hAPP(c_Groups_Oabs__class_Oabs(X20665),X20663)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__add__abs])]) ).
fof(i_0_9031,plain,
! [X30697,X30698,X30699,X30700,X30701] :
( ~ c_Finite__Set_Ofolding__one__idem(X30701,X30700,X30699)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30701),X30698))
| hAPP(X30699,hAPP(hAPP(c_Set_Oinsert(X30701),X30697),X30698)) = hAPP(hAPP(c_Finite__Set_Ofold(X30701,X30701,X30700),X30697),X30698) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oeq__fold__idem_H])]) ).
fof(i_0_9032,plain,
! [X24735,X24736,X24737] :
( ~ class_Lattices_Osemilattice__inf(X24737)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24737),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24737),X24736),X24735)),X24736)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__le1])]) ).
fof(i_0_9033,plain,
! [X24732,X24733,X24734] :
( ~ class_Lattices_Olattice(X24734)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24734),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24734),X24733),X24732)),X24733)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I1_J])]) ).
fof(i_0_9034,plain,
! [X24741,X24742,X24743] :
( ~ class_Lattices_Osemilattice__inf(X24743)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24743),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24743),X24742),X24741)),X24741)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__le2])]) ).
fof(i_0_9035,plain,
! [X24738,X24739,X24740] :
( ~ class_Lattices_Olattice(X24740)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24740),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24740),X24739),X24738)),X24738)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I2_J])]) ).
fof(i_0_9036,plain,
! [X22440,X22441,X22442] :
( ~ class_Orderings_Olinorder(X22442)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22442),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22442),X22441),X22440)),X22441)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__le1])]) ).
fof(i_0_9037,plain,
! [X22443,X22444,X22445] :
( ~ class_Orderings_Olinorder(X22445)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22445),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22445),X22444),X22443)),X22443)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__le2])]) ).
fof(i_0_9038,plain,
! [X20637] :
( ~ 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),X20637)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20637) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20637)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_expand__Suc])]) ).
fof(i_0_9039,plain,
! [X17712,X17713,X17714] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17714),X17713),X17712))
| c_Natural_Oevaln(X17714,X17713,esk13_3(X17712,X17713,X17714),X17712) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc__evaln])])]) ).
fof(i_0_9040,plain,
! [X17548,X17549,X17550,X17552,X17553,X17554,X17555] :
( ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17550),X17549),X17548))
| c_Natural_Oevaln(X17550,X17549,esk10_3(X17548,X17549,X17550),X17548) )
& ( ~ c_Natural_Oevaln(X17554,X17553,X17555,X17552)
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17554),X17553),X17552)) ) ),
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_9041,plain,
! [X27124,X27125,X27126] :
( ~ class_Orderings_Olinorder(X27126)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27126),X27125),X27124))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27126,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X27126),X27125)),c_SetInterval_Oord__class_OatLeastAtMost(X27126,X27125,X27124)) = hAPP(c_SetInterval_Oord__class_OatMost(X27126),X27124) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I10_J])]) ).
fof(i_0_9042,plain,
! [X27041,X27042,X27043] :
( ~ class_Orderings_Olinorder(X27043)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27043),X27042),X27041))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27043,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X27043),X27042)),c_SetInterval_Oord__class_OgreaterThanAtMost(X27043,X27042,X27041)) = hAPP(c_SetInterval_Oord__class_OatMost(X27043),X27041) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I9_J])]) ).
fof(i_0_9043,plain,
! [X27127,X27128,X27129] :
( ~ class_Orderings_Olinorder(X27129)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27129),X27128),X27127))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27129,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X27129),X27128)),c_SetInterval_Oord__class_OgreaterThanLessThan(X27129,X27128,X27127)) = hAPP(c_SetInterval_Oord__class_OlessThan(X27129),X27127) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I7_J])]) ).
fof(i_0_9044,plain,
! [X23286,X23287,X23288] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23288),hAPP(c_Groups_Ouminus__class_Ouminus(X23288),X23287)),X23286))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23288),X23287),X23286))
| ~ class_Rings_Ocomm__ring__1(X23288) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23288),X23287),X23286))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23288),hAPP(c_Groups_Ouminus__class_Ouminus(X23288),X23287)),X23286))
| ~ class_Rings_Ocomm__ring__1(X23288) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__dvd__iff])])]) ).
fof(i_0_9045,plain,
! [X23274,X23275,X23276] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23276),hAPP(c_Groups_Oabs__class_Oabs(X23276),X23275)),X23274))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23276),X23275),X23274))
| ~ class_Rings_Olinordered__idom(X23276) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23276),X23275),X23274))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23276),hAPP(c_Groups_Oabs__class_Oabs(X23276),X23275)),X23274))
| ~ class_Rings_Olinordered__idom(X23276) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__dvd__iff])])]) ).
fof(i_0_9046,plain,
! [X20657,X20658,X20659] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20659)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20659),hAPP(c_Groups_Oabs__class_Oabs(X20659),X20658)),X20657))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20659),X20658),X20657)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__D1])]) ).
fof(i_0_9047,plain,
! [X24830,X24831,X24832,X24833] :
( ~ class_Lattices_Odistrib__lattice(X24833)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24833),X24832),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24833),X24831),X24830)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24833),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24833),X24832),X24831)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24833),X24832),X24830)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__distrib1])]) ).
fof(i_0_9048,plain,
! [X24834,X24835,X24836,X24837] :
( ~ class_Lattices_Odistrib__lattice(X24837)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24837),X24836),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24837),X24835),X24834)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24837),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24837),X24836),X24835)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24837),X24836),X24834)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__inf__distrib1])]) ).
fof(i_0_9049,plain,
! [X22602,X22603,X22604,X22605] :
( ~ class_Orderings_Olinorder(X22605)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22605),X22604),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22605),X22603),X22602)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22605),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22605),X22604),X22603)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22605),X22604),X22602)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__inf__distrib1])]) ).
fof(i_0_9050,plain,
! [X22598,X22599,X22600,X22601] :
( ~ class_Orderings_Olinorder(X22601)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22601),X22600),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22601),X22599),X22598)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22601),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22601),X22600),X22599)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22601),X22600),X22598)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__distrib1])]) ).
fof(i_0_9051,plain,
! [X18854,X18855,X18856,X18857] :
( ~ class_Rings_Ocomm__semiring__1(X18857)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18857),X18856),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18857),X18855),X18854)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18857),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18857),X18856),X18855)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18857),X18856),X18854)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J])]) ).
fof(i_0_9052,plain,
! [X18733,X18734,X18735,X18736] :
( ~ class_Rings_Ocomm__semiring__1(X18736)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18736),X18735),X18734)),X18733) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18736),X18735),X18733)),X18734) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J])]) ).
fof(i_0_9053,plain,
! [X18199,X18200,X18201,X18202] :
( ~ class_Rings_Ocomm__semiring__1(X18202)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18202),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18202),X18201),X18200)),X18199) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18202),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18202),X18201),X18199)),X18200) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])]) ).
fof(i_0_9054,plain,
! [X28131] : c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X28131),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(X28131)),c_Option_Ooption_ONone(X28131)),hAPP(c_Set_Oimage(X28131,tc_Option_Ooption(X28131),c_Option_Ooption_OSome(X28131)),c_Orderings_Otop__class_Otop(tc_fun(X28131,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_UNIV__option__conv]) ).
fof(i_0_9055,plain,
! [X29404,X29405,X29406] : hAPP(c_Fun_Ocomp(X29406,X29406,X29405,c_Fun_Oid(X29406)),X29404) = X29404,
inference(variable_rename,[status(thm)],[fact_id__o]) ).
fof(i_0_9056,plain,
! [X32190,X32191,X32192] :
( ~ hBOOL(hAPP(hAPP(c_member(X32192),X32191),hAPP(c_List_Oset(X32192),X32190)))
| 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(X32192)),X32190))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__pos__if__in__set])]) ).
fof(i_0_9057,plain,
! [X28855,X28856,X28857] :
( ~ class_Groups_Oab__semigroup__mult(X28857)
| X28856 = c_Orderings_Obot__class_Obot(tc_fun(X28857,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28857),X28856))
| hBOOL(hAPP(hAPP(c_member(X28857),X28855),X28856))
| hAPP(c_Finite__Set_Ofold1(X28857,c_Groups_Otimes__class_Otimes(X28857)),hAPP(hAPP(c_Set_Oinsert(X28857),X28855),X28856)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X28857),X28855),hAPP(c_Finite__Set_Ofold1(X28857,c_Groups_Otimes__class_Otimes(X28857)),X28856)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5798])]) ).
fof(i_0_9058,plain,
! [X30575,X30576,X30577] :
( ~ c_Relation_Osingle__valued(X30577,X30577,X30576)
| c_Relation_Osingle__valued(X30577,X30577,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30577,X30577),tc_HOL_Obool),X30575),X30576)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__rel__pow])]) ).
fof(i_0_9059,plain,
! [X23008,X23009,X23010,X23011] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(X23011),X23010),X23009),X23008) = 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(X23011)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(X23011),X23010)),
inference(variable_rename,[status(thm)],[fact_Random__Sequence_Osingle__def]) ).
fof(i_0_9060,plain,
! [X29842,X29843,X29844,X29845,X29847,X29848,X29849,X29850,X29851] :
( ( ~ hBOOL(hAPP(c_Predicate_ODomainP(X29845,X29844,X29843),X29842))
| hBOOL(hAPP(hAPP(X29843,X29842),esk328_2(X29842,X29843))) )
& ( ~ hBOOL(hAPP(hAPP(X29848,X29847),X29849))
| hBOOL(hAPP(c_Predicate_ODomainP(X29851,X29850,X29848),X29847)) ) ),
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_9061,plain,
! [X28142,X28143,X28144,X28145,X28146] :
( ( hAPP(X28144,X28143) != hAPP(X28144,X28142)
| X28143 = X28142
| ~ c_Fun_Oinj__on(X28146,X28145,X28144,c_Orderings_Otop__class_Otop(tc_fun(X28146,tc_HOL_Obool))) )
& ( X28143 != X28142
| hAPP(X28144,X28143) = hAPP(X28144,X28142)
| ~ c_Fun_Oinj__on(X28146,X28145,X28144,c_Orderings_Otop__class_Otop(tc_fun(X28146,tc_HOL_Obool))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__eq])])]) ).
fof(i_0_9062,plain,
! [X28137,X28138,X28139,X28140,X28141] :
( ~ c_Fun_Oinj__on(X28141,X28140,X28139,c_Orderings_Otop__class_Otop(tc_fun(X28141,tc_HOL_Obool)))
| hAPP(X28139,X28138) != hAPP(X28139,X28137)
| X28138 = X28137 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_injD])]) ).
fof(i_0_9063,plain,
! [X25216,X25217] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25217),X25216))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25216),X25217))
| c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25216,X25217) = 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_9064,plain,
! [X30733,X30734,X30735] :
( ~ class_Orderings_Olinorder(X30735)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30735),X30734))
| c_Big__Operators_Olattice_OInf__fin(X30735,c_Orderings_Oord__class_Omin(X30735),hAPP(hAPP(c_Set_Oinsert(X30735),X30733),X30734)) = hAPP(hAPP(c_Finite__Set_Ofold(X30735,X30735,c_Orderings_Oord__class_Omin(X30735)),X30733),X30734) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oeq__fold__idem_H])]) ).
fof(i_0_9065,plain,
! [X30736,X30737,X30738] :
( ~ class_Orderings_Olinorder(X30738)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30738),X30737))
| c_Big__Operators_Olattice_OSup__fin(X30738,c_Orderings_Oord__class_Omax(X30738),hAPP(hAPP(c_Set_Oinsert(X30738),X30736),X30737)) = hAPP(hAPP(c_Finite__Set_Ofold(X30738,X30738,c_Orderings_Oord__class_Omax(X30738)),X30736),X30737) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oeq__fold__idem_H])]) ).
cnf(i_0_9066,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_9067,plain,
! [X19775,X19776,X19778] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk59_2(X19775,X19776)),X19775))
| ~ hBOOL(hAPP(X19776,X19775))
| hBOOL(hAPP(X19776,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19778),esk59_2(X19775,X19776)))
| ~ hBOOL(hAPP(X19776,X19778))
| ~ hBOOL(hAPP(X19776,X19775))
| hBOOL(hAPP(X19776,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( hBOOL(hAPP(X19776,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk59_2(X19775,X19776)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(X19776,X19775))
| hBOOL(hAPP(X19776,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_9068,plain,
! [X33591,X33592,X33593,X33594] : hAPP(c_List_Ofoldl(X33594,X33593,X33592,X33591),c_List_Olist_ONil(X33593)) = X33591,
inference(variable_rename,[status(thm)],[fact_foldl__Nil]) ).
fof(i_0_9069,plain,
! [X32908,X32909,X32910,X32911] : hAPP(c_List_Olist_Olist__case(X32911,X32910,X32909,X32908),c_List_Olist_ONil(X32910)) = X32909,
inference(variable_rename,[status(thm)],[fact_list_Osimps_I4_J]) ).
fof(i_0_9070,plain,
! [X29407,X29408,X29409] : hAPP(c_Fun_Ocomp(X29409,X29408,X29409,X29407),c_Fun_Oid(X29409)) = X29407,
inference(variable_rename,[status(thm)],[fact_o__id]) ).
fof(i_0_9071,plain,
! [X18171,X18172,X18173,X18174] : hAPP(c_Option_Ooption_Ooption__case(X18174,X18173,X18172,X18171),c_Option_Ooption_ONone(X18173)) = X18172,
inference(variable_rename,[status(thm)],[fact_option_Osimps_I4_J]) ).
fof(i_0_9072,plain,
! [X19384,X19385,X19386] :
( ( X19385 = c_Groups_Ozero__class_Ozero(X19386)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19386),X19385),X19384) != c_Groups_Ozero__class_Ozero(X19386)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19386),c_Groups_Ozero__class_Ozero(X19386)),X19384))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19386),c_Groups_Ozero__class_Ozero(X19386)),X19385))
| ~ class_Groups_Oordered__comm__monoid__add(X19386) )
& ( X19384 = c_Groups_Ozero__class_Ozero(X19386)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19386),X19385),X19384) != c_Groups_Ozero__class_Ozero(X19386)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19386),c_Groups_Ozero__class_Ozero(X19386)),X19384))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19386),c_Groups_Ozero__class_Ozero(X19386)),X19385))
| ~ class_Groups_Oordered__comm__monoid__add(X19386) )
& ( X19385 != c_Groups_Ozero__class_Ozero(X19386)
| X19384 != c_Groups_Ozero__class_Ozero(X19386)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19386),X19385),X19384) = c_Groups_Ozero__class_Ozero(X19386)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19386),c_Groups_Ozero__class_Ozero(X19386)),X19384))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19386),c_Groups_Ozero__class_Ozero(X19386)),X19385))
| ~ class_Groups_Oordered__comm__monoid__add(X19386) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff])])]) ).
fof(i_0_9073,negated_conjecture,
~ c_Hoare__Mirabelle_Otriple__valid(t_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
cnf(i_0_9074,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_9075,plain,
! [X20463,X20464,X20465] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20465),X20464))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20463),X20464)),X20465) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20463),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20464),X20465)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__assoc])]) ).
fof(i_0_9076,plain,
! [X20485,X20486,X20487] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20487),X20486))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20485),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20486),X20487)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20485),X20487)),X20486) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__right])]) ).
fof(i_0_9077,plain,
! [X20474,X20475,X20476] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20476),X20475))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20474),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20475),X20476)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20474),X20475)),X20476) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__assoc])]) ).
fof(i_0_9078,plain,
! [X19769,X19770,X19771] :
( ~ class_Lattices_Oboolean__algebra(X19771)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19771),X19770),X19769))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19771),hAPP(c_Groups_Ouminus__class_Ouminus(X19771),X19769)),hAPP(c_Groups_Ouminus__class_Ouminus(X19771),X19770))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__mono])]) ).
fof(i_0_9079,plain,
! [X19265,X19266,X19267] :
( ~ class_Groups_Oordered__ab__group__add(X19267)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19267),X19266),X19265))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19267),hAPP(c_Groups_Ouminus__class_Ouminus(X19267),X19265)),hAPP(c_Groups_Ouminus__class_Ouminus(X19267),X19266))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__neg__le])]) ).
cnf(i_0_9080,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_9081,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_9082,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_9083,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_9084,plain,
! [X18876] :
( ( ~ 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,X18876)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X18876)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X18876))
| 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,X18876))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__nat__eq])]) ).
fof(i_0_9085,plain,
! [X20020,X20021] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20021,X20020)),X20021)),
inference(variable_rename,[status(thm)],[fact_mod__less__eq__dividend]) ).
fof(i_0_9086,plain,
! [X27672] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X27672)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X27672)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X27672)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_greaterThan__Suc]) ).
fof(i_0_9087,plain,
! [X20780,X20781,X20782,X20783] :
( ~ class_Rings_Ocomm__semiring__1(X20783)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20783),hAPP(hAPP(c_Power_Opower__class_Opower(X20783),X20782),X20781)),hAPP(hAPP(c_Power_Opower__class_Opower(X20783),X20782),X20780)) = hAPP(hAPP(c_Power_Opower__class_Opower(X20783),X20782),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20781),X20780)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J])]) ).
fof(i_0_9088,plain,
! [X20985,X20986,X20987,X20988] :
( ~ class_Groups_Omonoid__mult(X20988)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20988),X20987),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20986),X20985)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20988),hAPP(hAPP(c_Power_Opower__class_Opower(X20988),X20987),X20986)),hAPP(hAPP(c_Power_Opower__class_Opower(X20988),X20987),X20985)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__add])]) ).
fof(i_0_9089,plain,
! [X30718,X30719,X30720] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X30720)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30720),X30719))
| hAPP(c_Finite__Set_Ofold1(X30720,c_Groups_Otimes__class_Otimes(X30720)),hAPP(hAPP(c_Set_Oinsert(X30720),X30718),X30719)) = hAPP(hAPP(c_Finite__Set_Ofold(X30720,X30720,c_Groups_Otimes__class_Otimes(X30720)),X30718),X30719) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__eq__fold__idem])]) ).
fof(i_0_9090,plain,
! [X18961,X18962,X18963,X18964,X18965,X18966] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18966)
| X18965 = c_Groups_Ozero__class_Ozero(X18966)
| X18964 != X18963
| X18962 = X18961
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18966),X18964),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18966),X18965),X18962)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18966),X18963),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18966),X18965),X18961)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__scale__eq__noteq])]) ).
fof(i_0_9091,plain,
! [X29995,X29996] : c_Hilbert__Choice_OEps(X29996,hAPP(hAPP(c_COMBC(X29996,X29996,tc_HOL_Obool),c_fequal),X29995)) = X29995,
inference(variable_rename,[status(thm)],[fact_some__eq__trivial]) ).
fof(i_0_9092,plain,
! [X23021,X23022] : c_HOL_OThe(X23022,hAPP(hAPP(c_COMBC(X23022,X23022,tc_HOL_Obool),c_fequal),X23021)) = X23021,
inference(variable_rename,[status(thm)],[fact_the__eq__trivial]) ).
fof(i_0_9093,plain,
! [X20436,X20437] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20437),X20436)),hAPP(c_Nat_OSuc,X20437))),
inference(variable_rename,[status(thm)],[fact_diff__less__Suc]) ).
fof(i_0_9094,plain,
! [X18384,X18385] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18385),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18385),X18384)))),
inference(variable_rename,[status(thm)],[fact_less__add__Suc1]) ).
fof(i_0_9095,plain,
! [X18386,X18387] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18387),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18386),X18387)))),
inference(variable_rename,[status(thm)],[fact_less__add__Suc2]) ).
fof(i_0_9096,plain,
! [X26525,X26526,X26527,X26528] :
( ~ class_Orderings_Oorder(X26528)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26528,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26528,X26527,X26526)),c_SetInterval_Oord__class_OgreaterThanAtMost(X26528,X26526,X26525)) = c_Orderings_Obot__class_Obot(tc_fun(X26528,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I16_J])]) ).
fof(i_0_9097,plain,
! [X26533,X26534,X26535,X26536] :
( ~ class_Orderings_Oorder(X26536)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26536,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26536,X26535,X26534)),c_SetInterval_Oord__class_OgreaterThanLessThan(X26536,X26534,X26533)) = c_Orderings_Obot__class_Obot(tc_fun(X26536,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I12_J])]) ).
fof(i_0_9098,plain,
! [X25842,X25843,X25844,X25845] :
( ~ class_Orderings_Oorder(X25845)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25845,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25845,X25844,X25843)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25845,X25843,X25842)) = c_Orderings_Obot__class_Obot(tc_fun(X25845,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I14_J])]) ).
fof(i_0_9099,plain,
! [X25857,X25858,X25859,X25860] :
( ~ class_Orderings_Oorder(X25860)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25860,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25860,X25859,X25858)),c_SetInterval_Oord__class_OgreaterThanLessThan(X25860,X25858,X25857)) = c_Orderings_Obot__class_Obot(tc_fun(X25860,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I10_J])]) ).
fof(i_0_9100,plain,
! [X26529,X26530,X26531,X26532] :
( ~ class_Orderings_Oorder(X26532)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26532,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X26532,X26531,X26530)),c_SetInterval_Oord__class_OatLeastAtMost(X26532,X26530,X26529)) = c_Orderings_Obot__class_Obot(tc_fun(X26532,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I13_J])]) ).
fof(i_0_9101,plain,
! [X23059,X23060] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23060,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X23060,tc_HOL_Obool))),X23059)),
inference(variable_rename,[status(thm)],[fact_empty__subsetI]) ).
fof(i_0_9102,plain,
! [X30342,X30343,X30344] :
( ~ c_Equiv__Relations_Oequiv(X30344,X30343,X30342)
| hAPP(hAPP(c_Relation_Orel__comp(X30344,X30344,X30344),hAPP(c_Relation_Oconverse(X30344,X30344),X30342)),X30342) = X30342 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__comp__eq])]) ).
fof(i_0_9103,plain,
! [X24996,X24997,X24998,X24999] :
( hBOOL(hAPP(hAPP(c_member(X24999),X24998),X24997))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24999,tc_HOL_Obool)),X24997),hAPP(hAPP(c_Set_Oinsert(X24999),X24998),X24996)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24999,tc_HOL_Obool)),X24997),X24996) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5807])]) ).
fof(i_0_9104,plain,
! [X17544,X17545,X17546,X17547] :
( ~ c_Natural_Oevaln(X17547,X17546,X17545,X17544)
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17547),X17546),X17544)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln__evalc])]) ).
fof(i_0_9105,plain,
! [X17401,X17402,X17403,X17404] : c_Natural_Oevaln(c_Com_Ocom_OAss(X17404,X17403),X17402,X17401,hAPP(hAPP(hAPP(c_Natural_Oupdate,X17402),X17404),hAPP(X17403,X17402))),
inference(variable_rename,[status(thm)],[fact_evaln_Oequations_I2_J]) ).
fof(i_0_9106,plain,
! [X17283,X17284,X17285,X17286] : c_Natural_Oevaln(c_Com_Ocom_OAss(X17286,X17285),X17284,X17283,hAPP(hAPP(hAPP(c_Natural_Oupdate,X17284),X17286),hAPP(X17285,X17284))),
inference(variable_rename,[status(thm)],[fact_evaln_OAssign]) ).
fof(i_0_9107,plain,
! [X19977,X19978] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19978))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19977))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(X19978,X19977))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J])]) ).
fof(i_0_9108,plain,
! [X23073,X23074,X23075] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23075,tc_HOL_Obool)),X23074),hAPP(hAPP(c_Set_Oinsert(X23075),X23073),X23074))),
inference(variable_rename,[status(thm)],[fact_subset__insertI]) ).
fof(i_0_9109,plain,
! [X20390,X20391,X20392] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20392),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20391,X20390)),X20390) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20392),X20391),X20390),
inference(variable_rename,[status(thm)],[fact_zdiff__zmod__right]) ).
fof(i_0_9110,plain,
! [X19877,X19878,X19879] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19879),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19878,X19877)),X19877) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19879),X19878),X19877),
inference(variable_rename,[status(thm)],[fact_zmod__simps_I3_J]) ).
fof(i_0_9111,plain,
! [X19874,X19875,X19876] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19876),X19875),X19874) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19876),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19875,X19874)),X19874),
inference(variable_rename,[status(thm)],[fact_zmod__zmult1__eq]) ).
fof(i_0_9112,plain,
! [X27108,X27109,X27110] :
( ~ class_Orderings_Olinorder(X27110)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27110),X27109),X27108))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27110,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X27110),X27109)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X27110,X27109),X27108)) = hAPP(c_SetInterval_Oord__class_OlessThan(X27110),X27108) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I8_J])]) ).
cnf(i_0_9113,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_9114,plain,
! [X26498,X26499] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26499),hAPP(c_Nat_OSuc,X26498)))
| c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26499,hAPP(c_Nat_OSuc,X26498)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X26498)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26499,X26498)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMostSuc__conv])]) ).
cnf(i_0_9115,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_9116,plain,
! [X28178] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X28178)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X28178),tc_HOL_Obool))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X28178),c_Orderings_Otop__class_Otop(tc_fun(X28178,tc_HOL_Obool)))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28178),c_Orderings_Otop__class_Otop(tc_fun(X28178,tc_HOL_Obool))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X28178)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X28178),tc_HOL_Obool)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__option__UNIV])]) ).
fof(i_0_9117,plain,
! [X18533,X18534,X18535] :
( ~ class_Rings_Olinordered__semidom(X18535)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18534),X18533))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18535),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18535),X18534)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18535),X18533))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__of__nat__less])]) ).
fof(i_0_9118,plain,
! [X27621,X27622,X27623,X27624] :
( ~ class_Orderings_Olinorder(X27624)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27624,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X27624),X27623)),c_SetInterval_Oord__class_OatLeastAtMost(X27624,X27622,X27621)) = c_SetInterval_Oord__class_OatLeastAtMost(X27624,hAPP(hAPP(c_Orderings_Oord__class_Omax(X27624),X27623),X27622),X27621) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostR2])]) ).
fof(i_0_9119,plain,
! [X27037,X27038,X27039,X27040] :
( ~ class_Orderings_Olinorder(X27040)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27040,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X27040),X27039)),c_SetInterval_Oord__class_OatLeastAtMost(X27040,X27038,X27037)) = c_SetInterval_Oord__class_OatLeastAtMost(X27040,X27038,hAPP(hAPP(c_Orderings_Oord__class_Omin(X27040),X27039),X27037)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostR1])]) ).
fof(i_0_9120,plain,
! [X18997,X18998] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18998),hAPP(c_Int_Onat,X18997)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18998)),X18997)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18998)),X18997))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18998),hAPP(c_Int_Onat,X18997))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__nat__eq__int__zless])]) ).
fof(i_0_9121,plain,
! [X26537,X26538] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26538),X26537))
| c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X26537,X26538) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26538),X26537))
| c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X26537,X26538) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),X26537),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26537),c_Groups_Oone__class_Oone(tc_Int_Oint)),X26538)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5810])]) ).
fof(i_0_9122,plain,
! [X20242,X20243] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20243))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20242))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X20243)),hAPP(c_Int_Onat,X20242)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(X20243,X20242)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J])]) ).
fof(i_0_9123,plain,
! [X33330,X33331,X33332,X33333] : hAPP(hAPP(c_List_Odrop(X33333),X33332),hAPP(hAPP(c_List_Otake(X33333),X33331),X33330)) = hAPP(hAPP(c_List_Otake(X33333),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33331),X33332)),hAPP(hAPP(c_List_Odrop(X33333),X33332),X33330)),
inference(variable_rename,[status(thm)],[fact_drop__take]) ).
fof(i_0_9124,plain,
! [X29507,X29508,X29509,X29510] : hAPP(hAPP(c_Relation_Orel__comp(X29510,X29509,X29508),X29507),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29509,X29508),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29510,X29508),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_rel__comp__empty2]) ).
fof(i_0_9125,plain,
! [X23457,X23458,X23459,X23460] : c_Product__Type_Ocurry(X23460,X23459,X23458,hAPP(c_Product__Type_Oprod_Oprod__case(X23460,X23459,X23458),X23457)) = X23457,
inference(variable_rename,[status(thm)],[fact_curry__split]) ).
fof(i_0_9126,plain,
! [X22247] :
( ~ 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),X22247)))
| 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),X22247)) = 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),X22247))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__pos__1__number__of])]) ).
fof(i_0_9127,plain,
! [X20025,X20026,X20027] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20027,X20026)),X20025) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20027),X20025),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20026),X20025)),
inference(variable_rename,[status(thm)],[fact_mod__mult__distrib]) ).
fof(i_0_9128,plain,
! [X23473,X23474,X23475] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23474))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23475),X23473),hAPP(hAPP(c_Power_Opower__class_Opower(X23475),X23473),X23474)))
| ~ class_Rings_Ocomm__semiring__1(X23475) )
& ( X23473 != c_Groups_Oone__class_Oone(X23475)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23475),X23473),hAPP(hAPP(c_Power_Opower__class_Opower(X23475),X23473),X23474)))
| ~ class_Rings_Ocomm__semiring__1(X23475) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__power])])]) ).
fof(i_0_9129,plain,
! [X23261,X23262,X23263,X23264] :
( ~ class_Rings_Ocomm__semiring__1(X23264)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23264),X23263),X23262))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23264),X23263),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23264),X23262),X23261))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult2])]) ).
fof(i_0_9130,plain,
! [X23257,X23258,X23259,X23260] :
( ~ class_Rings_Ocomm__semiring__1(X23260)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23260),X23259),X23258))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23260),X23259),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23260),X23257),X23258))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult])]) ).
fof(i_0_9131,plain,
! [X23965,X23966,X23967,X23968] :
( ~ class_Lattices_Osemilattice__sup(X23968)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23968),X23967),X23966))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23968),X23967),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23968),X23966),X23965))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__supI1])]) ).
fof(i_0_9132,plain,
! [X23969,X23970,X23971,X23972] :
( ~ class_Lattices_Osemilattice__sup(X23972)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23972),X23971),X23970))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23972),X23971),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23972),X23969),X23970))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__supI2])]) ).
fof(i_0_9133,plain,
! [X22685,X22686,X22687,X22688] :
( ~ class_Orderings_Olinorder(X22688)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22688),X22687),X22686))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22688),X22687),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22688),X22686),X22685))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__supI1])]) ).
fof(i_0_9134,plain,
! [X22681,X22682,X22683,X22684] :
( ~ class_Orderings_Olinorder(X22684)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22684),X22683),X22682))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22684),X22683),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22684),X22681),X22682))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__supI2])]) ).
fof(i_0_9135,plain,
! [X24127,X24128,X24129,X24130] :
( ~ class_Lattices_Osemilattice__sup(X24130)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24130),X24129),X24128))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24130),X24129),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24130),X24128),X24127))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__supI1])]) ).
fof(i_0_9136,plain,
! [X24123,X24124,X24125,X24126] :
( ~ class_Lattices_Osemilattice__sup(X24126)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24126),X24125),X24124))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24126),X24125),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24126),X24123),X24124))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__supI2])]) ).
fof(i_0_9137,plain,
! [X22582,X22583,X22584,X22585] :
( ~ class_Orderings_Olinorder(X22585)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22585),X22584),X22583))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22585),X22584),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22585),X22583),X22582))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oless__supI1])]) ).
fof(i_0_9138,plain,
! [X22586,X22587,X22588,X22589] :
( ~ class_Orderings_Olinorder(X22589)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22589),X22588),X22587))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22589),X22588),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22589),X22586),X22587))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oless__supI2])]) ).
cnf(i_0_9139,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_9140,plain,
! [X19680] : 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),X19680))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[fact_negative__zle__0]) ).
fof(i_0_9141,plain,
! [X33977,X33978,X33979,X33980,X33981] :
( ( c_List_Otranspose(X33978,X33977) != c_List_Olist_ONil(tc_List_Olist(X33978))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33978)),X33979),hAPP(c_List_Oset(tc_List_Olist(X33978)),X33977)))
| X33979 = c_List_Olist_ONil(X33978) )
& ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33981)),esk484_2(X33980,X33981)),hAPP(c_List_Oset(tc_List_Olist(X33981)),X33980)))
| c_List_Otranspose(X33981,X33980) = c_List_Olist_ONil(tc_List_Olist(X33981)) )
& ( esk484_2(X33980,X33981) != c_List_Olist_ONil(X33981)
| c_List_Otranspose(X33981,X33980) = c_List_Olist_ONil(tc_List_Olist(X33981)) ) ),
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_9142,plain,
! [X27336,X27337,X27338] :
( ~ class_Groups_Ocomm__monoid__add(X27338)
| hAPP(X27337,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(X27338)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27338),X27337),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X27336)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X27338),X27337),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27336)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__lb__Suc0__0__upt])]) ).
fof(i_0_9143,plain,
! [X25977,X25978,X25979] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25979,tc_fun(X25978,tc_HOL_Obool)),X25977),hAPP(c_COMBK(tc_fun(X25978,tc_HOL_Obool),X25979),c_Orderings_Obot__class_Obot(tc_fun(X25978,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25978,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_UN__empty2]) ).
fof(i_0_9144,plain,
! [X18315,X18316,X18317] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18317),X18316))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18316),X18315))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18317)),X18315)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__trans__Suc])]) ).
fof(i_0_9145,plain,
! [X22405] :
( ~ 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),X22405)))
| 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),X22405)) = 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),X22405))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__pos__1__number__of])]) ).
fof(i_0_9146,plain,
! [X19930,X19931] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19931))
| 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,X19930,X19931))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__sign])]) ).
fof(i_0_9147,plain,
! [X31986,X31987] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X31987,X31986) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X31987),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X31986),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(variable_rename,[status(thm)],[fact_greaterThanLessThan__upto]) ).
fof(i_0_9148,plain,
! [X32318,X32319,X32320,X32321,X32322] : hAPP(hAPP(c_List_Omap(X32322,X32321),X32320),hAPP(hAPP(c_List_Olist_OCons(X32322),X32319),X32318)) = hAPP(hAPP(c_List_Olist_OCons(X32321),hAPP(X32320,X32319)),hAPP(hAPP(c_List_Omap(X32322,X32321),X32320),X32318)),
inference(variable_rename,[status(thm)],[fact_map_Osimps_I2_J]) ).
fof(i_0_9149,plain,
! [X21614,X21615,X21616] :
( ~ class_Fields_Ofield__inverse__zero(X21616)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21616),c_Groups_Oone__class_Oone(X21616)),hAPP(hAPP(c_Power_Opower__class_Opower(X21616),X21615),X21614)) = hAPP(hAPP(c_Power_Opower__class_Opower(X21616),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21616),c_Groups_Oone__class_Oone(X21616)),X21615)),X21614) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one__over])]) ).
fof(i_0_9150,plain,
! [X19699] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19699))
| 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)),X19699))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__0__less])]) ).
fof(i_0_9151,plain,
! [X23615,X23616,X23617,X23618] :
( ~ hBOOL(hAPP(hAPP(c_member(X23618),X23617),X23616))
| hBOOL(hAPP(hAPP(c_member(X23618),X23617),hAPP(hAPP(c_Set_Oinsert(X23618),X23615),X23616))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insertI2])]) ).
fof(i_0_9152,plain,
! [X23582,X23583,X23584,X23585] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X23585),X23584),X23583))
| hBOOL(hAPP(hAPP(c_member(X23585),X23584),hAPP(hAPP(c_Set_Oinsert(X23585),X23582),X23583))) )
& ( X23584 != X23582
| hBOOL(hAPP(hAPP(c_member(X23585),X23584),hAPP(hAPP(c_Set_Oinsert(X23585),X23582),X23583))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5812])])]) ).
fof(i_0_9153,plain,
! [X19274,X19275,X19276] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19276),X19275),hAPP(c_Groups_Ouminus__class_Ouminus(X19276),X19274)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19276),X19274),hAPP(c_Groups_Ouminus__class_Ouminus(X19276),X19275)))
| ~ class_Groups_Oordered__ab__group__add(X19276) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19276),X19274),hAPP(c_Groups_Ouminus__class_Ouminus(X19276),X19275)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19276),X19275),hAPP(c_Groups_Ouminus__class_Ouminus(X19276),X19274)))
| ~ class_Groups_Oordered__ab__group__add(X19276) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__minus__iff])])]) ).
fof(i_0_9154,plain,
! [X18795,X18796,X18797] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18797),X18796),hAPP(c_Groups_Ouminus__class_Ouminus(X18797),X18795)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18797),X18795),hAPP(c_Groups_Ouminus__class_Ouminus(X18797),X18796)))
| ~ class_Groups_Oordered__ab__group__add(X18797) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18797),X18795),hAPP(c_Groups_Ouminus__class_Ouminus(X18797),X18796)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18797),X18796),hAPP(c_Groups_Ouminus__class_Ouminus(X18797),X18795)))
| ~ class_Groups_Oordered__ab__group__add(X18797) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__iff])])]) ).
fof(i_0_9155,plain,
! [X33720,X33721,X33722,X33723] :
( ( X33721 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33722)),X33723)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_List_Olast(X33722,hAPP(hAPP(c_List_Olist__update(X33722,X33723),X33721),X33720)) = X33720
| X33723 = c_List_Olist_ONil(X33722) )
& ( X33721 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33722)),X33723)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_List_Olast(X33722,hAPP(hAPP(c_List_Olist__update(X33722,X33723),X33721),X33720)) = c_List_Olast(X33722,X33723)
| X33723 = c_List_Olist_ONil(X33722) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__list__update])])]) ).
fof(i_0_9156,plain,
! [X19654,X19655] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19655),c_Groups_Osgn__class_Osgn(X19655,X19654)),c_Groups_Ozero__class_Ozero(X19655)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19655),X19654),c_Groups_Ozero__class_Ozero(X19655)))
| ~ class_Rings_Olinordered__idom(X19655) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19655),X19654),c_Groups_Ozero__class_Ozero(X19655)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19655),c_Groups_Osgn__class_Osgn(X19655,X19654)),c_Groups_Ozero__class_Ozero(X19655)))
| ~ class_Rings_Olinordered__idom(X19655) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__less])])]) ).
fof(i_0_9157,plain,
! [X33824,X33825,X33826] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33826),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33825)),X33824)))
| hAPP(hAPP(c_List_Otake(X33825),X33826),c_List_Obutlast(X33825,X33824)) = hAPP(hAPP(c_List_Otake(X33825),X33826),X33824) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__butlast])]) ).
fof(i_0_9158,plain,
! [X33757,X33758,X33759] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33759),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33758)),X33757)))
| c_List_Olast(X33758,hAPP(hAPP(c_List_Odrop(X33758),X33759),X33757)) = c_List_Olast(X33758,X33757) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__drop])]) ).
cnf(i_0_9159,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_9160,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_9161,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_9162,plain,
! [X22129,X22130,X22131,X22132,X22133,X22134] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22134,X22133,X22132),X22131),hAPP(hAPP(c_Product__Type_OPair(X22134,X22133),X22130),X22129)) = hAPP(hAPP(X22131,X22130),X22129),
inference(variable_rename,[status(thm)],[fact_prod_Osimps_I2_J]) ).
fof(i_0_9163,plain,
! [X22123,X22124,X22125,X22126,X22127,X22128] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22128,X22127,X22126),X22125),hAPP(hAPP(c_Product__Type_OPair(X22128,X22127),X22124),X22123)) = hAPP(hAPP(X22125,X22124),X22123),
inference(variable_rename,[status(thm)],[fact_split__conv]) ).
fof(i_0_9164,plain,
! [X25264,X25265,X25266] :
( ~ class_Orderings_Olinorder(X25266)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25266),X25265))
| ~ hBOOL(hAPP(hAPP(c_member(X25266),X25264),X25265))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X25266),X25264),c_Big__Operators_Olattice_OSup__fin(X25266,c_Orderings_Oord__class_Omax(X25266),X25265)) = c_Big__Operators_Olattice_OSup__fin(X25266,c_Orderings_Oord__class_Omax(X25266),X25265) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oin__idem])]) ).
fof(i_0_9165,plain,
! [X25413,X25414,X25415] :
( ~ class_Orderings_Olinorder(X25415)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25415),X25414))
| ~ hBOOL(hAPP(hAPP(c_member(X25415),X25413),X25414))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X25415),X25413),c_Big__Operators_Olattice_OInf__fin(X25415,c_Orderings_Oord__class_Omin(X25415),X25414)) = c_Big__Operators_Olattice_OInf__fin(X25415,c_Orderings_Oord__class_Omin(X25415),X25414) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oin__idem])]) ).
fof(i_0_9166,plain,
! [X23602,X23603,X23604] :
( hBOOL(hAPP(hAPP(c_member(X23604),X23603),X23602))
| hBOOL(hAPP(hAPP(c_member(X23604),X23603),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X23604,tc_HOL_Obool)),X23602))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5816])]) ).
fof(i_0_9167,plain,
! [X28492,X28493,X28494,X28495] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X28495),X28494),X28493))
| hAPP(c_Set_Ovimage(X28492,X28495,hAPP(c_COMBK(X28495,X28492),X28494)),X28493) = c_Orderings_Otop__class_Otop(tc_fun(X28492,tc_HOL_Obool)) )
& ( hBOOL(hAPP(hAPP(c_member(X28495),X28494),X28493))
| hAPP(c_Set_Ovimage(X28492,X28495,hAPP(c_COMBK(X28495,X28492),X28494)),X28493) = c_Orderings_Obot__class_Obot(tc_fun(X28492,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5817])]) ).
fof(i_0_9168,plain,
! [X26776,X26777,X26778,X26779,X26780] :
( ( X26779 = X26777
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26780,X26779),X26778) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26780,X26777),X26776)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26780),X26777),X26776))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26780),X26779),X26778))
| ~ class_Orderings_Olinorder(X26780) )
& ( X26778 = X26776
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26780,X26779),X26778) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26780,X26777),X26776)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26780),X26777),X26776))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26780),X26779),X26778))
| ~ class_Orderings_Olinorder(X26780) )
& ( X26779 != X26777
| X26778 != X26776
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26780,X26779),X26778) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26780,X26777),X26776)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26780),X26777),X26776))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26780),X26779),X26778))
| ~ class_Orderings_Olinorder(X26780) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__eq__iff])])]) ).
fof(i_0_9169,plain,
! [X26781,X26782,X26783,X26784,X26785] :
( ~ class_Orderings_Olinorder(X26785)
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26785,X26784),X26783) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26785,X26782),X26781)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26785),X26784),X26783))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26785),X26782),X26781))
| X26784 = X26782 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I1_J])]) ).
fof(i_0_9170,plain,
! [X26786,X26787,X26788,X26789,X26790] :
( ~ class_Orderings_Olinorder(X26790)
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26790,X26789),X26788) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26790,X26787),X26786)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26790),X26789),X26788))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26790),X26787),X26786))
| X26788 = X26786 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I2_J])]) ).
fof(i_0_9171,plain,
! [X24646,X24647,X24648,X24649,X24650] :
( ~ c_Finite__Set_Ofolding__one(X24650,X24649,X24648)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24650),X24647))
| hBOOL(hAPP(hAPP(c_member(X24650),X24646),X24647))
| X24647 = c_Orderings_Obot__class_Obot(tc_fun(X24650,tc_HOL_Obool))
| hAPP(X24648,hAPP(hAPP(c_Set_Oinsert(X24650),X24646),X24647)) = hAPP(hAPP(X24649,X24646),hAPP(X24648,X24647)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5818])]) ).
cnf(i_0_9172,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_9173,plain,
! [X22243,X22244] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22244))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22243))
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22244,X22243),c_Divides_OposDivAlg(X22244,X22243))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg__correct])]) ).
fof(i_0_9174,plain,
! [X32675,X32676,X32677,X32678,X32679] :
( X32679 = X32678
| hAPP(hAPP(c_List_Onth(X32677),hAPP(hAPP(c_List_Olist__update(X32677,X32676),X32679),X32675)),X32678) = hAPP(hAPP(c_List_Onth(X32677),X32676),X32678) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__list__update__neq])]) ).
fof(i_0_9175,plain,
! [X26864,X26865,X26866,X26867] :
( ~ class_Orderings_Oorder(X26867)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26867,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X26867,X26866,X26865)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26867,X26865),X26864)) = c_Orderings_Obot__class_Obot(tc_fun(X26867,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I9_J])]) ).
fof(i_0_9176,plain,
! [X30355,X30356,X30357,X30358] : hAPP(c_Relation_Oconverse(X30358,X30358),hAPP(hAPP(c_Relation_Oinv__image(X30357,X30358),X30356),X30355)) = hAPP(hAPP(c_Relation_Oinv__image(X30357,X30358),hAPP(c_Relation_Oconverse(X30357,X30357),X30356)),X30355),
inference(variable_rename,[status(thm)],[fact_converse__inv__image]) ).
fof(i_0_9177,plain,
! [X30727,X30728,X30729] :
( ~ class_Orderings_Olinorder(X30729)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30729),X30728))
| c_Big__Operators_Olinorder__class_OMin(X30729,hAPP(hAPP(c_Set_Oinsert(X30729),X30727),X30728)) = hAPP(hAPP(c_Finite__Set_Ofold(X30729,X30729,c_Orderings_Oord__class_Omin(X30729)),X30727),X30728) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oeq__fold__idem_H])]) ).
fof(i_0_9178,plain,
! [X30730,X30731,X30732] :
( ~ class_Orderings_Olinorder(X30732)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30732),X30731))
| c_Big__Operators_Olinorder__class_OMax(X30732,hAPP(hAPP(c_Set_Oinsert(X30732),X30730),X30731)) = hAPP(hAPP(c_Finite__Set_Ofold(X30732,X30732,c_Orderings_Oord__class_Omax(X30732)),X30730),X30731) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oeq__fold__idem_H])]) ).
fof(i_0_9179,plain,
! [X30724,X30725,X30726] :
( ~ class_Lattices_Olattice(X30726)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30726),X30725))
| c_Big__Operators_Olattice__class_OInf__fin(X30726,hAPP(hAPP(c_Set_Oinsert(X30726),X30724),X30725)) = hAPP(hAPP(c_Finite__Set_Ofold(X30726,X30726,c_Lattices_Osemilattice__inf__class_Oinf(X30726)),X30724),X30725) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oeq__fold__idem_H])]) ).
fof(i_0_9180,plain,
! [X30721,X30722,X30723] :
( ~ class_Lattices_Olattice(X30723)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30723),X30722))
| c_Big__Operators_Olattice__class_OSup__fin(X30723,hAPP(hAPP(c_Set_Oinsert(X30723),X30721),X30722)) = hAPP(hAPP(c_Finite__Set_Ofold(X30723,X30723,c_Lattices_Osemilattice__sup__class_Osup(X30723)),X30721),X30722) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oeq__fold__idem_H])]) ).
fof(i_0_9181,plain,
! [X21837,X21838] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X21838),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
| c_Random_Olog(X21838,X21837) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X21837),X21838))
| c_Random_Olog(X21838,X21837) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X21838),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X21837),X21838))
| c_Random_Olog(X21838,X21837) = 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(X21838,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X21837),X21838))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_log_Osimps])])]) ).
fof(i_0_9182,plain,
! [X23864,X23865] :
( ~ class_Rings_Oring__1(X23865)
| ~ hBOOL(hAPP(hAPP(c_member(X23865),X23864),c_Int_Oring__1__class_OInts(X23865)))
| hBOOL(hAPP(hAPP(c_member(X23865),hAPP(c_Groups_Ouminus__class_Ouminus(X23865),X23864)),c_Int_Oring__1__class_OInts(X23865))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__minus])]) ).
fof(i_0_9183,plain,
! [X23511,X23512] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23512))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23512),X23511))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23511),X23512)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5819])]) ).
fof(i_0_9184,plain,
! [X23389,X23390] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23390))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23390),X23389))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23389),X23390)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5820])]) ).
fof(i_0_9185,plain,
! [X23705,X23706] :
( ( ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X23706,tc_HOL_Obool)),X23705))
| hBOOL(hAPP(hAPP(c_member(X23706),X23705),c_Orderings_Obot__class_Obot(tc_fun(X23706,tc_HOL_Obool)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X23706),X23705),c_Orderings_Obot__class_Obot(tc_fun(X23706,tc_HOL_Obool))))
| hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X23706,tc_HOL_Obool)),X23705)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__empty__eq])]) ).
cnf(i_0_9186,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_9187,plain,
! [X21745,X21746,X21747] :
( ~ class_Fields_Olinordered__field__inverse__zero(X21747)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21747),c_Groups_Ozero__class_Ozero(X21747)),X21746))
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21747),hAPP(c_Groups_Oabs__class_Oabs(X21747),X21745)),X21746) = hAPP(c_Groups_Oabs__class_Oabs(X21747),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21747),X21745),X21746)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__div__pos])]) ).
fof(i_0_9188,plain,
! [X20825,X20826,X20827] :
( ~ class_Rings_Olinordered__idom(X20827)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20827),c_Groups_Ozero__class_Ozero(X20827)),X20826))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20827),hAPP(c_Groups_Oabs__class_Oabs(X20827),X20825)),X20826) = hAPP(c_Groups_Oabs__class_Oabs(X20827),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20827),X20825),X20826)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__pos])]) ).
fof(i_0_9189,plain,
! [X26414] : hAPP(c_Set_OPow(X26414),c_Orderings_Obot__class_Obot(tc_fun(X26414,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X26414,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X26414,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X26414,tc_HOL_Obool),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_Pow__empty]) ).
fof(i_0_9190,plain,
! [X27493,X27494] :
( hAPP(X27494,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),X27494),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27493)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X27494),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X27493)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__lb__Suc0__0])]) ).
fof(i_0_9191,plain,
! [X24935,X24936,X24937,X24938,X24939] :
( ~ class_Lattices_Olattice(X24939)
| hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24938,X24939)),X24937),X24936),X24935) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24939),hAPP(X24937,X24935)),hAPP(X24936,X24935)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__apply])]) ).
fof(i_0_9192,plain,
! [X24884,X24885,X24886,X24887,X24888] :
( ~ class_Lattices_Olattice(X24888)
| hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24887,X24888)),X24886),X24885),X24884) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24888),hAPP(X24886,X24884)),hAPP(X24885,X24884)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__fun__def])]) ).
fof(i_0_9193,plain,
! [X24131,X24132,X24133,X24134,X24135] :
( ~ class_Lattices_Olattice(X24135)
| hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24134,X24135)),X24133),X24132),X24131) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24135),hAPP(X24133,X24131)),hAPP(X24132,X24131)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__fun__def])]) ).
fof(i_0_9194,plain,
! [X24072,X24073,X24074,X24075,X24076] :
( ~ class_Lattices_Olattice(X24076)
| hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24075,X24076)),X24074),X24073),X24072) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24076),hAPP(X24074,X24072)),hAPP(X24073,X24072)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__apply])]) ).
fof(i_0_9195,plain,
! [X21878,X21879,X21880,X21881,X21882] :
( ~ class_Groups_Ominus(X21882)
| hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21881,X21882)),X21880),X21879),X21878) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21882),hAPP(X21880,X21878)),hAPP(X21879,X21878)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__diff__def])]) ).
fof(i_0_9196,plain,
! [X20264,X20265,X20266,X20267,X20268] :
( ~ class_Groups_Ominus(X20268)
| hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20267,X20268)),X20266),X20265),X20264) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20268),hAPP(X20266,X20264)),hAPP(X20265,X20264)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__apply])]) ).
fof(i_0_9197,plain,
! [X22237,X22238] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22238),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)),X22237))
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22238,X22237),c_Divides_OnegDivAlg(X22238,X22237))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negDivAlg__correct])]) ).
fof(i_0_9198,plain,
! [X19906,X19907] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19907),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19907),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19906,X19907))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__mod__bound])]) ).
fof(i_0_9199,plain,
! [X29427,X29428,X29429,X29430] :
( ~ c_Finite__Set_Ofolding(X29430,X29429,X29428,X29427)
| hAPP(X29427,c_Orderings_Obot__class_Obot(tc_fun(X29430,tc_HOL_Obool))) = c_Fun_Oid(X29429) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Oempty])]) ).
fof(i_0_9200,plain,
! [X22037,X22038] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22037))
| c_Divides_Odivmod__int(X22038,X22037) = c_Divides_OposDivAlg(X22038,X22037)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22038)) )
& ( X22038 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odivmod__int(X22038,X22037) = 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)),X22037))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22038)) )
& ( X22038 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odivmod__int(X22038,X22037) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22038),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22037)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22037))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22038)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22037))
| c_Divides_Odivmod__int(X22038,X22037) = c_Divides_OnegDivAlg(X22038,X22037)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22038)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22037))
| c_Divides_Odivmod__int(X22038,X22037) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22038),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22037)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22038)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5822])])]) ).
fof(i_0_9201,plain,
! [X22783,X22784] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X22784),X22783))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X22784)),hAPP(c_Code__Numeral_Onat__of,X22783))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X22784)),hAPP(c_Code__Numeral_Onat__of,X22783)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X22784),X22783)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__code__numeral__def])]) ).
fof(i_0_9202,plain,
! [X21917,X21918] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X21918)),hAPP(c_Code__Numeral_Oof__nat,X21917)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21918),X21917)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21918),X21917))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X21918)),hAPP(c_Code__Numeral_Oof__nat,X21917))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__code__numeral__code])]) ).
fof(i_0_9203,plain,
! [X19288,X19289] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19289)),hAPP(c_Nat_OSuc,X19288)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19289),X19288)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19289),X19288))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19289)),hAPP(c_Nat_OSuc,X19288))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__mono])]) ).
fof(i_0_9204,plain,
! [X22780,X22781] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X22781),X22780))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X22781)),hAPP(c_Code__Numeral_Onat__of,X22780))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X22781)),hAPP(c_Code__Numeral_Onat__of,X22780)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X22781),X22780)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__code__numeral__def])]) ).
fof(i_0_9205,plain,
! [X21909,X21910] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X21910)),hAPP(c_Code__Numeral_Oof__nat,X21909)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21910),X21909)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21910),X21909))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X21910)),hAPP(c_Code__Numeral_Oof__nat,X21909))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__code__numeral__code])]) ).
fof(i_0_9206,plain,
! [X18326,X18327] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18327)),hAPP(c_Nat_OSuc,X18326)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18327),X18326)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18327),X18326))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18327)),hAPP(c_Nat_OSuc,X18326))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__eq])]) ).
fof(i_0_9207,plain,
! [X18309,X18310] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18310)),hAPP(c_Nat_OSuc,X18309)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18310),X18309)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__SucD])]) ).
fof(i_0_9208,plain,
! [X32627,X32628,X32629,X32630] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32630),X32629))
| hAPP(hAPP(c_List_Onth(X32628),hAPP(hAPP(c_List_Otake(X32628),X32629),X32627)),X32630) = hAPP(hAPP(c_List_Onth(X32628),X32627),X32630) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__take])]) ).
fof(i_0_9209,plain,
! [X25023,X25024,X25025] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25025,tc_HOL_Obool)),X25024),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25025,tc_HOL_Obool)),X25023),X25024)) = c_Orderings_Obot__class_Obot(tc_fun(X25025,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Diff__disjoint]) ).
fof(i_0_9210,plain,
! [X34218,X34219,X34220,X34221] :
( ( hAPP(c_List_Orev(X34221),X34220) != hAPP(hAPP(c_List_Olist_OCons(X34221),X34219),X34218)
| X34220 = hAPP(hAPP(c_List_Oappend(X34221),hAPP(c_List_Orev(X34221),X34218)),hAPP(hAPP(c_List_Olist_OCons(X34221),X34219),c_List_Olist_ONil(X34221))) )
& ( X34220 != hAPP(hAPP(c_List_Oappend(X34221),hAPP(c_List_Orev(X34221),X34218)),hAPP(hAPP(c_List_Olist_OCons(X34221),X34219),c_List_Olist_ONil(X34221)))
| hAPP(c_List_Orev(X34221),X34220) = hAPP(hAPP(c_List_Olist_OCons(X34221),X34219),X34218) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__eq__Cons__iff])]) ).
fof(i_0_9211,plain,
! [X20797,X20798] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20798))
| 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),X20798),X20797))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J])]) ).
fof(i_0_9212,plain,
! [X20354,X20355] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20355),X20354)),X20355)),
inference(variable_rename,[status(thm)],[fact_diff__le__self]) ).
fof(i_0_9213,plain,
! [X20007,X20008] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20008),X20007)),X20008)),
inference(variable_rename,[status(thm)],[fact_div__le__dividend]) ).
fof(i_0_9214,plain,
! [X27122,X27123] :
( ~ class_Orderings_Olinorder(X27123)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27123,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X27123),X27122)),hAPP(hAPP(c_Set_Oinsert(X27123),X27122),c_Orderings_Obot__class_Obot(tc_fun(X27123,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(X27123),X27122) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I2_J])]) ).
fof(i_0_9215,plain,
! [X25267,X25268,X25269] :
( ~ class_Orderings_Olinorder(X25269)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25269),X25268))
| ~ hBOOL(hAPP(hAPP(c_member(X25269),X25267),X25268))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25269),c_Big__Operators_Olinorder__class_OMin(X25269,X25268)),X25267)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__le])]) ).
fof(i_0_9216,plain,
! [X20814,X20815,X20816] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20816),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20815),X20814)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20816),X20815)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20816),X20814)),
inference(variable_rename,[status(thm)],[fact_zpower__zadd__distrib]) ).
fof(i_0_9217,plain,
! [X20378,X20379,X20380] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20380),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20379),X20378)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20380),X20379)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20380),X20378)),
inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib2]) ).
fof(i_0_9218,plain,
! [X18872,X18873,X18874] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18874),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18873),X18872)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18874),X18873)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18874),X18872)),
inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib2]) ).
fof(i_0_9219,plain,
! [X20381,X20382,X20383] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20383),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20382),X20381)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20383),X20382)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20383),X20381)),
inference(variable_rename,[status(thm)],[fact_diff__mult__distrib2]) ).
fof(i_0_9220,plain,
! [X19277,X19278,X19279] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19279),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19278),X19277)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19279),X19278)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19279),X19277)),
inference(variable_rename,[status(thm)],[fact_add__mult__distrib2]) ).
fof(i_0_9221,plain,
! [X20253,X20254,X20255] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20255),X20254)),X20253) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20255),X20253)),X20254),
inference(variable_rename,[status(thm)],[fact_diff__commute]) ).
fof(i_0_9222,plain,
! [X19469,X19470] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19470),c_Groups_Ozero__class_Ozero(X19470)),hAPP(c_Groups_Ouminus__class_Ouminus(X19470),X19469)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19470),X19469),c_Groups_Ozero__class_Ozero(X19470)))
| ~ class_Groups_Oordered__ab__group__add(X19470) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19470),X19469),c_Groups_Ozero__class_Ozero(X19470)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19470),c_Groups_Ozero__class_Ozero(X19470)),hAPP(c_Groups_Ouminus__class_Ouminus(X19470),X19469)))
| ~ class_Groups_Oordered__ab__group__add(X19470) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__le__iff__le])])]) ).
fof(i_0_9223,plain,
! [X18877,X18878] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18878),c_Groups_Ozero__class_Ozero(X18878)),hAPP(c_Groups_Ouminus__class_Ouminus(X18878),X18877)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18878),X18877),c_Groups_Ozero__class_Ozero(X18878)))
| ~ class_Groups_Oordered__ab__group__add(X18878) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18878),X18877),c_Groups_Ozero__class_Ozero(X18878)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18878),c_Groups_Ozero__class_Ozero(X18878)),hAPP(c_Groups_Ouminus__class_Ouminus(X18878),X18877)))
| ~ class_Groups_Oordered__ab__group__add(X18878) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__less__iff__less])])]) ).
fof(i_0_9224,plain,
! [X17275,X17276,X17277] :
( ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(X17277,X17276,X17275)))
| hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X17276))) )
& ( ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X17276)))
| hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(X17277,X17276,X17275))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_Oequations_I8_J])]) ).
fof(i_0_9225,plain,
! [X17269,X17270,X17271] :
( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(X17271,X17270,X17269)))
| hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X17270))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WTs__elim__cases_I8_J])]) ).
fof(i_0_9226,plain,
! [X23211,X23212,X23213,X23214] :
( ~ class_Rings_Ocomm__semiring__1(X23214)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23214),X23213),X23212))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23214),X23212),X23211))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23214),X23213),X23211)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__trans])]) ).
fof(i_0_9227,plain,
! [X19088,X19089,X19090,X19091] :
( ~ class_Orderings_Opreorder(X19091)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19091),X19090),X19089))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19091),X19089),X19088))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19091),X19090),X19088)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).
fof(i_0_9228,plain,
! [X19081,X19082,X19083,X19084] :
( ~ class_Orderings_Oorder(X19084)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19084),X19083),X19082))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19084),X19081),X19083))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19084),X19081),X19082)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).
fof(i_0_9229,plain,
! [X19205,X19206,X19207,X19208] :
( ~ class_Orderings_Opreorder(X19208)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19208),X19207),X19206))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19208),X19206),X19205))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19208),X19207),X19205)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le__trans])]) ).
fof(i_0_9230,plain,
! [X19213,X19214,X19215,X19216] :
( ~ class_Orderings_Opreorder(X19216)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19216),X19215),X19214))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19216),X19214),X19213))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19216),X19215),X19213)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less__trans])]) ).
fof(i_0_9231,plain,
! [X18566,X18567,X18568,X18569] :
( ~ class_Orderings_Opreorder(X18569)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18569),X18568),X18567))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18569),X18567),X18566))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18569),X18568),X18566)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__trans])]) ).
fof(i_0_9232,plain,
! [X19209,X19210,X19211,X19212] :
( ~ class_Orderings_Oorder(X19212)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19212),X19211),X19210))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19212),X19209),X19211))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19212),X19209),X19210)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I7_J])]) ).
fof(i_0_9233,plain,
! [X19217,X19218,X19219,X19220] :
( ~ class_Orderings_Oorder(X19220)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19220),X19219),X19218))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19220),X19217),X19219))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19220),X19217),X19218)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])]) ).
fof(i_0_9234,plain,
! [X18562,X18563,X18564,X18565] :
( ~ class_Orderings_Oorder(X18565)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18565),X18564),X18563))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18565),X18562),X18564))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18565),X18562),X18563)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I10_J])]) ).
fof(i_0_9235,plain,
! [X22205] :
( X22205 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X22205),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_9236,plain,
! [X22245,X22246] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22246))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22245))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X22246,X22245) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X22246,X22245)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__pos])]) ).
fof(i_0_9237,plain,
! [X20274,X20275,X20276,X20277,X20278] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20278),X20277),X20276))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20278),X20275),X20274))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20278),X20277),X20276) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20278),X20275),X20274)
| ~ class_Groups_Oordered__ab__group__add(X20278) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20278),X20275),X20274))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20278),X20277),X20276))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20278),X20277),X20276) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20278),X20275),X20274)
| ~ class_Groups_Oordered__ab__group__add(X20278) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less__eq])])]) ).
fof(i_0_9238,plain,
! [X20289,X20290,X20291,X20292,X20293] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20293),X20292),X20291))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20293),X20290),X20289))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20293),X20292),X20291) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20293),X20290),X20289)
| ~ class_Groups_Oordered__ab__group__add(X20293) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20293),X20290),X20289))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20293),X20292),X20291))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20293),X20292),X20291) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20293),X20290),X20289)
| ~ class_Groups_Oordered__ab__group__add(X20293) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less])])]) ).
fof(i_0_9239,plain,
! [X20364,X20365,X20366] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20365),X20366) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20364),X20366)
| X20365 = X20364
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20366),X20364))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20366),X20365)) )
& ( X20365 != X20364
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20365),X20366) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20364),X20366)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20366),X20364))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20366),X20365)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__diff__iff])])]) ).
fof(i_0_9240,plain,
! [X23502,X23503] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23503),X23502))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23503)),X23502)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23503)),X23502))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23503),X23502)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_uminus__dvd__conv_I1_J])]) ).
fof(i_0_9241,plain,
! [X28645,X28646,X28647] : hAPP(hAPP(c_Product__Type_OSigma(X28647,X28646),X28645),hAPP(c_COMBK(tc_fun(X28646,tc_HOL_Obool),X28647),c_Orderings_Obot__class_Obot(tc_fun(X28646,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28647,X28646),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Sigma__empty2]) ).
cnf(i_0_9242,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_9243,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_9244,plain,
! [X18667,X18668,X18669] :
( ~ class_Rings_Ocomm__semiring__1(X18669)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18669),X18668),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18669),X18667),X18668)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18669),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18669),X18667),c_Groups_Oone__class_Oone(X18669))),X18668) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J])]) ).
cnf(i_0_9245,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_9246,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_9247,plain,
! [X22403,X22404] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22404))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22403))
| 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_OposDivAlg(X22404,X22403)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__pos])]) ).
fof(i_0_9248,plain,
! [X19284,X19285] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19285),X19284))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19284)),X19285)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19284)),X19285))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19285),X19284)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5826])]) ).
fof(i_0_9249,plain,
! [X26853,X26854,X26855,X26856] :
( ~ class_Orderings_Oorder(X26856)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26856,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26856,X26855),X26854)),c_SetInterval_Oord__class_OatLeastAtMost(X26856,X26854,X26853)) = c_Orderings_Obot__class_Obot(tc_fun(X26856,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I15_J])]) ).
fof(i_0_9250,plain,
! [X19365,X19366] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19366),c_Groups_Ozero__class_Ozero(X19366)),hAPP(c_Int_Oring__1__class_Oof__int(X19366),X19365)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19365))
| ~ class_Rings_Olinordered__idom(X19366) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19365))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19366),c_Groups_Ozero__class_Ozero(X19366)),hAPP(c_Int_Oring__1__class_Oof__int(X19366),X19365)))
| ~ class_Rings_Olinordered__idom(X19366) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__0__le__iff])])]) ).
fof(i_0_9251,plain,
! [X18646,X18647] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18647),c_Groups_Ozero__class_Ozero(X18647)),hAPP(c_Int_Oring__1__class_Oof__int(X18647),X18646)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18646))
| ~ class_Rings_Olinordered__idom(X18647) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18646))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18647),c_Groups_Ozero__class_Ozero(X18647)),hAPP(c_Int_Oring__1__class_Oof__int(X18647),X18646)))
| ~ class_Rings_Olinordered__idom(X18647) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__0__less__iff])])]) ).
fof(i_0_9252,plain,
! [X18489,X18490] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18490),c_Groups_Ozero__class_Ozero(X18490)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18490),X18489)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18489))
| ~ class_Rings_Olinordered__semidom(X18490) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18489))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18490),c_Groups_Ozero__class_Ozero(X18490)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18490),X18489)))
| ~ class_Rings_Olinordered__semidom(X18490) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__0__less__iff])])]) ).
fof(i_0_9253,plain,
! [X18139,X18140,X18141] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X18141,X18140,X18139)) = 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(X18140)),c_Com_Ocom_Ocom__size(X18139))),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_9254,plain,
! [X20706,X20707] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20707),hAPP(c_Groups_Oabs__class_Oabs(X20707),X20706)),c_Groups_Ozero__class_Ozero(X20707)))
| X20706 = c_Groups_Ozero__class_Ozero(X20707)
| ~ class_Groups_Oordered__ab__group__add__abs(X20707) )
& ( X20706 != c_Groups_Ozero__class_Ozero(X20707)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20707),hAPP(c_Groups_Oabs__class_Oabs(X20707),X20706)),c_Groups_Ozero__class_Ozero(X20707)))
| ~ class_Groups_Oordered__ab__group__add__abs(X20707) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__zero__iff])])]) ).
fof(i_0_9255,plain,
! [X23545,X23546] :
( X23546 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23545),X23546))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X23545)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X23546))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__imp__le__int])]) ).
fof(i_0_9256,plain,
! [X22239,X22240] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22240),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)),X22239))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X22240,X22239) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X22240,X22239)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__neg__pos])]) ).
fof(i_0_9257,plain,
! [X25418,X25419,X25420] :
( ~ class_Orderings_Olinorder(X25420)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25420),X25419))
| X25419 = c_Orderings_Obot__class_Obot(tc_fun(X25420,tc_HOL_Obool))
| c_Big__Operators_Olattice_OInf__fin(X25420,c_Orderings_Oord__class_Omin(X25420),hAPP(hAPP(c_Set_Oinsert(X25420),X25418),X25419)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25420),X25418),c_Big__Operators_Olattice_OInf__fin(X25420,c_Orderings_Oord__class_Omin(X25420),X25419)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oinsert__idem])]) ).
fof(i_0_9258,plain,
! [X25291,X25292,X25293] :
( ~ class_Orderings_Olinorder(X25293)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25293),X25292))
| X25292 = c_Orderings_Obot__class_Obot(tc_fun(X25293,tc_HOL_Obool))
| c_Big__Operators_Olattice_OSup__fin(X25293,c_Orderings_Oord__class_Omax(X25293),hAPP(hAPP(c_Set_Oinsert(X25293),X25291),X25292)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25293),X25291),c_Big__Operators_Olattice_OSup__fin(X25293,c_Orderings_Oord__class_Omax(X25293),X25292)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oinsert__idem])]) ).
fof(i_0_9259,plain,
! [X20710,X20711] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20711)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20711),hAPP(c_Groups_Oabs__class_Oabs(X20711),X20710)),c_Groups_Ozero__class_Ozero(X20711))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5827])]) ).
fof(i_0_9260,plain,
! [X18527,X18528] :
( ~ class_Rings_Olinordered__semidom(X18528)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18528),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18528),X18527)),c_Groups_Ozero__class_Ozero(X18528))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5828])]) ).
fof(i_0_9261,plain,
! [X23353,X23354,X23355] :
( ~ class_Divides_Osemiring__div(X23355)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23355),X23354),X23353))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23355),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23355),X23353),X23354)),X23354) = X23353 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__div__mult__self])]) ).
fof(i_0_9262,plain,
! [X20269,X20270,X20271] :
( ~ class_Rings_Oring__1(X20271)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20270),X20269))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20271),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20269),X20270)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20271),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20271),X20269)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20271),X20270)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__diff])]) ).
cnf(i_0_9263,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_9264,plain,
! [X21177,X21178] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21178),c_Int_OPls))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21178)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21177)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21177) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21177),c_Int_OPls))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21178)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21177)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21178)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21178),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21177),c_Int_OPls))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21178)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21177)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21178),X21177))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21178),c_Int_OPls)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5830])])]) ).
fof(i_0_9265,plain,
! [X21082,X21083] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21083)))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21083)),X21082) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21082) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21083)))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21083)),X21082) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21083)),X21082)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5831])]) ).
fof(i_0_9266,plain,
! [X22401,X22402] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22402),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)),X22401))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22402),X22401) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X22402,X22401)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__neg__pos])]) ).
fof(i_0_9267,plain,
! [X24551,X24552,X24553] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24553),hAPP(hAPP(c_Set_Oinsert(X24553),X24552),X24551)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24553),X24551)) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24553),X24551))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24553),hAPP(hAPP(c_Set_Oinsert(X24553),X24552),X24551))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__insert])]) ).
cnf(i_0_9268,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_9269,plain,
! [X31420,X31421,X31422] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31422)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31422),X31421))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X31422),X31420),c_Complete__Lattice_OInf__class_OInf(X31422,X31421)) = hAPP(hAPP(c_Finite__Set_Ofold(X31422,X31422,c_Lattices_Osemilattice__inf__class_Oinf(X31422)),X31420),X31421) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Inf__fold__inf])]) ).
fof(i_0_9270,plain,
! [X31415,X31416,X31417] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31417)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31417),X31416))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X31417),X31415),c_Complete__Lattice_OSup__class_OSup(X31417,X31416)) = hAPP(hAPP(c_Finite__Set_Ofold(X31417,X31417,c_Lattices_Osemilattice__sup__class_Osup(X31417)),X31415),X31416) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Sup__fold__sup])]) ).
cnf(i_0_9271,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_9272,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_9273,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_9274,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_9275,plain,
! [X25048,X25049] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25049,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25049,tc_HOL_Obool)),X25048)),X25048) = c_Orderings_Obot__class_Obot(tc_fun(X25049,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__disjoint2]) ).
fof(i_0_9276,plain,
! [X28224,X28225] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28225,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28225,tc_HOL_Obool)),X28224)),X28224) = c_Orderings_Otop__class_Otop(tc_fun(X28225,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__partition2]) ).
fof(i_0_9277,plain,
! [X28174,X28175] : c_Sum__Type_OPlus(X28175,X28174,c_Orderings_Otop__class_Otop(tc_fun(X28175,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X28174,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X28175,X28174),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_UNIV__Plus__UNIV]) ).
fof(i_0_9278,plain,
! [X27659,X27660,X27661] :
( ~ class_Orderings_Oorder(X27661)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27661,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X27661,X27660,X27659)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X27661),X27659)) = c_Orderings_Obot__class_Obot(tc_fun(X27661,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I7_J])]) ).
fof(i_0_9279,plain,
! [X27669,X27670,X27671] :
( ~ class_Orderings_Oorder(X27671)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27671,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X27671,X27670,X27669)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X27671),X27669)) = c_Orderings_Obot__class_Obot(tc_fun(X27671,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I5_J])]) ).
fof(i_0_9280,plain,
! [X27629,X27630,X27631] :
( ~ class_Orderings_Oorder(X27631)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27631,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X27631,X27630,X27629)),hAPP(c_SetInterval_Oord__class_OatLeast(X27631),X27629)) = c_Orderings_Obot__class_Obot(tc_fun(X27631,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I6_J])]) ).
fof(i_0_9281,plain,
! [X21843,X21844,X21845] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X21845),X21844))
| c_Random_Ominus__shift(X21843,X21845,X21844) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X21843),X21845)),X21844) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X21845),X21844))
| c_Random_Ominus__shift(X21843,X21845,X21844) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X21845),X21844) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5833])]) ).
fof(i_0_9282,plain,
! [X21168,X21169] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21169),c_Groups_Ozero__class_Ozero(X21169)),hAPP(c_Int_Onumber__class_Onumber__of(X21169),X21168)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X21168))
| ~ class_Int_Onumber__ring(X21169)
| ~ class_Rings_Olinordered__idom(X21169) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X21168))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21169),c_Groups_Ozero__class_Ozero(X21169)),hAPP(c_Int_Onumber__class_Onumber__of(X21169),X21168)))
| ~ class_Int_Onumber__ring(X21169)
| ~ class_Rings_Olinordered__idom(X21169) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I1_J])])]) ).
fof(i_0_9283,plain,
! [X21174,X21175] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21175),c_Groups_Ozero__class_Ozero(X21175)),hAPP(c_Int_Onumber__class_Onumber__of(X21175),X21174)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X21174))
| ~ class_Int_Onumber__ring(X21175)
| ~ class_Rings_Olinordered__idom(X21175) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X21174))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21175),c_Groups_Ozero__class_Ozero(X21175)),hAPP(c_Int_Onumber__class_Onumber__of(X21175),X21174)))
| ~ class_Int_Onumber__ring(X21175)
| ~ class_Rings_Olinordered__idom(X21175) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I1_J])])]) ).
fof(i_0_9284,plain,
! [X19779,X19780,X19781] :
( ( ~ hBOOL(hAPP(X19781,c_Divides_Odiv__class_Omod(tc_Int_Oint,X19780,X19779)))
| epred1_3(X19781,X19780,X19779) )
& ( ~ epred1_3(X19781,X19780,X19779)
| hBOOL(hAPP(X19781,c_Divides_Odiv__class_Omod(tc_Int_Oint,X19780,X19779))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5834])]) ).
fof(i_0_9285,plain,
! [X29790,X29791,X29792] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X29792,X29791)),X29790))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29792),hAPP(c_Relation_ODomain(X29792,X29791),X29790))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Domain])]) ).
fof(i_0_9286,plain,
! [X29699,X29700,X29701] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X29701,X29700)),X29699))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X29700),hAPP(c_Relation_ORange(X29701,X29700),X29699))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Range])]) ).
fof(i_0_9287,plain,
! [X28185,X28186,X28187,X28188] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X28188,X28187,X28186),X28185))
| X28186 != c_Orderings_Obot__class_Obot(tc_fun(X28188,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1Set__nonempty])]) ).
fof(i_0_9288,plain,
! [X21046,X21047] : hAPP(hAPP(c_Nitpick_Oint__gcd,X21047),X21046) = 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),X21047)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X21046)))),
inference(variable_rename,[status(thm)],[fact_Nitpick_Oint__gcd__def]) ).
fof(i_0_9289,plain,
! [X33359,X33360,X33361,X33362,X33363] : hAPP(hAPP(c_List_Odrop(X33363),X33362),hAPP(hAPP(c_List_Omap(X33361,X33363),X33360),X33359)) = hAPP(hAPP(c_List_Omap(X33361,X33363),X33360),hAPP(hAPP(c_List_Odrop(X33361),X33362),X33359)),
inference(variable_rename,[status(thm)],[fact_drop__map]) ).
fof(i_0_9290,plain,
! [X32659,X32660,X32661,X32662,X32663] : hAPP(hAPP(c_List_Otake(X32663),X32662),hAPP(hAPP(c_List_Omap(X32661,X32663),X32660),X32659)) = hAPP(hAPP(c_List_Omap(X32661,X32663),X32660),hAPP(hAPP(c_List_Otake(X32661),X32662),X32659)),
inference(variable_rename,[status(thm)],[fact_take__map]) ).
fof(i_0_9291,plain,
! [X33910,X33911,X33912,X33913] : hAPP(c_List_Ofilter(X33913,X33912),hAPP(hAPP(c_List_Oappend(X33913),X33911),X33910)) = hAPP(hAPP(c_List_Oappend(X33913),hAPP(c_List_Ofilter(X33913,X33912),X33911)),hAPP(c_List_Ofilter(X33913,X33912),X33910)),
inference(variable_rename,[status(thm)],[fact_filter__append]) ).
fof(i_0_9292,plain,
! [X32863,X32864] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X32864),X32863))
| c_List_Oupto(X32864,X32863) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X32864),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X32864),c_Groups_Oone__class_Oone(tc_Int_Oint)),X32863)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X32864),X32863))
| c_List_Oupto(X32864,X32863) = c_List_Olist_ONil(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5835])]) ).
fof(i_0_9293,plain,
! [X29580,X29581,X29582,X29583,X29584] :
( ( ~ c_Wellfounded_Owf(X29581,X29580)
| hBOOL(hAPP(hAPP(c_member(X29581),X29582),c_Wellfounded_Oacc(X29581,X29580))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X29584),esk316_2(X29583,X29584)),c_Wellfounded_Oacc(X29584,X29583)))
| c_Wellfounded_Owf(X29584,X29583) ) ),
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_9294,plain,
! [X25254,X25255] :
( ~ class_Groups_Olinordered__ab__group__add(X25255)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25255),X25254))
| X25254 = c_Orderings_Obot__class_Obot(tc_fun(X25255,tc_HOL_Obool))
| hAPP(c_Groups_Ouminus__class_Ouminus(X25255),c_Big__Operators_Olinorder__class_OMin(X25255,X25254)) = c_Big__Operators_Olinorder__class_OMax(X25255,hAPP(c_Set_Oimage(X25255,X25255,c_Groups_Ouminus__class_Ouminus(X25255)),X25254)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__Min__eq__Max])]) ).
fof(i_0_9295,plain,
! [X25256,X25257] :
( ~ class_Groups_Olinordered__ab__group__add(X25257)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25257),X25256))
| X25256 = c_Orderings_Obot__class_Obot(tc_fun(X25257,tc_HOL_Obool))
| hAPP(c_Groups_Ouminus__class_Ouminus(X25257),c_Big__Operators_Olinorder__class_OMax(X25257,X25256)) = c_Big__Operators_Olinorder__class_OMin(X25257,hAPP(c_Set_Oimage(X25257,X25257,c_Groups_Ouminus__class_Ouminus(X25257)),X25256)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__Max__eq__Min])]) ).
fof(i_0_9296,plain,
! [X31312,X31313] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31313),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31313,tc_HOL_Obool),X31312)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X31313,tc_HOL_Obool)),X31312)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UnionD])]) ).
fof(i_0_9297,plain,
! [X20222,X20223] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X20223))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20223),X20222)),X20223) = 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_9298,plain,
! [X19656,X19657] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19657),c_Groups_Ozero__class_Ozero(X19657)),c_Groups_Osgn__class_Osgn(X19657,X19656)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19657),c_Groups_Ozero__class_Ozero(X19657)),X19656))
| ~ class_Rings_Olinordered__idom(X19657) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19657),c_Groups_Ozero__class_Ozero(X19657)),X19656))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19657),c_Groups_Ozero__class_Ozero(X19657)),c_Groups_Osgn__class_Osgn(X19657,X19656)))
| ~ class_Rings_Olinordered__idom(X19657) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__greater])])]) ).
fof(i_0_9299,plain,
! [X23363,X23364,X23365] :
( ~ class_Divides_Oring__div(X23365)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23365),X23364),X23363))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23365),hAPP(c_Groups_Ouminus__class_Ouminus(X23365),X23363)),X23364) = hAPP(c_Groups_Ouminus__class_Ouminus(X23365),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23365),X23363),X23364)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__neg__div])]) ).
cnf(i_0_9300,plain,
c_Int_OBit0(X1) != c_Int_OBit1(X2),
inference(split_conjunct,[status(thm)],[i_0_5836]) ).
cnf(i_0_9301,plain,
c_Int_OBit1(X1) != c_Int_OBit0(X2),
inference(split_conjunct,[status(thm)],[i_0_5837]) ).
fof(i_0_9302,plain,
! [X19849,X19850,X19851,X19852] :
( ~ class_Divides_Osemiring__div(X19852)
| c_Divides_Odiv__class_Omod(X19852,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19852),X19851),X19850),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19852),X19851),X19849)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19852),X19851),c_Divides_Odiv__class_Omod(X19852,X19850,X19849)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__mult1])]) ).
fof(i_0_9303,plain,
! [X31065,X31066,X31067,X31068] :
( ( X31068 != c_Orderings_Obot__class_Obot(tc_fun(X31067,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31067,tc_fun(X31066,tc_HOL_Obool)),X31068),hAPP(c_COMBK(tc_fun(X31066,tc_HOL_Obool),X31067),X31065)) = c_Orderings_Otop__class_Otop(tc_fun(X31066,tc_HOL_Obool)) )
& ( X31068 = c_Orderings_Obot__class_Obot(tc_fun(X31067,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31067,tc_fun(X31066,tc_HOL_Obool)),X31068),hAPP(c_COMBK(tc_fun(X31066,tc_HOL_Obool),X31067),X31065)) = X31065 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__constant])]) ).
fof(i_0_9304,plain,
! [X25980,X25981,X25982,X25983] :
( ( X25983 != c_Orderings_Obot__class_Obot(tc_fun(X25982,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25982,tc_fun(X25981,tc_HOL_Obool)),X25983),hAPP(c_COMBK(tc_fun(X25981,tc_HOL_Obool),X25982),X25980)) = c_Orderings_Obot__class_Obot(tc_fun(X25981,tc_HOL_Obool)) )
& ( X25983 = c_Orderings_Obot__class_Obot(tc_fun(X25982,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25982,tc_fun(X25981,tc_HOL_Obool)),X25983),hAPP(c_COMBK(tc_fun(X25981,tc_HOL_Obool),X25982),X25980)) = X25980 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__constant])]) ).
fof(i_0_9305,plain,
! [X23005,X23006,X23007] : c_Random__Sequence_Oempty(X23007,X23006,X23005) = 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(X23007)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X23007)),
inference(variable_rename,[status(thm)],[fact_Random__Sequence_Oempty__def]) ).
fof(i_0_9306,plain,
! [X20095,X20096,X20097,X20098] :
( ( X20097 != c_Groups_Ozero__class_Ozero(X20098)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20098),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20098),X20097),X20096)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20098),X20097),X20095)) = c_Groups_Ozero__class_Ozero(X20098)
| ~ class_Divides_Osemiring__div(X20098) )
& ( X20097 = c_Groups_Ozero__class_Ozero(X20098)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20098),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20098),X20097),X20096)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20098),X20097),X20095)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20098),X20096),X20095)
| ~ class_Divides_Osemiring__div(X20098) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__mult1__if])])]) ).
fof(i_0_9307,plain,
! [X21569,X21570,X21571,X21572] :
( ~ class_Fields_Ofield__inverse__zero(X21572)
| X21571 = c_Groups_Ozero__class_Ozero(X21572)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21572),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21572),X21571),X21570)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21572),X21571),X21569)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21572),X21570),X21569) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__left])]) ).
fof(i_0_9308,plain,
! [X21565,X21566,X21567,X21568] :
( ~ class_Fields_Ofield__inverse__zero(X21568)
| X21567 = c_Groups_Ozero__class_Ozero(X21568)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21568),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21568),X21566),X21567)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21568),X21565),X21567)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21568),X21566),X21565) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__right])]) ).
fof(i_0_9309,plain,
! [X20081,X20082,X20083,X20084] :
( ~ class_Divides_Osemiring__div(X20084)
| X20083 = c_Groups_Ozero__class_Ozero(X20084)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20084),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20084),X20083),X20082)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20084),X20083),X20081)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20084),X20082),X20081) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__mult1])]) ).
fof(i_0_9310,plain,
! [X20085,X20086,X20087,X20088] :
( ~ class_Divides_Osemiring__div(X20088)
| X20087 = c_Groups_Ozero__class_Ozero(X20088)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20088),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20088),X20086),X20087)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20088),X20085),X20087)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20088),X20086),X20085) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__mult2])]) ).
cnf(i_0_9311,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_9312,plain,
! [X22005,X22006,X22007,X22008] : hAPP(c_Nat_Onat_Onat__rec(X22008,X22007,X22006),hAPP(c_Nat_OSuc,X22005)) = hAPP(hAPP(X22006,X22005),hAPP(c_Nat_Onat_Onat__rec(X22008,X22007,X22006),X22005)),
inference(variable_rename,[status(thm)],[fact_nat__rec__Suc]) ).
fof(i_0_9313,plain,
! [X19327,X19328,X19329] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19329),X19328))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19329),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19328),X19327))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add1])]) ).
fof(i_0_9314,plain,
! [X19308,X19309,X19310] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19310),X19309))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19310),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19309),X19308))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J])]) ).
fof(i_0_9315,plain,
! [X19330,X19331,X19332] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19332),X19331))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19332),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19330),X19331))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add2])]) ).
fof(i_0_9316,plain,
! [X19311,X19312,X19313] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19313),X19312))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19313),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19311),X19312))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I4_J])]) ).
fof(i_0_9317,plain,
! [X18458,X18459,X18460] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18460),X18459))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18460),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18459),X18458))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J])]) ).
fof(i_0_9318,plain,
! [X18349,X18350,X18351] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18351),X18350))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18351),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18350),X18349))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add1])]) ).
fof(i_0_9319,plain,
! [X18436,X18437,X18438] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18438),X18437))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18438),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18436),X18437))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J])]) ).
fof(i_0_9320,plain,
! [X18346,X18347,X18348] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18348),X18347))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18348),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18346),X18347))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add2])]) ).
fof(i_0_9321,plain,
! [X19896,X19897,X19898,X19899] :
( ~ class_Divides_Osemiring__div(X19899)
| c_Divides_Odiv__class_Omod(X19899,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19899),X19898),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19899),X19897),X19896)),X19897) = c_Divides_Odiv__class_Omod(X19899,X19898,X19897) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self2])]) ).
fof(i_0_9322,plain,
! [X19892,X19893,X19894,X19895] :
( ~ class_Divides_Osemiring__div(X19895)
| c_Divides_Odiv__class_Omod(X19895,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19895),X19894),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19895),X19893),X19892)),X19892) = c_Divides_Odiv__class_Omod(X19895,X19894,X19892) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self1])]) ).
fof(i_0_9323,plain,
! [X18376,X18377,X18379,X18380,X18381] :
( ( X18377 = hAPP(c_Nat_OSuc,esk37_2(X18376,X18377))
| X18377 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18377),hAPP(c_Nat_OSuc,X18376))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk37_2(X18376,X18377)),X18376))
| X18377 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18377),hAPP(c_Nat_OSuc,X18376))) )
& ( X18380 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18380),hAPP(c_Nat_OSuc,X18379))) )
& ( X18380 != hAPP(c_Nat_OSuc,X18381)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18381),X18379))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18380),hAPP(c_Nat_OSuc,X18379))) ) ),
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_9324,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_9325,plain,
! [X33462,X33463] :
( X33463 = c_List_Olist_ONil(X33462)
| hAPP(c_List_Orotate1(X33462),X33463) = hAPP(hAPP(c_List_Oappend(X33462),hAPP(c_List_Otl(X33462),X33463)),hAPP(hAPP(c_List_Olist_OCons(X33462),hAPP(c_List_Ohd(X33462),X33463)),c_List_Olist_ONil(X33462))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate1__hd__tl])]) ).
fof(i_0_9326,plain,
! [X26968,X26969,X26970,X26971,X26972,X26973] :
( ( X26973 != X26972
| hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26971,X26970),X26969),X26972),X26968),X26973) = X26968 )
& ( X26973 = X26972
| hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26971,X26970),X26969),X26972),X26968),X26973) = hAPP(X26969,X26973) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__apply])]) ).
fof(i_0_9327,plain,
! [X26955,X26956,X26957,X26958,X26959,X26960] :
( X26960 = X26959
| hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26958,X26957),X26956),X26959),X26955),X26960) = hAPP(X26956,X26960) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__other])]) ).
fof(i_0_9328,plain,
! [X26944,X26945,X26946,X26947,X26948,X26949] :
( ( X26949 != X26948
| hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26947,X26946),X26945),X26948),X26944),X26949) = X26944 )
& ( X26949 = X26948
| hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26947,X26946),X26945),X26948),X26944),X26949) = hAPP(X26945,X26949) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__def])]) ).
cnf(i_0_9329,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_9330,plain,
! [X32449,X32450,X32451,X32452] :
( ~ class_Groups_Ocomm__monoid__add(X32452)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X32452),X32451),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X32450,X32449))) = hAPP(c_List_Omonoid__add__class_Olistsum(X32452),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X32452),X32451),c_List_Oupto(X32450,X32449))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__set__upto__conv__listsum__int])]) ).
fof(i_0_9331,plain,
! [X32453,X32454,X32455,X32456] :
( ~ class_Groups_Ocomm__monoid__add(X32456)
| hAPP(c_List_Omonoid__add__class_Olistsum(X32456),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X32456),X32455),c_List_Oupto(X32454,X32453))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X32456),X32455),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X32454,X32453))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_interv__listsum__conv__setsum__set__int])]) ).
fof(i_0_9332,plain,
! [X24931,X24932,X24933,X24934] :
( ~ class_Lattices_Osemilattice__inf(X24934)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24934),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24934),X24933),X24932)),X24931) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24934),X24933),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24934),X24932),X24931)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__assoc])]) ).
fof(i_0_9333,plain,
! [X24923,X24924,X24925,X24926] :
( ~ class_Lattices_Osemilattice__inf(X24926)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24926),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24926),X24925),X24924)),X24923) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24926),X24925),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24926),X24924),X24923)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oassoc])]) ).
fof(i_0_9334,plain,
! [X24927,X24928,X24929,X24930] :
( ~ class_Lattices_Olattice(X24930)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24930),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24930),X24929),X24928)),X24927) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24930),X24929),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24930),X24928),X24927)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I2_J])]) ).
fof(i_0_9335,plain,
! [X24085,X24086,X24087,X24088] :
( ~ class_Lattices_Osemilattice__sup(X24088)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24088),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24088),X24087),X24086)),X24085) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24088),X24087),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24088),X24086),X24085)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Oassoc])]) ).
fof(i_0_9336,plain,
! [X24077,X24078,X24079,X24080] :
( ~ class_Lattices_Osemilattice__sup(X24080)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24080),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24080),X24079),X24078)),X24077) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24080),X24079),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24080),X24078),X24077)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__assoc])]) ).
fof(i_0_9337,plain,
! [X24081,X24082,X24083,X24084] :
( ~ class_Lattices_Olattice(X24084)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24084),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24084),X24083),X24082)),X24081) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24084),X24083),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24084),X24082),X24081)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I6_J])]) ).
fof(i_0_9338,plain,
! [X22648,X22649,X22650,X22651] :
( ~ class_Orderings_Olinorder(X22651)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22651),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22651),X22650),X22649)),X22648) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22651),X22650),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22651),X22649),X22648)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__assoc])]) ).
fof(i_0_9339,plain,
! [X22644,X22645,X22646,X22647] :
( ~ class_Orderings_Olinorder(X22647)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22647),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22647),X22646),X22645)),X22644) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22647),X22646),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22647),X22645),X22644)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oassoc])]) ).
fof(i_0_9340,plain,
! [X22514,X22515,X22516,X22517] :
( ~ class_Orderings_Olinorder(X22517)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22517),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22517),X22516),X22515)),X22514) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22517),X22516),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22517),X22515),X22514)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oassoc])]) ).
fof(i_0_9341,plain,
! [X22510,X22511,X22512,X22513] :
( ~ class_Orderings_Olinorder(X22513)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22513),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22513),X22512),X22511)),X22510) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22513),X22512),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22513),X22511),X22510)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__assoc])]) ).
fof(i_0_9342,plain,
! [X20937,X20938,X20939] :
( ~ class_Groups_Omonoid__mult(X20939)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20939),hAPP(hAPP(c_Power_Opower__class_Opower(X20939),X20938),X20937)),X20938) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20939),X20938),hAPP(hAPP(c_Power_Opower__class_Opower(X20939),X20938),X20937)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__commutes])]) ).
fof(i_0_9343,plain,
! [X18773,X18774,X18775,X18776] :
( ~ class_Groups_Oab__semigroup__mult(X18776)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18776),X18775),X18774)),X18773) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18776),X18775),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18776),X18774),X18773)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__mult__class_Omult__ac_I1_J])]) ).
fof(i_0_9344,plain,
! [X18726,X18727,X18728,X18729] :
( ~ class_Rings_Ocomm__semiring__1(X18729)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18729),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18729),X18728),X18727)),X18726) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18729),X18728),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18729),X18727),X18726)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J])]) ).
fof(i_0_9345,plain,
! [X18195,X18196,X18197,X18198] :
( ~ class_Rings_Ocomm__semiring__1(X18198)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18198),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18198),X18197),X18196)),X18195) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18198),X18197),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18198),X18196),X18195)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])]) ).
fof(i_0_9346,plain,
! [X18046,X18047,X18048,X18049] :
( ~ class_Groups_Oab__semigroup__add(X18049)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18049),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18049),X18048),X18047)),X18046) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18049),X18048),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18049),X18047),X18046)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])]) ).
fof(i_0_9347,plain,
! [X21480,X21481,X21482,X21483] :
( ~ class_Rings_Odivision__ring(X21483)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21483),X21482),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21483),X21481),X21480)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21483),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21483),X21482),X21481)),X21480) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times__divide__eq__right])]) ).
fof(i_0_9348,plain,
! [X18717,X18718,X18719,X18720] :
( ~ class_Rings_Ocomm__semiring__1(X18720)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18720),X18719),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18720),X18718),X18717)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18720),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18720),X18719),X18718)),X18717) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J])]) ).
fof(i_0_9349,plain,
! [X18191,X18192,X18193,X18194] :
( ~ class_Rings_Ocomm__semiring__1(X18194)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18194),X18193),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18194),X18192),X18191)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18194),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18194),X18193),X18192)),X18191) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J])]) ).
fof(i_0_9350,plain,
! [X33760,X33761] :
( X33761 = c_List_Olist_ONil(X33760)
| c_List_Olast(X33760,X33761) = hAPP(hAPP(c_List_Onth(X33760),X33761),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33760)),X33761)),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_9351,plain,
! [X18781,X18782] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18781),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Oring__1__class_Oof__int(X18782),X18781) = hAPP(c_Groups_Ouminus__class_Ouminus(X18782),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18782),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X18781))))
| ~ class_Rings_Oring__1(X18782) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18781),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Oring__1__class_Oof__int(X18782),X18781) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18782),hAPP(c_Int_Onat,X18781))
| ~ class_Rings_Oring__1(X18782) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5841])])]) ).
fof(i_0_9352,plain,
! [X23807,X23808] :
( ~ class_Int_Onumber__ring(X23808)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X23807))
| hBOOL(hAPP(hAPP(c_member(X23808),hAPP(c_Int_Onumber__class_Onumber__of(X23808),X23807)),c_Nat_Osemiring__1__class_ONats(X23808))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__number__of])]) ).
fof(i_0_9353,plain,
! [X26364,X26365] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26365),X26364))
| hAPP(c_Finite__Set_Ocard(tc_fun(X26365,tc_HOL_Obool)),hAPP(c_Set_OPow(X26365),X26364)) = 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(X26365),X26364)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Pow])]) ).
fof(i_0_9354,plain,
! [X27636] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X27636)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),X27636)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X27636),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_atLeast__Suc]) ).
fof(i_0_9355,plain,
! [X25064,X25065,X25066] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25066,tc_HOL_Obool)),X25065),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25066,tc_HOL_Obool)),X25064)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25066,tc_HOL_Obool)),X25065),X25064),
inference(variable_rename,[status(thm)],[fact_Diff__Compl]) ).
fof(i_0_9356,plain,
! [X25061,X25062,X25063] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25063,tc_HOL_Obool)),X25062),X25061) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25063,tc_HOL_Obool)),X25062),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25063,tc_HOL_Obool)),X25061)),
inference(variable_rename,[status(thm)],[fact_Diff__eq]) ).
fof(i_0_9357,plain,
! [X19005] :
( ~ class_Rings_Olinordered__semidom(X19005)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19005),c_Groups_Ozero__class_Ozero(X19005)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19005),c_Groups_Oone__class_Oone(X19005)),c_Groups_Oone__class_Oone(X19005)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])]) ).
fof(i_0_9358,plain,
! [X25554,X25555] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X25555,X25554)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25554),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25555),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(variable_rename,[status(thm)],[fact_card__greaterThanLessThan__int]) ).
fof(i_0_9359,plain,
! [X25424,X25425,X25426] :
( ~ class_Orderings_Olinorder(X25426)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25426),X25425))
| ~ hBOOL(hAPP(hAPP(c_member(X25426),X25424),X25425))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X25426),X25424),c_Big__Operators_Olattice_OInf__fin(X25426,c_Orderings_Oord__class_Omin(X25426),X25425)) = X25424 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf__absorb])]) ).
fof(i_0_9360,plain,
! [X25297,X25298,X25299] :
( ~ class_Orderings_Olinorder(X25299)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25299),X25298))
| ~ hBOOL(hAPP(hAPP(c_member(X25299),X25297),X25298))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X25299),X25297),c_Big__Operators_Olattice_OSup__fin(X25299,c_Orderings_Oord__class_Omax(X25299),X25298)) = X25297 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup__absorb])]) ).
fof(i_0_9361,plain,
! [X19471,X19472] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19472),X19471),hAPP(c_Groups_Ouminus__class_Ouminus(X19472),X19471)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19472),X19471),c_Groups_Ozero__class_Ozero(X19472)))
| ~ class_Groups_Olinordered__ab__group__add(X19472) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19472),X19471),c_Groups_Ozero__class_Ozero(X19472)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19472),X19471),hAPP(c_Groups_Ouminus__class_Ouminus(X19472),X19471)))
| ~ class_Groups_Olinordered__ab__group__add(X19472) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__minus__self__iff])])]) ).
fof(i_0_9362,plain,
! [X18883,X18884] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18884),X18883),hAPP(c_Groups_Ouminus__class_Ouminus(X18884),X18883)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18884),X18883),c_Groups_Ozero__class_Ozero(X18884)))
| ~ class_Rings_Olinordered__idom(X18884) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18884),X18883),c_Groups_Ozero__class_Ozero(X18884)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18884),X18883),hAPP(c_Groups_Ouminus__class_Ouminus(X18884),X18883)))
| ~ class_Rings_Olinordered__idom(X18884) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__self__iff])])]) ).
fof(i_0_9363,plain,
! [X25026,X25027,X25028] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25028,tc_HOL_Obool)),X25027),X25026) != c_Orderings_Obot__class_Obot(tc_fun(X25028,tc_HOL_Obool))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25028,tc_HOL_Obool)),X25027),X25026) = X25027 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__triv])]) ).
fof(i_0_9364,plain,
! [X32806,X32807,X32808,X32809,X32810] :
( ~ class_Orderings_Olinorder(X32810)
| hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32809,X32810,X32808),X32807),X32806) != c_List_Olist_ONil(X32809) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__not__Nil])]) ).
fof(i_0_9365,plain,
! [X25701,X25702,X25703,X25704] :
( ~ class_Groups_Ocomm__monoid__mult(X25704)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25703),X25702))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25703,X25704),hAPP(c_COMBK(X25704,X25703),X25701)),X25702) = hAPP(hAPP(c_Power_Opower__class_Opower(X25704),X25701),hAPP(c_Finite__Set_Ocard(X25703),X25702)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__constant])]) ).
fof(i_0_9366,plain,
! [X28823,X28824,X28825] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X28825)
| X28824 = c_Orderings_Obot__class_Obot(tc_fun(X28825,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28825),X28824))
| hAPP(c_Finite__Set_Ofold1(X28825,c_Groups_Otimes__class_Otimes(X28825)),hAPP(hAPP(c_Set_Oinsert(X28825),X28823),X28824)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X28825),X28823),hAPP(c_Finite__Set_Ofold1(X28825,c_Groups_Otimes__class_Otimes(X28825)),X28824)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__insert__idem])]) ).
fof(i_0_9367,plain,
! [X26836,X26837,X26838,X26839] :
( ~ class_Orderings_Oorder(X26839)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26839,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26839,X26838),X26837)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26839,X26837),X26836)) = c_Orderings_Obot__class_Obot(tc_fun(X26839,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I11_J])]) ).
fof(i_0_9368,plain,
! [X21968,X21969] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21969),hAPP(c_Nat_OSuc,X21968)) = 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),X21969),X21968)),
inference(variable_rename,[status(thm)],[fact_diff__Suc]) ).
fof(i_0_9369,plain,
! [X33115,X33116,X33117,X33118] : hAPP(hAPP(c_List_Oappend(X33118),hAPP(hAPP(c_List_Oappend(X33118),X33117),X33116)),X33115) = hAPP(hAPP(c_List_Oappend(X33118),X33117),hAPP(hAPP(c_List_Oappend(X33118),X33116),X33115)),
inference(variable_rename,[status(thm)],[fact_append__assoc]) ).
fof(i_0_9370,plain,
! [X33039,X33040,X33041,X33042] : hAPP(hAPP(c_List_Oappend(X33042),hAPP(hAPP(c_List_Olist_OCons(X33042),X33041),X33040)),X33039) = hAPP(hAPP(c_List_Olist_OCons(X33042),X33041),hAPP(hAPP(c_List_Oappend(X33042),X33040),X33039)),
inference(variable_rename,[status(thm)],[fact_append__Cons]) ).
fof(i_0_9371,plain,
! [X23541,X23542] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23542),X23541))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23541))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23542),X23541)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__imp__le])]) ).
fof(i_0_9372,plain,
! [X23465,X23466] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23466),X23465))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23465))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23466),X23465)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__imp__le])]) ).
fof(i_0_9373,plain,
! [X33542,X33543,X33544] :
( X33544 = c_List_Olist_ONil(X33543)
| hAPP(hAPP(c_List_Otake(X33543),hAPP(c_Nat_OSuc,X33542)),X33544) = hAPP(hAPP(c_List_Olist_OCons(X33543),hAPP(c_List_Ohd(X33543),X33544)),hAPP(hAPP(c_List_Otake(X33543),X33542),hAPP(c_List_Otl(X33543),X33544))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__Suc])]) ).
fof(i_0_9374,plain,
! [X27063] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X27063))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X27063) = 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,X27063))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__atLeastZeroLessThan__int])]) ).
fof(i_0_9375,plain,
! [X32575,X32576,X32577,X32578] :
( ( X32578 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Onth(X32577),hAPP(hAPP(c_List_Olist_OCons(X32577),X32576),X32575)),X32578) = X32576 )
& ( X32578 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Onth(X32577),hAPP(hAPP(c_List_Olist_OCons(X32577),X32576),X32575)),X32578) = hAPP(hAPP(c_List_Onth(X32577),X32575),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X32578),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_9376,plain,
! [X24372,X24373,X24374,X24375] :
( ( X24375 != c_Orderings_Obot__class_Obot(tc_fun(X24374,tc_HOL_Obool))
| hAPP(c_Set_Oimage(X24374,X24373,hAPP(c_COMBK(X24373,X24374),X24372)),X24375) = c_Orderings_Obot__class_Obot(tc_fun(X24373,tc_HOL_Obool)) )
& ( X24375 = c_Orderings_Obot__class_Obot(tc_fun(X24374,tc_HOL_Obool))
| hAPP(c_Set_Oimage(X24374,X24373,hAPP(c_COMBK(X24373,X24374),X24372)),X24375) = hAPP(hAPP(c_Set_Oinsert(X24373),X24372),c_Orderings_Obot__class_Obot(tc_fun(X24373,tc_HOL_Obool))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__constant__conv])]) ).
cnf(i_0_9377,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_9378,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_9379,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_9380,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_9381,plain,
! [X17593,X17594,X17595] :
( ( hBOOL(hAPP(c_Com_OWT,X17594))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X17595,X17594,X17593))) )
& ( hBOOL(hAPP(c_Com_OWT,X17593))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X17595,X17594,X17593))) )
& ( ~ hBOOL(hAPP(c_Com_OWT,X17594))
| ~ hBOOL(hAPP(c_Com_OWT,X17593))
| hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X17595,X17594,X17593))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_Oequations_I5_J])])]) ).
fof(i_0_9382,plain,
! [X17435,X17436,X17437] :
( ( hBOOL(hAPP(c_Com_OWT,X17436))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X17437,X17436,X17435))) )
& ( hBOOL(hAPP(c_Com_OWT,X17435))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X17437,X17436,X17435))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5842])])]) ).
fof(i_0_9383,plain,
! [X17567,X17568,X17569] :
( ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X17569,X17568,X17567)))
| hBOOL(hAPP(c_Com_OWT,X17567)) )
& ( ~ hBOOL(hAPP(c_Com_OWT,X17567))
| hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X17569,X17568,X17567))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_Oequations_I3_J])]) ).
fof(i_0_9384,plain,
! [X17456,X17457,X17458] :
( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X17458,X17457,X17456)))
| hBOOL(hAPP(c_Com_OWT,X17456)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WTs__elim__cases_I3_J])]) ).
fof(i_0_9385,plain,
! [X32445,X32446,X32447,X32448] :
( ~ class_Groups_Ocomm__monoid__add(X32448)
| ~ hBOOL(hAPP(c_List_Odistinct(X32447),X32446))
| hAPP(c_List_Omonoid__add__class_Olistsum(X32448),hAPP(hAPP(c_List_Omap(X32447,X32448),X32445),X32446)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32447,X32448),X32445),hAPP(c_List_Oset(X32447),X32446)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__distinct__conv__setsum__set])]) ).
fof(i_0_9386,plain,
! [X20945,X20946,X20947,X20948] :
( ~ class_Groups_Omonoid__mult(X20948)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20948),X20947),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20946),X20945)) = hAPP(hAPP(c_Power_Opower__class_Opower(X20948),hAPP(hAPP(c_Power_Opower__class_Opower(X20948),X20947),X20946)),X20945) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult])]) ).
fof(i_0_9387,plain,
! [X20684,X20685,X20686,X20687] :
( ~ class_Rings_Ocomm__semiring__1(X20687)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20687),hAPP(hAPP(c_Power_Opower__class_Opower(X20687),X20686),X20685)),X20684) = hAPP(hAPP(c_Power_Opower__class_Opower(X20687),X20686),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20685),X20684)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J])]) ).
fof(i_0_9388,plain,
! [X19869,X19870,X19871] :
( ~ class_Divides_Oring__div(X19871)
| c_Divides_Odiv__class_Omod(X19871,hAPP(c_Groups_Ouminus__class_Ouminus(X19871),X19870),X19869) = c_Divides_Odiv__class_Omod(X19871,hAPP(c_Groups_Ouminus__class_Ouminus(X19871),c_Divides_Odiv__class_Omod(X19871,X19870,X19869)),X19869) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__minus__eq])]) ).
fof(i_0_9389,plain,
! [X33539,X33540,X33541] : hAPP(c_List_Otl(X33541),hAPP(hAPP(c_List_Otake(X33541),X33540),X33539)) = hAPP(hAPP(c_List_Otake(X33541),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33540),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(X33541),X33539)),
inference(variable_rename,[status(thm)],[fact_tl__take]) ).
fof(i_0_9390,plain,
! [X20989,X20990,X20991] :
( ~ class_Rings_Olinordered__idom(X20991)
| hAPP(c_Groups_Oabs__class_Oabs(X20991),hAPP(hAPP(c_Power_Opower__class_Opower(X20991),hAPP(c_Groups_Ouminus__class_Ouminus(X20991),X20990)),X20989)) = hAPP(c_Groups_Oabs__class_Oabs(X20991),hAPP(hAPP(c_Power_Opower__class_Opower(X20991),X20990),X20989)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__power__minus])]) ).
cnf(i_0_9391,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_9392,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_9393,plain,
! [X26974,X26975,X26976,X26977,X26978] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26978,X26977),X26976),X26975),X26974),X26975) = X26974,
inference(variable_rename,[status(thm)],[fact_fun__upd__same]) ).
fof(i_0_9394,plain,
! [X25353,X25354,X25355] :
( ~ class_Orderings_Olinorder(X25355)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25355),X25354))
| hBOOL(hAPP(hAPP(c_member(X25355),X25353),X25354))
| X25354 = c_Orderings_Obot__class_Obot(tc_fun(X25355,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMin(X25355,hAPP(hAPP(c_Set_Oinsert(X25355),X25353),X25354)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25355),X25353),c_Big__Operators_Olinorder__class_OMin(X25355,X25354)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5845])]) ).
fof(i_0_9395,plain,
! [X25356,X25357,X25358] :
( ~ class_Orderings_Olinorder(X25358)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25358),X25357))
| hBOOL(hAPP(hAPP(c_member(X25358),X25356),X25357))
| X25357 = c_Orderings_Obot__class_Obot(tc_fun(X25358,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMax(X25358,hAPP(hAPP(c_Set_Oinsert(X25358),X25356),X25357)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25358),X25356),c_Big__Operators_Olinorder__class_OMax(X25358,X25357)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5846])]) ).
fof(i_0_9396,plain,
! [X25350,X25351,X25352] :
( ~ class_Lattices_Olattice(X25352)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25352),X25351))
| hBOOL(hAPP(hAPP(c_member(X25352),X25350),X25351))
| X25351 = c_Orderings_Obot__class_Obot(tc_fun(X25352,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OInf__fin(X25352,hAPP(hAPP(c_Set_Oinsert(X25352),X25350),X25351)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25352),X25350),c_Big__Operators_Olattice__class_OInf__fin(X25352,X25351)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5847])]) ).
fof(i_0_9397,plain,
! [X25117,X25118,X25119] :
( ~ class_Lattices_Olattice(X25119)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25119),X25118))
| hBOOL(hAPP(hAPP(c_member(X25119),X25117),X25118))
| X25118 = c_Orderings_Obot__class_Obot(tc_fun(X25119,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OSup__fin(X25119,hAPP(hAPP(c_Set_Oinsert(X25119),X25117),X25118)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25119),X25117),c_Big__Operators_Olattice__class_OSup__fin(X25119,X25118)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5848])]) ).
fof(i_0_9398,plain,
! [X28208,X28209] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28209),c_Orderings_Otop__class_Otop(tc_fun(X28209,tc_HOL_Obool))))
| hAPP(c_Finite__Set_Ocard(X28209),X28208) != hAPP(c_Finite__Set_Ocard(X28209),c_Orderings_Otop__class_Otop(tc_fun(X28209,tc_HOL_Obool)))
| X28208 = c_Orderings_Otop__class_Otop(tc_fun(X28209,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__eq__UNIV__imp__eq__UNIV])]) ).
fof(i_0_9399,plain,
! [X33396,X33397,X33398,X33399] :
( ( X33399 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Odrop(X33398),X33399),hAPP(hAPP(c_List_Olist_OCons(X33398),X33397),X33396)) = hAPP(hAPP(c_List_Olist_OCons(X33398),X33397),X33396) )
& ( X33399 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Odrop(X33398),X33399),hAPP(hAPP(c_List_Olist_OCons(X33398),X33397),X33396)) = hAPP(hAPP(c_List_Odrop(X33398),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33399),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X33396) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_drop__Cons_H])]) ).
fof(i_0_9400,plain,
! [X21071] : 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,X21071))))),
inference(variable_rename,[status(thm)],[fact_neg__zminus__int]) ).
fof(i_0_9401,plain,
! [X23082,X23083,X23084,X23085] :
( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X23085),X23084),X23083),X23082))
| X23084 = X23082
| hBOOL(hAPP(X23083,X23082)) )
& ( X23084 != X23082
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X23085),X23084),X23083),X23082)) )
& ( ~ hBOOL(hAPP(X23083,X23082))
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X23085),X23084),X23083),X23082)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__code])])]) ).
fof(i_0_9402,plain,
! [X23289,X23290,X23291] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23291),X23290),hAPP(c_Groups_Ouminus__class_Ouminus(X23291),X23289)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23291),X23290),X23289))
| ~ class_Rings_Ocomm__ring__1(X23291) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23291),X23290),X23289))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23291),X23290),hAPP(c_Groups_Ouminus__class_Ouminus(X23291),X23289)))
| ~ class_Rings_Ocomm__ring__1(X23291) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__minus__iff])])]) ).
fof(i_0_9403,plain,
! [X23271,X23272,X23273] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23273),X23272),hAPP(c_Groups_Oabs__class_Oabs(X23273),X23271)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23273),X23272),X23271))
| ~ class_Rings_Olinordered__idom(X23273) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23273),X23272),X23271))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23273),X23272),hAPP(c_Groups_Oabs__class_Oabs(X23273),X23271)))
| ~ class_Rings_Olinordered__idom(X23273) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__abs__iff])])]) ).
fof(i_0_9404,plain,
! [X26993,X26994,X26995] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X26995),X26994),hAPP(c_SetInterval_Oord__class_OatMost(X26995),X26993)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26995),X26994),X26993))
| ~ class_Orderings_Oord(X26995) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26995),X26994),X26993))
| hBOOL(hAPP(hAPP(c_member(X26995),X26994),hAPP(c_SetInterval_Oord__class_OatMost(X26995),X26993)))
| ~ class_Orderings_Oord(X26995) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atMost__iff])])]) ).
fof(i_0_9405,plain,
! [X27605,X27606,X27607] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X27607),X27606),hAPP(c_SetInterval_Oord__class_OatLeast(X27607),X27605)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27607),X27605),X27606))
| ~ class_Orderings_Oord(X27607) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27607),X27605),X27606))
| hBOOL(hAPP(hAPP(c_member(X27607),X27606),hAPP(c_SetInterval_Oord__class_OatLeast(X27607),X27605)))
| ~ class_Orderings_Oord(X27607) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeast__iff])])]) ).
fof(i_0_9406,plain,
! [X27078,X27079,X27080] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X27080),X27079),hAPP(c_SetInterval_Oord__class_OlessThan(X27080),X27078)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27080),X27079),X27078))
| ~ class_Orderings_Oord(X27080) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27080),X27079),X27078))
| hBOOL(hAPP(hAPP(c_member(X27080),X27079),hAPP(c_SetInterval_Oord__class_OlessThan(X27080),X27078)))
| ~ class_Orderings_Oord(X27080) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lessThan__iff])])]) ).
fof(i_0_9407,plain,
! [X27649,X27650,X27651] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X27651),X27650),hAPP(c_SetInterval_Oord__class_OgreaterThan(X27651),X27649)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27651),X27649),X27650))
| ~ class_Orderings_Oord(X27651) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27651),X27649),X27650))
| hBOOL(hAPP(hAPP(c_member(X27651),X27650),hAPP(c_SetInterval_Oord__class_OgreaterThan(X27651),X27649)))
| ~ class_Orderings_Oord(X27651) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThan__iff])])]) ).
fof(i_0_9408,plain,
! [X26868,X26869,X26870] :
( ~ class_Groups_Oordered__ab__group__add(X26870)
| hAPP(c_Set_Oimage(X26870,X26870,c_Groups_Ouminus__class_Ouminus(X26870)),c_SetInterval_Oord__class_OgreaterThanAtMost(X26870,X26869,X26868)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26870,hAPP(c_Groups_Ouminus__class_Ouminus(X26870),X26868)),hAPP(c_Groups_Ouminus__class_Ouminus(X26870),X26869)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThanAtMost])]) ).
fof(i_0_9409,plain,
! [X27573,X27574,X27575,X27576,X27577] :
( ~ c_Finite__Set_Ofolding__one__idem(X27577,X27576,X27575)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27577),X27574))
| ~ hBOOL(hAPP(hAPP(c_member(X27577),X27573),X27574))
| hAPP(hAPP(X27576,X27573),hAPP(X27575,X27574)) = hAPP(X27575,X27574) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oin__idem])]) ).
fof(i_0_9410,plain,
! [X25270,X25271,X25272] :
( ~ class_Orderings_Olinorder(X25272)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25272),X25271))
| ~ hBOOL(hAPP(hAPP(c_member(X25272),X25270),X25271))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25272),X25270),c_Big__Operators_Olinorder__class_OMax(X25272,X25271))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__ge])]) ).
fof(i_0_9411,plain,
! [X32585,X32586] :
( ~ class_Groups_Ocomm__monoid__add(X32586)
| hAPP(c_List_Omonoid__add__class_Olistsum(X32586),X32585) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X32586),hAPP(c_List_Onth(X32586),X32585)),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(X32586)),X32585))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__setsum__nth])]) ).
fof(i_0_9412,plain,
! [X20272,X20273] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20273),X20272))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20272)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20273)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20272),X20273)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiff__int])]) ).
fof(i_0_9413,plain,
! [X23537,X23538] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23538),X23537))
| hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23537),X23538)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X23537)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X23538)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__div])]) ).
fof(i_0_9414,plain,
! [X18977] : 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)),X18977)),X18977) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_odd__nonzero]) ).
fof(i_0_9415,plain,
! [X29819,X29820] : hAPP(c_Relation_OField(X29820),X29819) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29820,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X29820,X29820),X29819)),hAPP(c_Relation_ORange(X29820,X29820),X29819)),
inference(variable_rename,[status(thm)],[fact_Field__def]) ).
cnf(i_0_9416,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_9417,plain,
! [X26434,X26435] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26435,X26434) = 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),X26435),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X26434))),
inference(variable_rename,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__functions_I2_J]) ).
fof(i_0_9418,plain,
! [X32865,X32866,X32867] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32867))
| c_List_Osublist(X32866,hAPP(hAPP(c_List_Olist_OCons(X32866),X32865),c_List_Olist_ONil(X32866)),X32867) = hAPP(hAPP(c_List_Olist_OCons(X32866),X32865),c_List_Olist_ONil(X32866)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32867))
| c_List_Osublist(X32866,hAPP(hAPP(c_List_Olist_OCons(X32866),X32865),c_List_Olist_ONil(X32866)),X32867) = c_List_Olist_ONil(X32866) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5850])]) ).
fof(i_0_9419,plain,
! [X20109,X20110] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20110))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20110),X20109)),X20110) = X20109 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self1__is__m])]) ).
fof(i_0_9420,plain,
! [X20107,X20108] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20108))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20107),X20108)),X20108) = X20107 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self__is__m])]) ).
fof(i_0_9421,plain,
! [X20586,X20587] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X20587,X20586) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X20587,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20586)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X20587,X20586) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X20587,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20586)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20587,X20586)),X20586) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zminus2__eq__if])]) ).
fof(i_0_9422,plain,
! [X28149,X28150] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28150,tc_HOL_Obool)),X28149),c_Orderings_Otop__class_Otop(tc_fun(X28150,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_subset__UNIV]) ).
fof(i_0_9423,plain,
! [X21048] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21048)))
| 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),X21048)) = 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),X21048)))
| 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),X21048)) = 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),X21048))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5851])]) ).
cnf(i_0_9424,plain,
c_Relation_Osingle__valued(X1,X1,c_Relation_OId(X1)),
inference(split_conjunct,[status(thm)],[i_0_5852]) ).
fof(i_0_9425,plain,
! [X23170,X23171,X23172] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23172),X23171))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23171),X23170))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23172),X23170)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Oorder__trans])]) ).
fof(i_0_9426,plain,
! [X19065,X19066,X19067] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19067),X19066))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19066),X19065))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19067),X19065)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__trans])]) ).
fof(i_0_9427,plain,
! [X19744,X19745,X19746] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19746),X19745))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19745),X19744))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19746),X19744)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__trans])]) ).
fof(i_0_9428,plain,
! [X23228,X23229,X23230,X23231] :
( ~ class_Divides_Osemiring__div(X23231)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23231),X23230),X23229))
| c_Divides_Odiv__class_Omod(X23231,c_Divides_Odiv__class_Omod(X23231,X23228,X23229),X23230) = c_Divides_Odiv__class_Omod(X23231,X23228,X23230) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mod__cancel])]) ).
fof(i_0_9429,plain,
! [X17262,X17263,X17264] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,X17264,X17263,X17262)
| X17262 = X17264 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln__elim__cases_I1_J])]) ).
fof(i_0_9430,plain,
! [X18665,X18666] :
( ~ class_Rings_Ocomm__semiring__1(X18666)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18666),X18665),X18665) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18666),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18666),c_Groups_Oone__class_Oone(X18666)),c_Groups_Oone__class_Oone(X18666))),X18665) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J])]) ).
fof(i_0_9431,plain,
! [X19166,X19167,X19168] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19168),X19167),X19166))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19168),X19167),X19166))
| ~ class_Orderings_Opreorder(X19168) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19168),X19166),X19167))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19168),X19167),X19166))
| ~ class_Orderings_Opreorder(X19168) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19168),X19167),X19166))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19168),X19166),X19167))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19168),X19167),X19166))
| ~ class_Orderings_Opreorder(X19168) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5853])])]) ).
fof(i_0_9432,plain,
! [X18335,X18336,X18337,X18338] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18338),X18337))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18336),X18337) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18338),X18335)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18336),X18335)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__eq__less])]) ).
fof(i_0_9433,plain,
! [X23366,X23367,X23368] :
( ~ class_Divides_Oring__div(X23368)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23368),X23367),X23366))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23368),X23366),hAPP(c_Groups_Ouminus__class_Ouminus(X23368),X23367)) = hAPP(c_Groups_Ouminus__class_Ouminus(X23368),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23368),X23366),X23367)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__div__neg])]) ).
fof(i_0_9434,plain,
! [X19294,X19295] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19295)),X19294))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19295),X19294)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leD])]) ).
fof(i_0_9435,plain,
! [X19516,X19517] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19517),X19516))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19517)),X19516)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19517)),X19516))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19517),X19516)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le])]) ).
fof(i_0_9436,plain,
! [X19512,X19513] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19513)),X19512))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19513),X19512)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19513),X19512))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19513)),X19512)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__eq])]) ).
fof(i_0_9437,plain,
! [X19504,X19505] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19505)),X19504))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19505),X19504)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__lessD])]) ).
fof(i_0_9438,plain,
! [X18311,X18312] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18312)),X18311))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18312),X18311)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessD])]) ).
fof(i_0_9439,plain,
! [X25512,X25513,X25514] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25514),X25513))
| hBOOL(hAPP(hAPP(c_member(X25514),X25512),X25513))
| hAPP(c_Finite__Set_Ocard(X25514),hAPP(hAPP(c_Set_Oinsert(X25514),X25512),X25513)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X25514),X25513)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5854])]) ).
fof(i_0_9440,plain,
! [X33348,X33349,X33350,X33351] : hAPP(hAPP(c_List_Odrop(X33351),X33350),hAPP(hAPP(c_List_Odrop(X33351),X33349),X33348)) = hAPP(hAPP(c_List_Odrop(X33351),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33350),X33349)),X33348),
inference(variable_rename,[status(thm)],[fact_drop__drop]) ).
fof(i_0_9441,plain,
! [X32640,X32641,X32642,X32643] : hAPP(hAPP(c_List_Otake(X32643),X32642),hAPP(hAPP(c_List_Otake(X32643),X32641),X32640)) = hAPP(hAPP(c_List_Otake(X32643),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X32642),X32641)),X32640),
inference(variable_rename,[status(thm)],[fact_take__take]) ).
fof(i_0_9442,plain,
! [X19983,X19984,X19985] :
( ( ~ hBOOL(hAPP(X19985,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19984),X19983)))
| epred2_3(X19985,X19984,X19983) )
& ( ~ epred2_3(X19985,X19984,X19983)
| hBOOL(hAPP(X19985,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19984),X19983))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5855])]) ).
fof(i_0_9443,plain,
! [X31367,X31368,X31369] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31369)
| ~ hBOOL(hAPP(hAPP(c_member(X31369),X31368),X31367))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31369),c_Complete__Lattice_OInf__class_OInf(X31369,X31367)),X31368)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__lower])]) ).
fof(i_0_9444,plain,
! [X19530,X19532,X19533,X19535] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk52_1(X19530)))
| hBOOL(hAPP(X19530,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19532))) )
& ( ~ hBOOL(hAPP(X19530,esk52_1(X19530)))
| hBOOL(hAPP(X19530,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19532))) )
& ( ~ hBOOL(hAPP(X19533,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk53_1(X19533))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19535))
| hBOOL(hAPP(X19533,X19535)) ) ),
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_9445,plain,
! [X20038,X20039] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20039))
| hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20039),X20038)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X20039)),hAPP(c_Int_Onat,X20038)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__div__distrib])]) ).
fof(i_0_9446,plain,
! [X19361,X19362] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19362))
| hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19362),X19361)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X19362)),hAPP(c_Int_Onat,X19361)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__distrib])]) ).
fof(i_0_9447,plain,
! [X26444,X26445] :
( ~ c_Nat__Transfer_Ois__nat(X26445)
| ~ c_Nat__Transfer_Ois__nat(X26444)
| c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X26445,X26444) = 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,X26445),hAPP(c_Int_Onat,X26444))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__int__nat__set__functions])]) ).
fof(i_0_9448,plain,
! [X34202] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X34202)),c_List_Otranspose__rel(X34202)),c_List_Olist_ONil(tc_List_Olist(X34202))))
| c_List_Otranspose(X34202,c_List_Olist_ONil(tc_List_Olist(X34202))) = c_List_Olist_ONil(tc_List_Olist(X34202)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose_Opsimps_I1_J])]) ).
fof(i_0_9449,plain,
! [X20022,X20023,X20024] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20024),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20023,X20022)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20024),X20023),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20024),X20022)),
inference(variable_rename,[status(thm)],[fact_mod__mult__distrib2]) ).
fof(i_0_9450,plain,
! [X24409,X24410] :
( ( X24410 != X24409
| hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X24410) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X24409) )
& ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X24410) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X24409)
| X24410 = X24409 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I3_J])]) ).
fof(i_0_9451,plain,
! [X33119,X33120,X33121] : hAPP(c_List_Oset(X33121),hAPP(hAPP(c_List_Oappend(X33121),X33120),X33119)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X33121,tc_HOL_Obool)),hAPP(c_List_Oset(X33121),X33120)),hAPP(c_List_Oset(X33121),X33119)),
inference(variable_rename,[status(thm)],[fact_set__append]) ).
fof(i_0_9452,plain,
! [X18252,X18253] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18253),X18252))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18253)),hAPP(c_Nat_OSuc,X18252))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mono])]) ).
fof(i_0_9453,plain,
! [X23622,X23623,X23624,X23625] :
( ( hAPP(hAPP(c_Set_Oinsert(X23625),X23624),X23623) != hAPP(hAPP(c_Set_Oinsert(X23625),X23624),X23622)
| X23623 = X23622
| hBOOL(hAPP(hAPP(c_member(X23625),X23624),X23622))
| hBOOL(hAPP(hAPP(c_member(X23625),X23624),X23623)) )
& ( X23623 != X23622
| hAPP(hAPP(c_Set_Oinsert(X23625),X23624),X23623) = hAPP(hAPP(c_Set_Oinsert(X23625),X23624),X23622)
| hBOOL(hAPP(hAPP(c_member(X23625),X23624),X23622))
| hBOOL(hAPP(hAPP(c_member(X23625),X23624),X23623)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5856])])]) ).
fof(i_0_9454,plain,
! [X20973,X20974,X20975,X20976] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X20976),X20975),X20974) != hAPP(hAPP(c_Power_Opower__class_Opower(X20976),X20975),X20973)
| X20974 = X20973
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20976),c_Groups_Oone__class_Oone(X20976)),X20975))
| ~ class_Rings_Olinordered__semidom(X20976) )
& ( X20974 != X20973
| hAPP(hAPP(c_Power_Opower__class_Opower(X20976),X20975),X20974) = hAPP(hAPP(c_Power_Opower__class_Opower(X20976),X20975),X20973)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20976),c_Groups_Oone__class_Oone(X20976)),X20975))
| ~ class_Rings_Olinordered__semidom(X20976) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inject__exp])])]) ).
fof(i_0_9455,plain,
! [X32912,X32913,X32914] : c_List_Olistset(X32914,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X32914,tc_HOL_Obool)),X32913),X32912)) = c_List_Oset__Cons(X32914,X32913,c_List_Olistset(X32914,X32912)),
inference(variable_rename,[status(thm)],[fact_listset_Osimps_I2_J]) ).
fof(i_0_9456,plain,
! [X31190,X31191] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31191)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31191),X31190))
| c_Complete__Lattice_OSup__class_OSup(X31191,X31190) = hAPP(hAPP(c_Finite__Set_Ofold(X31191,X31191,c_Lattices_Osemilattice__sup__class_Osup(X31191)),c_Orderings_Obot__class_Obot(X31191)),X31190) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fold__sup])]) ).
fof(i_0_9457,plain,
! [X31188,X31189] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31189)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31189),X31188))
| c_Complete__Lattice_OInf__class_OInf(X31189,X31188) = hAPP(hAPP(c_Finite__Set_Ofold(X31189,X31189,c_Lattices_Osemilattice__inf__class_Oinf(X31189)),c_Orderings_Otop__class_Otop(X31189)),X31188) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fold__inf])]) ).
fof(i_0_9458,plain,
! [X20922,X20923] :
( ( X20923 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20922),X20923) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X20923 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20922),X20923) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20922),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20922),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20923),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_9459,plain,
! [X26471,X26472,X26473] :
( ~ class_Groups_Oordered__ab__group__add(X26473)
| hAPP(c_Set_Oimage(X26473,X26473,c_Groups_Ouminus__class_Ouminus(X26473)),c_SetInterval_Oord__class_OatLeastAtMost(X26473,X26472,X26471)) = c_SetInterval_Oord__class_OatLeastAtMost(X26473,hAPP(c_Groups_Ouminus__class_Ouminus(X26473),X26471),hAPP(c_Groups_Ouminus__class_Ouminus(X26473),X26472)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeastAtMost])]) ).
fof(i_0_9460,plain,
! [X25688,X25689,X25690] :
( ~ class_Groups_Oordered__ab__group__add(X25690)
| hAPP(c_Set_Oimage(X25690,X25690,c_Groups_Ouminus__class_Ouminus(X25690)),c_SetInterval_Oord__class_OgreaterThanLessThan(X25690,X25689,X25688)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X25690,hAPP(c_Groups_Ouminus__class_Ouminus(X25690),X25688),hAPP(c_Groups_Ouminus__class_Ouminus(X25690),X25689)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThanLessThan])]) ).
fof(i_0_9461,plain,
! [X25477,X25478,X25479] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25479),X25477),X25478))
| hAPP(c_Finite__Set_Ocard(X25479),hAPP(hAPP(c_Set_Oinsert(X25479),X25477),X25478)) = hAPP(c_Finite__Set_Ocard(X25479),X25478)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25479),X25478)) )
& ( hBOOL(hAPP(hAPP(c_member(X25479),X25477),X25478))
| hAPP(c_Finite__Set_Ocard(X25479),hAPP(hAPP(c_Set_Oinsert(X25479),X25477),X25478)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X25479),X25478))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25479),X25478)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5857])])]) ).
fof(i_0_9462,plain,
! [X27121] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X27121)) = 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),X27121))),
inference(variable_rename,[status(thm)],[fact_lessThan__Suc__eq__insert__0]) ).
fof(i_0_9463,plain,
! [X22158,X22159] : c_Code__Numeral_Odiv__mod__code__numeral(X22159,X22158) = 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),X22159),X22158)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X22159,X22158)),
inference(variable_rename,[status(thm)],[fact_div__mod__code__numeral__def]) ).
fof(i_0_9464,plain,
! [X22024,X22025] : c_Divides_Odivmod__int(X22025,X22024) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22025),X22024)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X22025,X22024)),
inference(variable_rename,[status(thm)],[fact_divmod__int__mod__div]) ).
fof(i_0_9465,plain,
! [X19884,X19885] : 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,X19885,X19884)),X19884) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19885),X19884),
inference(variable_rename,[status(thm)],[fact_zminus__zmod]) ).
fof(i_0_9466,plain,
! [X19550,X19551] :
( ( hAPP(c_Int_Onat,X19551) != hAPP(c_Int_Onat,X19550)
| X19551 = X19550
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19550))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19551)) )
& ( X19551 != X19550
| hAPP(c_Int_Onat,X19551) = hAPP(c_Int_Onat,X19550)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19550))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19551)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__relations_I1_J])])]) ).
fof(i_0_9467,plain,
! [X19536,X19537] :
( ( hAPP(c_Int_Onat,X19537) != hAPP(c_Int_Onat,X19536)
| X19537 = X19536
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19536))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19537)) )
& ( X19537 != X19536
| hAPP(c_Int_Onat,X19537) = hAPP(c_Int_Onat,X19536)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19536))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19537)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__nat__nat__iff])])]) ).
fof(i_0_9468,plain,
! [X18513,X18514,X18516,X18517,X18518] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18514),X18513))
| X18513 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18514),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,esk42_2(X18513,X18514)))) )
& ( X18516 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18517),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X18518)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18517),X18516)) ) ),
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_9469,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_9470,plain,
! [X20499,X20500] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20500),X20499)),X20499) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20500),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20500,X20499)),
inference(variable_rename,[status(thm)],[fact_div__mod__equality_H]) ).
fof(i_0_9471,plain,
! [X20469,X20470] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20470),X20469))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20469),X20470)),X20470) = X20469 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse2])]) ).
fof(i_0_9472,plain,
! [X18526] :
( ( ~ 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),X18526)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18526)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18526))
| 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),X18526))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__int__conv])]) ).
fof(i_0_9473,plain,
! [X20924,X20925] :
( ( X20925 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20924))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20925) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20924) )
& ( 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),X20924)))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20925) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20924) )
& ( X20925 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20924))
| ~ 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),X20924)))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20925) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20924) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__eq__iff__number__of])])]) ).
fof(i_0_9474,plain,
! [X27352,X27353,X27354,X27355,X27356] :
( hAPP(X27356,X27355) != hAPP(c_Option_Ooption_OSome(X27354),X27353)
| hBOOL(hAPP(hAPP(c_member(X27354),X27353),c_Map_Oran(X27352,X27354,X27356))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ranI])]) ).
fof(i_0_9475,plain,
! [X27798,X27799,X27800,X27801,X27802] :
( hAPP(X27802,X27801) != hAPP(c_Option_Ooption_OSome(X27800),X27799)
| hBOOL(hAPP(hAPP(c_member(X27798),X27801),c_Map_Odom(X27798,X27800,X27802))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_domI])]) ).
fof(i_0_9476,plain,
! [X26376,X26377] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X26377,tc_HOL_Obool)),hAPP(c_Set_OPow(X26377),X26376)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X26377),X26376)) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26377),X26376))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X26377,tc_HOL_Obool)),hAPP(c_Set_OPow(X26377),X26376))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Pow__iff])]) ).
fof(i_0_9477,plain,
! [X29837,X29838,X29839,X29840,X29841] :
( ~ hBOOL(hAPP(hAPP(X29841,X29840),X29839))
| hBOOL(hAPP(c_Predicate_ODomainP(X29838,X29837,X29841),X29840)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainP_Ointros])]) ).
fof(i_0_9478,plain,
! [X29737,X29738,X29739,X29740,X29741] :
( ~ hBOOL(hAPP(hAPP(X29741,X29740),X29739))
| hBOOL(hAPP(c_Predicate_ORangeP(X29738,X29737,X29741),X29739)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeP_Ointros])]) ).
fof(i_0_9479,plain,
! [X32821,X32822] :
( ( ~ 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(X32822)),X32821)))
| X32821 != c_List_Olist_ONil(X32822) )
& ( X32821 = c_List_Olist_ONil(X32822)
| 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(X32822)),X32821))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__greater__0__conv])]) ).
fof(i_0_9480,plain,
! [X27618,X27619,X27620] :
( ~ class_Orderings_Oorder(X27620)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27620,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X27620,X27619),X27618)),hAPP(c_SetInterval_Oord__class_OatLeast(X27620),X27618)) = c_Orderings_Obot__class_Obot(tc_fun(X27620,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I8_J])]) ).
fof(i_0_9481,plain,
! [X19506,X19507] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19506),hAPP(c_Nat_OSuc,X19507)))
| X19506 = X19507
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19507),X19506)) )
& ( X19506 != X19507
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19506),hAPP(c_Nat_OSuc,X19507)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19507),X19506)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq])])]) ).
cnf(i_0_9482,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_9483,plain,
! [X19926,X19927] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19927))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19927),X19926))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X19927,X19926) = X19927 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__pos__trivial])]) ).
fof(i_0_9484,plain,
! [X27600,X27601] :
( ~ class_Orderings_Oorder(X27601)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27601,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X27601),X27600)),hAPP(c_SetInterval_Oord__class_OatLeast(X27601),X27600)) = hAPP(hAPP(c_Set_Oinsert(X27601),X27600),c_Orderings_Obot__class_Obot(tc_fun(X27601,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atMost__Int__atLeast])]) ).
fof(i_0_9485,plain,
! [X18330,X18331] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18331),X18330))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18330),hAPP(c_Nat_OSuc,X18331))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18330),hAPP(c_Nat_OSuc,X18331)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18331),X18330)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5860])]) ).
cnf(i_0_9486,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_9487,plain,
! [X33063,X33064,X33065] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33065)),hAPP(hAPP(c_List_Oappend(X33065),X33064),X33063)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33065)),X33064)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33065)),X33063)),
inference(variable_rename,[status(thm)],[fact_length__append]) ).
fof(i_0_9488,plain,
! [X24470,X24471] :
( ( X24471 != X24470
| hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X24471) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X24470)
| ~ c_Nat__Transfer_Onat__set(X24470)
| ~ c_Nat__Transfer_Onat__set(X24471) )
& ( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X24471) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X24470)
| X24471 = X24470
| ~ c_Nat__Transfer_Onat__set(X24470)
| ~ c_Nat__Transfer_Onat__set(X24471) ) ),
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_9489,plain,
! [X17103,X17104,X17105,X17106,X17107,X17108,X17109] :
( ( X17108 = X17105
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17109),X17108),X17107),X17106) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17109),X17105),X17104),X17103) )
& ( X17107 = X17104
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17109),X17108),X17107),X17106) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17109),X17105),X17104),X17103) )
& ( X17106 = X17103
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17109),X17108),X17107),X17106) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17109),X17105),X17104),X17103) )
& ( X17108 != X17105
| X17107 != X17104
| X17106 != X17103
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17109),X17108),X17107),X17106) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17109),X17105),X17104),X17103) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_triple_Oinject])])]) ).
fof(i_0_9490,plain,
! [X25613,X25614,X25615,X25616,X25617] :
( ~ class_Rings_Ocomm__semiring__1(X25616)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25615),X25614))
| ~ hBOOL(hAPP(hAPP(c_member(X25615),X25617),X25614))
| hAPP(X25613,X25617) != c_Groups_Ozero__class_Ozero(X25616)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25615,X25616),X25613),X25614) = c_Groups_Ozero__class_Ozero(X25616) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__zero])])]) ).
fof(i_0_9491,plain,
! [X20045,X20046,X20047] :
( ( X20047 != 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),X20047),X20046)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20047),X20045)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X20047 = 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),X20047),X20046)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20047),X20045)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20046),X20045) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__div__cancel__disj])]) ).
fof(i_0_9492,plain,
! [X26386,X26387] : hBOOL(hAPP(hAPP(c_member(tc_fun(X26387,tc_HOL_Obool)),X26386),hAPP(c_Set_OPow(X26387),X26386))),
inference(variable_rename,[status(thm)],[fact_Pow__top]) ).
fof(i_0_9493,plain,
! [X34215,X34216,X34217] : hAPP(c_List_Orev(X34217),hAPP(hAPP(c_List_Olist_OCons(X34217),X34216),X34215)) = hAPP(hAPP(c_List_Oappend(X34217),hAPP(c_List_Orev(X34217),X34215)),hAPP(hAPP(c_List_Olist_OCons(X34217),X34216),c_List_Olist_ONil(X34217))),
inference(variable_rename,[status(thm)],[fact_rev_Osimps_I2_J]) ).
cnf(i_0_9494,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_9495,plain,
! [X20129,X20130] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20130))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20130),X20129))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20130),X20129) = 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_9496,plain,
! [X20116,X20117] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20117),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)),X20117))
| X20116 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20117),X20116) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20116),X20117))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20117))
| X20116 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20117),X20116) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20117),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20117),X20116))
| X20116 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20117),X20116) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20116),X20117))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20117),X20116))
| X20116 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20117),X20116) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( X20116 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20117),X20116) = 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)),X20117))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20117),X20116))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20117),X20116) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20117),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20116),X20117))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20117),X20116) = 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_9497,plain,
! [X25336,X25337] :
( ~ class_Lattices_Olattice(X25337)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25337),X25336))
| X25336 = c_Orderings_Obot__class_Obot(tc_fun(X25337,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25337),c_Big__Operators_Olattice__class_OInf__fin(X25337,X25336)),c_Big__Operators_Olattice__class_OSup__fin(X25337,X25336))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__le__Sup])]) ).
fof(i_0_9498,plain,
! [X28342,X28343,X28344,X28345,X28346] :
( ~ c_Equiv__Relations_Oequivp(X28346,X28345)
| ~ hBOOL(hAPP(hAPP(X28345,X28344),X28343))
| ~ hBOOL(hAPP(hAPP(X28345,X28343),X28342))
| hBOOL(hAPP(hAPP(X28345,X28344),X28342)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__transp])]) ).
fof(i_0_9499,plain,
! [X27578,X27579,X27580,X27581,X27582] :
( ~ c_Finite__Set_Ofolding__one__idem(X27582,X27581,X27580)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27582),X27579))
| X27579 = c_Orderings_Obot__class_Obot(tc_fun(X27582,tc_HOL_Obool))
| hAPP(X27580,hAPP(hAPP(c_Set_Oinsert(X27582),X27578),X27579)) = hAPP(hAPP(X27581,X27578),hAPP(X27580,X27579)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oinsert__idem])]) ).
fof(i_0_9500,plain,
! [X19865,X19866,X19867,X19868] :
( ~ class_Divides_Oring__div(X19868)
| c_Divides_Odiv__class_Omod(X19868,X19867,X19866) != c_Divides_Odiv__class_Omod(X19868,X19865,X19866)
| c_Divides_Odiv__class_Omod(X19868,hAPP(c_Groups_Ouminus__class_Ouminus(X19868),X19867),X19866) = c_Divides_Odiv__class_Omod(X19868,hAPP(c_Groups_Ouminus__class_Ouminus(X19868),X19865),X19866) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__minus__cong])]) ).
fof(i_0_9501,plain,
! [X31442,X31443] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X31443,tc_HOL_Obool),X31442) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X31443,tc_HOL_Obool),tc_fun(X31443,tc_HOL_Obool)),X31442),c_COMBI(tc_fun(X31443,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_Union__def]) ).
fof(i_0_9502,plain,
! [X31440,X31441] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X31441,tc_HOL_Obool),X31440) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X31441,tc_HOL_Obool),tc_fun(X31441,tc_HOL_Obool)),X31440),c_COMBI(tc_fun(X31441,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_Inter__def]) ).
fof(i_0_9503,plain,
! [X20847] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X20847)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| X20847 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( X20847 != 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),X20847)),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_9504,plain,
! [X19664] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19664)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X19664 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X19664 != 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),X19664)),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_9505,plain,
! [X31593,X31594,X31595] : c_Map_Omap__add(X31595,X31594,hAPP(c_COMBK(tc_Option_Ooption(X31594),X31595),c_Option_Ooption_ONone(X31594)),X31593) = X31593,
inference(variable_rename,[status(thm)],[fact_empty__map__add]) ).
fof(i_0_9506,plain,
! [X31596,X31597,X31598] : c_Map_Omap__add(X31598,X31597,X31596,hAPP(c_COMBK(tc_Option_Ooption(X31597),X31598),c_Option_Ooption_ONone(X31597))) = X31596,
inference(variable_rename,[status(thm)],[fact_map__add__empty]) ).
fof(i_0_9507,plain,
! [X20928,X20929] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20929))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X20929)),X20928) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20929),X20928)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J])]) ).
fof(i_0_9508,plain,
! [X20926,X20927] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20927))
| hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20927),X20926)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X20927)),X20926) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__eq])]) ).
fof(i_0_9509,plain,
! [X20348,X20349,X20350] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20350),X20349)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20350),X20348)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20349),X20348),
inference(variable_rename,[status(thm)],[fact_diff__cancel]) ).
fof(i_0_9510,plain,
! [X20351,X20352,X20353] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20353),X20352)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20351),X20352)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20353),X20351),
inference(variable_rename,[status(thm)],[fact_diff__cancel2]) ).
fof(i_0_9511,plain,
! [X20688,X20689,X20690] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20690),X20689)),X20688) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20690),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20689),X20688)),
inference(variable_rename,[status(thm)],[fact_zpower__zpower]) ).
fof(i_0_9512,plain,
! [X20345,X20346,X20347] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20347),X20346)),X20345) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20347),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20346),X20345)),
inference(variable_rename,[status(thm)],[fact_diff__diff__left]) ).
fof(i_0_9513,plain,
! [X18730,X18731,X18732] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18732),X18731)),X18730) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18732),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18731),X18730)),
inference(variable_rename,[status(thm)],[fact_zmult__assoc]) ).
fof(i_0_9514,plain,
! [X19050,X19051,X19052] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19052),X19051)),X19050) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19052),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19051),X19050)),
inference(variable_rename,[status(thm)],[fact_nat__mult__assoc]) ).
fof(i_0_9515,plain,
! [X18584,X18585,X18586] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18586),X18585)),X18584) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18586),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18585),X18584)),
inference(variable_rename,[status(thm)],[fact_zadd__assoc]) ).
fof(i_0_9516,plain,
! [X18076,X18077,X18078] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18078),X18077)),X18076) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18078),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18077),X18076)),
inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).
fof(i_0_9517,plain,
! [X20015,X20016,X20017] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20017),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20016),X20015)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20017),X20016)),X20015),
inference(variable_rename,[status(thm)],[fact_div__mult2__eq]) ).
fof(i_0_9518,plain,
! [X29912,X29913,X29914] :
( ~ hBOOL(hAPP(hAPP(c_member(X29913),X29914),c_Orderings_Obot__class_Obot(tc_fun(X29913,tc_HOL_Obool))))
| hBOOL(hAPP(X29912,X29914)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ball__empty])]) ).
fof(i_0_9519,plain,
! [X27111,X27112,X27113] :
( ~ class_Orderings_Oorder(X27113)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27113,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X27113),X27112)),c_SetInterval_Oord__class_OatLeastAtMost(X27113,X27112,X27111)) = c_Orderings_Obot__class_Obot(tc_fun(X27113,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I4_J])]) ).
fof(i_0_9520,plain,
! [X27044,X27045,X27046] :
( ~ class_Orderings_Oorder(X27046)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27046,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X27046),X27045)),c_SetInterval_Oord__class_OgreaterThanAtMost(X27046,X27045,X27044)) = c_Orderings_Obot__class_Obot(tc_fun(X27046,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I3_J])]) ).
fof(i_0_9521,plain,
! [X27047,X27048,X27049] :
( ~ class_Orderings_Oorder(X27049)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27049,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X27049),X27048)),c_SetInterval_Oord__class_OgreaterThanLessThan(X27049,X27048,X27047)) = c_Orderings_Obot__class_Obot(tc_fun(X27049,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I1_J])]) ).
fof(i_0_9522,plain,
! [X19920,X19921] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19921),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19920),X19921))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X19921,X19920) = X19921 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__neg__neg__trivial])]) ).
fof(i_0_9523,plain,
! [X31824,X31825,X31826,X31827] : hAPP(c_List_Oset(X31827),hAPP(hAPP(c_List_Omap(X31826,X31827),X31825),X31824)) = hAPP(c_Set_Oimage(X31826,X31827,X31825),hAPP(c_List_Oset(X31826),X31824)),
inference(variable_rename,[status(thm)],[fact_set__map]) ).
fof(i_0_9524,plain,
! [X33389,X33390,X33391] : hAPP(hAPP(c_List_Oappend(X33391),hAPP(hAPP(c_List_Otake(X33391),X33390),X33389)),hAPP(hAPP(c_List_Odrop(X33391),X33390),X33389)) = X33389,
inference(variable_rename,[status(thm)],[fact_append__take__drop__id]) ).
fof(i_0_9525,plain,
! [X18574] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18574)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[i_0_5863]) ).
fof(i_0_9526,plain,
! [X20013,X20014] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X20014),X20013) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20014,X20013)),X20013),
inference(variable_rename,[status(thm)],[fact_mod__Suc__eq__Suc__mod]) ).
fof(i_0_9527,plain,
! [X18150,X18151] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X18151,X18150)) = 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(X18151)),c_Com_Ocom_Ocom__size(X18150))),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_9528,plain,
! [X21176] :
( ( ~ 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),X21176)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X21176)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X21176))
| 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),X21176))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__0__number__of])]) ).
fof(i_0_9529,plain,
! [X17272,X17273,X17274] :
( ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X17274)))
| hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(X17273,X17274,X17272))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_OCall])]) ).
fof(i_0_9530,plain,
! [X20138,X20139] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20139),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20138),X20139))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20139),X20138) = 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_9531,plain,
( c_Int_OMin = X1
| c_Int_OMin != c_Int_OBit1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_5864]) ).
cnf(i_0_9532,plain,
( X1 = c_Int_OMin
| c_Int_OBit1(X1) != c_Int_OMin ),
inference(split_conjunct,[status(thm)],[i_0_5865]) ).
fof(i_0_9533,plain,
! [X32652,X32653,X32654,X32655] : hAPP(hAPP(c_List_Otake(X32655),hAPP(c_Nat_OSuc,X32654)),hAPP(hAPP(c_List_Olist_OCons(X32655),X32653),X32652)) = hAPP(hAPP(c_List_Olist_OCons(X32655),X32653),hAPP(hAPP(c_List_Otake(X32655),X32654),X32652)),
inference(variable_rename,[status(thm)],[fact_take__Suc__Cons]) ).
fof(i_0_9534,plain,
! [X32156,X32157,X32158,X32159,X32160,X32161,X32162] :
( hAPP(hAPP(c_List_Omap(X32162,X32161),X32160),X32159) != hAPP(hAPP(c_List_Omap(X32158,X32161),X32157),X32156)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32162)),X32159) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32158)),X32156) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__eq__imp__length__eq])]) ).
cnf(i_0_9535,plain,
c_Int_OBit1(X1) != c_Int_OPls,
inference(split_conjunct,[status(thm)],[i_0_5866]) ).
cnf(i_0_9536,plain,
c_Int_OPls != c_Int_OBit1(X1),
inference(split_conjunct,[status(thm)],[i_0_5867]) ).
fof(i_0_9537,plain,
! [X24411] : 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)),X24411)) = X24411,
inference(variable_rename,[status(thm)],[fact_transfer__int__nat__set__return__embed]) ).
fof(i_0_9538,plain,
! [X22296,X22297,X22298,X22299,X22300] :
( hAPP(c_Product__Type_Ofst(X22300,X22299),hAPP(hAPP(c_Product__Type_OPair(X22300,X22299),X22298),X22297)) != X22296
| X22298 = X22296 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fst__eqD])]) ).
fof(i_0_9539,plain,
! [X22180,X22181,X22182,X22183,X22184] :
( hAPP(c_Product__Type_Osnd(X22184,X22183),hAPP(hAPP(c_Product__Type_OPair(X22184,X22183),X22182),X22181)) != X22180
| X22181 = X22180 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snd__eqD])]) ).
fof(i_0_9540,plain,
! [X24476] :
( ~ c_Nat__Transfer_Onat__set(X24476)
| 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),X24476)) = X24476 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__return__embed])]) ).
fof(i_0_9541,plain,
! [X24487,X24488] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X24488,X24488)),X24487))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24488),hAPP(c_Relation_OField(X24488),X24487))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Field])]) ).
fof(i_0_9542,plain,
! [X26871,X26872,X26873] :
( ~ class_Groups_Oordered__ab__group__add(X26873)
| hAPP(c_Set_Oimage(X26873,X26873,c_Groups_Ouminus__class_Ouminus(X26873)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26873,X26872),X26871)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X26873,hAPP(c_Groups_Ouminus__class_Ouminus(X26873),X26871),hAPP(c_Groups_Ouminus__class_Ouminus(X26873),X26872)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeastLessThan])]) ).
fof(i_0_9543,plain,
! [X18318,X18319] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18319),X18318))
| hAPP(c_Nat_OSuc,X18319) = X18318
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18319)),X18318)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessI])]) ).
fof(i_0_9544,plain,
! [X24664,X24666,X24667,X24668] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X24664))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X24666),X24664))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24666),esk126_1(X24664))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk127_2(X24667,X24668)),X24667))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X24667)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk127_2(X24667,X24668)),X24668))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X24667)) ) ),
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_9545,plain,
! [X24670,X24672,X24673,X24674] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X24670))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X24672),X24670))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24672),esk128_1(X24670))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk129_2(X24673,X24674)),X24673))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X24673)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk129_2(X24673,X24674)),X24674))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X24673)) ) ),
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_9546,plain,
! [X20696,X20697] :
( ( ~ 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),X20696)))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20697),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20696)) = hAPP(c_Int_Onumber__class_Onumber__of(X20697),X20696)
| ~ class_Int_Onumber__ring(X20697) )
& ( 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),X20696)))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20697),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20696)) = c_Groups_Ozero__class_Ozero(X20697)
| ~ class_Int_Onumber__ring(X20697) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5868])])]) ).
fof(i_0_9547,plain,
! [X20858,X20859,X20860] :
( ~ class_Int_Onumber__ring(X20860)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20860),hAPP(c_Int_Onumber__class_Onumber__of(X20860),X20859)),hAPP(c_Int_Onumber__class_Onumber__of(X20860),X20858)) = hAPP(c_Int_Onumber__class_Onumber__of(X20860),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20859),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20858))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__number__of__eq])]) ).
fof(i_0_9548,plain,
! [X25480,X25481,X25482] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25482),X25481))
| hBOOL(hAPP(hAPP(c_member(X25482),X25480),X25481))
| hAPP(c_Finite__Set_Ocard(X25482),hAPP(hAPP(c_Set_Oinsert(X25482),X25480),X25481)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X25482),X25481)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5869])]) ).
fof(i_0_9549,plain,
! [X18660] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X18660)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18660)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18660))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X18660))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__nat__eq])]) ).
fof(i_0_9550,plain,
! [X19193,X19194,X19195] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19195),X19194),X19193))
| X19194 = X19193
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19195),X19194),X19193))
| ~ class_Orderings_Olinorder(X19195) )
& ( X19194 != X19193
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19195),X19194),X19193))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19195),X19194),X19193))
| ~ class_Orderings_Olinorder(X19195) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5870])])]) ).
fof(i_0_9551,plain,
! [X33821,X33822,X33823] : c_List_Obutlast(X33823,hAPP(hAPP(c_List_Oappend(X33823),X33822),hAPP(hAPP(c_List_Olist_OCons(X33823),X33821),c_List_Olist_ONil(X33823)))) = X33822,
inference(variable_rename,[status(thm)],[fact_butlast__snoc]) ).
fof(i_0_9552,plain,
! [X33754,X33755,X33756] : c_List_Olast(X33756,hAPP(hAPP(c_List_Oappend(X33756),X33755),hAPP(hAPP(c_List_Olist_OCons(X33756),X33754),c_List_Olist_ONil(X33756)))) = X33754,
inference(variable_rename,[status(thm)],[fact_last__snoc]) ).
fof(i_0_9553,plain,
! [X30233,X30234] : hAPP(hAPP(c_Relation_Orel__comp(X30234,X30234,X30234),c_Transitive__Closure_Ortrancl(X30234,X30233)),c_Transitive__Closure_Ortrancl(X30234,X30233)) = c_Transitive__Closure_Ortrancl(X30234,X30233),
inference(variable_rename,[status(thm)],[fact_rtrancl__idemp__self__comp]) ).
fof(i_0_9554,plain,
! [X22314,X22315,X22316] : hAPP(c_Product__Type_Ofst(X22316,X22315),X22314) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22316,X22315,X22316),c_COMBK(X22316,X22315)),X22314),
inference(variable_rename,[status(thm)],[fact_fst__def]) ).
fof(i_0_9555,plain,
! [X31871] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X31871)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X31871),tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[i_0_5871]) ).
fof(i_0_9556,plain,
! [X30428,X30429] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X30429,X30429)),X30428))
| ~ c_Wellfounded_Oacyclic(X30429,X30428)
| c_Wellfounded_Owf(X30429,hAPP(c_Relation_Oconverse(X30429,X30429),X30428)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__acyclic__wf__converse])]) ).
fof(i_0_9557,plain,
! [X19122,X19123,X19124] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19124),X19123),X19122))
| X19123 != X19122
| ~ class_Orderings_Oorder(X19124) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19124),X19122),X19123))
| X19123 != X19122
| ~ class_Orderings_Oorder(X19124) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19124),X19123),X19122))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19124),X19122),X19123))
| X19123 = X19122
| ~ class_Orderings_Oorder(X19124) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__iff])])]) ).
fof(i_0_9558,plain,
! [X19111,X19112,X19113] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19113),X19111),X19112))
| X19111 = X19112
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19113),X19112),X19111))
| ~ class_Orderings_Oorder(X19113) )
& ( X19111 != X19112
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19113),X19111),X19112))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19113),X19112),X19111))
| ~ class_Orderings_Oorder(X19113) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym__conv])])]) ).
fof(i_0_9559,plain,
! [X19092,X19093,X19094] :
( ~ class_Orderings_Oorder(X19094)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19094),X19093),X19092))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19094),X19092),X19093))
| X19093 = X19092 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym])]) ).
fof(i_0_9560,plain,
! [X19085,X19086,X19087] :
( ~ class_Orderings_Oorder(X19087)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19087),X19086),X19085))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19087),X19085),X19086))
| X19085 = X19086 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I5_J])]) ).
fof(i_0_9561,plain,
! [X17761,X17762,X17763] :
( hBOOL(hAPP(X17763,X17762))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17763,X17761)),X17762),X17762)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5872])]) ).
fof(i_0_9562,plain,
! [X20373,X20374] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20374),X20373))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20373,X20374) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20373),X20374),X20374) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__mod__geq])]) ).
fof(i_0_9563,plain,
! [X25218,X25219] :
( X25219 != X25218
| c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25219,X25218) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X25219),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_9564,plain,
! [X23504,X23505] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23505),X23504))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23505),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23504))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23505),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X23504)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23505),X23504)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_uminus__dvd__conv_I2_J])]) ).
fof(i_0_9565,plain,
! [X20449,X20450] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20450),X20449))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20449)),X20450) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20449),X20450)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__le])]) ).
fof(i_0_9566,plain,
! [X18626,X18627,X18628] :
( ~ class_Orderings_Opreorder(X18628)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18628),X18627),X18626))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18628),X18626),X18627)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5873])]) ).
fof(i_0_9567,plain,
! [X18617,X18618,X18619] :
( ~ class_Orderings_Opreorder(X18619)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18619),X18618),X18617))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18619),X18617),X18618)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5874])]) ).
fof(i_0_9568,plain,
! [X18614,X18615,X18616] :
( ~ class_Orderings_Opreorder(X18616)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18616),X18615),X18614))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18616),X18614),X18615)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5875])]) ).
fof(i_0_9569,plain,
! [X18559,X18560,X18561] :
( ~ class_Orderings_Opreorder(X18561)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18561),X18560),X18559))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18561),X18559),X18560)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5876])]) ).
fof(i_0_9570,plain,
! [X19157,X19158,X19159] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19159),X19158),X19157))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19159),X19157),X19158))
| ~ class_Orderings_Olinorder(X19159) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19159),X19157),X19158))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19159),X19158),X19157))
| ~ class_Orderings_Olinorder(X19159) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5877])])]) ).
fof(i_0_9571,plain,
! [X19187,X19188,X19189] :
( ~ class_Orderings_Olinorder(X19189)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19189),X19188),X19187))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19189),X19187),X19188)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5878])]) ).
fof(i_0_9572,plain,
! [X19154,X19155,X19156] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19156),X19155),X19154))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19156),X19154),X19155))
| ~ class_Orderings_Olinorder(X19156) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19156),X19154),X19155))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19156),X19155),X19154))
| ~ class_Orderings_Olinorder(X19156) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5879])])]) ).
fof(i_0_9573,plain,
! [X18599,X18600,X18601] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18601),X18600),X18599))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18601),X18599),X18600))
| X18600 = X18599
| ~ class_Orderings_Olinorder(X18601) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18601),X18599),X18600))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18601),X18600),X18599))
| ~ class_Orderings_Olinorder(X18601) )
& ( X18600 != X18599
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18601),X18600),X18599))
| ~ class_Orderings_Olinorder(X18601) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5880])])]) ).
fof(i_0_9574,plain,
! [X18629,X18630,X18631] :
( ~ class_Orderings_Oorder(X18631)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18631),X18630),X18629))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18631),X18629),X18630)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5881])]) ).
fof(i_0_9575,plain,
! [X20742,X20743] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20743)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20743),hAPP(c_Groups_Ouminus__class_Ouminus(X20743),X20742)),hAPP(c_Groups_Oabs__class_Oabs(X20743),X20742))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__minus__self])]) ).
fof(i_0_9576,plain,
! [X19455,X19456] :
( ~ class_Rings_Olinordered__ring(X19456)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19456),c_Groups_Ozero__class_Ozero(X19456)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19456),X19455),X19455))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__square])]) ).
fof(i_0_9577,plain,
! [X18967,X18968] :
( ~ class_Rings_Olinordered__semidom(X18968)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18968),X18967),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18968),X18967),c_Groups_Oone__class_Oone(X18968)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__one])]) ).
fof(i_0_9578,plain,
! [X20712,X20713] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20713),c_Groups_Ozero__class_Ozero(X20713)),hAPP(c_Groups_Oabs__class_Oabs(X20713),X20712)))
| X20712 != c_Groups_Ozero__class_Ozero(X20713)
| ~ class_Groups_Oordered__ab__group__add__abs(X20713) )
& ( X20712 = c_Groups_Ozero__class_Ozero(X20713)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20713),c_Groups_Ozero__class_Ozero(X20713)),hAPP(c_Groups_Oabs__class_Oabs(X20713),X20712)))
| ~ class_Groups_Oordered__ab__group__add__abs(X20713) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__abs__iff])])]) ).
fof(i_0_9579,plain,
! [X22048,X22049,X22050,X22051] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X22051,X22050),X22049))
| ~ hBOOL(hAPP(hAPP(X22050,X22048),X22049))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X22051,X22050),X22048)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__downward])]) ).
fof(i_0_9580,plain,
! [X21140,X21141] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21141),c_Int_OPls))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21141)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21140)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21141),c_Int_OPls))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21141)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21140)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21141),X21140)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5882])]) ).
fof(i_0_9581,plain,
! [X33458,X33459] :
( X33459 = c_List_Olist_ONil(X33458)
| hBOOL(hAPP(hAPP(c_member(X33458),hAPP(c_List_Ohd(X33458),X33459)),hAPP(c_List_Oset(X33458),X33459))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__in__set])]) ).
fof(i_0_9582,plain,
! [X25220] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25220,X25220) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X25220),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_9583,plain,
! [X20758,X20759,X20760] :
( ~ class_Rings_Ocomm__semiring__1(X20760)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20760),hAPP(hAPP(c_Power_Opower__class_Opower(X20760),X20759),X20758)),X20759) = hAPP(hAPP(c_Power_Opower__class_Opower(X20760),X20759),hAPP(c_Nat_OSuc,X20758)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J])]) ).
fof(i_0_9584,plain,
! [X20977,X20978,X20979] :
( ~ class_Groups_Omonoid__mult(X20979)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20979),X20978),hAPP(c_Nat_OSuc,X20977)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20979),hAPP(hAPP(c_Power_Opower__class_Opower(X20979),X20978),X20977)),X20978) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc2])]) ).
fof(i_0_9585,plain,
! [X17516,X17517,X17518,X17519] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17519),X17518),X17517))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17519),X17518),X17516))
| X17516 = X17517 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com__det])]) ).
fof(i_0_9586,plain,
! [X27094,X27095,X27096,X27097,X27098] :
( hAPP(X27098,X27097) != hAPP(c_Option_Ooption_OSome(X27096),X27095)
| hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X27094,tc_Option_Ooption(X27096)),X27098),X27097),hAPP(c_Option_Ooption_OSome(X27096),X27095)) = X27098 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__upd__triv])]) ).
fof(i_0_9587,plain,
! [X17178,X17179,X17180,X17181,X17182] :
( ~ c_Groups_Osemigroup(X17182,X17181)
| hAPP(hAPP(X17181,hAPP(hAPP(X17181,X17180),X17179)),X17178) = hAPP(hAPP(X17181,X17180),hAPP(hAPP(X17181,X17179),X17178)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semigroup_Oassoc])]) ).
fof(i_0_9588,plain,
! [X32342,X32343,X32344] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32344)),hAPP(hAPP(c_List_Olist_OCons(X32344),X32343),X32342)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32344)),X32342)),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_9589,plain,
! [X19524,X19525,X19527,X19528] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19525))
| ~ hBOOL(hAPP(X19524,X19525))
| hBOOL(hAPP(X19524,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk50_1(X19524)))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk51_1(X19527)))
| ~ hBOOL(hAPP(X19527,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19528))) )
& ( hBOOL(hAPP(X19527,esk51_1(X19527)))
| ~ hBOOL(hAPP(X19527,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19528))) ) ),
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_9590,plain,
! [X19508,X19509] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19509),X19508))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19509)),X19508)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leI])]) ).
fof(i_0_9591,plain,
! [X25282,X25283,X25284] :
( ~ class_Lattices_Olattice(X25284)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25284),X25283))
| ~ hBOOL(hAPP(hAPP(c_member(X25284),X25282),X25283))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25284),X25282),c_Big__Operators_Olattice__class_OInf__fin(X25284,X25283)) = c_Big__Operators_Olattice__class_OInf__fin(X25284,X25283) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oin__idem])]) ).
fof(i_0_9592,plain,
! [X25087,X25088,X25089] :
( ~ class_Lattices_Olattice(X25089)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25089),X25088))
| ~ hBOOL(hAPP(hAPP(c_member(X25089),X25087),X25088))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25089),X25087),c_Big__Operators_Olattice__class_OSup__fin(X25089,X25088)) = c_Big__Operators_Olattice__class_OSup__fin(X25089,X25088) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oin__idem])]) ).
fof(i_0_9593,plain,
! [X25288,X25289,X25290] :
( ~ class_Orderings_Olinorder(X25290)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25290),X25289))
| ~ hBOOL(hAPP(hAPP(c_member(X25290),X25288),X25289))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X25290),X25288),c_Big__Operators_Olinorder__class_OMax(X25290,X25289)) = c_Big__Operators_Olinorder__class_OMax(X25290,X25289) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oin__idem])]) ).
fof(i_0_9594,plain,
! [X25285,X25286,X25287] :
( ~ class_Orderings_Olinorder(X25287)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25287),X25286))
| ~ hBOOL(hAPP(hAPP(c_member(X25287),X25285),X25286))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X25287),X25285),c_Big__Operators_Olinorder__class_OMin(X25287,X25286)) = c_Big__Operators_Olinorder__class_OMin(X25287,X25286) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oin__idem])]) ).
fof(i_0_9595,plain,
! [X31363,X31364,X31365] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31365)
| ~ hBOOL(hAPP(hAPP(c_member(X31365),X31364),X31363))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31365),X31364),c_Complete__Lattice_OSup__class_OSup(X31365,X31363))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__upper])]) ).
cnf(i_0_9596,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_9597,plain,
! [X27114,X27115,X27116] :
( ~ class_Orderings_Oorder(X27116)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27116,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X27116),X27115)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X27116,X27115),X27114)) = c_Orderings_Obot__class_Obot(tc_fun(X27116,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I2_J])]) ).
fof(i_0_9598,plain,
! [X25483,X25484] :
( ( X25483 != c_Orderings_Obot__class_Obot(tc_fun(X25484,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(X25484),X25483))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X25484),X25483))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X25484),X25483))) )
& ( X25483 = c_Orderings_Obot__class_Obot(tc_fun(X25484,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25484),X25483))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X25484),X25483))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__gt__0__iff])])]) ).
fof(i_0_9599,plain,
! [X32523,X32524,X32525,X32526] : hAPP(hAPP(c_List_Onth(X32526),hAPP(hAPP(c_List_Olist_OCons(X32526),X32525),X32524)),hAPP(c_Nat_OSuc,X32523)) = hAPP(hAPP(c_List_Onth(X32526),X32524),X32523),
inference(variable_rename,[status(thm)],[fact_nth__Cons__Suc]) ).
fof(i_0_9600,plain,
! [X33495,X33496,X33497,X33498] : hAPP(hAPP(c_List_Omap(X33498,X33497),X33496),hAPP(c_List_Otl(X33498),X33495)) = hAPP(c_List_Otl(X33497),hAPP(hAPP(c_List_Omap(X33498,X33497),X33496),X33495)),
inference(variable_rename,[status(thm)],[fact_map__tl]) ).
fof(i_0_9601,plain,
! [X34253,X34254,X34255,X34256] : hAPP(c_List_Orev(X34256),hAPP(hAPP(c_List_Omap(X34255,X34256),X34254),X34253)) = hAPP(hAPP(c_List_Omap(X34255,X34256),X34254),hAPP(c_List_Orev(X34255),X34253)),
inference(variable_rename,[status(thm)],[fact_rev__map]) ).
fof(i_0_9602,plain,
! [X23494,X23495] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23495),X23494))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23494),X23495))
| hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X23495) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X23494) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__antisym__abs])]) ).
fof(i_0_9603,plain,
! [X23630,X23631] : ~ hBOOL(hAPP(hAPP(c_member(X23631),X23630),c_Orderings_Obot__class_Obot(tc_fun(X23631,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[i_0_5884]) ).
fof(i_0_9604,plain,
! [X23580,X23581] : ~ hBOOL(hAPP(hAPP(c_member(X23581),X23580),c_Orderings_Obot__class_Obot(tc_fun(X23581,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[i_0_5885]) ).
fof(i_0_9605,plain,
! [X23360,X23361,X23362] :
( ~ class_Divides_Osemiring__div(X23362)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23362),X23361),X23360))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23362),X23361),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23362),X23360),X23361)) = X23360 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__div__cancel])]) ).
fof(i_0_9606,plain,
! [X19538,X19539,X19541,X19542] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk54_1(X19538)))
| ~ hBOOL(hAPP(X19538,X19539)) )
& ( hBOOL(hAPP(X19538,hAPP(c_Int_Onat,esk54_1(X19538))))
| ~ hBOOL(hAPP(X19538,X19539)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19542))
| ~ hBOOL(hAPP(X19541,hAPP(c_Int_Onat,X19542)))
| hBOOL(hAPP(X19541,esk55_1(X19541))) ) ),
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_9607,plain,
! [X25459,X25460] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X25460),X25459)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X25460),X25459)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__ge__0__finite])]) ).
cnf(i_0_9608,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_9609,plain,
! [X20531] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20531))
| hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20531),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X20531 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__pred])]) ).
fof(i_0_9610,plain,
! [X23079,X23080,X23081] :
( hAPP(hAPP(c_Set_Oinsert(X23081),X23080),c_Orderings_Obot__class_Obot(tc_fun(X23081,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(X23081),X23079),c_Orderings_Obot__class_Obot(tc_fun(X23081,tc_HOL_Obool)))
| X23080 = X23079 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singleton__inject])]) ).
fof(i_0_9611,plain,
! [X28298] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X28298),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,X28298)) = X28298 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__inverse])]) ).
fof(i_0_9612,plain,
! [X21725,X21726,X21727,X21728] :
( ( X21726 = c_Groups_Ozero__class_Ozero(X21728)
| X21727 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21728),hAPP(c_Int_Onumber__class_Onumber__of(X21728),X21725)),X21726)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21728),X21727),X21726) != hAPP(c_Int_Onumber__class_Onumber__of(X21728),X21725)
| ~ class_Fields_Ofield__inverse__zero(X21728)
| ~ class_Int_Onumber(X21728) )
& ( X21726 != c_Groups_Ozero__class_Ozero(X21728)
| hAPP(c_Int_Onumber__class_Onumber__of(X21728),X21725) = c_Groups_Ozero__class_Ozero(X21728)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21728),X21727),X21726) != hAPP(c_Int_Onumber__class_Onumber__of(X21728),X21725)
| ~ class_Fields_Ofield__inverse__zero(X21728)
| ~ class_Int_Onumber(X21728) )
& ( X21726 = c_Groups_Ozero__class_Ozero(X21728)
| X21726 != c_Groups_Ozero__class_Ozero(X21728)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21728),X21727),X21726) = hAPP(c_Int_Onumber__class_Onumber__of(X21728),X21725)
| ~ class_Fields_Ofield__inverse__zero(X21728)
| ~ class_Int_Onumber(X21728) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(X21728),X21725) != c_Groups_Ozero__class_Ozero(X21728)
| X21726 != c_Groups_Ozero__class_Ozero(X21728)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21728),X21727),X21726) = hAPP(c_Int_Onumber__class_Onumber__of(X21728),X21725)
| ~ class_Fields_Ofield__inverse__zero(X21728)
| ~ class_Int_Onumber(X21728) )
& ( X21726 = c_Groups_Ozero__class_Ozero(X21728)
| X21727 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21728),hAPP(c_Int_Onumber__class_Onumber__of(X21728),X21725)),X21726)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21728),X21727),X21726) = hAPP(c_Int_Onumber__class_Onumber__of(X21728),X21725)
| ~ class_Fields_Ofield__inverse__zero(X21728)
| ~ class_Int_Onumber(X21728) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(X21728),X21725) != c_Groups_Ozero__class_Ozero(X21728)
| X21727 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21728),hAPP(c_Int_Onumber__class_Onumber__of(X21728),X21725)),X21726)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21728),X21727),X21726) = hAPP(c_Int_Onumber__class_Onumber__of(X21728),X21725)
| ~ class_Fields_Ofield__inverse__zero(X21728)
| ~ class_Int_Onumber(X21728) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of])])]) ).
fof(i_0_9613,plain,
! [X21729,X21730,X21731,X21732] :
( ( X21729 = c_Groups_Ozero__class_Ozero(X21732)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21732),hAPP(c_Int_Onumber__class_Onumber__of(X21732),X21731)),X21729) = X21730
| hAPP(c_Int_Onumber__class_Onumber__of(X21732),X21731) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21732),X21730),X21729)
| ~ class_Fields_Ofield__inverse__zero(X21732)
| ~ class_Int_Onumber(X21732) )
& ( X21729 != c_Groups_Ozero__class_Ozero(X21732)
| hAPP(c_Int_Onumber__class_Onumber__of(X21732),X21731) = c_Groups_Ozero__class_Ozero(X21732)
| hAPP(c_Int_Onumber__class_Onumber__of(X21732),X21731) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21732),X21730),X21729)
| ~ class_Fields_Ofield__inverse__zero(X21732)
| ~ class_Int_Onumber(X21732) )
& ( X21729 = c_Groups_Ozero__class_Ozero(X21732)
| X21729 != c_Groups_Ozero__class_Ozero(X21732)
| hAPP(c_Int_Onumber__class_Onumber__of(X21732),X21731) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21732),X21730),X21729)
| ~ class_Fields_Ofield__inverse__zero(X21732)
| ~ class_Int_Onumber(X21732) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(X21732),X21731) != c_Groups_Ozero__class_Ozero(X21732)
| X21729 != c_Groups_Ozero__class_Ozero(X21732)
| hAPP(c_Int_Onumber__class_Onumber__of(X21732),X21731) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21732),X21730),X21729)
| ~ class_Fields_Ofield__inverse__zero(X21732)
| ~ class_Int_Onumber(X21732) )
& ( X21729 = c_Groups_Ozero__class_Ozero(X21732)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21732),hAPP(c_Int_Onumber__class_Onumber__of(X21732),X21731)),X21729) != X21730
| hAPP(c_Int_Onumber__class_Onumber__of(X21732),X21731) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21732),X21730),X21729)
| ~ class_Fields_Ofield__inverse__zero(X21732)
| ~ class_Int_Onumber(X21732) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(X21732),X21731) != c_Groups_Ozero__class_Ozero(X21732)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21732),hAPP(c_Int_Onumber__class_Onumber__of(X21732),X21731)),X21729) != X21730
| hAPP(c_Int_Onumber__class_Onumber__of(X21732),X21731) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21732),X21730),X21729)
| ~ class_Fields_Ofield__inverse__zero(X21732)
| ~ class_Int_Onumber(X21732) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of])])]) ).
fof(i_0_9614,plain,
! [X19292,X19293] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19293),hAPP(c_Nat_OSuc,X19292)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19293),X19292))
| X19293 = hAPP(c_Nat_OSuc,X19292) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5886])]) ).
fof(i_0_9615,plain,
! [X19286,X19287] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19287),hAPP(c_Nat_OSuc,X19286)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19287),X19286))
| X19287 = hAPP(c_Nat_OSuc,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),hAPP(c_Nat_OSuc,X19286))) )
& ( X19287 != hAPP(c_Nat_OSuc,X19286)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19287),hAPP(c_Nat_OSuc,X19286))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__eq])])]) ).
fof(i_0_9616,plain,
! [X33839,X33840] :
( X33840 = c_List_Olist_ONil(X33839)
| hAPP(hAPP(c_List_Oappend(X33839),c_List_Obutlast(X33839,X33840)),hAPP(hAPP(c_List_Olist_OCons(X33839),c_List_Olast(X33839,X33840)),c_List_Olist_ONil(X33839))) = X33840 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__butlast__last__id])]) ).
cnf(i_0_9617,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_9618,plain,
! [X17596,X17597,X17598] :
( ~ hBOOL(hAPP(c_Com_OWT,X17598))
| ~ hBOOL(hAPP(c_Com_OWT,X17597))
| hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X17596,X17598,X17597))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_OIf])]) ).
fof(i_0_9619,plain,
! [X22317,X22318,X22319] : hAPP(hAPP(c_Product__Type_OPair(X22319,X22318),hAPP(c_Product__Type_Ofst(X22319,X22318),X22317)),hAPP(c_Product__Type_Osnd(X22319,X22318),X22317)) = X22317,
inference(variable_rename,[status(thm)],[fact_pair__collapse]) ).
fof(i_0_9620,plain,
! [X22320,X22321,X22322] : X22322 = hAPP(hAPP(c_Product__Type_OPair(X22321,X22320),hAPP(c_Product__Type_Ofst(X22321,X22320),X22322)),hAPP(c_Product__Type_Osnd(X22321,X22320),X22322)),
inference(variable_rename,[status(thm)],[fact_surjective__pairing]) ).
fof(i_0_9621,plain,
! [X26874,X26875] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26875),X26874))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26875),hAPP(c_Nat_OSuc,X26874)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X26874),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26875),X26874)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26875),X26874))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26875),hAPP(c_Nat_OSuc,X26874)) = 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_9622,plain,
! [X32739,X32740,X32741,X32742] :
( ~ class_Orderings_Olinorder(X32742)
| hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32741,X32742,X32740),X32739),c_List_Olist_ONil(X32741)) = hAPP(hAPP(c_List_Olist_OCons(X32741),X32739),c_List_Olist_ONil(X32741)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__key_Osimps_I1_J])]) ).
fof(i_0_9623,plain,
! [X26985,X26986,X26987,X26988,X26989] :
( ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26989,X26988),X26987),X26986),X26985) != X26987
| hAPP(X26987,X26986) = X26985 )
& ( hAPP(X26987,X26986) != X26985
| hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26989,X26988),X26987),X26986),X26985) = X26987 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__idem__iff])]) ).
fof(i_0_9624,plain,
! [X34403,X34404,X34405] :
( ~ hBOOL(hAPP(c_List_Odistinct(X34405),X34404))
| hBOOL(hAPP(c_List_Odistinct(X34405),c_List_OtakeWhile(X34405,X34403,X34404))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__takeWhile])]) ).
fof(i_0_9625,plain,
! [X32389,X32390,X32391] :
( ~ hBOOL(hAPP(c_List_Odistinct(X32391),X32390))
| hBOOL(hAPP(c_List_Odistinct(X32391),c_List_Osublist(X32391,X32390,X32389))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__sublistI])]) ).
fof(i_0_9626,plain,
! [X32026,X32027,X32028] :
( ~ hBOOL(hAPP(c_List_Odistinct(X32028),X32027))
| hBOOL(hAPP(c_List_Odistinct(X32028),c_List_Oremove1(X32028,X32026,X32027))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__remove1])]) ).
fof(i_0_9627,plain,
! [X32022,X32023,X32024,X32025] : c_List_Oremove1(X32025,X32024,c_List_Oremove1(X32025,X32023,X32022)) = c_List_Oremove1(X32025,X32023,c_List_Oremove1(X32025,X32024,X32022)),
inference(variable_rename,[status(thm)],[fact_remove1__commute]) ).
fof(i_0_9628,plain,
! [X30787,X30788,X30789,X30790,X30791,X30792] :
( ~ c_Finite__Set_Ofun__left__comm(X30792,X30791,X30790)
| hAPP(hAPP(X30790,X30789),hAPP(hAPP(X30790,X30788),X30787)) = hAPP(hAPP(X30790,X30788),hAPP(hAPP(X30790,X30789),X30787)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__left__comm])]) ).
fof(i_0_9629,plain,
! [X24704,X24705,X24706] :
( ~ class_Lattices_Olattice(X24706)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24706),X24705))
| ~ hBOOL(hAPP(hAPP(c_member(X24706),X24704),X24705))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24706),X24704),c_Big__Operators_Olattice__class_OSup__fin(X24706,X24705)) = X24704 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Sup__absorb])]) ).
fof(i_0_9630,plain,
! [X25279,X25280,X25281] :
( ~ class_Lattices_Olattice(X25281)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25281),X25280))
| ~ hBOOL(hAPP(hAPP(c_member(X25281),X25279),X25280))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25281),X25279),c_Big__Operators_Olattice__class_OInf__fin(X25281,X25280)) = X25279 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Inf__absorb])]) ).
fof(i_0_9631,plain,
! [X29757] : c_Wellfounded_OwfP(X29757,hAPP(c_COMBK(tc_fun(X29757,tc_HOL_Obool),X29757),hAPP(c_COMBK(tc_HOL_Obool,X29757),c_fFalse))),
inference(variable_rename,[status(thm)],[fact_wfP__empty]) ).
fof(i_0_9632,plain,
! [X33906,X33907,X33908,X33909] :
( ( ~ hBOOL(hAPP(X33909,X33908))
| hAPP(c_List_Ofilter(X33907,X33909),hAPP(hAPP(c_List_Olist_OCons(X33907),X33908),X33906)) = hAPP(hAPP(c_List_Olist_OCons(X33907),X33908),hAPP(c_List_Ofilter(X33907,X33909),X33906)) )
& ( hBOOL(hAPP(X33909,X33908))
| hAPP(c_List_Ofilter(X33907,X33909),hAPP(hAPP(c_List_Olist_OCons(X33907),X33908),X33906)) = hAPP(c_List_Ofilter(X33907,X33909),X33906) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5889])]) ).
fof(i_0_9633,plain,
! [X23268,X23269,X23270] :
( ~ class_Rings_Ocomm__semiring__1(X23270)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23270),X23269),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23270),X23269),X23268))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__triv__left])]) ).
fof(i_0_9634,plain,
! [X23265,X23266,X23267] :
( ~ class_Rings_Ocomm__semiring__1(X23267)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23267),X23266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23267),X23265),X23266))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__triv__right])]) ).
fof(i_0_9635,plain,
! [X23949,X23950,X23951] :
( ~ class_Lattices_Osemilattice__sup(X23951)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23951),X23950),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23951),X23950),X23949))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__ge1])]) ).
fof(i_0_9636,plain,
! [X23946,X23947,X23948] :
( ~ class_Lattices_Olattice(X23948)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23948),X23947),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23948),X23947),X23946))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I3_J])]) ).
fof(i_0_9637,plain,
! [X23955,X23956,X23957] :
( ~ class_Lattices_Osemilattice__sup(X23957)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23957),X23956),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23957),X23955),X23956))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__ge2])]) ).
fof(i_0_9638,plain,
! [X23952,X23953,X23954] :
( ~ class_Lattices_Olattice(X23954)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23954),X23953),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23954),X23952),X23953))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I4_J])]) ).
fof(i_0_9639,plain,
! [X22699,X22700,X22701] :
( ~ class_Orderings_Olinorder(X22701)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22701),X22700),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22701),X22700),X22699))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__maxI1])]) ).
fof(i_0_9640,plain,
! [X22696,X22697,X22698] :
( ~ class_Orderings_Olinorder(X22698)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22698),X22697),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22698),X22696),X22697))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__maxI2])]) ).
fof(i_0_9641,plain,
! [X29149,X29150,X29151] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X29151),X29150),hAPP(c_Set_OCollect(X29151),X29149)))
| hBOOL(hAPP(X29149,X29150)) )
& ( ~ hBOOL(hAPP(X29149,X29150))
| hBOOL(hAPP(hAPP(c_member(X29151),X29150),hAPP(c_Set_OCollect(X29151),X29149))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__Collect__eq])]) ).
fof(i_0_9642,plain,
! [X29146,X29147,X29148] :
( ~ hBOOL(hAPP(hAPP(c_member(X29148),X29147),hAPP(c_Set_OCollect(X29148),X29146)))
| hBOOL(hAPP(X29146,X29147)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_CollectD])]) ).
fof(i_0_9643,plain,
! [X29143,X29144,X29145] :
( ~ hBOOL(hAPP(hAPP(c_member(X29145),X29144),hAPP(c_Set_OCollect(X29145),X29143)))
| hBOOL(hAPP(X29143,X29144)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_CollectE])]) ).
fof(i_0_9644,plain,
! [X19019] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19019))
| hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,X19019)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X19019)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__nat__eq__nat__zadd1])]) ).
cnf(i_0_9645,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_9646,plain,
! [X32323,X32324,X32325,X32326] :
( ( X32326 != X32325
| c_List_Oremove1(X32324,X32326,hAPP(hAPP(c_List_Olist_OCons(X32324),X32325),X32323)) = X32323 )
& ( X32326 = X32325
| c_List_Oremove1(X32324,X32326,hAPP(hAPP(c_List_Olist_OCons(X32324),X32325),X32323)) = hAPP(hAPP(c_List_Olist_OCons(X32324),X32325),c_List_Oremove1(X32324,X32326,X32323)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remove1_Osimps_I2_J])]) ).
fof(i_0_9647,plain,
! [X23453,X23454,X23455,X23456] :
( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23456),X23454),X23455) != X23453
| X23454 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23456),X23453),X23455)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23456),X23455),X23454))
| X23455 = c_Groups_Ozero__class_Ozero(X23456)
| ~ class_Divides_Osemiring__div(X23456) )
& ( X23454 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23456),X23453),X23455)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X23456),X23454),X23455) = X23453
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23456),X23455),X23454))
| X23455 = c_Groups_Ozero__class_Ozero(X23456)
| ~ class_Divides_Osemiring__div(X23456) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__div__eq__mult])])]) ).
fof(i_0_9648,plain,
! [X18328,X18329] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18329),hAPP(c_Nat_OSuc,X18328)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18329),X18328))
| X18329 = X18328 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18329),X18328))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18329),hAPP(c_Nat_OSuc,X18328))) )
& ( X18329 != X18328
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18329),hAPP(c_Nat_OSuc,X18328))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq])])]) ).
fof(i_0_9649,plain,
! [X18324,X18325] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18325),hAPP(c_Nat_OSuc,X18324)))
| X18325 = X18324
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18325),X18324)) )
& ( X18325 != X18324
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18325),hAPP(c_Nat_OSuc,X18324)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18325),X18324)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5890])])]) ).
fof(i_0_9650,plain,
! [X18322,X18323] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18323),X18322))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18323),hAPP(c_Nat_OSuc,X18322)))
| X18322 = X18323 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5891])]) ).
fof(i_0_9651,plain,
! [X18313,X18314] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18314),hAPP(c_Nat_OSuc,X18313)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18314),X18313))
| X18314 = X18313 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5892])]) ).
cnf(i_0_9652,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_9653,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_9654,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_9655,plain,
! [X26260,X26261,X26262] : hAPP(c_Relation_OImage(X26262,X26262,c_Relation_OId__on(X26262,X26261)),X26260) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26262,tc_HOL_Obool)),X26261),X26260),
inference(variable_rename,[status(thm)],[fact_Image__Id__on]) ).
fof(i_0_9656,plain,
! [X24919,X24920,X24921,X24922] :
( ~ class_Lattices_Osemilattice__inf(X24922)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24922),X24921),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24922),X24920),X24919)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24922),X24920),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24922),X24921),X24919)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__left__commute])]) ).
fof(i_0_9657,plain,
! [X24911,X24912,X24913,X24914] :
( ~ class_Lattices_Osemilattice__inf(X24914)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24914),X24913),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24914),X24912),X24911)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24914),X24912),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24914),X24913),X24911)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oleft__commute])]) ).
fof(i_0_9658,plain,
! [X24915,X24916,X24917,X24918] :
( ~ class_Lattices_Olattice(X24918)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24918),X24917),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24918),X24916),X24915)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24918),X24916),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24918),X24917),X24915)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I3_J])]) ).
fof(i_0_9659,plain,
! [X24097,X24098,X24099,X24100] :
( ~ class_Lattices_Osemilattice__sup(X24100)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24100),X24099),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24100),X24098),X24097)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24100),X24098),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24100),X24099),X24097)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Oleft__commute])]) ).
fof(i_0_9660,plain,
! [X24089,X24090,X24091,X24092] :
( ~ class_Lattices_Osemilattice__sup(X24092)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24092),X24091),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24092),X24090),X24089)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24092),X24090),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24092),X24091),X24089)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__left__commute])]) ).
fof(i_0_9661,plain,
! [X24093,X24094,X24095,X24096] :
( ~ class_Lattices_Olattice(X24096)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24096),X24095),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24096),X24094),X24093)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24096),X24094),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24096),X24095),X24093)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I7_J])]) ).
fof(i_0_9662,plain,
! [X22640,X22641,X22642,X22643] :
( ~ class_Orderings_Olinorder(X22643)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22643),X22642),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22643),X22641),X22640)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22643),X22641),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22643),X22642),X22640)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__left__commute])]) ).
fof(i_0_9663,plain,
! [X22636,X22637,X22638,X22639] :
( ~ class_Orderings_Olinorder(X22639)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22639),X22638),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22639),X22637),X22636)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22639),X22637),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22639),X22638),X22636)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oleft__commute])]) ).
fof(i_0_9664,plain,
! [X22522,X22523,X22524,X22525] :
( ~ class_Orderings_Olinorder(X22525)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22525),X22524),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22525),X22523),X22522)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22525),X22523),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22525),X22524),X22522)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oleft__commute])]) ).
fof(i_0_9665,plain,
! [X22518,X22519,X22520,X22521] :
( ~ class_Orderings_Olinorder(X22521)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22521),X22520),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22521),X22519),X22518)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22521),X22519),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22521),X22520),X22518)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__left__commute])]) ).
fof(i_0_9666,plain,
! [X18713,X18714,X18715,X18716] :
( ~ class_Rings_Ocomm__semiring__1(X18716)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18716),X18715),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18716),X18714),X18713)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18716),X18714),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18716),X18715),X18713)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J])]) ).
fof(i_0_9667,plain,
! [X18187,X18188,X18189,X18190] :
( ~ class_Rings_Ocomm__semiring__1(X18190)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18190),X18189),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18190),X18188),X18187)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18190),X18188),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18190),X18189),X18187)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])]) ).
fof(i_0_9668,plain,
! [X18810,X18811,X18812] :
( ~ class_Groups_Ogroup__add(X18812)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18812),X18811),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18812),hAPP(c_Groups_Ouminus__class_Ouminus(X18812),X18811)),X18810)) = X18810 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__minus__cancel])]) ).
fof(i_0_9669,plain,
! [X19763,X19764,X19765] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19765),X19764) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19765),X19763)
| X19764 = X19763
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19765)) )
& ( X19764 != X19763
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19765),X19764) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19765),X19763)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19765)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel1])])]) ).
fof(i_0_9670,plain,
! [X19514,X19515] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19515),hAPP(c_Nat_OSuc,X19514)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19515),X19514)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19515),X19514))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19515),hAPP(c_Nat_OSuc,X19514))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le])]) ).
fof(i_0_9671,plain,
! [X20949] : 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),X20949)) = 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),X20949))),
inference(variable_rename,[status(thm)],[fact_one__div__nat__number__of]) ).
fof(i_0_9672,plain,
! [X18654,X18655,X18656,X18657,X18658] :
( ( X18654 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18656)
| hBOOL(hAPP(X18655,X18656))
| ~ hBOOL(hAPP(X18655,hAPP(c_Int_Onat,X18654))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18654),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(X18655,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X18655,hAPP(c_Int_Onat,X18654))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18657),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X18657 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk46_2(X18657,X18658))
| hBOOL(hAPP(X18658,hAPP(c_Int_Onat,X18657))) )
& ( ~ hBOOL(hAPP(X18658,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X18657 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk46_2(X18657,X18658))
| hBOOL(hAPP(X18658,hAPP(c_Int_Onat,X18657))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18657),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(X18658,esk46_2(X18657,X18658)))
| hBOOL(hAPP(X18658,hAPP(c_Int_Onat,X18657))) )
& ( ~ hBOOL(hAPP(X18658,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X18658,esk46_2(X18657,X18658)))
| hBOOL(hAPP(X18658,hAPP(c_Int_Onat,X18657))) ) ),
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_9673,plain,
! [X33343,X33344,X33345] :
( ~ hBOOL(hAPP(c_List_Odistinct(X33345),X33344))
| hBOOL(hAPP(c_List_Odistinct(X33345),hAPP(hAPP(c_List_Odrop(X33345),X33343),X33344))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__drop])]) ).
fof(i_0_9674,plain,
! [X32637,X32638,X32639] :
( ~ hBOOL(hAPP(c_List_Odistinct(X32639),X32638))
| hBOOL(hAPP(c_List_Odistinct(X32639),hAPP(hAPP(c_List_Otake(X32639),X32637),X32638))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__take])]) ).
fof(i_0_9675,plain,
! [X24540,X24541,X24542] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24542),X24541))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24542),hAPP(hAPP(c_Set_Oinsert(X24542),X24540),X24541))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite_OinsertI])]) ).
fof(i_0_9676,plain,
! [X26429,X26430] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26430,X26429)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X26430),hAPP(c_Nat_OSuc,X26429)),
inference(variable_rename,[status(thm)],[fact_image__Suc__atLeastAtMost]) ).
fof(i_0_9677,plain,
! [X31069,X31070,X31071] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31071,tc_fun(X31070,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X31071,tc_HOL_Obool))),X31069) = c_Orderings_Otop__class_Otop(tc_fun(X31070,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_INT__empty]) ).
fof(i_0_9678,plain,
! [X20920,X20921] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20921)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20920)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20921),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20920))),
inference(variable_rename,[status(thm)],[fact_minus__numeral__code_I6_J]) ).
fof(i_0_9679,plain,
! [X28228,X28229] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28229,tc_HOL_Obool)),X28228) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28229,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X28229,tc_HOL_Obool))),X28228),
inference(variable_rename,[status(thm)],[fact_Compl__eq__Diff__UNIV]) ).
fof(i_0_9680,plain,
! [X33795,X33796,X33797,X33798] : hAPP(hAPP(c_List_Omap(X33798,X33797),X33796),c_List_Obutlast(X33798,X33795)) = c_List_Obutlast(X33797,hAPP(hAPP(c_List_Omap(X33798,X33797),X33796),X33795)),
inference(variable_rename,[status(thm)],[fact_map__butlast]) ).
fof(i_0_9681,plain,
! [X25277,X25278] :
( ~ class_Orderings_Olinorder(X25278)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25278),X25277))
| X25277 = c_Orderings_Obot__class_Obot(tc_fun(X25278,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X25278),c_Big__Operators_Olinorder__class_OMin(X25278,X25277)),X25277)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__in])]) ).
fof(i_0_9682,plain,
! [X25275,X25276] :
( ~ class_Orderings_Olinorder(X25276)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25276),X25275))
| X25275 = c_Orderings_Obot__class_Obot(tc_fun(X25276,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X25276),c_Big__Operators_Olinorder__class_OMax(X25276,X25275)),X25275)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__in])]) ).
fof(i_0_9683,plain,
! [X19544,X19546,X19547,X19549] :
( ( ~ hBOOL(hAPP(X19544,esk56_1(X19544)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19546))
| hBOOL(hAPP(X19544,hAPP(c_Int_Onat,X19546))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk57_1(X19547)))
| hBOOL(hAPP(X19547,X19549)) )
& ( ~ hBOOL(hAPP(X19547,hAPP(c_Int_Onat,esk57_1(X19547))))
| hBOOL(hAPP(X19547,X19549)) ) ),
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_9684,plain,
! [X23644,X23645,X23646] : hBOOL(hAPP(hAPP(c_member(X23646),X23645),hAPP(hAPP(c_Set_Oinsert(X23646),X23645),X23644))),
inference(variable_rename,[status(thm)],[fact_insertI1]) ).
fof(i_0_9685,plain,
! [X20049,X20050] :
( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20050,X20049)) != X20049
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X20050),X20049) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20050,X20049)) = X20049
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X20050),X20049) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20050,X20049)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__Suc])]) ).
cnf(i_0_9686,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_9687,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_9688,plain,
! [X23091,X23092,X23093,X23094] : hAPP(hAPP(c_Set_Oinsert(X23094),X23093),hAPP(hAPP(c_Set_Oinsert(X23094),X23092),X23091)) = hAPP(hAPP(c_Set_Oinsert(X23094),X23092),hAPP(hAPP(c_Set_Oinsert(X23094),X23093),X23091)),
inference(variable_rename,[status(thm)],[fact_insert__commute]) ).
fof(i_0_9689,plain,
! [X24613,X24614,X24615,X24616] :
( ~ c_Finite__Set_Ofolding__one(X24616,X24615,X24614)
| hAPP(X24614,hAPP(hAPP(c_Set_Oinsert(X24616),X24613),c_Orderings_Obot__class_Obot(tc_fun(X24616,tc_HOL_Obool)))) = X24613 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Osingleton])]) ).
fof(i_0_9690,plain,
! [X20492,X20493] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20493),hAPP(c_Nat_OSuc,X20492)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20493),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X20492),
inference(variable_rename,[status(thm)],[fact_diff__Suc__eq__diff__pred]) ).
fof(i_0_9691,plain,
! [X18494,X18495] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk40_2(X18494,X18495)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18495),X18494)) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18495),esk40_2(X18494,X18495)) = X18494
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18495),X18494)) ) ),
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_9692,plain,
! [X30652,X30653,X30654,X30655] : hAPP(hAPP(c_Finite__Set_Ofold(X30655,X30654,X30653),X30652),c_Orderings_Obot__class_Obot(tc_fun(X30655,tc_HOL_Obool))) = X30652,
inference(variable_rename,[status(thm)],[fact_fold__empty]) ).
fof(i_0_9693,plain,
! [X33364,X33365,X33366] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33366)),hAPP(hAPP(c_List_Odrop(X33366),X33365),X33364)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33366)),X33364)),X33365),
inference(variable_rename,[status(thm)],[fact_length__drop]) ).
fof(i_0_9694,plain,
! [X32649,X32650,X32651] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32651)),hAPP(hAPP(c_List_Otake(X32651),X32650),X32649)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32651)),X32649)),X32650),
inference(variable_rename,[status(thm)],[fact_length__take]) ).
cnf(i_0_9695,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_9696,plain,
! [X28248] :
( ~ class_Nat_Osemiring__char__0(X28248)
| c_Fun_Oinj__on(tc_Nat_Onat,X28248,c_Nat_Osemiring__1__class_Oof__nat(X28248),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_9697,plain,
! [X17780,X17781,X17782,X17783] :
( hBOOL(hAPP(X17783,X17782))
| c_Natural_Oevaln(c_Com_Ocom_OWhile(X17783,X17781),X17782,X17780,X17782) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5899])]) ).
fof(i_0_9698,plain,
! [X33480,X33481,X33482] : hAPP(hAPP(c_List_Otake(X33482),X33481),hAPP(c_List_Otl(X33482),X33480)) = hAPP(c_List_Otl(X33482),hAPP(hAPP(c_List_Otake(X33482),hAPP(c_Nat_OSuc,X33481)),X33480)),
inference(variable_rename,[status(thm)],[fact_take__tl]) ).
fof(i_0_9699,plain,
! [X18491,X18492] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18492),X18491))
| X18491 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18492),esk39_2(X18491,X18492))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__Suc__add])])]) ).
fof(i_0_9700,plain,
! [X18388,X18389,X18391,X18392,X18393] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18389),X18388))
| X18388 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18389),esk38_2(X18388,X18389))) )
& ( X18391 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18392),X18393))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18392),X18391)) ) ),
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_9701,plain,
! [X26451,X26452,X26453] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X26453,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(X26453,X26452,X26451)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26453),X26452),X26451))
| ~ class_Orderings_Oorder(X26453) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26453),X26452),X26451))
| c_Orderings_Obot__class_Obot(tc_fun(X26453,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(X26453,X26452,X26451)
| ~ class_Orderings_Oorder(X26453) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5900])])]) ).
fof(i_0_9702,plain,
! [X25832,X25833,X25834] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X25834,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(X25834,X25833,X25832)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25834),X25833),X25832))
| ~ class_Orderings_Oorder(X25834) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25834),X25833),X25832))
| c_Orderings_Obot__class_Obot(tc_fun(X25834,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X25834,X25833,X25832)
| ~ class_Orderings_Oorder(X25834) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5901])])]) ).
fof(i_0_9703,plain,
! [X26448,X26449,X26450] :
( ( c_SetInterval_Oord__class_OatLeastAtMost(X26450,X26449,X26448) != c_Orderings_Obot__class_Obot(tc_fun(X26450,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26450),X26449),X26448))
| ~ class_Orderings_Oorder(X26450) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26450),X26449),X26448))
| c_SetInterval_Oord__class_OatLeastAtMost(X26450,X26449,X26448) = c_Orderings_Obot__class_Obot(tc_fun(X26450,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X26450) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5902])])]) ).
fof(i_0_9704,plain,
! [X25835,X25836,X25837] :
( ( c_SetInterval_Oord__class_OgreaterThanAtMost(X25837,X25836,X25835) != c_Orderings_Obot__class_Obot(tc_fun(X25837,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25837),X25836),X25835))
| ~ class_Orderings_Oorder(X25837) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25837),X25836),X25835))
| c_SetInterval_Oord__class_OgreaterThanAtMost(X25837,X25836,X25835) = c_Orderings_Obot__class_Obot(tc_fun(X25837,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X25837) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5903])])]) ).
fof(i_0_9705,plain,
! [X26923] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X26923) = 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),X26923))),
inference(variable_rename,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__functions_I1_J]) ).
fof(i_0_9706,plain,
! [X21611,X21612,X21613] :
( ~ class_Fields_Olinordered__field(X21613)
| X21612 = c_Groups_Ozero__class_Ozero(X21613)
| hAPP(c_Groups_Oabs__class_Oabs(X21613),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21613),X21611),X21612)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21613),hAPP(c_Groups_Oabs__class_Oabs(X21613),X21611)),hAPP(c_Groups_Oabs__class_Oabs(X21613),X21612)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__abs__divide])]) ).
fof(i_0_9707,plain,
! [X30037,X30038] :
( ( hBOOL(hAPP(hAPP(c_member(X30038),esk356_2(X30037,X30038)),X30037))
| hAPP(c_Finite__Set_Ocard(X30038),X30037) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30038),X30037)) )
& ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Finite__Set_Ocard(X30038),X30037) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30038),X30037)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oneutral])])])]) ).
fof(i_0_9708,plain,
! [X25046,X25047] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25047,tc_HOL_Obool)),X25046),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25047,tc_HOL_Obool)),X25046)) = c_Orderings_Obot__class_Obot(tc_fun(X25047,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__disjoint]) ).
fof(i_0_9709,plain,
! [X28226,X28227] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28227,tc_HOL_Obool)),X28226),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28227,tc_HOL_Obool)),X28226)) = c_Orderings_Otop__class_Otop(tc_fun(X28227,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__partition]) ).
fof(i_0_9710,plain,
! [X26574,X26575,X26576] : c_Fun_Oinj__on(X26576,tc_sum(X26576,X26575),c_Sum__Type_OInl(X26576,X26575),X26574),
inference(variable_rename,[status(thm)],[fact_inj__Inl]) ).
fof(i_0_9711,plain,
! [X26580,X26581,X26582] : c_Fun_Oinj__on(X26582,tc_sum(X26581,X26582),c_Sum__Type_OInr(X26582,X26581),X26580),
inference(variable_rename,[status(thm)],[fact_inj__Inr]) ).
fof(i_0_9712,plain,
! [X26571,X26572,X26573] : c_Fun_Oinj__on(X26573,X26572,X26571,c_Orderings_Obot__class_Obot(tc_fun(X26573,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_inj__on__empty]) ).
fof(i_0_9713,plain,
! [X23197,X23198] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23198),X23197))
| X23198 != X23197 )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23197),X23198))
| X23198 != X23197 )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23198),X23197))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23197),X23198))
| X23198 = X23197 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Oeq__iff])])]) ).
fof(i_0_9714,plain,
! [X23195,X23196] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23196),X23195))
| X23196 = X23195
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23196),X23195)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23195),X23196))
| X23196 = X23195
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23196),X23195)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23196),X23195))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23195),X23196))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23196),X23195)) )
& ( X23196 != X23195
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23196),X23195)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5904])])]) ).
fof(i_0_9715,plain,
! [X23193,X23194] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23194),X23193))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23194),X23193))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23193),X23194)) )
& ( X23194 != X23193
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23194),X23193))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23193),X23194)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23194),X23193))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23194),X23193))
| X23194 = X23193 )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23193),X23194))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23194),X23193))
| X23194 = X23193 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5905])])]) ).
fof(i_0_9716,plain,
! [X23191,X23192] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23192),X23191))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23192),X23191))
| X23192 = X23191 )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23191),X23192))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23192),X23191))
| X23192 = X23191 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5906])])]) ).
fof(i_0_9717,plain,
! [X23187,X23188] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23187),X23188))
| X23187 = X23188
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23188),X23187)) )
& ( X23187 != X23188
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23187),X23188))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23188),X23187)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Oantisym__conv])])]) ).
fof(i_0_9718,plain,
! [X23185,X23186] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23186),X23185))
| X23186 = X23185
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23186),X23185)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23185),X23186))
| X23186 = X23185
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23186),X23185)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5907])])]) ).
fof(i_0_9719,plain,
! [X23183,X23184] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23184),X23183))
| X23184 = X23183
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23184),X23183)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23183),X23184))
| X23184 = X23183
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23184),X23183)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5908])])]) ).
fof(i_0_9720,plain,
! [X23175,X23176] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23176),X23175))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23175),X23176))
| X23176 = X23175 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__antisym])]) ).
fof(i_0_9721,plain,
! [X23173,X23174] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23174),X23173))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23173),X23174))
| X23174 = X23173 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Oantisym])]) ).
fof(i_0_9722,plain,
! [X19063,X19064] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19064),X19063))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19063),X19064))
| X19064 = X19063 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__antisym])]) ).
fof(i_0_9723,plain,
! [X19742,X19743] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19743),X19742))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19742),X19743))
| X19743 = X19742 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__antisym])]) ).
cnf(i_0_9724,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_9725,plain,
! [X21087] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21087))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X21087) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X21087),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__minus1])]) ).
fof(i_0_9726,plain,
! [X17153,X17154] : X17154 = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17153),esk5_2(X17153,X17154)),esk6_2(X17153,X17154)),esk7_2(X17153,X17154)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_triple_Oexhaust])])]) ).
fof(i_0_9727,plain,
! [X25312,X25313,X25314] :
( ~ class_Orderings_Olinorder(X25314)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25314),X25313))
| X25313 = c_Orderings_Obot__class_Obot(tc_fun(X25314,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMin(X25314,hAPP(hAPP(c_Set_Oinsert(X25314),X25312),X25313)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25314),X25312),c_Big__Operators_Olinorder__class_OMin(X25314,X25313)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__insert])]) ).
fof(i_0_9728,plain,
! [X25315,X25316,X25317] :
( ~ class_Orderings_Olinorder(X25317)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25317),X25316))
| X25316 = c_Orderings_Obot__class_Obot(tc_fun(X25317,tc_HOL_Obool))
| c_Big__Operators_Olinorder__class_OMax(X25317,hAPP(hAPP(c_Set_Oinsert(X25317),X25315),X25316)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25317),X25315),c_Big__Operators_Olinorder__class_OMax(X25317,X25316)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__insert])]) ).
fof(i_0_9729,plain,
! [X25309,X25310,X25311] :
( ~ class_Lattices_Olattice(X25311)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25311),X25310))
| X25310 = c_Orderings_Obot__class_Obot(tc_fun(X25311,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OInf__fin(X25311,hAPP(hAPP(c_Set_Oinsert(X25311),X25309),X25310)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25311),X25309),c_Big__Operators_Olattice__class_OInf__fin(X25311,X25310)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oinsert__idem])]) ).
fof(i_0_9730,plain,
! [X25108,X25109,X25110] :
( ~ class_Lattices_Olattice(X25110)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25110),X25109))
| X25109 = c_Orderings_Obot__class_Obot(tc_fun(X25110,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OSup__fin(X25110,hAPP(hAPP(c_Set_Oinsert(X25110),X25108),X25109)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25110),X25108),c_Big__Operators_Olattice__class_OSup__fin(X25110,X25109)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oinsert__idem])]) ).
fof(i_0_9731,plain,
! [X23943,X23944,X23945] :
( ( X23944 = c_Orderings_Obot__class_Obot(tc_fun(X23945,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23945,tc_HOL_Obool)),X23944),X23943) != c_Orderings_Obot__class_Obot(tc_fun(X23945,tc_HOL_Obool)) )
& ( X23943 = c_Orderings_Obot__class_Obot(tc_fun(X23945,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23945,tc_HOL_Obool)),X23944),X23943) != c_Orderings_Obot__class_Obot(tc_fun(X23945,tc_HOL_Obool)) )
& ( X23944 != c_Orderings_Obot__class_Obot(tc_fun(X23945,tc_HOL_Obool))
| X23943 != c_Orderings_Obot__class_Obot(tc_fun(X23945,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23945,tc_HOL_Obool)),X23944),X23943) = c_Orderings_Obot__class_Obot(tc_fun(X23945,tc_HOL_Obool)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__empty])])]) ).
fof(i_0_9732,plain,
! [X33122,X33123,X33124] :
( ~ class_Groups_Omonoid__add(X33124)
| hAPP(c_List_Omonoid__add__class_Olistsum(X33124),hAPP(hAPP(c_List_Oappend(X33124),X33123),X33122)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X33124),hAPP(c_List_Omonoid__add__class_Olistsum(X33124),X33123)),hAPP(c_List_Omonoid__add__class_Olistsum(X33124),X33122)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__append])]) ).
fof(i_0_9733,plain,
! [X21503,X21504,X21505] :
( ~ class_Fields_Olinordered__field__inverse__zero(X21505)
| hAPP(c_Groups_Oabs__class_Oabs(X21505),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21505),X21504),X21503)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21505),hAPP(c_Groups_Oabs__class_Oabs(X21505),X21504)),hAPP(c_Groups_Oabs__class_Oabs(X21505),X21503)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__divide])]) ).
fof(i_0_9734,plain,
! [X20666,X20667,X20668] :
( ~ class_Rings_Olinordered__idom(X20668)
| hAPP(c_Groups_Oabs__class_Oabs(X20668),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20668),X20667),X20666)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20668),hAPP(c_Groups_Oabs__class_Oabs(X20668),X20667)),hAPP(c_Groups_Oabs__class_Oabs(X20668),X20666)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult])]) ).
fof(i_0_9735,plain,
! [X24982,X24983,X24984] :
( ~ class_Lattices_Oboolean__algebra(X24984)
| hAPP(c_Groups_Ouminus__class_Ouminus(X24984),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24984),X24983),X24982)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24984),hAPP(c_Groups_Ouminus__class_Ouminus(X24984),X24983)),hAPP(c_Groups_Ouminus__class_Ouminus(X24984),X24982)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__inf])]) ).
fof(i_0_9736,plain,
! [X24985,X24986,X24987] :
( ~ class_Lattices_Oboolean__algebra(X24987)
| hAPP(c_Groups_Ouminus__class_Ouminus(X24987),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24987),X24986),X24985)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24987),hAPP(c_Groups_Ouminus__class_Ouminus(X24987),X24986)),hAPP(c_Groups_Ouminus__class_Ouminus(X24987),X24985)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__sup])]) ).
fof(i_0_9737,plain,
! [X22716,X22717,X22718] :
( ~ class_Groups_Olinordered__ab__group__add(X22718)
| hAPP(c_Groups_Ouminus__class_Ouminus(X22718),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22718),X22717),X22716)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22718),hAPP(c_Groups_Ouminus__class_Ouminus(X22718),X22717)),hAPP(c_Groups_Ouminus__class_Ouminus(X22718),X22716)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__max__eq__min])]) ).
fof(i_0_9738,plain,
! [X22713,X22714,X22715] :
( ~ class_Groups_Olinordered__ab__group__add(X22715)
| hAPP(c_Groups_Ouminus__class_Ouminus(X22715),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22715),X22714),X22713)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22715),hAPP(c_Groups_Ouminus__class_Ouminus(X22715),X22714)),hAPP(c_Groups_Ouminus__class_Ouminus(X22715),X22713)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__min__eq__max])]) ).
fof(i_0_9739,plain,
! [X18804,X18805,X18806] :
( ~ class_Groups_Oab__group__add(X18806)
| hAPP(c_Groups_Ouminus__class_Ouminus(X18806),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18806),X18805),X18804)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18806),hAPP(c_Groups_Ouminus__class_Ouminus(X18806),X18805)),hAPP(c_Groups_Ouminus__class_Ouminus(X18806),X18804)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__distrib])]) ).
fof(i_0_9740,plain,
! [X18807,X18808,X18809] :
( ~ class_Groups_Ogroup__add(X18809)
| hAPP(c_Groups_Ouminus__class_Ouminus(X18809),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18809),X18808),X18807)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18809),hAPP(c_Groups_Ouminus__class_Ouminus(X18809),X18807)),hAPP(c_Groups_Ouminus__class_Ouminus(X18809),X18808)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add])]) ).
cnf(i_0_9741,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_9742,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_9743,plain,
! [X26637,X26638,X26639] : hAPP(c_Set_Oimage(X26638,tc_fun(X26638,tc_HOL_Obool),X26639),X26637) != hAPP(c_Set_OPow(X26638),X26637),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cantors__paradox])]) ).
fof(i_0_9744,plain,
! [X22381,X22382,X22383] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22381,tc_HOL_Obool)),X22383),X22382))
| X22383 != X22382 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22381,tc_HOL_Obool)),X22382),X22383))
| X22383 != X22382 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5910])])]) ).
fof(i_0_9745,plain,
! [X22371,X22372,X22373] :
( X22373 != X22372
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22371,tc_HOL_Obool)),X22373),X22372)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD1])]) ).
fof(i_0_9746,plain,
! [X22374,X22375,X22376] :
( X22376 != X22375
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22374,tc_HOL_Obool)),X22375),X22376)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD2])]) ).
fof(i_0_9747,plain,
! [X19283] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19283)),X19283)),
inference(variable_rename,[status(thm)],[i_0_5911]) ).
fof(i_0_9748,plain,
! [X20231,X20232] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20232))
| c_SMT_Oz3div(X20231,X20232) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20231),X20232) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20232))
| c_SMT_Oz3div(X20231,X20232) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20231),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20232))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5912])]) ).
fof(i_0_9749,plain,
! [X33752,X33753] :
( X33753 = c_List_Olist_ONil(X33752)
| hBOOL(hAPP(hAPP(c_member(X33752),c_List_Olast(X33752,X33753)),hAPP(c_List_Oset(X33752),X33753))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__in__set])]) ).
fof(i_0_9750,plain,
! [X19260,X19261,X19262] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19262)),X19261) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19262)),X19260)
| X19261 = X19260 )
& ( X19261 != X19260
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19262)),X19261) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19262)),X19260) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__cancel1])]) ).
fof(i_0_9751,plain,
! [X22099,X22100,X22101,X22102,X22103,X22104] :
( ( X22102 = X22100
| hAPP(hAPP(c_Product__Type_OPair(X22104,X22103),X22102),X22101) != hAPP(hAPP(c_Product__Type_OPair(X22104,X22103),X22100),X22099) )
& ( X22101 = X22099
| hAPP(hAPP(c_Product__Type_OPair(X22104,X22103),X22102),X22101) != hAPP(hAPP(c_Product__Type_OPair(X22104,X22103),X22100),X22099) )
& ( X22102 != X22100
| X22101 != X22099
| hAPP(hAPP(c_Product__Type_OPair(X22104,X22103),X22102),X22101) = hAPP(hAPP(c_Product__Type_OPair(X22104,X22103),X22100),X22099) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pair__eq])])]) ).
fof(i_0_9752,plain,
! [X22093,X22094,X22095,X22096,X22097,X22098] :
( ( X22096 = X22094
| hAPP(hAPP(c_Product__Type_OPair(X22098,X22097),X22096),X22095) != hAPP(hAPP(c_Product__Type_OPair(X22098,X22097),X22094),X22093) )
& ( X22095 = X22093
| hAPP(hAPP(c_Product__Type_OPair(X22098,X22097),X22096),X22095) != hAPP(hAPP(c_Product__Type_OPair(X22098,X22097),X22094),X22093) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pair__inject])])]) ).
fof(i_0_9753,plain,
! [X20588,X20589] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X20589,X20588) != 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),X20589),X20588) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X20589,X20588) = 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),X20589),X20588) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20588),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20589,X20588)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zminus1__eq__if])]) ).
fof(i_0_9754,plain,
! [X20339,X20340] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20340),X20339))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20340,X20339) = X20340 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20340),X20339))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20340,X20339) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20340),X20339),X20339) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5913])]) ).
fof(i_0_9755,plain,
! [X20337,X20338] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20338),X20337))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20338,X20337) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20338),X20337),X20337) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5914])]) ).
fof(i_0_9756,plain,
! [X22366,X22367] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22367,tc_HOL_Obool)),X22366),X22366)),
inference(variable_rename,[status(thm)],[fact_subset__refl]) ).
fof(i_0_9757,plain,
! [X26812,X26813] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26813),X26812)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X26813)),hAPP(c_Nat_OSuc,X26812)),
inference(variable_rename,[status(thm)],[fact_image__Suc__atLeastLessThan]) ).
fof(i_0_9758,plain,
! [X34269,X34270,X34271] : hAPP(c_List_Orev(X34271),hAPP(hAPP(c_List_Oappend(X34271),X34270),X34269)) = hAPP(hAPP(c_List_Oappend(X34271),hAPP(c_List_Orev(X34271),X34269)),hAPP(c_List_Orev(X34271),X34270)),
inference(variable_rename,[status(thm)],[fact_rev__append]) ).
fof(i_0_9759,plain,
! [X33412,X33413,X33414,X33415] :
( hAPP(c_List_Orotate1(X33415),c_List_Olist_ONil(X33415)) = c_List_Olist_ONil(X33415)
& hAPP(c_List_Orotate1(X33414),hAPP(hAPP(c_List_Olist_OCons(X33414),X33413),X33412)) = hAPP(hAPP(c_List_Oappend(X33414),X33412),hAPP(hAPP(c_List_Olist_OCons(X33414),X33413),c_List_Olist_ONil(X33414))) ),
inference(variable_rename,[status(thm)],[fact_rotate__simps]) ).
fof(i_0_9760,plain,
! [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(c_Nat_OSuc,X19290))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__SucI])]) ).
fof(i_0_9761,plain,
! [X19510,X19511] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19511),X19510))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19511),hAPP(c_Nat_OSuc,X19510))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__less__Suc])]) ).
fof(i_0_9762,plain,
! [X18320,X18321] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18321),X18320))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18321),hAPP(c_Nat_OSuc,X18320))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__SucI])]) ).
fof(i_0_9763,plain,
! [X32002,X32003] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X32003,X32002) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X32003),c_Groups_Oone__class_Oone(tc_Int_Oint)),X32002)),
inference(variable_rename,[status(thm)],[fact_greaterThanAtMost__upto]) ).
fof(i_0_9764,plain,
! [X23873,X23874] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23874),X23873),X23873) != c_Groups_Ozero__class_Ozero(X23874)
| X23873 = c_Groups_Ozero__class_Ozero(X23874)
| ~ hBOOL(hAPP(hAPP(c_member(X23874),X23873),c_Int_Oring__1__class_OInts(X23874)))
| ~ class_Int_Oring__char__0(X23874) )
& ( X23873 != c_Groups_Ozero__class_Ozero(X23874)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X23874),X23873),X23873) = c_Groups_Ozero__class_Ozero(X23874)
| ~ hBOOL(hAPP(hAPP(c_member(X23874),X23873),c_Int_Oring__1__class_OInts(X23874)))
| ~ class_Int_Oring__char__0(X23874) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__double__eq__0__iff])])]) ).
fof(i_0_9765,plain,
! [X21127] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21127))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),X21127) = 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_9766,plain,
! [X24942,X24943,X24944] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24944,tc_HOL_Obool)),X24943),X24942) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24944,tc_HOL_Obool)),X24942),X24943),
inference(variable_rename,[status(thm)],[fact_Int__commute]) ).
fof(i_0_9767,plain,
! [X24067,X24068,X24069] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24069,tc_HOL_Obool)),X24068),X24067) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24069,tc_HOL_Obool)),X24067),X24068),
inference(variable_rename,[status(thm)],[fact_Un__commute]) ).
fof(i_0_9768,plain,
! [X17110,X17111,X17112,X17113,X17114] : c_Hoare__Mirabelle_Otriple_Otriple__size(X17114,X17113,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17114),X17112),X17111),X17110)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_triple_Osize_I1_J]) ).
fof(i_0_9769,plain,
! [X18644] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk45_1(X18644)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18644)) )
& ( X18644 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk45_1(X18644))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18644)) ) ),
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_9770,plain,
! [X21573,X21574,X21575,X21576,X21577] :
( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21577),X21574),X21576) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21577),X21573),X21575)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21577),X21574),X21575) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21577),X21573),X21576)
| X21575 = c_Groups_Ozero__class_Ozero(X21577)
| X21576 = c_Groups_Ozero__class_Ozero(X21577)
| ~ class_Fields_Ofield(X21577) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21577),X21574),X21575) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21577),X21573),X21576)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21577),X21574),X21576) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21577),X21573),X21575)
| X21575 = c_Groups_Ozero__class_Ozero(X21577)
| X21576 = c_Groups_Ozero__class_Ozero(X21577)
| ~ class_Fields_Ofield(X21577) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__eq__eq])])]) ).
fof(i_0_9771,plain,
! [X20590,X20591] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20591),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20590),X20591)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20590),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20590,X20591)),
inference(variable_rename,[status(thm)],[fact_zmult__div__cancel]) ).
fof(i_0_9772,plain,
! [X20497,X20498] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20498),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20497),X20498)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20497),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20497,X20498)),
inference(variable_rename,[status(thm)],[fact_mult__div__cancel]) ).
fof(i_0_9773,plain,
! [X22794,X22795] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X22795),X22794) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X22795)),hAPP(c_Code__Numeral_Onat__of,X22794))),
inference(variable_rename,[status(thm)],[fact_minus__code__numeral__def]) ).
fof(i_0_9774,plain,
! [X22798,X22799] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X22799),X22798) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X22799)),hAPP(c_Code__Numeral_Onat__of,X22798))),
inference(variable_rename,[status(thm)],[fact_div__code__numeral__def]) ).
fof(i_0_9775,plain,
! [X22800,X22801] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),X22801),X22800) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X22801)),hAPP(c_Code__Numeral_Onat__of,X22800))),
inference(variable_rename,[status(thm)],[fact_times__code__numeral__def]) ).
fof(i_0_9776,plain,
! [X22796,X22797] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X22797),X22796) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X22797)),hAPP(c_Code__Numeral_Onat__of,X22796))),
inference(variable_rename,[status(thm)],[fact_plus__code__numeral__def]) ).
fof(i_0_9777,plain,
! [X20362,X20363] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20363),X20362))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20362),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20362),X20363)) = X20363 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__cancel])]) ).
fof(i_0_9778,plain,
! [X23531,X23532] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23532),X23531))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23532),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X23531),X23532)) = X23531 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__mult__div__cancel])]) ).
fof(i_0_9779,plain,
! [X20477,X20478] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20478),X20477))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20478),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20477),X20478)) = X20477 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse])]) ).
fof(i_0_9780,plain,
! [X21961,X21962,X21963,X21964] : c_Nat_Onat_Onat__case(X21964,X21963,X21962,hAPP(c_Nat_OSuc,X21961)) = hAPP(X21962,X21961),
inference(variable_rename,[status(thm)],[fact_nat__case__Suc]) ).
fof(i_0_9781,plain,
! [X32478,X32479,X32480] :
( ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X32478) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X32479),hAPP(c_List_Oset(tc_Nat_Onat),X32478)))
| X32479 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk448_1(X32480)),hAPP(c_List_Oset(tc_Nat_Onat),X32480)))
| hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X32480) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( esk448_1(X32480) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X32480) = 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_9782,plain,
! [X17570,X17571,X17572] :
( ~ hBOOL(hAPP(c_Com_OWT,X17572))
| hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X17571,X17570,X17572))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_OLocal])]) ).
fof(i_0_9783,plain,
! [X19178,X19179,X19180] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19180),X19179),X19178))
| X19179 = X19178
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19180),X19179),X19178))
| ~ class_Orderings_Olinorder(X19180) )
& ( X19179 != X19178
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19180),X19179),X19178))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19180),X19179),X19178))
| ~ class_Orderings_Olinorder(X19180) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5915])])]) ).
fof(i_0_9784,plain,
! [X19202,X19203,X19204] :
( ~ class_Orderings_Oorder(X19204)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19204),X19203),X19202))
| X19202 = X19203
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19204),X19203),X19202)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I11_J])]) ).
fof(i_0_9785,plain,
! [X19199,X19200,X19201] :
( ~ class_Orderings_Oorder(X19201)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19201),X19200),X19199))
| X19200 = X19199
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19201),X19200),X19199)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans])]) ).
fof(i_0_9786,plain,
! [X19196,X19197,X19198] :
( ~ class_Orderings_Oorder(X19198)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19198),X19197),X19196))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19198),X19197),X19196))
| X19197 = X19196 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq])]) ).
fof(i_0_9787,plain,
! [X19181,X19182,X19183] :
( ~ class_Orderings_Oorder(X19183)
| X19182 = X19181
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19183),X19182),X19181))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19183),X19182),X19181)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans])]) ).
fof(i_0_9788,plain,
! [X19169,X19170,X19171] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19171),X19170),X19169))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19171),X19170),X19169))
| X19170 = X19169
| ~ class_Orderings_Oorder(X19171) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19171),X19170),X19169))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19171),X19170),X19169))
| ~ class_Orderings_Oorder(X19171) )
& ( X19170 != X19169
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19171),X19170),X19169))
| ~ class_Orderings_Oorder(X19171) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less])])]) ).
fof(i_0_9789,plain,
! [X19163,X19164,X19165] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19165),X19164),X19163))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19165),X19164),X19163))
| ~ class_Orderings_Oorder(X19165) )
& ( X19164 != X19163
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19165),X19164),X19163))
| ~ class_Orderings_Oorder(X19165) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19165),X19164),X19163))
| X19164 = X19163
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19165),X19164),X19163))
| ~ class_Orderings_Oorder(X19165) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le])])]) ).
fof(i_0_9790,plain,
! [X19184,X19185,X19186] :
( ~ class_Orderings_Oorder(X19186)
| X19185 = X19184
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19186),X19184),X19185))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19186),X19184),X19185)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I12_J])]) ).
fof(i_0_9791,plain,
! [X20802,X20803,X20804] :
( ~ class_Int_Onumber__ring(X20804)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20804),hAPP(c_Int_Onumber__class_Onumber__of(X20804),X20803)),hAPP(c_Int_Onumber__class_Onumber__of(X20804),X20802)) = hAPP(c_Int_Onumber__class_Onumber__of(X20804),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20803),X20802)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__simps_I32_J])]) ).
fof(i_0_9792,plain,
! [X20791,X20792,X20793] :
( ~ class_Int_Onumber__ring(X20793)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20793),hAPP(c_Int_Onumber__class_Onumber__of(X20793),X20792)),hAPP(c_Int_Onumber__class_Onumber__of(X20793),X20791)) = hAPP(c_Int_Onumber__class_Onumber__of(X20793),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20792),X20791)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__eq])]) ).
fof(i_0_9793,plain,
! [X20811,X20812,X20813] :
( ~ class_Int_Onumber__ring(X20813)
| hAPP(c_Int_Onumber__class_Onumber__of(X20813),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20812),X20811)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20813),hAPP(c_Int_Onumber__class_Onumber__of(X20813),X20812)),hAPP(c_Int_Onumber__class_Onumber__of(X20813),X20811)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__diff])]) ).
fof(i_0_9794,plain,
! [X20799,X20800,X20801] :
( ~ class_Int_Onumber__ring(X20801)
| hAPP(c_Int_Onumber__class_Onumber__of(X20801),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20800),X20799)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20801),hAPP(c_Int_Onumber__class_Onumber__of(X20801),X20800)),hAPP(c_Int_Onumber__class_Onumber__of(X20801),X20799)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__mult])]) ).
fof(i_0_9795,plain,
! [X20794,X20795,X20796] :
( ~ class_Int_Onumber__ring(X20796)
| hAPP(c_Int_Onumber__class_Onumber__of(X20796),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20795),X20794)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20796),hAPP(c_Int_Onumber__class_Onumber__of(X20796),X20795)),hAPP(c_Int_Onumber__class_Onumber__of(X20796),X20794)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__add])]) ).
fof(i_0_9796,plain,
! [X20261,X20262,X20263] :
( ~ class_Rings_Oring__1(X20263)
| hAPP(c_Int_Oring__1__class_Oof__int(X20263),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20262),X20261)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20263),hAPP(c_Int_Oring__1__class_Oof__int(X20263),X20262)),hAPP(c_Int_Oring__1__class_Oof__int(X20263),X20261)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__diff])]) ).
fof(i_0_9797,plain,
! [X18699,X18700,X18701] :
( ~ class_Rings_Oring__1(X18701)
| hAPP(c_Int_Oring__1__class_Oof__int(X18701),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18700),X18699)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18701),hAPP(c_Int_Oring__1__class_Oof__int(X18701),X18700)),hAPP(c_Int_Oring__1__class_Oof__int(X18701),X18699)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__mult])]) ).
fof(i_0_9798,plain,
! [X18988,X18989,X18990] :
( ~ class_Rings_Oring__1(X18990)
| hAPP(c_Int_Oring__1__class_Oof__int(X18990),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18989),X18988)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18990),hAPP(c_Int_Oring__1__class_Oof__int(X18990),X18989)),hAPP(c_Int_Oring__1__class_Oof__int(X18990),X18988)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__add])]) ).
fof(i_0_9799,plain,
! [X18777,X18778,X18779] :
( ~ class_Rings_Osemiring__1(X18779)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18779),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18778),X18777)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18779),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18779),X18778)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18779),X18777)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__mult])]) ).
fof(i_0_9800,plain,
! [X18539,X18540,X18541] :
( ~ class_Rings_Osemiring__1(X18541)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18541),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18540),X18539)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18541),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18541),X18540)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18541),X18539)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__add])]) ).
fof(i_0_9801,plain,
! [X21814,X21815] :
( ~ class_Fields_Ofield__inverse__zero(X21815)
| ~ class_Int_Onumber__ring(X21815)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21815),hAPP(c_Int_Onumber__class_Onumber__of(X21815),c_Int_OMin)),X21814) = hAPP(c_Groups_Ouminus__class_Ouminus(X21815),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21815),c_Groups_Oone__class_Oone(X21815)),X21814)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus1__divide])]) ).
fof(i_0_9802,plain,
! [X27188,X27189,X27190] :
( ~ class_Groups_Ocomm__monoid__add(X27190)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27189,X27190),hAPP(c_COMBK(X27190,X27189),c_Groups_Ozero__class_Ozero(X27190))),X27188) = c_Groups_Ozero__class_Ozero(X27190) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__0])]) ).
fof(i_0_9803,plain,
! [X25597,X25598,X25599] :
( ~ class_Groups_Ocomm__monoid__mult(X25599)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25598,X25599),hAPP(c_COMBK(X25599,X25598),c_Groups_Oone__class_Oone(X25599))),X25597) = c_Groups_Oone__class_Oone(X25599) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__1])]) ).
fof(i_0_9804,plain,
! [X26921,X26922] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26922),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26921) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X26922,X26921),
inference(variable_rename,[status(thm)],[fact_atLeastPlusOneLessThan__greaterThanLessThan__int]) ).
fof(i_0_9805,plain,
! [X19190,X19191,X19192] :
( ~ class_Orderings_Opreorder(X19192)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19192),X19191),X19190))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19192),X19191),X19190)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__le])]) ).
fof(i_0_9806,plain,
! [X22068,X22069] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22069),X22068)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22069),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22068)),
inference(variable_rename,[status(thm)],[fact_negateSnd__eq]) ).
fof(i_0_9807,plain,
! [X21125,X21126] :
( ~ class_Int_Onumber__ring(X21126)
| ~ class_Rings_Olinordered__idom(X21126)
| hAPP(c_Groups_Oabs__class_Oabs(X21126),hAPP(hAPP(c_Power_Opower__class_Opower(X21126),hAPP(c_Int_Onumber__class_Onumber__of(X21126),c_Int_OMin)),X21125)) = c_Groups_Oone__class_Oone(X21126) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__power__minus__one])]) ).
fof(i_0_9808,plain,
! [X26817,X26818,X26819] :
( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26819,X26818),X26817) != c_Orderings_Obot__class_Obot(tc_fun(X26819,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26819),X26818),X26817))
| ~ class_Orderings_Oorder(X26819) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26819),X26818),X26817))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26819,X26818),X26817) = c_Orderings_Obot__class_Obot(tc_fun(X26819,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X26819) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5916])])]) ).
fof(i_0_9809,plain,
! [X26820,X26821,X26822] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X26822,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26822,X26821),X26820)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26822),X26821),X26820))
| ~ class_Orderings_Oorder(X26822) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26822),X26821),X26820))
| c_Orderings_Obot__class_Obot(tc_fun(X26822,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26822,X26821),X26820)
| ~ class_Orderings_Oorder(X26822) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5917])])]) ).
cnf(i_0_9810,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_9811,plain,
! [X24965,X24966] :
( ~ c_Nat__Transfer_Onat__set(X24966)
| ~ c_Nat__Transfer_Onat__set(X24965)
| c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X24966),X24965)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J])]) ).
fof(i_0_9812,plain,
! [X24463,X24464] :
( ~ c_Nat__Transfer_Onat__set(X24464)
| ~ c_Nat__Transfer_Onat__set(X24463)
| c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X24464),X24463)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J])]) ).
fof(i_0_9813,plain,
! [X19564,X19565,X19567,X19568,X19569] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19565),X19564))
| X19564 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19565),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk58_2(X19564,X19565))) )
& ( X19567 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19568),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19569))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19568),X19567)) ) ),
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_9814,plain,
! [X33892,X33893,X33894,X33895] : hAPP(c_List_Ofilter(X33895,X33894),c_List_Oremove1(X33895,X33893,X33892)) = c_List_Oremove1(X33895,X33893,hAPP(c_List_Ofilter(X33895,X33894),X33892)),
inference(variable_rename,[status(thm)],[fact_filter__remove1]) ).
fof(i_0_9815,plain,
! [X33835,X33836,X33837,X33838] :
( ( X33835 != c_List_Olist_ONil(X33838)
| hAPP(hAPP(c_List_Oappend(X33838),X33837),hAPP(hAPP(c_List_Olist_OCons(X33838),X33836),c_List_Olist_ONil(X33838))) != X33835 )
& ( c_List_Obutlast(X33838,X33835) = X33837
| hAPP(hAPP(c_List_Oappend(X33838),X33837),hAPP(hAPP(c_List_Olist_OCons(X33838),X33836),c_List_Olist_ONil(X33838))) != X33835 )
& ( c_List_Olast(X33838,X33835) = X33836
| hAPP(hAPP(c_List_Oappend(X33838),X33837),hAPP(hAPP(c_List_Olist_OCons(X33838),X33836),c_List_Olist_ONil(X33838))) != X33835 )
& ( X33835 = c_List_Olist_ONil(X33838)
| c_List_Obutlast(X33838,X33835) != X33837
| c_List_Olast(X33838,X33835) != X33836
| hAPP(hAPP(c_List_Oappend(X33838),X33837),hAPP(hAPP(c_List_Olist_OCons(X33838),X33836),c_List_Olist_ONil(X33838))) = X33835 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snoc__eq__iff__butlast])])]) ).
fof(i_0_9816,plain,
! [X19010] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19010),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| X19010 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,esk47_1(X19010)))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negD])])]) ).
fof(i_0_9817,plain,
! [X23861,X23862] :
( ~ class_Int_Onumber__ring(X23862)
| hBOOL(hAPP(hAPP(c_member(X23862),hAPP(c_Int_Onumber__class_Onumber__of(X23862),X23861)),c_Int_Oring__1__class_OInts(X23862))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__number__of])]) ).
fof(i_0_9818,plain,
! [X23871,X23872] :
( ~ class_Rings_Oring__1(X23872)
| hBOOL(hAPP(hAPP(c_member(X23872),hAPP(c_Int_Oring__1__class_Oof__int(X23872),X23871)),c_Int_Oring__1__class_OInts(X23872))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__of__int])]) ).
fof(i_0_9819,plain,
! [X23866,X23867] :
( ~ class_Rings_Oring__1(X23867)
| hBOOL(hAPP(hAPP(c_member(X23867),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X23867),X23866)),c_Int_Oring__1__class_OInts(X23867))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__of__nat])]) ).
fof(i_0_9820,plain,
! [X23817,X23818] :
( ~ class_Rings_Osemiring__1(X23818)
| hBOOL(hAPP(hAPP(c_member(X23818),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X23818),X23817)),c_Nat_Osemiring__1__class_ONats(X23818))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__in__Nats])]) ).
fof(i_0_9821,plain,
! [X20597] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20597))
| hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20597),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X20597 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__1])]) ).
fof(i_0_9822,plain,
! [X20596] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20596))
| X20596 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20596),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_9823,plain,
! [X28241] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X28241)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_nat__of]) ).
fof(i_0_9824,plain,
! [X20101,X20102,X20103] :
( ~ class_Divides_Osemiring__div(X20103)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20103),c_Divides_Odiv__class_Omod(X20103,X20102,X20101)),X20101) = c_Groups_Ozero__class_Ozero(X20103) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__trivial])]) ).
fof(i_0_9825,plain,
! [X21903] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X21903) = 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),X21903),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[fact_negDivAlg__minus1]) ).
fof(i_0_9826,plain,
! [X26494,X26495] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26495))
| c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X26495,X26494)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__function__closures])]) ).
fof(i_0_9827,plain,
! [X25416,X25417] :
( ~ class_Orderings_Olinorder(X25417)
| c_Big__Operators_Olattice_OInf__fin(X25417,c_Orderings_Oord__class_Omin(X25417),hAPP(hAPP(c_Set_Oinsert(X25417),X25416),c_Orderings_Obot__class_Obot(tc_fun(X25417,tc_HOL_Obool)))) = X25416 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Osingleton])]) ).
fof(i_0_9828,plain,
! [X25273,X25274] :
( ~ class_Orderings_Olinorder(X25274)
| c_Big__Operators_Olattice_OSup__fin(X25274,c_Orderings_Oord__class_Omax(X25274),hAPP(hAPP(c_Set_Oinsert(X25274),X25273),c_Orderings_Obot__class_Obot(tc_fun(X25274,tc_HOL_Obool)))) = X25273 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Osingleton])]) ).
fof(i_0_9829,plain,
! [X19667] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X19667))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19667)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19667))
| 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_int__one__le__iff__zero__less])]) ).
fof(i_0_9830,plain,
! [X24806,X24807] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24807,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X24807,tc_HOL_Obool))),X24806) = c_Orderings_Obot__class_Obot(tc_fun(X24807,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Int__empty__left]) ).
fof(i_0_9831,plain,
! [X28168,X28169] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28169,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X28169,tc_HOL_Obool))),X28168) = c_Orderings_Otop__class_Otop(tc_fun(X28169,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Un__UNIV__left]) ).
fof(i_0_9832,plain,
! [X23306,X23307] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23307,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X23307,tc_HOL_Obool))),X23306) = c_Orderings_Obot__class_Obot(tc_fun(X23307,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_empty__Diff]) ).
fof(i_0_9833,plain,
! [X28613,X28614,X28615] : hAPP(hAPP(c_Product__Type_OSigma(X28615,X28614),c_Orderings_Obot__class_Obot(tc_fun(X28615,tc_HOL_Obool))),X28613) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28615,X28614),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Sigma__empty1]) ).
fof(i_0_9834,plain,
! [X19040] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19040),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19040),X19040))),
inference(variable_rename,[status(thm)],[fact_le__square]) ).
fof(i_0_9835,plain,
! [X19316,X19317] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19317),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19317),X19316))),
inference(variable_rename,[status(thm)],[fact_le__add1]) ).
fof(i_0_9836,plain,
! [X19314,X19315] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19315),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19314),X19315))),
inference(variable_rename,[status(thm)],[fact_le__add2]) ).
fof(i_0_9837,plain,
! [X21721,X21722,X21723,X21724] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(X21724),X21722) = c_Groups_Ozero__class_Ozero(X21724)
| X21723 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21724),X21721),hAPP(c_Int_Onumber__class_Onumber__of(X21724),X21722))
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21724),X21723),hAPP(c_Int_Onumber__class_Onumber__of(X21724),X21722)) != X21721
| ~ class_Fields_Ofield__inverse__zero(X21724)
| ~ class_Int_Onumber(X21724) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(X21724),X21722) != c_Groups_Ozero__class_Ozero(X21724)
| X21721 = c_Groups_Ozero__class_Ozero(X21724)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21724),X21723),hAPP(c_Int_Onumber__class_Onumber__of(X21724),X21722)) != X21721
| ~ class_Fields_Ofield__inverse__zero(X21724)
| ~ class_Int_Onumber(X21724) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(X21724),X21722) = c_Groups_Ozero__class_Ozero(X21724)
| hAPP(c_Int_Onumber__class_Onumber__of(X21724),X21722) != c_Groups_Ozero__class_Ozero(X21724)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21724),X21723),hAPP(c_Int_Onumber__class_Onumber__of(X21724),X21722)) = X21721
| ~ class_Fields_Ofield__inverse__zero(X21724)
| ~ class_Int_Onumber(X21724) )
& ( X21721 != c_Groups_Ozero__class_Ozero(X21724)
| hAPP(c_Int_Onumber__class_Onumber__of(X21724),X21722) != c_Groups_Ozero__class_Ozero(X21724)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21724),X21723),hAPP(c_Int_Onumber__class_Onumber__of(X21724),X21722)) = X21721
| ~ class_Fields_Ofield__inverse__zero(X21724)
| ~ class_Int_Onumber(X21724) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(X21724),X21722) = c_Groups_Ozero__class_Ozero(X21724)
| X21723 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21724),X21721),hAPP(c_Int_Onumber__class_Onumber__of(X21724),X21722))
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21724),X21723),hAPP(c_Int_Onumber__class_Onumber__of(X21724),X21722)) = X21721
| ~ class_Fields_Ofield__inverse__zero(X21724)
| ~ class_Int_Onumber(X21724) )
& ( X21721 != c_Groups_Ozero__class_Ozero(X21724)
| X21723 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21724),X21721),hAPP(c_Int_Onumber__class_Onumber__of(X21724),X21722))
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21724),X21723),hAPP(c_Int_Onumber__class_Onumber__of(X21724),X21722)) = X21721
| ~ class_Fields_Ofield__inverse__zero(X21724)
| ~ class_Int_Onumber(X21724) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of1])])]) ).
fof(i_0_9838,plain,
! [X21733,X21734,X21735,X21736] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(X21736),X21733) = c_Groups_Ozero__class_Ozero(X21736)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21736),X21735),hAPP(c_Int_Onumber__class_Onumber__of(X21736),X21733)) = X21734
| X21735 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21736),X21734),hAPP(c_Int_Onumber__class_Onumber__of(X21736),X21733))
| ~ class_Fields_Ofield__inverse__zero(X21736)
| ~ class_Int_Onumber(X21736) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(X21736),X21733) != c_Groups_Ozero__class_Ozero(X21736)
| X21735 = c_Groups_Ozero__class_Ozero(X21736)
| X21735 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21736),X21734),hAPP(c_Int_Onumber__class_Onumber__of(X21736),X21733))
| ~ class_Fields_Ofield__inverse__zero(X21736)
| ~ class_Int_Onumber(X21736) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(X21736),X21733) = c_Groups_Ozero__class_Ozero(X21736)
| hAPP(c_Int_Onumber__class_Onumber__of(X21736),X21733) != c_Groups_Ozero__class_Ozero(X21736)
| X21735 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21736),X21734),hAPP(c_Int_Onumber__class_Onumber__of(X21736),X21733))
| ~ class_Fields_Ofield__inverse__zero(X21736)
| ~ class_Int_Onumber(X21736) )
& ( X21735 != c_Groups_Ozero__class_Ozero(X21736)
| hAPP(c_Int_Onumber__class_Onumber__of(X21736),X21733) != c_Groups_Ozero__class_Ozero(X21736)
| X21735 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21736),X21734),hAPP(c_Int_Onumber__class_Onumber__of(X21736),X21733))
| ~ class_Fields_Ofield__inverse__zero(X21736)
| ~ class_Int_Onumber(X21736) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(X21736),X21733) = c_Groups_Ozero__class_Ozero(X21736)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21736),X21735),hAPP(c_Int_Onumber__class_Onumber__of(X21736),X21733)) != X21734
| X21735 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21736),X21734),hAPP(c_Int_Onumber__class_Onumber__of(X21736),X21733))
| ~ class_Fields_Ofield__inverse__zero(X21736)
| ~ class_Int_Onumber(X21736) )
& ( X21735 != c_Groups_Ozero__class_Ozero(X21736)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21736),X21735),hAPP(c_Int_Onumber__class_Onumber__of(X21736),X21733)) != X21734
| X21735 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21736),X21734),hAPP(c_Int_Onumber__class_Onumber__of(X21736),X21733))
| ~ class_Fields_Ofield__inverse__zero(X21736)
| ~ class_Int_Onumber(X21736) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of1])])]) ).
fof(i_0_9839,plain,
! [X18271,X18272,X18273] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18272),X18273))
| hBOOL(hAPP(hAPP(X18271,X18272),X18273))
| X18273 = X18272
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18273),X18272)) )
& ( ~ hBOOL(hAPP(hAPP(X18271,X18272),X18273))
| hBOOL(hAPP(hAPP(X18271,X18272),X18273))
| X18273 = X18272
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18273),X18272)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18272),X18273))
| hBOOL(hAPP(hAPP(X18271,X18272),X18273))
| ~ hBOOL(hAPP(hAPP(X18271,X18272),X18273))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18273),X18272)) )
& ( ~ hBOOL(hAPP(hAPP(X18271,X18272),X18273))
| hBOOL(hAPP(hAPP(X18271,X18272),X18273))
| ~ hBOOL(hAPP(hAPP(X18271,X18272),X18273))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18273),X18272)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18272),X18273))
| hBOOL(hAPP(hAPP(X18271,X18272),X18273))
| X18273 = X18272
| ~ hBOOL(hAPP(hAPP(X18271,X18272),X18273)) )
& ( ~ hBOOL(hAPP(hAPP(X18271,X18272),X18273))
| hBOOL(hAPP(hAPP(X18271,X18272),X18273))
| X18273 = X18272
| ~ hBOOL(hAPP(hAPP(X18271,X18272),X18273)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18272),X18273))
| hBOOL(hAPP(hAPP(X18271,X18272),X18273))
| ~ hBOOL(hAPP(hAPP(X18271,X18272),X18273))
| ~ hBOOL(hAPP(hAPP(X18271,X18272),X18273)) )
& ( ~ hBOOL(hAPP(hAPP(X18271,X18272),X18273))
| hBOOL(hAPP(hAPP(X18271,X18272),X18273))
| ~ hBOOL(hAPP(hAPP(X18271,X18272),X18273))
| ~ hBOOL(hAPP(hAPP(X18271,X18272),X18273)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__cases])])]) ).
fof(i_0_9840,plain,
! [X25452] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X25452) = 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)),X25452)),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J]) ).
fof(i_0_9841,plain,
! [X33087,X33088,X33089,X33090,X33091,X33092] :
( hAPP(hAPP(c_List_Oappend(X33092),X33091),X33090) != X33089
| X33088 != hAPP(hAPP(c_List_Oappend(X33092),X33090),X33087)
| hAPP(hAPP(c_List_Oappend(X33092),X33091),X33088) = hAPP(hAPP(c_List_Oappend(X33092),X33089),X33087) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__eq__appendI])]) ).
fof(i_0_9842,plain,
! [X33043,X33044,X33045,X33046,X33047,X33048] :
( hAPP(hAPP(c_List_Olist_OCons(X33048),X33047),X33046) != X33045
| X33044 != hAPP(hAPP(c_List_Oappend(X33048),X33046),X33043)
| hAPP(hAPP(c_List_Olist_OCons(X33048),X33047),X33044) = hAPP(hAPP(c_List_Oappend(X33048),X33045),X33043) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__eq__appendI])]) ).
fof(i_0_9843,plain,
! [X18581,X18582,X18583] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18583),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18582),X18581)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18582),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18583),X18581)),
inference(variable_rename,[status(thm)],[fact_zadd__left__commute]) ).
fof(i_0_9844,plain,
! [X18079,X18080,X18081] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18081),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18080),X18079)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18080),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18081),X18079)),
inference(variable_rename,[status(thm)],[fact_nat__add__left__commute]) ).
fof(i_0_9845,plain,
! [X32000,X32001] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X32001),X32000) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X32001,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X32000),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(variable_rename,[status(thm)],[fact_atLeastLessThan__upto]) ).
fof(i_0_9846,plain,
! [X22719,X22720] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22720),X22719)),X22719) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X22720),X22719),
inference(variable_rename,[status(thm)],[fact_nat__minus__add__max]) ).
fof(i_0_9847,plain,
! [X22792] :
( ~ class_Orderings_Olinorder(X22792)
| c_Orderings_Oord_Omax(X22792,hAPP(c_COMBC(X22792,X22792,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X22792))) = c_Orderings_Oord__class_Omin(X22792) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dual__max])]) ).
fof(i_0_9848,plain,
! [X22727] :
( ~ class_Orderings_Olinorder(X22727)
| c_Orderings_Oord_Omin(X22727,hAPP(c_COMBC(X22727,X22727,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X22727))) = c_Orderings_Oord__class_Omax(X22727) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dual__min])]) ).
fof(i_0_9849,plain,
! [X33595] :
( ~ class_Groups_Omonoid__add(X33595)
| c_List_Omonoid__add__class_Olistsum(X33595) = c_List_Ofoldl(X33595,X33595,c_Groups_Oplus__class_Oplus(X33595),c_Groups_Ozero__class_Ozero(X33595)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__foldl])]) ).
fof(i_0_9850,plain,
! [X23740,X23741,X23742] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X23742),X23741),c_Option_Oset(X23742,X23740)))
| X23740 = hAPP(c_Option_Ooption_OSome(X23742),X23741) )
& ( X23740 != hAPP(c_Option_Ooption_OSome(X23742),X23741)
| hBOOL(hAPP(hAPP(c_member(X23742),X23741),c_Option_Oset(X23742,X23740))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_elem__set])]) ).
fof(i_0_9851,plain,
! [X20089,X20090,X20091] :
( ~ class_Divides_Osemiring__div(X20091)
| X20090 = c_Groups_Ozero__class_Ozero(X20091)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20091),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20091),X20090),X20089)),X20090) = X20089 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self1__is__id])]) ).
fof(i_0_9852,plain,
! [X20092,X20093,X20094] :
( ~ class_Divides_Osemiring__div(X20094)
| X20093 = c_Groups_Ozero__class_Ozero(X20094)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20094),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20094),X20092),X20093)),X20093) = X20092 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self2__is__id])]) ).
fof(i_0_9853,plain,
! [X20466,X20467,X20468] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20467),X20468) != X20466
| X20467 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20466),X20468)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20468),X20467)) )
& ( X20467 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20466),X20468)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20467),X20468) = X20466
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20468),X20467)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__diff__is__add])])]) ).
fof(i_0_9854,plain,
! [X19880,X19881] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X19881,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19880)) = 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),X19881),X19880)),
inference(variable_rename,[status(thm)],[fact_zmod__zminus2]) ).
fof(i_0_9855,plain,
! [X18124,X18125,X18126,X18127] : c_Com_Ovname_Ovname__rec(X18127,X18126,X18125,c_Com_Ovname_OGlb(X18124)) = hAPP(X18126,X18124),
inference(variable_rename,[status(thm)],[fact_vname_Orecs_I1_J]) ).
fof(i_0_9856,plain,
! [X17933,X17934,X17935,X17936] : c_Com_Ovname_Ovname__rec(X17936,X17935,X17934,c_Com_Ovname_OLoc(X17933)) = hAPP(X17934,X17933),
inference(variable_rename,[status(thm)],[fact_vname_Orecs_I2_J]) ).
fof(i_0_9857,plain,
! [X18128,X18129,X18130,X18131] : c_Com_Ovname_Ovname__case(X18131,X18130,X18129,c_Com_Ovname_OGlb(X18128)) = hAPP(X18130,X18128),
inference(variable_rename,[status(thm)],[fact_vname_Osimps_I5_J]) ).
fof(i_0_9858,plain,
! [X17929,X17930,X17931,X17932] : c_Com_Ovname_Ovname__case(X17932,X17931,X17930,c_Com_Ovname_OLoc(X17929)) = hAPP(X17930,X17929),
inference(variable_rename,[status(thm)],[fact_vname_Osimps_I6_J]) ).
fof(i_0_9859,plain,
! [X27803,X27804,X27805,X27806,X27807] :
( hAPP(X27807,X27806) != hAPP(c_Option_Ooption_OSome(X27805),X27804)
| hAPP(hAPP(c_Set_Oinsert(X27803),X27806),c_Map_Odom(X27803,X27805,X27807)) = c_Map_Odom(X27803,X27805,X27807) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__dom])]) ).
fof(i_0_9860,plain,
! [X29887,X29888] :
( ( c_Wellfounded_Oacyclic(X29888,X29887)
| ~ c_Nitpick_Owf_H(X29888,X29887) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X29888,X29888)),X29887))
| c_Nitpick_Ounknown(tc_HOL_Obool)
| ~ c_Nitpick_Owf_H(X29888,X29887) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X29888,X29888)),X29887))
| ~ c_Wellfounded_Oacyclic(X29888,X29887)
| c_Nitpick_Owf_H(X29888,X29887) )
& ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
| ~ c_Wellfounded_Oacyclic(X29888,X29887)
| c_Nitpick_Owf_H(X29888,X29887) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Owf_H__def])])]) ).
fof(i_0_9861,plain,
! [X29865,X29866] :
( ( ~ c_Wellfounded_Owf(X29866,X29865)
| c_Wellfounded_Oacyclic(X29866,X29865)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X29866,X29866)),X29865)) )
& ( ~ c_Wellfounded_Oacyclic(X29866,X29865)
| c_Wellfounded_Owf(X29866,X29865)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X29866,X29866)),X29865)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__iff__acyclic__if__finite])])]) ).
fof(i_0_9862,plain,
! [X29863,X29864] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X29864,X29864)),X29863))
| ~ c_Wellfounded_Oacyclic(X29864,X29863)
| c_Wellfounded_Owf(X29864,X29863) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__acyclic__wf])]) ).
fof(i_0_9863,plain,
! [X34208,X34209] : c_Fun_Oinj__on(tc_List_Olist(X34209),tc_List_Olist(X34209),c_List_Orev(X34209),X34208),
inference(variable_rename,[status(thm)],[fact_inj__on__rev]) ).
fof(i_0_9864,plain,
! [X33885,X33886,X33887] :
( ~ hBOOL(hAPP(c_List_Odistinct(X33887),X33886))
| hBOOL(hAPP(c_List_Odistinct(X33887),hAPP(c_List_Ofilter(X33887,X33885),X33886))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__filter])]) ).
fof(i_0_9865,plain,
! [X17115,X17116,X17117,X17118] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(X17118)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17118),X17117),X17116),X17115)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_triple_Osize_I2_J]) ).
fof(i_0_9866,plain,
! [X28354,X28355,X28356,X28357,X28358,X28359,X28360,X28363] :
( ( ~ hBOOL(hAPP(hAPP(X28354,X28356),X28357))
| hAPP(X28354,X28356) = hAPP(X28354,X28357)
| ~ c_Equiv__Relations_Oequivp(X28355,X28354) )
& ( hAPP(X28354,X28358) != hAPP(X28354,X28359)
| hBOOL(hAPP(hAPP(X28354,X28358),X28359))
| ~ c_Equiv__Relations_Oequivp(X28355,X28354) )
& ( ~ hBOOL(hAPP(hAPP(X28360,esk273_1(X28360)),esk274_1(X28360)))
| hAPP(X28360,esk273_1(X28360)) != hAPP(X28360,esk274_1(X28360))
| c_Equiv__Relations_Oequivp(X28363,X28360) )
& ( hBOOL(hAPP(hAPP(X28360,esk273_1(X28360)),esk274_1(X28360)))
| hAPP(X28360,esk273_1(X28360)) = hAPP(X28360,esk274_1(X28360))
| c_Equiv__Relations_Oequivp(X28363,X28360) ) ),
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_9867,plain,
! [X20294,X20295,X20296] :
( ~ class_Groups_Ogroup__add(X20296)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20296),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20296),X20295),X20294)),X20294) = X20295 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__cancel])]) ).
fof(i_0_9868,plain,
! [X20297,X20298,X20299] :
( ~ class_Groups_Ogroup__add(X20299)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20299),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20299),X20298),X20297)),X20297) = X20298 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__cancel])]) ).
fof(i_0_9869,plain,
! [X29793,X29794,X29795] : hAPP(c_Set_Oimage(tc_prod(X29795,X29794),X29795,c_Product__Type_Ofst(X29795,X29794)),X29793) = hAPP(c_Relation_ODomain(X29795,X29794),X29793),
inference(variable_rename,[status(thm)],[fact_fst__eq__Domain]) ).
fof(i_0_9870,plain,
! [X29702,X29703,X29704] : hAPP(c_Set_Oimage(tc_prod(X29704,X29703),X29703,c_Product__Type_Osnd(X29704,X29703)),X29702) = hAPP(c_Relation_ORange(X29704,X29703),X29702),
inference(variable_rename,[status(thm)],[fact_snd__eq__Range]) ).
fof(i_0_9871,plain,
! [X18248,X18249] :
( ( hBOOL(hAPP(X18249,hAPP(c_Nat_OSuc,esk35_2(X18248,X18249))))
| hBOOL(hAPP(X18249,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X18249,X18248)) )
& ( ~ hBOOL(hAPP(X18249,esk35_2(X18248,X18249)))
| hBOOL(hAPP(X18249,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X18249,X18248)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__induct])])])]) ).
fof(i_0_9872,plain,
! [X30482,X30483,X30484] :
( ( ~ c_Relation_Ototal__on(X30484,X30483,hAPP(c_Relation_Oconverse(X30484,X30484),X30482))
| c_Relation_Ototal__on(X30484,X30483,X30482) )
& ( ~ c_Relation_Ototal__on(X30484,X30483,X30482)
| c_Relation_Ototal__on(X30484,X30483,hAPP(c_Relation_Oconverse(X30484,X30484),X30482)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_total__on__converse])]) ).
fof(i_0_9873,plain,
! [X30350,X30351,X30352] :
( ( ~ c_Relation_Orefl__on(X30352,X30351,hAPP(c_Relation_Oconverse(X30352,X30352),X30350))
| c_Relation_Orefl__on(X30352,X30351,X30350) )
& ( ~ c_Relation_Orefl__on(X30352,X30351,X30350)
| c_Relation_Orefl__on(X30352,X30351,hAPP(c_Relation_Oconverse(X30352,X30352),X30350)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__converse])]) ).
fof(i_0_9874,plain,
! [X18142,X18143,X18144] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(X18144,X18143,X18142)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X18142)),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_9875,plain,
! [X25453] :
( ~ c_Nat__Transfer_Onat__set(X25453)
| hAPP(c_Finite__Set_Ocard(tc_Int_Oint),X25453) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X25453)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J])]) ).
fof(i_0_9876,plain,
! [X24474,X24475] :
( ~ c_Nat__Transfer_Onat__set(X24475)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24474),X24475))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24474)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J])]) ).
fof(i_0_9877,plain,
! [X24465,X24466,X24467] :
( ( ~ c_Nat__Transfer_Onat__set(X24465)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24466),X24465))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24466)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk124_1(X24467)),X24467))
| c_Nat__Transfer_Onat__set(X24467) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk124_1(X24467)))
| c_Nat__Transfer_Onat__set(X24467) ) ),
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_9878,plain,
! [X29044] : c_Relation_Orefl__on(X29044,c_Orderings_Obot__class_Obot(tc_fun(X29044,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29044,X29044),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_refl__on__empty]) ).
fof(i_0_9879,plain,
! [X27474,X27475] : hAPP(c_Finite__Set_Ocard(X27475),X27474) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27475,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X27475),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X27474),
inference(variable_rename,[status(thm)],[fact_card__eq__setsum]) ).
fof(i_0_9880,plain,
! [X21998,X21999,X22000,X22001] :
( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22001,X22000),X21999))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22001,X22000),X21998))
| X21999 = X21998 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__unique])]) ).
fof(i_0_9881,plain,
! [X26569,X26570] :
( ~ class_Groups_Oordered__ab__group__add(X26570)
| c_Fun_Oinj__on(X26570,X26570,c_Groups_Ouminus__class_Ouminus(X26570),X26569) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__uminus])]) ).
fof(i_0_9882,plain,
! [X22802,X22803] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X22803,X22802) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,X22803),hAPP(c_Code__Numeral_Onat__of,X22802))),
inference(variable_rename,[status(thm)],[fact_mod__code__numeral__def]) ).
fof(i_0_9883,plain,
! [X32527,X32528,X32529] : hAPP(hAPP(c_List_Onth(X32529),hAPP(hAPP(c_List_Olist_OCons(X32529),X32528),X32527)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X32528,
inference(variable_rename,[status(thm)],[fact_nth__Cons__0]) ).
fof(i_0_9884,plain,
! [X24319,X24320,X24321,X24322] :
( ( hAPP(c_Set_Oimage(X24322,X24321,X24320),X24319) != c_Orderings_Obot__class_Obot(tc_fun(X24321,tc_HOL_Obool))
| X24319 = c_Orderings_Obot__class_Obot(tc_fun(X24322,tc_HOL_Obool)) )
& ( X24319 != c_Orderings_Obot__class_Obot(tc_fun(X24322,tc_HOL_Obool))
| hAPP(c_Set_Oimage(X24322,X24321,X24320),X24319) = c_Orderings_Obot__class_Obot(tc_fun(X24321,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__is__empty])]) ).
fof(i_0_9885,plain,
! [X24326,X24327,X24328,X24329] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X24329,tc_HOL_Obool)) != hAPP(c_Set_Oimage(X24328,X24329,X24327),X24326)
| X24326 = c_Orderings_Obot__class_Obot(tc_fun(X24328,tc_HOL_Obool)) )
& ( X24326 != c_Orderings_Obot__class_Obot(tc_fun(X24328,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(X24329,tc_HOL_Obool)) = hAPP(c_Set_Oimage(X24328,X24329,X24327),X24326) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_empty__is__image])]) ).
fof(i_0_9886,plain,
! [X26577,X26578] : c_Fun_Oinj__on(X26578,tc_Option_Ooption(X26578),c_Option_Ooption_OSome(X26578),X26577),
inference(variable_rename,[status(thm)],[fact_inj__Some]) ).
fof(i_0_9887,plain,
! [X32813,X32814] : c_List_Olistrelp(X32814,X32813,c_List_Olist_ONil(X32814),c_List_Olist_ONil(X32814)),
inference(variable_rename,[status(thm)],[fact_listrelp_ONil]) ).
fof(i_0_9888,plain,
! [X32811,X32812] : c_List_Olistrelp(X32812,X32811,c_List_Olist_ONil(X32812),c_List_Olist_ONil(X32812)),
inference(variable_rename,[status(thm)],[fact_listrelp_Oequations_I1_J]) ).
fof(i_0_9889,plain,
! [X33454,X33455,X33456,X33457] :
( X33457 = c_List_Olist_ONil(X33456)
| hAPP(c_List_Ohd(X33455),hAPP(hAPP(c_List_Omap(X33456,X33455),X33454),X33457)) = hAPP(X33454,hAPP(c_List_Ohd(X33456),X33457)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__map])]) ).
fof(i_0_9890,plain,
! [X18212,X18213,X18214] :
( ~ class_Rings_Osemiring__1(X18214)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X18214,X18213,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18212) = X18212 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I1_J])]) ).
fof(i_0_9891,plain,
! [X26464,X26465,X26466,X26467] :
( ( X26466 = X26465
| c_SetInterval_Oord__class_OatLeastAtMost(X26467,X26466,X26465) != hAPP(hAPP(c_Set_Oinsert(X26467),X26464),c_Orderings_Obot__class_Obot(tc_fun(X26467,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(X26467) )
& ( X26465 = X26464
| c_SetInterval_Oord__class_OatLeastAtMost(X26467,X26466,X26465) != hAPP(hAPP(c_Set_Oinsert(X26467),X26464),c_Orderings_Obot__class_Obot(tc_fun(X26467,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(X26467) )
& ( X26466 != X26465
| X26465 != X26464
| c_SetInterval_Oord__class_OatLeastAtMost(X26467,X26466,X26465) = hAPP(hAPP(c_Set_Oinsert(X26467),X26464),c_Orderings_Obot__class_Obot(tc_fun(X26467,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(X26467) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton__iff])])]) ).
fof(i_0_9892,plain,
! [X29879,X29880,X29881,X29882,X29883] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(X29883),X29882),X29881),X29880),X29879) = c_New__DSequence_Opos__single(X29883,X29882),
inference(variable_rename,[status(thm)],[fact_pos__single__def]) ).
fof(i_0_9893,plain,
! [X29867,X29868,X29869,X29870,X29871] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(X29871),X29870),X29869),X29868),X29867) = c_New__DSequence_Oneg__single(X29871,X29870),
inference(variable_rename,[status(thm)],[fact_neg__single__def]) ).
fof(i_0_9894,plain,
! [X20950,X20951,X20952] :
( ~ class_Rings_Olinordered__idom(X20952)
| hAPP(c_Groups_Oabs__class_Oabs(X20952),hAPP(hAPP(c_Power_Opower__class_Opower(X20952),X20951),X20950)) = hAPP(hAPP(c_Power_Opower__class_Opower(X20952),hAPP(c_Groups_Oabs__class_Oabs(X20952),X20951)),X20950) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__abs])]) ).
fof(i_0_9895,plain,
! [X21496,X21497,X21498] :
( ~ class_Rings_Odivision__ring(X21498)
| hAPP(c_Groups_Ouminus__class_Ouminus(X21498),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21498),X21497),X21496)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21498),hAPP(c_Groups_Ouminus__class_Ouminus(X21498),X21497)),X21496) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__left])]) ).
fof(i_0_9896,plain,
! [X18679,X18680,X18681] :
( ~ class_Rings_Oring(X18681)
| hAPP(c_Groups_Ouminus__class_Ouminus(X18681),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18681),X18680),X18679)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18681),hAPP(c_Groups_Ouminus__class_Ouminus(X18681),X18680)),X18679) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__left])]) ).
fof(i_0_9897,plain,
! [X21061,X21062,X21063,X21064] : hAPP(hAPP(c_Power_Opower_Opower(X21064,X21063,X21062),X21061),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X21063,
inference(variable_rename,[status(thm)],[fact_power_Opower_Opower__0]) ).
fof(i_0_9898,plain,
! [X33984,X33985,X33986] : c_List_Omap__filter(X33986,X33985,X33984,c_List_Olist_ONil(X33986)) = c_List_Olist_ONil(X33985),
inference(variable_rename,[status(thm)],[fact_map__filter__simps_I2_J]) ).
cnf(i_0_9899,plain,
( X1 = X2
| c_Code__Numeral_OSuc__code__numeral(X1) != c_Code__Numeral_OSuc__code__numeral(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5919]) ).
fof(i_0_9900,plain,
! [X26454,X26455,X26456] :
( ~ class_Orderings_Oorder(X26456)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26456),X26455),X26454))
| c_SetInterval_Oord__class_OatLeastAtMost(X26456,X26454,X26455) = c_Orderings_Obot__class_Obot(tc_fun(X26456,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastatMost__empty])]) ).
fof(i_0_9901,plain,
! [X25829,X25830,X25831] :
( ~ class_Orderings_Oorder(X25831)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25831),X25830),X25829))
| c_SetInterval_Oord__class_OgreaterThanAtMost(X25831,X25829,X25830) = c_Orderings_Obot__class_Obot(tc_fun(X25831,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThanAtMost__empty])]) ).
fof(i_0_9902,plain,
! [X25685,X25686,X25687] :
( ~ class_Orderings_Oorder(X25687)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25687),X25686),X25685))
| c_SetInterval_Oord__class_OgreaterThanLessThan(X25687,X25685,X25686) = c_Orderings_Obot__class_Obot(tc_fun(X25687,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThanLessThan__empty])]) ).
fof(i_0_9903,plain,
! [X23388] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23388),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X23388 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X23388 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23388),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_9904,plain,
! [X33513,X33514,X33515] :
( X33515 = c_List_Olist_ONil(X33514)
| hAPP(c_List_Otl(X33514),hAPP(hAPP(c_List_Oappend(X33514),X33515),X33513)) = hAPP(hAPP(c_List_Oappend(X33514),hAPP(c_List_Otl(X33514),X33515)),X33513) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tl__append2])]) ).
fof(i_0_9905,plain,
! [X20069,X20070] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20070,X20069)),X20069) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zmod__zdiv__trivial]) ).
fof(i_0_9906,plain,
! [X22305,X22306,X22307,X22308] :
( hAPP(c_Product__Type_Ofst(X22308,X22307),X22306) != hAPP(c_Product__Type_Ofst(X22308,X22307),X22305)
| hAPP(c_Product__Type_Osnd(X22308,X22307),X22306) != hAPP(c_Product__Type_Osnd(X22308,X22307),X22305)
| X22306 = X22305 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_prod__eqI])]) ).
fof(i_0_9907,plain,
! [X22301,X22302,X22303,X22304] :
( ( hAPP(c_Product__Type_Ofst(X22302,X22301),X22304) = hAPP(c_Product__Type_Ofst(X22302,X22301),X22303)
| X22304 != X22303 )
& ( hAPP(c_Product__Type_Osnd(X22302,X22301),X22304) = hAPP(c_Product__Type_Osnd(X22302,X22301),X22303)
| X22304 != X22303 )
& ( hAPP(c_Product__Type_Ofst(X22302,X22301),X22304) != hAPP(c_Product__Type_Ofst(X22302,X22301),X22303)
| hAPP(c_Product__Type_Osnd(X22302,X22301),X22304) != hAPP(c_Product__Type_Osnd(X22302,X22301),X22303)
| X22304 = X22303 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pair__fst__snd__eq])])]) ).
fof(i_0_9908,plain,
! [X29395,X29396] : c_Fun_Oinj__on(X29396,X29396,c_Fun_Oid(X29396),X29395),
inference(variable_rename,[status(thm)],[fact_inj__on__id]) ).
fof(i_0_9909,plain,
! [X26602,X26603] : c_Fun_Oinj__on(X26603,X26603,c_COMBI(X26603),X26602),
inference(variable_rename,[status(thm)],[fact_inj__on__id2]) ).
fof(i_0_9910,plain,
! [X19372,X19373,X19374] :
( ~ class_Rings_Olinordered__idom(X19374)
| c_Groups_Osgn__class_Osgn(X19374,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19374),X19373),X19372)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19374),c_Groups_Osgn__class_Osgn(X19374,X19373)),c_Groups_Osgn__class_Osgn(X19374,X19372)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__times])]) ).
fof(i_0_9911,plain,
! [X34088,X34089,X34090] :
( ~ class_Orderings_Olinorder(X34090)
| ~ c_List_Olinorder__class_Osorted(X34090,X34089)
| ~ hBOOL(hAPP(c_List_Odistinct(X34090),X34089))
| ~ c_List_Olinorder__class_Osorted(X34090,X34088)
| ~ hBOOL(hAPP(c_List_Odistinct(X34090),X34088))
| hAPP(c_List_Oset(X34090),X34089) != hAPP(c_List_Oset(X34090),X34088)
| X34089 = X34088 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__distinct__set__unique])]) ).
fof(i_0_9912,plain,
! [X33376,X33377,X33378,X33379] : hAPP(hAPP(c_List_Odrop(X33379),hAPP(c_Nat_OSuc,X33378)),hAPP(hAPP(c_List_Olist_OCons(X33379),X33377),X33376)) = hAPP(hAPP(c_List_Odrop(X33379),X33378),X33376),
inference(variable_rename,[status(thm)],[fact_drop__Suc__Cons]) ).
cnf(i_0_9913,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_9914,plain,
! [X20671,X20672,X20673] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20673)
| hAPP(c_Groups_Oabs__class_Oabs(X20673),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20673),X20672),X20671)) = hAPP(c_Groups_Oabs__class_Oabs(X20673),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20673),X20671),X20672)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__commute])]) ).
cnf(i_0_9915,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_5920]) ).
fof(i_0_9916,plain,
! [X21958,X21959,X21960] : c_Nat_Onat_Onat__case(X21960,X21959,X21958,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X21959,
inference(variable_rename,[status(thm)],[fact_nat__case__0]) ).
fof(i_0_9917,plain,
! [X21940,X21941,X21942] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X21942,X21941,X21940,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X21941,
inference(variable_rename,[status(thm)],[fact_code__numeral_Orecs_I1_J]) ).
fof(i_0_9918,plain,
! [X21834,X21835,X21836] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X21836,X21835,X21834,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X21835,
inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I4_J]) ).
fof(i_0_9919,plain,
! [X19999,X20000] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20000)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19999)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20000),X19999)),
inference(variable_rename,[status(thm)],[fact_Divides_Otransfer__int__nat__functions_I1_J]) ).
fof(i_0_9920,plain,
! [X20898,X20899] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20899)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20898)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20899),X20898)),
inference(variable_rename,[status(thm)],[fact_times__numeral__code_I5_J]) ).
fof(i_0_9921,plain,
! [X19562,X19563] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19563)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19562)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19563),X19562)),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J]) ).
fof(i_0_9922,plain,
! [X19560,X19561] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19561)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19560)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19561),X19560)),
inference(variable_rename,[status(thm)],[fact_zmult__int]) ).
fof(i_0_9923,plain,
! [X20896,X20897] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20897)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20896)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20897),X20896)),
inference(variable_rename,[status(thm)],[fact_plus__numeral__code_I9_J]) ).
fof(i_0_9924,plain,
! [X18552,X18553] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18553)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18552)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18553),X18552)),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J]) ).
fof(i_0_9925,plain,
! [X18521,X18522] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18522)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18521)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18522),X18521)),
inference(variable_rename,[status(thm)],[fact_zadd__int]) ).
cnf(i_0_9926,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_5921]) ).
fof(i_0_9927,plain,
! [X18867,X18868] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18868),X18867)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X18868)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X18867)),
inference(variable_rename,[status(thm)],[fact_zminus__zadd__distrib]) ).
fof(i_0_9928,plain,
! [X19997,X19998] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19998),X19997)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19998)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19997)),
inference(variable_rename,[status(thm)],[fact_zdiv__int]) ).
fof(i_0_9929,plain,
! [X19558,X19559] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19559),X19558)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19559)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19558)),
inference(variable_rename,[status(thm)],[fact_int__mult]) ).
fof(i_0_9930,plain,
! [X28153,X28154] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28154,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X28154,tc_HOL_Obool))),X28153) = X28153,
inference(variable_rename,[status(thm)],[fact_Int__UNIV__left]) ).
fof(i_0_9931,plain,
! [X23939,X23940] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23940,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X23940,tc_HOL_Obool))),X23939) = X23939,
inference(variable_rename,[status(thm)],[fact_Un__empty__left]) ).
fof(i_0_9932,plain,
! [X18784,X18785] :
( ( X18785 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18785),X18784) != 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)),X18785)) )
& ( X18784 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18785),X18784) != 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)),X18785)) )
& ( X18785 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X18784 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18785),X18784) = 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)),X18785)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff])])]) ).
cnf(i_0_9933,plain,
c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
inference(split_conjunct,[status(thm)],[fact_succ__Pls]) ).
fof(i_0_9934,plain,
! [X28683,X28684,X28685] : hAPP(c_Finite__Set_Ofold1(X28685,X28684),hAPP(hAPP(c_Set_Oinsert(X28685),X28683),c_Orderings_Obot__class_Obot(tc_fun(X28685,tc_HOL_Obool)))) = X28683,
inference(variable_rename,[status(thm)],[fact_fold1__singleton]) ).
fof(i_0_9935,plain,
! [X32697,X32698,X32699,X32700] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32700)),hAPP(hAPP(c_List_Olist__update(X32700,X32699),X32698),X32697)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32700)),X32699),
inference(variable_rename,[status(thm)],[fact_length__list__update]) ).
fof(i_0_9936,plain,
! [X32152,X32153,X32154,X32155] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32155)),hAPP(hAPP(c_List_Omap(X32154,X32155),X32153),X32152)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32154)),X32152),
inference(variable_rename,[status(thm)],[fact_length__map]) ).
fof(i_0_9937,plain,
! [X17267,X17268] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X17268,X17267,X17268),
inference(variable_rename,[status(thm)],[fact_evaln_Oequations_I1_J]) ).
fof(i_0_9938,plain,
! [X17265,X17266] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X17266,X17265,X17266),
inference(variable_rename,[status(thm)],[fact_evaln_OSkip]) ).
fof(i_0_9939,plain,
! [X20640,X20641,X20642] :
( ~ class_Rings_Oring__1(X20642)
| hAPP(c_Int_Oring__1__class_Oof__int(X20642),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20641),X20640)) = hAPP(hAPP(c_Power_Opower__class_Opower(X20642),hAPP(c_Int_Oring__1__class_Oof__int(X20642),X20641)),X20640) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__power])]) ).
fof(i_0_9940,plain,
! [X20942,X20943,X20944] :
( ~ class_Rings_Osemiring__1(X20944)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20944),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20943),X20942)) = hAPP(hAPP(c_Power_Opower__class_Opower(X20944),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20944),X20943)),X20942) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__power])]) ).
fof(i_0_9941,plain,
! [X19349,X19350] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19350),X19349))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19350),X19349)) )
& ( X19350 != X19349
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19350),X19349)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19350),X19349))
| X19350 = X19349
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19350),X19349)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__le])])]) ).
fof(i_0_9942,plain,
! [X19306,X19307] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19307),X19306))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19307),X19306)) )
& ( X19307 != X19306
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19307),X19306)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19307),X19306))
| X19307 = X19306
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19307),X19306)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__le])])]) ).
fof(i_0_9943,plain,
! [X19304,X19305] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19305),X19304))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19305),X19304))
| X19305 = X19304 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19305),X19304))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19305),X19304)) )
& ( X19305 != X19304
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19305),X19304)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq])])]) ).
fof(i_0_9944,plain,
! [X19300,X19301] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19301),X19300))
| X19301 = X19300
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19301),X19300)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less])]) ).
fof(i_0_9945,plain,
! [X28686,X28687,X28688,X28689] :
( X28689 != c_Finite__Set_Ofold1(X28688,X28687)
| hAPP(X28689,hAPP(hAPP(c_Set_Oinsert(X28688),X28686),c_Orderings_Obot__class_Obot(tc_fun(X28688,tc_HOL_Obool)))) = X28686 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__singleton__def])]) ).
fof(i_0_9946,plain,
! [X33537,X33538] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33538)),hAPP(c_List_Otl(X33538),X33537)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33538)),X33537)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_length__tl]) ).
fof(i_0_9947,plain,
! [X29097,X29098,X29099,X29100,X29101] :
( ~ c_Finite__Set_Ofun__left__comm__idem(X29101,X29100,X29099)
| hAPP(hAPP(X29099,X29098),hAPP(hAPP(X29099,X29098),X29097)) = hAPP(hAPP(X29099,X29098),X29097) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__left__idem])]) ).
fof(i_0_9948,plain,
! [X24469] : 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)),X24469)),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J]) ).
fof(i_0_9949,plain,
! [X26427,X26428] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X26428,X26427))),
inference(variable_rename,[status(thm)],[fact_finite__atLeastAtMost__int]) ).
fof(i_0_9950,plain,
! [X25797,X25798] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X25798,X25797))),
inference(variable_rename,[status(thm)],[fact_finite__greaterThanAtMost__int]) ).
fof(i_0_9951,plain,
! [X25566,X25567] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X25567,X25566))),
inference(variable_rename,[status(thm)],[fact_finite__greaterThanLessThan__int]) ).
fof(i_0_9952,plain,
! [X26425,X26426] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26426,X26425))),
inference(variable_rename,[status(thm)],[fact_finite__atLeastAtMost]) ).
fof(i_0_9953,plain,
! [X25795,X25796] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X25796,X25795))),
inference(variable_rename,[status(thm)],[fact_finite__greaterThanAtMost]) ).
fof(i_0_9954,plain,
! [X25781,X25782] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X25782,X25781))),
inference(variable_rename,[status(thm)],[fact_finite__greaterThanLessThan]) ).
fof(i_0_9955,plain,
! [X18375] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18375),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X18375 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X18375 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18375),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_9956,plain,
! [X26579] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X26579),
inference(variable_rename,[status(thm)],[fact_inj__Suc]) ).
fof(i_0_9957,plain,
! [X19302,X19303] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),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_less__imp__le__nat])]) ).
fof(i_0_9958,plain,
! [X19298,X19299] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19299),X19298))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19299),X19298)) )
& ( X19299 != X19298
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19299),X19298)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le])])]) ).
fof(i_0_9959,plain,
! [X19296,X19297] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19297),X19296))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19297),X19296)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J])]) ).
fof(i_0_9960,plain,
! [X26814,X26815,X26816] :
( ~ class_Orderings_Oorder(X26816)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26816),X26815),X26814))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26816,X26814),X26815) = c_Orderings_Obot__class_Obot(tc_fun(X26816,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__empty])]) ).
fof(i_0_9961,plain,
! [X23671,X23672,X23673] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X23673),X23672),hAPP(c_fequal,X23671)))
| X23672 = X23671 )
& ( X23672 != X23671
| hBOOL(hAPP(hAPP(c_member(X23673),X23672),hAPP(c_fequal,X23671))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__mem])]) ).
fof(i_0_9962,plain,
! [X33748,X33749,X33750,X33751] :
( X33751 = c_List_Olist_ONil(X33750)
| c_List_Olast(X33749,hAPP(hAPP(c_List_Omap(X33750,X33749),X33748),X33751)) = hAPP(X33748,c_List_Olast(X33750,X33751)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__map])]) ).
fof(i_0_9963,plain,
! [X32779,X32780,X32781] : hAPP(c_Map_Omap__of(X32781,X32780,c_List_Olist_ONil(tc_prod(X32781,X32780))),X32779) = c_Option_Ooption_ONone(X32780),
inference(variable_rename,[status(thm)],[fact_map__of_Osimps_I1_J]) ).
fof(i_0_9964,plain,
! [X32776,X32777,X32778] : hAPP(c_Map_Omap__of(X32778,X32777,c_List_Olist_ONil(tc_prod(X32778,X32777))),X32776) = c_Option_Ooption_ONone(X32777),
inference(variable_rename,[status(thm)],[fact_map__of__Cons__code_I1_J]) ).
cnf(i_0_9965,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_5922]) ).
fof(i_0_9966,plain,
! [X18813,X18814,X18815] :
( ~ class_Groups_Ogroup__add(X18815)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18815),hAPP(c_Groups_Ouminus__class_Ouminus(X18815),X18814)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18815),X18814),X18813)) = X18813 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__cancel])]) ).
fof(i_0_9967,plain,
! [X23632,X23633,X23634,X23635,X23636] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X23633),X23634),X23632))
| X23632 != c_Orderings_Obot__class_Obot(tc_fun(X23633,tc_HOL_Obool)) )
& ( X23635 = c_Orderings_Obot__class_Obot(tc_fun(X23636,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X23636),esk106_2(X23635,X23636)),X23635)) ) ),
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_9968,plain,
! [X23638,X23639,X23641,X23642,X23643] :
( ( hBOOL(hAPP(hAPP(c_member(X23639),esk107_2(X23638,X23639)),X23638))
| X23638 = c_Orderings_Obot__class_Obot(tc_fun(X23639,tc_HOL_Obool)) )
& ( X23641 != c_Orderings_Obot__class_Obot(tc_fun(X23642,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X23642),X23643),X23641)) ) ),
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_5923])])])])]) ).
fof(i_0_9969,plain,
! [X32008,X32009,X32010] :
( hBOOL(hAPP(hAPP(c_member(X32010),X32009),hAPP(c_List_Oset(X32010),X32008)))
| c_List_Oremove1(X32010,X32009,X32008) = X32008 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5924])]) ).
cnf(i_0_9970,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_5925]) ).
fof(i_0_9971,plain,
! [X19701,X19702] :
( ~ class_Rings_Oring__1(X19702)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19701))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X19702),hAPP(c_Int_Onat,X19701)) = hAPP(c_Int_Oring__1__class_Oof__int(X19702),X19701) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__nat])]) ).
fof(i_0_9972,plain,
! [X19882,X19883] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19883),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19882)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19883,X19882)),
inference(variable_rename,[status(thm)],[fact_zmod__zminus__zminus]) ).
fof(i_0_9973,plain,
! [X20079,X20080] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20080),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20079)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20080,X20079)),
inference(variable_rename,[status(thm)],[fact_Divides_Otransfer__int__nat__functions_I2_J]) ).
fof(i_0_9974,plain,
! [X20077,X20078] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20078,X20077)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20078),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20077)),
inference(variable_rename,[status(thm)],[fact_zmod__int]) ).
fof(i_0_9975,plain,
! [X19012,X19013] :
( ( X19012 != c_Groups_Ozero__class_Ozero(X19013)
| c_Groups_Osgn__class_Osgn(X19013,X19012) = c_Groups_Ozero__class_Ozero(X19013)
| ~ class_Groups_Osgn__if(X19013) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19013),c_Groups_Ozero__class_Ozero(X19013)),X19012))
| c_Groups_Osgn__class_Osgn(X19013,X19012) = c_Groups_Oone__class_Oone(X19013)
| X19012 = c_Groups_Ozero__class_Ozero(X19013)
| ~ class_Groups_Osgn__if(X19013) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19013),c_Groups_Ozero__class_Ozero(X19013)),X19012))
| c_Groups_Osgn__class_Osgn(X19013,X19012) = hAPP(c_Groups_Ouminus__class_Ouminus(X19013),c_Groups_Oone__class_Oone(X19013))
| X19012 = c_Groups_Ozero__class_Ozero(X19013)
| ~ class_Groups_Osgn__if(X19013) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5926])])]) ).
fof(i_0_9976,plain,
! [X32441,X32442] :
( ~ class_Groups_Ocomm__monoid__add(X32442)
| ~ hBOOL(hAPP(c_List_Odistinct(X32442),X32441))
| hAPP(c_List_Omonoid__add__class_Olistsum(X32442),X32441) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32442,X32442),c_COMBI(X32442)),hAPP(c_List_Oset(X32442),X32441)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__listsum__conv__Setsum])]) ).
fof(i_0_9977,plain,
! [X20761,X20762,X20763] :
( ~ class_Rings_Ocomm__semiring__1(X20763)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20763),X20762),hAPP(hAPP(c_Power_Opower__class_Opower(X20763),X20762),X20761)) = hAPP(hAPP(c_Power_Opower__class_Opower(X20763),X20762),hAPP(c_Nat_OSuc,X20761)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J])]) ).
fof(i_0_9978,plain,
! [X20980,X20981,X20982] :
( ~ class_Power_Opower(X20982)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20982),X20981),hAPP(c_Nat_OSuc,X20980)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20982),X20981),hAPP(hAPP(c_Power_Opower__class_Opower(X20982),X20981),X20980)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc])]) ).
fof(i_0_9979,plain,
! [X20764,X20765,X20766] :
( ~ class_Rings_Ocomm__semiring__1(X20766)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20766),X20765),hAPP(c_Nat_OSuc,X20764)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20766),X20765),hAPP(hAPP(c_Power_Opower__class_Opower(X20766),X20765),X20764)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J])]) ).
fof(i_0_9980,plain,
! [X27665,X27666] :
( ~ class_Groups_Oordered__ab__group__add(X27666)
| hAPP(c_Set_Oimage(X27666,X27666,c_Groups_Ouminus__class_Ouminus(X27666)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X27666),X27665)) = hAPP(c_SetInterval_Oord__class_OlessThan(X27666),hAPP(c_Groups_Ouminus__class_Ouminus(X27666),X27665)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThan])]) ).
fof(i_0_9981,plain,
! [X27632,X27633] :
( ~ class_Groups_Oordered__ab__group__add(X27633)
| hAPP(c_Set_Oimage(X27633,X27633,c_Groups_Ouminus__class_Ouminus(X27633)),hAPP(c_SetInterval_Oord__class_OatLeast(X27633),X27632)) = hAPP(c_SetInterval_Oord__class_OatMost(X27633),hAPP(c_Groups_Ouminus__class_Ouminus(X27633),X27632)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeast])]) ).
fof(i_0_9982,plain,
! [X27667,X27668] :
( ~ class_Groups_Oordered__ab__group__add(X27668)
| hAPP(c_Set_Oimage(X27668,X27668,c_Groups_Ouminus__class_Ouminus(X27668)),hAPP(c_SetInterval_Oord__class_OlessThan(X27668),X27667)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X27668),hAPP(c_Groups_Ouminus__class_Ouminus(X27668),X27667)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__lessThan])]) ).
fof(i_0_9983,plain,
! [X27634,X27635] :
( ~ class_Groups_Oordered__ab__group__add(X27635)
| hAPP(c_Set_Oimage(X27635,X27635,c_Groups_Ouminus__class_Ouminus(X27635)),hAPP(c_SetInterval_Oord__class_OatMost(X27635),X27634)) = hAPP(c_SetInterval_Oord__class_OatLeast(X27635),hAPP(c_Groups_Ouminus__class_Ouminus(X27635),X27634)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__atMost])]) ).
cnf(i_0_9984,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_5927]) ).
cnf(i_0_9985,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_9986,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_5927]) ).
fof(i_0_9987,plain,
! [X19958,X19959] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19959))
| c_SMT_Oz3mod(X19958,X19959) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X19958,X19959) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19959))
| c_SMT_Oz3mod(X19958,X19959) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X19958,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19959)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5929])]) ).
fof(i_0_9988,plain,
! [X20704,X20705] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20705)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20705),c_Groups_Ozero__class_Ozero(X20705)),X20704))
| hAPP(c_Groups_Oabs__class_Oabs(X20705),X20704) = X20704 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonneg])]) ).
fof(i_0_9989,plain,
! [X20714,X20715] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20715)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20715),c_Groups_Ozero__class_Ozero(X20715)),X20714))
| hAPP(c_Groups_Oabs__class_Oabs(X20715),X20714) = X20714 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__pos])]) ).
fof(i_0_9990,plain,
! [X20843,X20844] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20844),X20843),c_Groups_Ozero__class_Ozero(X20844)))
| hAPP(c_Groups_Oabs__class_Oabs(X20844),X20843) = hAPP(c_Groups_Ouminus__class_Ouminus(X20844),X20843)
| ~ class_Groups_Oabs__if(X20844) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20844),X20843),c_Groups_Ozero__class_Ozero(X20844)))
| hAPP(c_Groups_Oabs__class_Oabs(X20844),X20843) = X20843
| ~ class_Groups_Oabs__if(X20844) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5930])])]) ).
fof(i_0_9991,plain,
! [X20839,X20840] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20840)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20840),X20839),c_Groups_Ozero__class_Ozero(X20840)))
| hAPP(c_Groups_Oabs__class_Oabs(X20840),X20839) = hAPP(c_Groups_Ouminus__class_Ouminus(X20840),X20839) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonpos])]) ).
fof(i_0_9992,plain,
! [X20845,X20846] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20846)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20846),X20845),c_Groups_Ozero__class_Ozero(X20846)))
| hAPP(c_Groups_Oabs__class_Oabs(X20846),X20845) = hAPP(c_Groups_Ouminus__class_Ouminus(X20846),X20845) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__neg])]) ).
fof(i_0_9993,plain,
! [X19016,X19017] :
( ( c_Groups_Osgn__class_Osgn(X19017,X19016) != hAPP(c_Groups_Ouminus__class_Ouminus(X19017),c_Groups_Oone__class_Oone(X19017))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19017),X19016),c_Groups_Ozero__class_Ozero(X19017)))
| ~ class_Rings_Olinordered__idom(X19017) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19017),X19016),c_Groups_Ozero__class_Ozero(X19017)))
| c_Groups_Osgn__class_Osgn(X19017,X19016) = hAPP(c_Groups_Ouminus__class_Ouminus(X19017),c_Groups_Oone__class_Oone(X19017))
| ~ class_Rings_Olinordered__idom(X19017) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__1__neg])])]) ).
fof(i_0_9994,plain,
! [X19014,X19015] :
( ~ class_Rings_Olinordered__idom(X19015)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19015),X19014),c_Groups_Ozero__class_Ozero(X19015)))
| c_Groups_Osgn__class_Osgn(X19015,X19014) = hAPP(c_Groups_Ouminus__class_Ouminus(X19015),c_Groups_Oone__class_Oone(X19015)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__neg])]) ).
fof(i_0_9995,plain,
! [X28347,X28348,X28349,X28350] :
( ~ c_Equiv__Relations_Oequivp(X28350,X28349)
| ~ hBOOL(hAPP(hAPP(X28349,X28348),X28347))
| hBOOL(hAPP(hAPP(X28349,X28347),X28348)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__symp])]) ).
fof(i_0_9996,plain,
! [X23337,X23338,X23339] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23339),X23338),X23337))
| c_Divides_Odiv__class_Omod(X23339,X23337,X23338) = c_Groups_Ozero__class_Ozero(X23339)
| ~ class_Divides_Osemiring__div(X23339) )
& ( c_Divides_Odiv__class_Omod(X23339,X23337,X23338) != c_Groups_Ozero__class_Ozero(X23339)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23339),X23338),X23337))
| ~ class_Divides_Osemiring__div(X23339) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__eq__mod__eq__0])])]) ).
fof(i_0_9997,plain,
! [X23334,X23335,X23336] :
( ~ class_Divides_Osemiring__div(X23336)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23336),X23335),X23334))
| c_Divides_Odiv__class_Omod(X23336,X23334,X23335) = c_Groups_Ozero__class_Ozero(X23336) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__imp__mod__0])]) ).
fof(i_0_9998,plain,
! [X33827,X33828] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33828)),c_List_Obutlast(X33828,X33827)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33828)),X33827)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_length__butlast]) ).
fof(i_0_9999,plain,
! [X19468] :
( ~ class_Rings_Olinordered__semidom(X19468)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19468),c_Groups_Oone__class_Oone(X19468)),c_Groups_Ozero__class_Ozero(X19468))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5931])]) ).
fof(i_0_10000,plain,
! [X18956] :
( ~ class_Rings_Olinordered__semidom(X18956)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18956),c_Groups_Oone__class_Oone(X18956)),c_Groups_Ozero__class_Ozero(X18956))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5932])]) ).
fof(i_0_10001,plain,
! [X20447,X20448] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20448),X20447))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20447),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20448),X20447)) = X20448 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5933])]) ).
fof(i_0_10002,plain,
! [X33670,X33671] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33671)),c_List_Olist_ONil(X33671)),c_List_Olists(X33671,X33670))),
inference(variable_rename,[status(thm)],[fact_lists_ONil]) ).
fof(i_0_10003,plain,
! [X19703,X19704] :
( ~ class_Rings_Olinordered__idom(X19704)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19704),c_Groups_Ozero__class_Ozero(X19704)),X19703))
| c_Groups_Osgn__class_Osgn(X19704,X19703) = c_Groups_Oone__class_Oone(X19704) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__pos])]) ).
fof(i_0_10004,plain,
! [X19028,X19029] :
( ( c_Groups_Osgn__class_Osgn(X19029,X19028) != c_Groups_Oone__class_Oone(X19029)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19029),c_Groups_Ozero__class_Ozero(X19029)),X19028))
| ~ class_Rings_Olinordered__idom(X19029) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19029),c_Groups_Ozero__class_Ozero(X19029)),X19028))
| c_Groups_Osgn__class_Osgn(X19029,X19028) = c_Groups_Oone__class_Oone(X19029)
| ~ class_Rings_Olinordered__idom(X19029) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__1__pos])])]) ).
fof(i_0_10005,plain,
! [X21601,X21602,X21603] :
( ~ class_Rings_Odivision__ring(X21603)
| X21602 = c_Groups_Ozero__class_Ozero(X21603)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21603),hAPP(c_Groups_Ouminus__class_Ouminus(X21603),X21601)),hAPP(c_Groups_Ouminus__class_Ouminus(X21603),X21602)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21603),X21601),X21602) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__minus__divide__divide])]) ).
fof(i_0_10006,plain,
! [X33700] : c_List_Olists(X33700,c_Orderings_Obot__class_Obot(tc_fun(X33700,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X33700)),c_List_Olist_ONil(X33700)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X33700),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_lists__empty]) ).
fof(i_0_10007,plain,
! [X32896] : c_List_Olistset(X32896,c_List_Olist_ONil(tc_fun(X32896,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X32896)),c_List_Olist_ONil(X32896)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X32896),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_listset_Osimps_I1_J]) ).
fof(i_0_10008,plain,
! [X29121,X29122,X29123] :
( ~ hBOOL(hAPP(X29123,X29122))
| hBOOL(hAPP(hAPP(c_member(X29121),X29122),hAPP(c_Set_OCollect(X29121),X29123))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_CollectI])]) ).
fof(i_0_10009,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_10010,plain,
! [X33346,X33347] :
( ( ~ hBOOL(hAPP(c_List_Odistinct(X33347),hAPP(c_List_Orotate1(X33347),X33346)))
| hBOOL(hAPP(c_List_Odistinct(X33347),X33346)) )
& ( ~ hBOOL(hAPP(c_List_Odistinct(X33347),X33346))
| hBOOL(hAPP(c_List_Odistinct(X33347),hAPP(c_List_Orotate1(X33347),X33346))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct1__rotate])]) ).
fof(i_0_10011,plain,
! [X24599,X24600] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X24600),c_Orderings_Obot__class_Obot(tc_fun(X24600,tc_HOL_Obool))),X24599) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X24600,tc_HOL_Obool),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_quotient__empty]) ).
fof(i_0_10012,plain,
! [X29439,X29440] : hAPP(c_Product__Type_Oprod_Oprod__case(X29440,X29439,tc_prod(X29440,X29439)),c_Product__Type_OPair(X29440,X29439)) = c_Fun_Oid(tc_prod(X29440,X29439)),
inference(variable_rename,[status(thm)],[fact_split__Pair]) ).
fof(i_0_10013,plain,
! [X24759,X24760,X24761] :
( ~ class_Lattices_Osemilattice__inf(X24761)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24761),X24760),X24759))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24761),X24760),X24759) = X24760 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__absorb1])]) ).
fof(i_0_10014,plain,
! [X24744,X24745,X24746] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24746),X24745),X24744))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24746),X24745),X24744) = X24745
| ~ class_Lattices_Osemilattice__inf(X24746) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24746),X24745),X24744) != X24745
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24746),X24745),X24744))
| ~ class_Lattices_Osemilattice__inf(X24746) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__inf])])]) ).
fof(i_0_10015,plain,
! [X24762,X24763,X24764] :
( ~ class_Lattices_Osemilattice__inf(X24764)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24764),X24763),X24762))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24764),X24762),X24763) = X24763 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__absorb2])]) ).
fof(i_0_10016,plain,
! [X23973,X23974,X23975] :
( ~ class_Lattices_Osemilattice__sup(X23975)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23975),X23974),X23973))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23975),X23974),X23973) = X23973 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__absorb2])]) ).
fof(i_0_10017,plain,
! [X23958,X23959,X23960] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23960),X23959),X23958))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23960),X23959),X23958) = X23958
| ~ class_Lattices_Osemilattice__sup(X23960) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23960),X23959),X23958) != X23958
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23960),X23959),X23958))
| ~ class_Lattices_Osemilattice__sup(X23960) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__sup])])]) ).
fof(i_0_10018,plain,
! [X23976,X23977,X23978] :
( ~ class_Lattices_Osemilattice__sup(X23978)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23978),X23977),X23976))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23978),X23976),X23977) = X23976 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__absorb1])]) ).
fof(i_0_10019,plain,
! [X22693,X22694,X22695] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22695),X22694),X22693))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22695),X22694),X22693) = X22693
| ~ class_Orderings_Olinorder(X22695) )
& ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X22695),X22694),X22693) != X22693
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22695),X22694),X22693))
| ~ class_Orderings_Olinorder(X22695) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__iff__sup])])]) ).
fof(i_0_10020,plain,
! [X22678,X22679,X22680] :
( ~ class_Orderings_Olinorder(X22680)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22680),X22679),X22678))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22680),X22679),X22678) = X22678 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__absorb2])]) ).
fof(i_0_10021,plain,
! [X22675,X22676,X22677] :
( ~ class_Orderings_Olinorder(X22677)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22677),X22676),X22675))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22677),X22675),X22676) = X22675 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__absorb1])]) ).
fof(i_0_10022,plain,
! [X22461,X22462,X22463] :
( ~ class_Orderings_Olinorder(X22463)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22463),X22462),X22461))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22463),X22462),X22461) = X22462 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__absorb1])]) ).
fof(i_0_10023,plain,
! [X22446,X22447,X22448] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22448),X22447),X22446))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22448),X22447),X22446) = X22447
| ~ class_Orderings_Olinorder(X22448) )
& ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X22448),X22447),X22446) != X22447
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22448),X22447),X22446))
| ~ class_Orderings_Olinorder(X22448) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__iff__inf])])]) ).
fof(i_0_10024,plain,
! [X22464,X22465,X22466] :
( ~ class_Orderings_Olinorder(X22466)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22466),X22465),X22464))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22466),X22464),X22465) = X22465 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__absorb2])]) ).
fof(i_0_10025,plain,
! [X31374,X31375] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31375)
| c_Complete__Lattice_OSup__class_OSup(X31375,hAPP(hAPP(c_Set_Oinsert(X31375),X31374),c_Orderings_Obot__class_Obot(tc_fun(X31375,tc_HOL_Obool)))) = X31374 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__singleton])]) ).
fof(i_0_10026,plain,
! [X31385,X31386] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31386)
| c_Complete__Lattice_OInf__class_OInf(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_Inf__singleton])]) ).
fof(i_0_10027,plain,
! [X25260,X25261] :
( ~ class_Orderings_Olinorder(X25261)
| c_Big__Operators_Olinorder__class_OMin(X25261,hAPP(hAPP(c_Set_Oinsert(X25261),X25260),c_Orderings_Obot__class_Obot(tc_fun(X25261,tc_HOL_Obool)))) = X25260 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Osingleton])]) ).
fof(i_0_10028,plain,
! [X25258,X25259] :
( ~ class_Orderings_Olinorder(X25259)
| c_Big__Operators_Olinorder__class_OMax(X25259,hAPP(hAPP(c_Set_Oinsert(X25259),X25258),c_Orderings_Obot__class_Obot(tc_fun(X25259,tc_HOL_Obool)))) = X25258 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Osingleton])]) ).
fof(i_0_10029,plain,
! [X25262,X25263] :
( ~ class_Lattices_Olattice(X25263)
| c_Big__Operators_Olattice__class_OInf__fin(X25263,hAPP(hAPP(c_Set_Oinsert(X25263),X25262),c_Orderings_Obot__class_Obot(tc_fun(X25263,tc_HOL_Obool)))) = X25262 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Osingleton])]) ).
fof(i_0_10030,plain,
! [X25067,X25068] :
( ~ class_Lattices_Olattice(X25068)
| c_Big__Operators_Olattice__class_OSup__fin(X25068,hAPP(hAPP(c_Set_Oinsert(X25068),X25067),c_Orderings_Obot__class_Obot(tc_fun(X25068,tc_HOL_Obool)))) = X25067 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Osingleton])]) ).
fof(i_0_10031,plain,
! [X19500,X19501] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19501)),X19500) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19500),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19501),X19500)),
inference(variable_rename,[status(thm)],[fact_mult__Suc]) ).
fof(i_0_10032,plain,
! [X23203,X23204,X23205,X23206] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X23206,X23205,X23204)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X23206,X23203,X23205)
| c_Hoare__Mirabelle_Ohoare__derivs(X23206,X23203,X23204) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_cut])]) ).
cnf(i_0_10033,plain,
( c_Int_OBit1(X1) = c_Int_OMin
| X1 != c_Int_OMin ),
inference(split_conjunct,[status(thm)],[i_0_5865]) ).
cnf(i_0_10034,plain,
( c_Int_OMin = c_Int_OBit1(X1)
| c_Int_OMin != X1 ),
inference(split_conjunct,[status(thm)],[i_0_5864]) ).
cnf(i_0_10035,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_10036,plain,
! [X20343,X20344] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20344),X20343)),X20344) = X20343,
inference(variable_rename,[status(thm)],[fact_diff__add__inverse]) ).
fof(i_0_10037,plain,
! [X20341,X20342] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20342),X20341)),X20341) = X20342,
inference(variable_rename,[status(thm)],[fact_diff__add__inverse2]) ).
fof(i_0_10038,plain,
! [X31309,X31310,X31311] :
( ~ c_Equiv__Relations_Oequiv(X31311,X31310,X31309)
| c_Complete__Lattice_OSup__class_OSup(tc_fun(X31311,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(X31311),X31310),X31309)) = X31310 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Union__quotient])]) ).
fof(i_0_10039,plain,
! [X21493,X21494,X21495] :
( ~ class_Fields_Ofield__inverse__zero(X21495)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21495),hAPP(c_Groups_Ouminus__class_Ouminus(X21495),X21494)),hAPP(c_Groups_Ouminus__class_Ouminus(X21495),X21493)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21495),X21494),X21493) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__divide])]) ).
fof(i_0_10040,plain,
! [X20669,X20670] :
( ~ class_Rings_Olinordered__idom(X20670)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20670),hAPP(c_Groups_Oabs__class_Oabs(X20670),X20669)),hAPP(c_Groups_Oabs__class_Oabs(X20670),X20669)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20670),X20669),X20669) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__self])]) ).
fof(i_0_10041,plain,
! [X18685,X18686,X18687] :
( ~ class_Rings_Oring(X18687)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18687),hAPP(c_Groups_Ouminus__class_Ouminus(X18687),X18686)),hAPP(c_Groups_Ouminus__class_Ouminus(X18687),X18685)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18687),X18686),X18685) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__minus])]) ).
fof(i_0_10042,plain,
! [X18682,X18683,X18684] :
( ~ class_Rings_Oring(X18684)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18684),hAPP(c_Groups_Ouminus__class_Ouminus(X18684),X18683)),X18682) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18684),X18683),hAPP(c_Groups_Ouminus__class_Ouminus(X18684),X18682)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__commute])]) ).
fof(i_0_10043,plain,
! [X29766,X29767,X29768,X29769,X29770] :
( ( ~ c_Wellfounded_OwfP(X29767,X29766)
| hBOOL(hAPP(c_Wellfounded_Oaccp(X29767,X29766),X29768)) )
& ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X29770,X29769),esk325_2(X29769,X29770)))
| c_Wellfounded_OwfP(X29770,X29769) ) ),
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_10044,plain,
! [X21604,X21605,X21606] :
( ~ class_Rings_Odivision__ring(X21606)
| X21605 = c_Groups_Ozero__class_Ozero(X21606)
| hAPP(c_Groups_Ouminus__class_Ouminus(X21606),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21606),X21604),X21605)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21606),X21604),hAPP(c_Groups_Ouminus__class_Ouminus(X21606),X21605)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__minus__divide__right])]) ).
cnf(i_0_10045,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_5934]) ).
fof(i_0_10046,plain,
! [X24601,X24602,X24603] :
( ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X24603,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(X24603),X24602),X24601)
| X24602 = c_Orderings_Obot__class_Obot(tc_fun(X24603,tc_HOL_Obool)) )
& ( X24602 != c_Orderings_Obot__class_Obot(tc_fun(X24603,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X24603,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X24603),X24602),X24601) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__is__empty2])]) ).
fof(i_0_10047,plain,
! [X24604,X24605,X24606] :
( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(X24606),X24605),X24604) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X24606,tc_HOL_Obool),tc_HOL_Obool))
| X24605 = c_Orderings_Obot__class_Obot(tc_fun(X24606,tc_HOL_Obool)) )
& ( X24605 != c_Orderings_Obot__class_Obot(tc_fun(X24606,tc_HOL_Obool))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(X24606),X24605),X24604) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X24606,tc_HOL_Obool),tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__is__empty])]) ).
fof(i_0_10048,plain,
! [X25861,X25862] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X25862,X25861)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25861),X25862)),
inference(variable_rename,[status(thm)],[fact_card__greaterThanAtMost__int]) ).
fof(i_0_10049,plain,
! [X18596,X18597,X18598] :
( ( X18597 = X18596
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18598),X18597),X18596))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18598),X18596),X18597))
| ~ class_Orderings_Olinorder(X18598) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18598),X18597),X18596))
| X18597 != X18596
| ~ class_Orderings_Olinorder(X18598) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18598),X18596),X18597))
| X18597 != X18596
| ~ class_Orderings_Olinorder(X18598) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff])])]) ).
fof(i_0_10050,plain,
! [X18608,X18609,X18610] :
( ~ class_Orderings_Olinorder(X18610)
| X18609 = X18608
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18610),X18609),X18608))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18610),X18608),X18609)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5935])]) ).
fof(i_0_10051,plain,
! [X18605,X18606,X18607] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18607),X18605),X18606))
| X18605 = X18606
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18607),X18606),X18605))
| ~ class_Orderings_Olinorder(X18607) )
& ( X18605 != X18606
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18607),X18605),X18606))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18607),X18606),X18605))
| ~ class_Orderings_Olinorder(X18607) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5936])])]) ).
fof(i_0_10052,plain,
! [X18602,X18603,X18604] :
( ~ class_Orderings_Olinorder(X18604)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18604),X18603),X18602))
| X18603 = X18602
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18604),X18602),X18603)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__less__linear])]) ).
fof(i_0_10053,plain,
! [X18556,X18557,X18558] :
( ~ class_Orderings_Olinorder(X18558)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18558),X18557),X18556))
| X18557 = X18556
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18558),X18556),X18557)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5937])]) ).
fof(i_0_10054,plain,
! [X18439,X18440,X18441] :
( ~ class_Rings_Olinordered__idom(X18441)
| X18440 = X18439
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18441),X18440),X18439))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18441),X18439),X18440)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5938])]) ).
fof(i_0_10055,plain,
! [X19794,X19795,X19796] :
( ~ class_Divides_Osemiring__div(X19796)
| c_Divides_Odiv__class_Omod(X19796,c_Divides_Odiv__class_Omod(X19796,X19795,X19794),X19794) = c_Divides_Odiv__class_Omod(X19796,X19795,X19794) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mod__trivial])]) ).
fof(i_0_10056,plain,
! [X24804,X24805] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24805,tc_HOL_Obool)),X24804),c_Orderings_Obot__class_Obot(tc_fun(X24805,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X24805,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Int__empty__right]) ).
fof(i_0_10057,plain,
! [X28166,X28167] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28167,tc_HOL_Obool)),X28166),c_Orderings_Otop__class_Otop(tc_fun(X28167,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X28167,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Un__UNIV__right]) ).
fof(i_0_10058,plain,
! [X28201,X28202] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28202,tc_HOL_Obool)),X28201),c_Orderings_Otop__class_Otop(tc_fun(X28202,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X28202,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Diff__UNIV]) ).
fof(i_0_10059,plain,
! [X29777,X29778] : hAPP(c_Relation_ODomain(X29778,X29777),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29778,X29777),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X29778,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Domain__empty]) ).
fof(i_0_10060,plain,
! [X29690,X29691] : hAPP(c_Relation_ORange(X29691,X29690),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29691,X29690),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X29690,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Range__empty]) ).
fof(i_0_10061,plain,
! [X26936,X26937,X26938,X26939] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26939,X26938),X26937),X26936),hAPP(X26937,X26936)) = X26937,
inference(variable_rename,[status(thm)],[fact_fun__upd__triv]) ).
fof(i_0_10062,plain,
! [X22292,X22293,X22294,X22295] : hAPP(c_Product__Type_Ofst(X22295,X22294),hAPP(hAPP(c_Product__Type_OPair(X22295,X22294),X22293),X22292)) = X22293,
inference(variable_rename,[status(thm)],[fact_fst__conv]) ).
fof(i_0_10063,plain,
! [X22185,X22186,X22187,X22188] : hAPP(c_Product__Type_Osnd(X22188,X22187),hAPP(hAPP(c_Product__Type_OPair(X22188,X22187),X22186),X22185)) = X22185,
inference(variable_rename,[status(thm)],[fact_snd__conv]) ).
cnf(i_0_10064,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_10065,plain,
! [X19318,X19319,X19321,X19322,X19323] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19319),X19318))
| X19318 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19319),esk49_2(X19318,X19319)) )
& ( X19321 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19322),X19323)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19322),X19321)) ) ),
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_10066,plain,
! [X23612,X23613,X23614] :
( ~ hBOOL(hAPP(hAPP(c_member(X23614),X23613),X23612))
| hAPP(hAPP(c_Set_Oinsert(X23614),X23613),X23612) = X23612 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__absorb])]) ).
fof(i_0_10067,plain,
! [X23482,X23483] : c_Set_Othe__elem(X23483,hAPP(hAPP(c_Set_Oinsert(X23483),X23482),c_Orderings_Obot__class_Obot(tc_fun(X23483,tc_HOL_Obool)))) = X23482,
inference(variable_rename,[status(thm)],[fact_the__elem__eq]) ).
fof(i_0_10068,plain,
! [X19125,X19126,X19127] :
( ~ class_Orderings_Olinorder(X19127)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19127),X19126),X19125))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19127),X19125),X19126)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__linear])]) ).
fof(i_0_10069,plain,
! [X19073,X19074,X19075] :
( ~ class_Orderings_Olinorder(X19075)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19075),X19074),X19073))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19075),X19073),X19074)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5939])]) ).
fof(i_0_10070,plain,
! [X19172,X19173,X19174] :
( ~ class_Orderings_Olinorder(X19174)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19174),X19173),X19172))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19174),X19172),X19173)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5940])]) ).
fof(i_0_10071,plain,
! [X19175,X19176,X19177] :
( ~ class_Orderings_Olinorder(X19177)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19177),X19176),X19175))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19177),X19175),X19176)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5941])]) ).
fof(i_0_10072,plain,
! [X19160,X19161,X19162] :
( ~ class_Orderings_Olinorder(X19162)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19162),X19161),X19160))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19162),X19160),X19161)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear])]) ).
fof(i_0_10073,plain,
! [X26950,X26951,X26952,X26953,X26954] :
( hAPP(X26954,X26953) != X26952
| hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X26951,X26950),X26954),X26953),X26952) = X26954 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__idem])]) ).
cnf(i_0_10074,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_5942]) ).
cnf(i_0_10075,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_5943]) ).
fof(i_0_10076,plain,
! [X32409,X32410,X32411] :
( ~ class_Groups_Omonoid__add(X32411)
| hAPP(c_List_Omonoid__add__class_Olistsum(X32411),hAPP(hAPP(c_List_Olist_OCons(X32411),X32410),X32409)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X32411),X32410),hAPP(c_List_Omonoid__add__class_Olistsum(X32411),X32409)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__simps_I2_J])]) ).
fof(i_0_10077,plain,
! [X21490,X21491,X21492] :
( ~ class_Fields_Ofield__inverse__zero(X21492)
| hAPP(c_Groups_Ouminus__class_Ouminus(X21492),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21492),X21491),X21490)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21492),X21491),hAPP(c_Groups_Ouminus__class_Ouminus(X21492),X21490)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__right])]) ).
fof(i_0_10078,plain,
! [X18676,X18677,X18678] :
( ~ class_Rings_Oring(X18678)
| hAPP(c_Groups_Ouminus__class_Ouminus(X18678),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18678),X18677),X18676)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18678),X18677),hAPP(c_Groups_Ouminus__class_Ouminus(X18678),X18676)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__right])]) ).
fof(i_0_10079,plain,
! [X18043,X18044,X18045] : c_Option_Ooption_Ooption__size(X18045,X18044,hAPP(c_Option_Ooption_OSome(X18045),X18043)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X18044,X18043)),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_10080,plain,
! [X33942,X33943] : c_List_Opartition(X33943,X33942,c_List_Olist_ONil(X33943)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33943),tc_List_Olist(X33943)),c_List_Olist_ONil(X33943)),c_List_Olist_ONil(X33943)),
inference(variable_rename,[status(thm)],[fact_partition_Osimps_I1_J]) ).
cnf(i_0_10081,plain,
c_Int_Osucc(c_Int_Opred(X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_5944]) ).
fof(i_0_10082,plain,
! [X32828,X32829,X32830] : hAPP(hAPP(c_List_Otake(X32830),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X32830),X32829),X32828)) = hAPP(hAPP(c_List_Olist_OCons(X32830),X32829),c_List_Olist_ONil(X32830)),
inference(variable_rename,[status(thm)],[fact_take__1__Cons]) ).
fof(i_0_10083,plain,
! [X29559,X29560,X29561,X29562] :
( ~ c_Wellfounded_Owf(X29562,X29561)
| c_Wellfounded_Owf(X29560,hAPP(hAPP(c_Relation_Oinv__image(X29562,X29560),X29561),X29559)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__inv__image])]) ).
fof(i_0_10084,plain,
! [X24193,X24194,X24195,X24196] :
( ~ c_FunDef_Oreduction__pair(X24196,X24195)
| c_FunDef_Oreduction__pair(X24194,hAPP(hAPP(c_FunDef_Orp__inv__image(X24196,X24194),X24195),X24193)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rp__inv__image__rp])]) ).
fof(i_0_10085,plain,
! [X23131,X23132] :
( ~ class_Rings_Ocomm__semiring__1(X23132)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23132),c_Groups_Ozero__class_Ozero(X23132)),X23131))
| X23131 = c_Groups_Ozero__class_Ozero(X23132) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__0__left])]) ).
fof(i_0_10086,plain,
! [X19829,X19830,X19831] :
( ~ class_Divides_Osemiring__div(X19831)
| c_Divides_Odiv__class_Omod(X19831,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19831),X19830),X19829),X19830) = c_Divides_Odiv__class_Omod(X19831,X19829,X19830) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__self1])]) ).
fof(i_0_10087,plain,
! [X19832,X19833,X19834] :
( ~ class_Divides_Osemiring__div(X19834)
| c_Divides_Odiv__class_Omod(X19834,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19834),X19833),X19832),X19832) = c_Divides_Odiv__class_Omod(X19834,X19833,X19832) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__self2])]) ).
fof(i_0_10088,plain,
! [X33380,X33381,X33382,X33383,X33384] :
( hAPP(hAPP(c_List_Odrop(X33384),X33383),X33382) != hAPP(hAPP(c_List_Olist_OCons(X33384),X33381),X33380)
| hAPP(hAPP(c_List_Onth(X33384),X33382),X33383) = X33381 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__via__drop])]) ).
fof(i_0_10089,plain,
! [X22652,X22653] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X22653)),hAPP(c_Nat_OSuc,X22652)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X22653),X22652)),
inference(variable_rename,[status(thm)],[fact_max__Suc__Suc]) ).
fof(i_0_10090,plain,
! [X22488,X22489] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X22489)),hAPP(c_Nat_OSuc,X22488)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X22489),X22488)),
inference(variable_rename,[status(thm)],[fact_min__Suc__Suc]) ).
fof(i_0_10091,plain,
! [X21887,X21888] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X21888)),hAPP(c_Code__Numeral_Oof__nat,X21887)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21888),X21887)),
inference(variable_rename,[status(thm)],[fact_times__code__numeral__code]) ).
fof(i_0_10092,plain,
! [X21915,X21916] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X21916)),hAPP(c_Code__Numeral_Oof__nat,X21915)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21916),X21915)),
inference(variable_rename,[status(thm)],[fact_plus__code__numeral__code]) ).
fof(i_0_10093,plain,
! [X20916,X20917] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20917)),X20916) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20917),X20916)),
inference(variable_rename,[status(thm)],[fact_zpower__int]) ).
fof(i_0_10094,plain,
! [X20914,X20915] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20915)),X20914) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20915),X20914)),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J]) ).
fof(i_0_10095,plain,
! [X18721,X18722] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X18722)),X18721) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18722),X18721)),
inference(variable_rename,[status(thm)],[fact_zmult__zminus]) ).
fof(i_0_10096,plain,
! [X20918,X20919] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20919),X20918)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20919)),X20918),
inference(variable_rename,[status(thm)],[fact_int__power]) ).
cnf(i_0_10097,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_5945]) ).
fof(i_0_10098,plain,
! [X20708,X20709] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20709)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20709),c_Groups_Ozero__class_Ozero(X20709)),hAPP(c_Groups_Oabs__class_Oabs(X20709),X20708))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__zero])]) ).
fof(i_0_10099,plain,
! [X19481,X19482] :
( ~ class_Rings_Olinordered__semidom(X19482)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19482),c_Groups_Ozero__class_Ozero(X19482)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X19482),X19481))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__0__le__iff])]) ).
fof(i_0_10100,plain,
! [X19479,X19480] :
( ~ class_Rings_Olinordered__semidom(X19480)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19480),c_Groups_Ozero__class_Ozero(X19480)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X19480),X19479))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__imp__of__nat])]) ).
fof(i_0_10101,plain,
! [X24908,X24909,X24910] :
( ~ class_Lattices_Osemilattice__inf(X24910)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24910),X24909),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24910),X24909),X24908)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24910),X24909),X24908) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__left__idem])]) ).
fof(i_0_10102,plain,
! [X24902,X24903,X24904] :
( ~ class_Lattices_Osemilattice__inf(X24904)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24904),X24903),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24904),X24903),X24902)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24904),X24903),X24902) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oleft__idem])]) ).
fof(i_0_10103,plain,
! [X24905,X24906,X24907] :
( ~ class_Lattices_Olattice(X24907)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24907),X24906),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24907),X24906),X24905)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24907),X24906),X24905) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I4_J])]) ).
fof(i_0_10104,plain,
! [X24107,X24108,X24109] :
( ~ class_Lattices_Osemilattice__sup(X24109)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24109),X24108),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24109),X24108),X24107)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24109),X24108),X24107) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Oleft__idem])]) ).
fof(i_0_10105,plain,
! [X24101,X24102,X24103] :
( ~ class_Lattices_Osemilattice__sup(X24103)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24103),X24102),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24103),X24102),X24101)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24103),X24102),X24101) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__left__idem])]) ).
fof(i_0_10106,plain,
! [X24104,X24105,X24106] :
( ~ class_Lattices_Olattice(X24106)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24106),X24105),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24106),X24105),X24104)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24106),X24105),X24104) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I8_J])]) ).
fof(i_0_10107,plain,
! [X22633,X22634,X22635] :
( ~ class_Orderings_Olinorder(X22635)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22635),X22634),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22635),X22634),X22633)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22635),X22634),X22633) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__left__idem])]) ).
fof(i_0_10108,plain,
! [X22630,X22631,X22632] :
( ~ class_Orderings_Olinorder(X22632)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22632),X22631),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22632),X22631),X22630)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22632),X22631),X22630) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oleft__idem])]) ).
fof(i_0_10109,plain,
! [X22529,X22530,X22531] :
( ~ class_Orderings_Olinorder(X22531)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22531),X22530),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22531),X22530),X22529)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22531),X22530),X22529) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oleft__idem])]) ).
fof(i_0_10110,plain,
! [X22526,X22527,X22528] :
( ~ class_Orderings_Olinorder(X22528)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22528),X22527),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22528),X22527),X22526)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22528),X22527),X22526) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__left__idem])]) ).
fof(i_0_10111,plain,
! [X19936,X19937,X19938] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X19938)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19938),X19937),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19938),X19937),X19936)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19938),X19937),X19936) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__idem])]) ).
fof(i_0_10112,plain,
! [X33473,X33474,X33475] : hAPP(hAPP(c_List_Odrop(X33475),X33474),hAPP(c_List_Otl(X33475),X33473)) = hAPP(c_List_Otl(X33475),hAPP(hAPP(c_List_Odrop(X33475),X33474),X33473)),
inference(variable_rename,[status(thm)],[fact_drop__tl]) ).
fof(i_0_10113,plain,
! [X33470,X33471,X33472] : hAPP(c_List_Otl(X33472),hAPP(hAPP(c_List_Odrop(X33472),X33471),X33470)) = hAPP(hAPP(c_List_Odrop(X33472),X33471),hAPP(c_List_Otl(X33472),X33470)),
inference(variable_rename,[status(thm)],[fact_tl__drop]) ).
fof(i_0_10114,plain,
! [X32283,X32284,X32285] : hAPP(c_List_Oset(X32285),hAPP(hAPP(c_List_Olist_OCons(X32285),X32284),X32283)) = hAPP(hAPP(c_Set_Oinsert(X32285),X32284),hAPP(c_List_Oset(X32285),X32283)),
inference(variable_rename,[status(thm)],[fact_List_Oset_Osimps_I2_J]) ).
fof(i_0_10115,plain,
! [X26496,X26497] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26497,X26496)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X26496)),X26497),
inference(variable_rename,[status(thm)],[fact_card__atLeastAtMost]) ).
fof(i_0_10116,plain,
! [X23619,X23620,X23621] :
( X23621 != c_Orderings_Obot__class_Obot(tc_fun(X23620,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X23620),X23619),X23621)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5946])]) ).
fof(i_0_10117,plain,
! [X29426] : hAPP(c_Set_Oimage(X29426,X29426,c_Fun_Oid(X29426)),c_Orderings_Otop__class_Otop(tc_fun(X29426,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X29426,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_surj__id]) ).
fof(i_0_10118,plain,
! [X29997,X29998,X30000,X30001,X30002] :
( ( ~ hBOOL(hAPP(X29998,c_Hilbert__Choice_OEps(X29997,X29998)))
| hBOOL(hAPP(X29998,esk351_2(X29997,X29998))) )
& ( ~ hBOOL(hAPP(X30001,X30002))
| hBOOL(hAPP(X30001,c_Hilbert__Choice_OEps(X30000,X30001))) ) ),
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_10119,plain,
! [X33900,X33901,X33902] : hAPP(c_Product__Type_Ofst(tc_List_Olist(X33902),tc_List_Olist(X33902)),c_List_Opartition(X33902,X33901,X33900)) = hAPP(c_List_Ofilter(X33902,X33901),X33900),
inference(variable_rename,[status(thm)],[fact_partition__filter1]) ).
fof(i_0_10120,plain,
! [X21057] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X21057))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21057)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21057))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X21057)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5947])]) ).
fof(i_0_10121,plain,
! [X23061] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X23061)),
inference(variable_rename,[status(thm)],[fact_dvd__1__left]) ).
fof(i_0_10122,plain,
! [X28338,X28339] : hBOOL(hAPP(hAPP(c_member(X28339),X28338),c_Orderings_Otop__class_Otop(tc_fun(X28339,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_iso__tuple__UNIV__I]) ).
fof(i_0_10123,plain,
! [X28129,X28130] : hBOOL(hAPP(hAPP(c_member(X28130),X28129),c_Orderings_Otop__class_Otop(tc_fun(X28130,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_UNIV__I]) ).
fof(i_0_10124,plain,
! [X19691,X19692] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19692))
| X19692 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19691)
| hAPP(c_Int_Onat,X19692) != X19691 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19692))
| X19691 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Int_Onat,X19692) != X19691 )
& ( ~ 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__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19692))
| hAPP(c_Int_Onat,X19692) = X19691 )
& ( X19691 != 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)),X19692))
| hAPP(c_Int_Onat,X19692) = X19691 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19692))
| X19692 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19691)
| hAPP(c_Int_Onat,X19692) = X19691 )
& ( X19691 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X19692 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19691)
| hAPP(c_Int_Onat,X19692) = X19691 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5948])])]) ).
fof(i_0_10125,plain,
! [X19693,X19694] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19693))
| X19693 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19694)
| X19694 != hAPP(c_Int_Onat,X19693) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19693))
| X19694 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X19694 != hAPP(c_Int_Onat,X19693) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19693))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19693))
| X19694 = hAPP(c_Int_Onat,X19693) )
& ( X19694 != 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)),X19693))
| X19694 = hAPP(c_Int_Onat,X19693) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19693))
| X19693 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19694)
| X19694 = hAPP(c_Int_Onat,X19693) )
& ( X19694 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X19693 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19694)
| X19694 = hAPP(c_Int_Onat,X19693) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5949])])]) ).
fof(i_0_10126,plain,
! [X22430,X22431,X22432] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X22432,tc_HOL_Obool)),X22431) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X22432,tc_HOL_Obool)),X22430)
| X22431 = X22430 )
& ( X22431 != X22430
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X22432,tc_HOL_Obool)),X22431) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X22432,tc_HOL_Obool)),X22430) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__eq__Compl__iff])]) ).
fof(i_0_10127,plain,
! [X21874,X21875,X21876,X21877] :
( ~ class_Groups_Ouminus(X21877)
| hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X21876,X21877)),X21875),X21874) = hAPP(c_Groups_Ouminus__class_Ouminus(X21877),hAPP(X21875,X21874)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__Compl__def])]) ).
fof(i_0_10128,plain,
! [X19941,X19942,X19943,X19944] :
( ~ class_Groups_Ouminus(X19944)
| hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19943,X19944)),X19942),X19941) = hAPP(c_Groups_Ouminus__class_Ouminus(X19944),hAPP(X19942,X19941)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_uminus__apply])]) ).
fof(i_0_10129,plain,
! [X19671] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19671))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X19671)) = X19671 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19671))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X19671)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5950])]) ).
fof(i_0_10130,plain,
! [X19668] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19668))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X19668)) = X19668 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__0__le])]) ).
fof(i_0_10131,plain,
! [X20594,X20595] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20595),X20594))
| c_Nat__Transfer_Otsub(X20594,X20595) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20594),X20595) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20595),X20594))
| c_Nat__Transfer_Otsub(X20594,X20595) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5951])]) ).
fof(i_0_10132,plain,
! [X20501,X20502] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20502),X20501))
| c_Nat__Transfer_Otsub(X20501,X20502) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20501),X20502) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tsub__eq])]) ).
fof(i_0_10133,plain,
! [X21928,X21929] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,X21929)),hAPP(c_Code__Numeral_Oof__nat,X21928)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21929),X21928)),
inference(variable_rename,[status(thm)],[fact_subtract__code__numeral__code]) ).
fof(i_0_10134,plain,
! [X31674,X31675] : c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,X31675,X31674) = c_Smallcheck_Ofull__small_H(X31675,hAPP(c_Code__Numeral_Oint__of,X31674),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X31674))),
inference(variable_rename,[status(thm)],[fact_full__small__int__def]) ).
fof(i_0_10135,plain,
! [X19669,X19670] :
( ( X19670 = hAPP(c_Int_Onat,X19669)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19670) != X19669 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19669))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19670) != X19669 )
& ( X19670 != hAPP(c_Int_Onat,X19669)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19669))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19670) = X19669 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__eq__iff])])]) ).
fof(i_0_10136,plain,
! [X28861,X28862,X28863,X28864] :
( ~ c_Big__Operators_Osemilattice__big(X28864,X28863,X28862)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28864),X28861))
| hAPP(X28862,X28861) = hAPP(c_Finite__Set_Ofold1(X28864,X28863),X28861) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semilattice__big_OF__eq])]) ).
fof(i_0_10137,plain,
! [X28736,X28737,X28738,X28739] :
( ~ c_Finite__Set_Ofolding__one(X28739,X28738,X28737)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28739),X28736))
| hAPP(X28737,X28736) = hAPP(c_Finite__Set_Ofold1(X28739,X28738),X28736) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Oeq__fold])]) ).
fof(i_0_10138,plain,
! [X21078,X21079] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21078)))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X21079),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21078)) = c_Groups_Ozero__class_Ozero(X21079)
| ~ class_Int_Onumber__ring(X21079) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21078)))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X21079),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21078)) = hAPP(c_Int_Onumber__class_Onumber__of(X21079),X21078)
| ~ class_Int_Onumber__ring(X21079) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5952])])]) ).
fof(i_0_10139,plain,
! [X31354] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X31354,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X31354,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X31354,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Union__UNIV]) ).
fof(i_0_10140,plain,
! [X31267] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X31267,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X31267,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X31267,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Union__empty]) ).
fof(i_0_10141,plain,
! [X31366] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X31366,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X31366,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X31366,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Inter__UNIV]) ).
fof(i_0_10142,plain,
! [X31257] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X31257,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X31257,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X31257,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Inter__empty]) ).
cnf(i_0_10143,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_10144,plain,
! [X23095,X23096,X23097] : hAPP(hAPP(c_Set_Oinsert(X23097),X23096),hAPP(hAPP(c_Set_Oinsert(X23097),X23096),X23095)) = hAPP(hAPP(c_Set_Oinsert(X23097),X23096),X23095),
inference(variable_rename,[status(thm)],[fact_insert__absorb2]) ).
cnf(i_0_10145,plain,
c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
inference(split_conjunct,[status(thm)],[fact_Bit1__Min]) ).
fof(i_0_10146,plain,
! [X31082,X31083,X31084,X31085] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31085)
| X31084 = c_Orderings_Obot__class_Obot(tc_fun(X31083,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31083,X31085),X31084),hAPP(c_COMBK(X31085,X31083),X31082)) = X31082 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__const])]) ).
fof(i_0_10147,plain,
! [X25963,X25964,X25965,X25966] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X25966)
| X25965 = c_Orderings_Obot__class_Obot(tc_fun(X25964,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25964,X25966),X25965),hAPP(c_COMBK(X25966,X25964),X25963)) = X25963 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__const])]) ).
fof(i_0_10148,plain,
! [X28120,X28121,X28122] :
( ~ class_Lattices_Oboolean__algebra(X28122)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X28122),X28121),X28120) != c_Orderings_Obot__class_Obot(X28122)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X28122),X28121),X28120) != c_Orderings_Otop__class_Otop(X28122)
| hAPP(c_Groups_Ouminus__class_Ouminus(X28122),X28121) = X28120 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__unique])]) ).
fof(i_0_10149,plain,
! [X19502,X19503] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19503),hAPP(c_Nat_OSuc,X19502)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19503),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19503),X19502)),
inference(variable_rename,[status(thm)],[fact_mult__Suc__right]) ).
cnf(i_0_10150,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_5953]) ).
fof(i_0_10151,plain,
! [X26913] : 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)),X26913))),
inference(variable_rename,[status(thm)],[fact_finite__atLeastZeroLessThan__int]) ).
fof(i_0_10152,plain,
! [X33975,X33976] : c_List_Otranspose(X33976,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X33976)),c_List_Olist_ONil(X33976)),X33975)) = c_List_Otranspose(X33976,X33975),
inference(variable_rename,[status(thm)],[fact_transpose_Osimps_I2_J]) ).
fof(i_0_10153,plain,
! [X33888,X33889,X33890,X33891] :
( hBOOL(hAPP(X33891,X33890))
| c_List_Oremove1(X33889,X33890,hAPP(c_List_Ofilter(X33889,X33891),X33888)) = hAPP(c_List_Ofilter(X33889,X33891),X33888) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5954])]) ).
fof(i_0_10154,plain,
! [X24448] : hAPP(c_Relation_OField(X24448),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X24448,X24448),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X24448,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Field__empty]) ).
fof(i_0_10155,plain,
! [X20018,X20019] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20019),X20018))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20019,X20018) = X20019 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__less])]) ).
fof(i_0_10156,plain,
! [X26503,X26504] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26504),c_Groups_Oone__class_Oone(tc_Int_Oint)),X26503) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X26504,X26503),
inference(variable_rename,[status(thm)],[fact_atLeastPlusOneAtMost__greaterThanAtMost__int]) ).
fof(i_0_10157,plain,
! [X31376,X31377,X31378] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31378)
| c_Complete__Lattice_OSup__class_OSup(X31378,hAPP(hAPP(c_Set_Oinsert(X31378),X31377),X31376)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X31378),X31377),c_Complete__Lattice_OSup__class_OSup(X31378,X31376)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__insert])]) ).
fof(i_0_10158,plain,
! [X31389,X31390,X31391] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31391)
| c_Complete__Lattice_OInf__class_OInf(X31391,hAPP(hAPP(c_Set_Oinsert(X31391),X31390),X31389)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X31391),X31390),c_Complete__Lattice_OInf__class_OInf(X31391,X31389)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__insert])]) ).
fof(i_0_10159,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_10160,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_10161,plain,
! [X31682,X31683] : hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),X31683),X31682) = c_Smallcheck_Osmall_H(X31683,hAPP(c_Code__Numeral_Oint__of,X31682),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X31682))),
inference(variable_rename,[status(thm)],[fact_small__int__def]) ).
fof(i_0_10162,plain,
! [X33799,X33800,X33801] :
( ( X33801 != c_List_Olist_ONil(X33800)
| c_List_Obutlast(X33800,hAPP(hAPP(c_List_Oappend(X33800),X33799),X33801)) = c_List_Obutlast(X33800,X33799) )
& ( X33801 = c_List_Olist_ONil(X33800)
| c_List_Obutlast(X33800,hAPP(hAPP(c_List_Oappend(X33800),X33799),X33801)) = hAPP(hAPP(c_List_Oappend(X33800),X33799),c_List_Obutlast(X33800,X33801)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast__append])]) ).
fof(i_0_10163,plain,
! [X33802,X33803,X33804] :
( ( X33804 != c_List_Olist_ONil(X33803)
| c_List_Obutlast(X33803,hAPP(hAPP(c_List_Olist_OCons(X33803),X33802),X33804)) = c_List_Olist_ONil(X33803) )
& ( X33804 = c_List_Olist_ONil(X33803)
| c_List_Obutlast(X33803,hAPP(hAPP(c_List_Olist_OCons(X33803),X33802),X33804)) = hAPP(hAPP(c_List_Olist_OCons(X33803),X33802),c_List_Obutlast(X33803,X33804)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast_Osimps_I2_J])]) ).
fof(i_0_10164,plain,
! [X28454,X28455,X28456] : hAPP(c_Set_Ovimage(X28456,X28455,X28454),c_Orderings_Otop__class_Otop(tc_fun(X28455,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X28456,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_vimage__UNIV]) ).
fof(i_0_10165,plain,
! [X28415,X28416,X28417] : hAPP(c_Set_Ovimage(X28417,X28416,X28415),c_Orderings_Obot__class_Obot(tc_fun(X28416,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X28417,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_vimage__empty]) ).
fof(i_0_10166,plain,
! [X24330,X24331,X24332] : hAPP(c_Relation_OImage(X24332,X24331,X24330),c_Orderings_Obot__class_Obot(tc_fun(X24332,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X24331,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Image__empty]) ).
fof(i_0_10167,plain,
! [X24323,X24324,X24325] : hAPP(c_Set_Oimage(X24325,X24324,X24323),c_Orderings_Obot__class_Obot(tc_fun(X24325,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X24324,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_image__empty]) ).
fof(i_0_10168,plain,
! [X33672,X33673,X33674] :
( ~ c_Relation_Orefl__on(X33674,X33673,X33672)
| c_Relation_Orefl__on(tc_List_Olist(X33674),c_List_Olists(X33674,X33673),c_List_Olistrel(X33674,X33672)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__refl__on])]) ).
fof(i_0_10169,plain,
! [X33675,X33676,X33677] :
( ~ c_Equiv__Relations_Oequiv(X33677,X33676,X33675)
| c_Equiv__Relations_Oequiv(tc_List_Olist(X33677),c_List_Olists(X33677,X33676),c_List_Olistrel(X33677,X33675)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__listrel])]) ).
fof(i_0_10170,plain,
! [X23686,X23687,X23688] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X23688),X23687),X23686))
| hBOOL(hAPP(X23686,X23687)) )
& ( ~ hBOOL(hAPP(X23686,X23687))
| hBOOL(hAPP(hAPP(c_member(X23688),X23687),X23686)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])]) ).
fof(i_0_10171,plain,
! [X18145,X18146,X18147] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X18147,X18146,X18145)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X18145)),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_10172,plain,
! [X23248,X23249,X23250,X23251] :
( ~ class_Rings_Odvd(X23251)
| X23250 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23251),X23249),X23248)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23251),X23249),X23250)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvdI])]) ).
cnf(i_0_10173,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_5955]) ).
fof(i_0_10174,plain,
! [X20442,X20443] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20443),X20442) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| 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),X20443),X20442))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20443),X20442) = 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_10175,plain,
! [X20440,X20441] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20441),X20440))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20441),X20440) = 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_10176,plain,
! [X20043,X20044] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20044),X20043))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20044),X20043) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__less])]) ).
fof(i_0_10177,plain,
! [X28151,X28152] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28152,tc_HOL_Obool)),X28151),c_Orderings_Otop__class_Otop(tc_fun(X28152,tc_HOL_Obool))) = X28151,
inference(variable_rename,[status(thm)],[fact_Int__UNIV__right]) ).
fof(i_0_10178,plain,
! [X23941,X23942] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23942,tc_HOL_Obool)),X23941),c_Orderings_Obot__class_Obot(tc_fun(X23942,tc_HOL_Obool))) = X23941,
inference(variable_rename,[status(thm)],[fact_Un__empty__right]) ).
fof(i_0_10179,plain,
! [X23308,X23309] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23309,tc_HOL_Obool)),X23308),c_Orderings_Obot__class_Obot(tc_fun(X23309,tc_HOL_Obool))) = X23308,
inference(variable_rename,[status(thm)],[fact_Diff__empty]) ).
fof(i_0_10180,plain,
! [X22428,X22429] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X22429,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X22429,tc_HOL_Obool)),X22428)) = X22428,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
fof(i_0_10181,plain,
! [X30453,X30454] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X30454,X30454),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X30453) = X30453,
inference(variable_rename,[status(thm)],[fact_rel__pow__1]) ).
fof(i_0_10182,plain,
! [X27812,X27813] : c_Map_Odom(X27813,X27812,hAPP(c_COMBK(tc_Option_Ooption(X27812),X27813),c_Option_Ooption_ONone(X27812))) = c_Orderings_Obot__class_Obot(tc_fun(X27813,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_dom__empty]) ).
fof(i_0_10183,plain,
! [X27395,X27396] : c_Map_Oran(X27396,X27395,hAPP(c_COMBK(tc_Option_Ooption(X27395),X27396),c_Option_Ooption_ONone(X27395))) = c_Orderings_Obot__class_Obot(tc_fun(X27395,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_ran__empty]) ).
fof(i_0_10184,plain,
! [X21077] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21077)))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21077)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21077)))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21077)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21077) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5956])]) ).
fof(i_0_10185,plain,
! [X32680,X32681,X32682] : hAPP(hAPP(c_List_Olist__update(X32682,X32681),X32680),hAPP(hAPP(c_List_Onth(X32682),X32681),X32680)) = X32681,
inference(variable_rename,[status(thm)],[fact_list__update__id]) ).
fof(i_0_10186,plain,
! [X18690,X18691,X18692] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18692),X18691),X18691) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18692),X18690),X18690)
| X18691 = X18690
| X18691 = hAPP(c_Groups_Ouminus__class_Ouminus(X18692),X18690)
| ~ class_Rings_Oidom(X18692) )
& ( X18691 != X18690
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18692),X18691),X18691) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18692),X18690),X18690)
| ~ class_Rings_Oidom(X18692) )
& ( X18691 != hAPP(c_Groups_Ouminus__class_Ouminus(X18692),X18690)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18692),X18691),X18691) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18692),X18690),X18690)
| ~ class_Rings_Oidom(X18692) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__iff])])]) ).
fof(i_0_10187,plain,
! [X18094,X18095] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18095)),X18094) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18095),X18094)),
inference(variable_rename,[status(thm)],[fact_add__Suc]) ).
fof(i_0_10188,plain,
! [X33811,X33812,X33813] : hAPP(hAPP(c_List_Odrop(X33813),X33812),c_List_Obutlast(X33813,X33811)) = c_List_Obutlast(X33813,hAPP(hAPP(c_List_Odrop(X33813),X33812),X33811)),
inference(variable_rename,[status(thm)],[fact_drop__butlast]) ).
fof(i_0_10189,plain,
! [X33814,X33815,X33816] : c_List_Obutlast(X33816,hAPP(hAPP(c_List_Odrop(X33816),X33815),X33814)) = hAPP(hAPP(c_List_Odrop(X33816),X33815),c_List_Obutlast(X33816,X33814)),
inference(variable_rename,[status(thm)],[fact_butlast__drop]) ).
fof(i_0_10190,plain,
! [X21870] :
( ( X21870 = 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)),X21870)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X21870))
| X21870 != 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_10191,plain,
! [X29779,X29780,X29781] :
( ( hAPP(c_Relation_ODomain(X29781,X29780),X29779) != c_Orderings_Obot__class_Obot(tc_fun(X29781,tc_HOL_Obool))
| X29779 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29781,X29780),tc_HOL_Obool)) )
& ( X29779 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29781,X29780),tc_HOL_Obool))
| hAPP(c_Relation_ODomain(X29781,X29780),X29779) = c_Orderings_Obot__class_Obot(tc_fun(X29781,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Domain__empty__iff])]) ).
fof(i_0_10192,plain,
! [X29692,X29693,X29694] :
( ( hAPP(c_Relation_ORange(X29694,X29693),X29692) != c_Orderings_Obot__class_Obot(tc_fun(X29693,tc_HOL_Obool))
| X29692 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29694,X29693),tc_HOL_Obool)) )
& ( X29692 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29694,X29693),tc_HOL_Obool))
| hAPP(c_Relation_ORange(X29694,X29693),X29692) = c_Orderings_Obot__class_Obot(tc_fun(X29693,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Range__empty__iff])]) ).
fof(i_0_10193,plain,
! [X20852] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20852),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X20852) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20852) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20852),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X20852) = X20852 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5957])]) ).
fof(i_0_10194,plain,
! [X20809,X20810] :
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20810),X20809)) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X20810) = 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_10195,plain,
! [X18589,X18590] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18590),X18589))
| X18590 = X18589
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18589),X18590)) ),
inference(variable_rename,[status(thm)],[fact_zless__linear]) ).
fof(i_0_10196,plain,
! [X18264,X18265] :
( X18265 = X18264
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18265),X18264))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18264),X18265)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5958])]) ).
fof(i_0_10197,plain,
! [X18262,X18263] :
( ( X18263 = X18262
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18263),X18262))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18262),X18263)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18263),X18262))
| X18263 != X18262 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18262),X18263))
| X18263 != X18262 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__neq__iff])])]) ).
fof(i_0_10198,plain,
! [X26919,X26920] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X26920),X26919)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26919),X26920)),
inference(variable_rename,[status(thm)],[fact_card__atLeastLessThan__int]) ).
cnf(i_0_10199,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_5959]) ).
fof(i_0_10200,plain,
! [X20655,X20656] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20656)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20656),X20655),hAPP(c_Groups_Oabs__class_Oabs(X20656),X20655))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__self])]) ).
fof(i_0_10201,plain,
! [X25783,X25784] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X25784,X25783)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25783),hAPP(c_Nat_OSuc,X25784)),
inference(variable_rename,[status(thm)],[fact_card__greaterThanLessThan]) ).
fof(i_0_10202,plain,
! [X19068,X19069] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19069),X19068))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19068),X19069)) ),
inference(variable_rename,[status(thm)],[fact_zle__linear]) ).
fof(i_0_10203,plain,
! [X19749,X19750] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19750),X19749))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19749),X19750)) ),
inference(variable_rename,[status(thm)],[fact_nat__le__linear]) ).
fof(i_0_10204,plain,
! [X20028,X20029] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20029)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20028)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20029),X20028),
inference(variable_rename,[status(thm)],[fact_zdiv__zminus__zminus]) ).
fof(i_0_10205,plain,
! [X20030,X20031] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20031),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20030)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20031)),X20030),
inference(variable_rename,[status(thm)],[fact_zdiv__zminus2]) ).
fof(i_0_10206,plain,
! [X33467,X33468,X33469] : hAPP(hAPP(c_List_Odrop(X33469),hAPP(c_Nat_OSuc,X33468)),X33467) = hAPP(hAPP(c_List_Odrop(X33469),X33468),hAPP(c_List_Otl(X33469),X33467)),
inference(variable_rename,[status(thm)],[fact_drop__Suc]) ).
fof(i_0_10207,plain,
! [X27814,X27815,X27816] :
( ( c_Map_Odom(X27816,X27815,X27814) != c_Orderings_Obot__class_Obot(tc_fun(X27816,tc_HOL_Obool))
| X27814 = hAPP(c_COMBK(tc_Option_Ooption(X27815),X27816),c_Option_Ooption_ONone(X27815)) )
& ( X27814 != hAPP(c_COMBK(tc_Option_Ooption(X27815),X27816),c_Option_Ooption_ONone(X27815))
| c_Map_Odom(X27816,X27815,X27814) = c_Orderings_Obot__class_Obot(tc_fun(X27816,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dom__eq__empty__conv])]) ).
fof(i_0_10208,plain,
! [X18497] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18497))
| X18497 = hAPP(c_Nat_OSuc,esk41_1(X18497)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0__implies__Suc])])]) ).
fof(i_0_10209,plain,
! [X18371,X18373,X18374] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18371))
| X18371 = hAPP(c_Nat_OSuc,esk36_1(X18371)) )
& ( X18373 != hAPP(c_Nat_OSuc,X18374)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18373)) ) ),
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_10210,plain,
! [X28783,X28784] :
( ~ class_Orderings_Olinorder(X28784)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28784),X28783))
| c_Big__Operators_Olattice_OInf__fin(X28784,c_Orderings_Oord__class_Omin(X28784),X28783) = hAPP(c_Finite__Set_Ofold1(X28784,c_Orderings_Oord__class_Omin(X28784)),X28783) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_OF__eq])]) ).
fof(i_0_10211,plain,
! [X28785,X28786] :
( ~ class_Orderings_Olinorder(X28786)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28786),X28785))
| c_Big__Operators_Olattice_OSup__fin(X28786,c_Orderings_Oord__class_Omax(X28786),X28785) = hAPP(c_Finite__Set_Ofold1(X28786,c_Orderings_Oord__class_Omax(X28786)),X28785) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_OF__eq])]) ).
fof(i_0_10212,plain,
! [X32146] :
( ~ class_Orderings_Olinorder(X32146)
| c_Finite__Set_Ofun__left__comm(X32146,tc_List_Olist(X32146),c_List_Olinorder__class_Oinsort__key(X32146,X32146,c_COMBI(X32146))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__insort])]) ).
fof(i_0_10213,plain,
! [X19018] :
( ( X19018 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Groups_Osgn__class_Osgn(tc_Int_Oint,X19018) = 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)),X19018))
| c_Groups_Osgn__class_Osgn(tc_Int_Oint,X19018) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| X19018 = 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)),X19018))
| c_Groups_Osgn__class_Osgn(tc_Int_Oint,X19018) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
| X19018 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5960])])]) ).
fof(i_0_10214,plain,
! [X33486,X33487] :
( ~ hBOOL(hAPP(c_List_Odistinct(X33487),X33486))
| hBOOL(hAPP(c_List_Odistinct(X33487),hAPP(c_List_Otl(X33487),X33486))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__tl])]) ).
fof(i_0_10215,plain,
! [X26914,X26915] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X26915),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26914),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X26915,X26914),
inference(variable_rename,[status(thm)],[fact_atLeastLessThanPlusOne__atLeastAtMost__int]) ).
fof(i_0_10216,plain,
! [X21058] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X21058))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21058),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21058),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X21058)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__def])]) ).
fof(i_0_10217,plain,
! [X32170,X32171] :
( hAPP(c_Finite__Set_Ocard(X32171),hAPP(c_List_Oset(X32171),X32170)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32171)),X32170)
| hBOOL(hAPP(c_List_Odistinct(X32171),X32170)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__distinct])]) ).
fof(i_0_10218,plain,
! [X20503,X20504] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20504),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20503)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20504),X20503)),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J]) ).
fof(i_0_10219,plain,
! [X34240,X34241,X34242] :
( ( hAPP(hAPP(c_List_Olist_OCons(X34242),X34241),c_List_Olist_ONil(X34242)) != hAPP(c_List_Orev(X34242),X34240)
| X34240 = hAPP(hAPP(c_List_Olist_OCons(X34242),X34241),c_List_Olist_ONil(X34242)) )
& ( X34240 != hAPP(hAPP(c_List_Olist_OCons(X34242),X34241),c_List_Olist_ONil(X34242))
| hAPP(hAPP(c_List_Olist_OCons(X34242),X34241),c_List_Olist_ONil(X34242)) = hAPP(c_List_Orev(X34242),X34240) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singleton__rev__conv])]) ).
fof(i_0_10220,plain,
! [X34243,X34244,X34245] :
( ( hAPP(c_List_Orev(X34245),X34244) != hAPP(hAPP(c_List_Olist_OCons(X34245),X34243),c_List_Olist_ONil(X34245))
| X34244 = hAPP(hAPP(c_List_Olist_OCons(X34245),X34243),c_List_Olist_ONil(X34245)) )
& ( X34244 != hAPP(hAPP(c_List_Olist_OCons(X34245),X34243),c_List_Olist_ONil(X34245))
| hAPP(c_List_Orev(X34245),X34244) = hAPP(hAPP(c_List_Olist_OCons(X34245),X34243),c_List_Olist_ONil(X34245)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__singleton__conv])]) ).
fof(i_0_10221,plain,
! [X18132,X18133] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(X18133,X18132)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X18132)),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_10222,plain,
! [X33207,X33208] : c_List_Olistrel1(X33208,hAPP(c_Relation_Oconverse(X33208,X33208),X33207)) = hAPP(c_Relation_Oconverse(tc_List_Olist(X33208),tc_List_Olist(X33208)),c_List_Olistrel1(X33208,X33207)),
inference(variable_rename,[status(thm)],[fact_listrel1__converse]) ).
fof(i_0_10223,plain,
! [X20300,X20301,X20302] :
( ~ class_Groups_Oab__group__add(X20302)
| hAPP(c_Groups_Ouminus__class_Ouminus(X20302),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20302),X20301),X20300)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20302),X20300),X20301) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__diff__eq])]) ).
cnf(i_0_10224,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_5757]) ).
fof(i_0_10225,plain,
! [X29577,X29578,X29579] :
( ~ c_Wellfounded_Owf(X29579,X29578)
| hBOOL(hAPP(hAPP(c_member(X29579),X29577),c_Wellfounded_Oacc(X29579,X29578))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__wfD])]) ).
fof(i_0_10226,plain,
! [X18694,X18695] :
( ~ class_Rings_Ocomm__ring__1(X18695)
| hAPP(c_Groups_Ouminus__class_Ouminus(X18695),X18694) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18695),hAPP(c_Groups_Ouminus__class_Ouminus(X18695),c_Groups_Oone__class_Oone(X18695))),X18694) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J])]) ).
fof(i_0_10227,plain,
! [X26911,X26912] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X26912),X26911))),
inference(variable_rename,[status(thm)],[fact_finite__atLeastLessThan__int]) ).
fof(i_0_10228,plain,
! [X26774,X26775] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26775),X26774))),
inference(variable_rename,[status(thm)],[fact_finite__atLeastLessThan]) ).
fof(i_0_10229,plain,
! [X18122] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18122)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X18122)),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_10230,plain,
c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_5961]) ).
fof(i_0_10231,plain,
! [X18623,X18624,X18625] :
( ~ class_Orderings_Oorder(X18625)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18625),X18624),X18623))
| X18623 != X18624 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2])]) ).
fof(i_0_10232,plain,
! [X18620,X18621,X18622] :
( ~ class_Orderings_Oorder(X18622)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18622),X18621),X18620))
| X18621 != X18620 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq])]) ).
fof(i_0_10233,plain,
! [X18611,X18612,X18613] :
( ~ class_Orderings_Oorder(X18613)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18613),X18612),X18611))
| X18612 != X18611 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__neq])]) ).
fof(i_0_10234,plain,
! [X23536] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23536),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X23536) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X23536) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X23536),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd1__eq])]) ).
cnf(i_0_10235,plain,
c_Wellfounded_Owf(X1,hAPP(c_Wellfounded_Omeasure(X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_5962]) ).
fof(i_0_10236,plain,
! [X23277,X23278,X23279] :
( ~ class_Rings_Olinordered__idom(X23279)
| hAPP(c_Groups_Oabs__class_Oabs(X23279),X23278) != hAPP(c_Groups_Oabs__class_Oabs(X23279),X23277)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23279),X23278),X23277)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__if__abs__eq])]) ).
fof(i_0_10237,plain,
! [X20256,X20257,X20258,X20259,X20260] :
( ( X20259 != X20258
| X20257 = X20256
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20260),X20259),X20258) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20260),X20257),X20256)
| ~ class_Groups_Oab__group__add(X20260) )
& ( X20257 != X20256
| X20259 = X20258
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20260),X20259),X20258) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20260),X20257),X20256)
| ~ class_Groups_Oab__group__add(X20260) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__eq])])]) ).
fof(i_0_10238,plain,
! [X31884,X31885,X31886,X31887] : hAPP(hAPP(c_Option_Omap(X31887,X31886),X31885),hAPP(c_Option_Ooption_OSome(X31887),X31884)) = hAPP(c_Option_Ooption_OSome(X31886),hAPP(X31885,X31884)),
inference(variable_rename,[status(thm)],[fact_option__map__Some]) ).
fof(i_0_10239,plain,
! [X34304,X34305,X34306] : hAPP(c_List_Orev(X34306),hAPP(c_List_Ofilter(X34306,X34305),X34304)) = hAPP(c_List_Ofilter(X34306,X34305),hAPP(c_List_Orev(X34306),X34304)),
inference(variable_rename,[status(thm)],[fact_rev__filter]) ).
fof(i_0_10240,plain,
! [X19918,X19919] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19919),X19918) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X19919,X19918) != 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_10241,plain,
! [X19916,X19917] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X19917,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19916)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X19917,X19916) != 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_10242,plain,
! [X18594,X18595] :
( ~ class_Orderings_Opreorder(X18595)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18595),X18594),X18594)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5963])]) ).
fof(i_0_10243,plain,
! [X18304] :
( ( X18304 = 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)),X18304)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18304))
| X18304 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neq0__conv])]) ).
fof(i_0_10244,plain,
! [X18066,X18067,X18068,X18069] :
( ~ class_Groups_Ocancel__semigroup__add(X18069)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18069),X18068),X18067) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18069),X18066),X18067)
| X18068 = X18066 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq])]) ).
fof(i_0_10245,plain,
! [X18054,X18055,X18056,X18057] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18057),X18056),X18055) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18057),X18054),X18055)
| X18056 = X18054
| ~ class_Groups_Ocancel__semigroup__add(X18057) )
& ( X18056 != X18054
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18057),X18056),X18055) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18057),X18054),X18055)
| ~ class_Groups_Ocancel__semigroup__add(X18057) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__cancel])])]) ).
fof(i_0_10246,plain,
! [X18062,X18063,X18064,X18065] :
( ~ class_Groups_Ocancel__ab__semigroup__add(X18065)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18065),X18064),X18063) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18065),X18064),X18062)
| X18063 = X18062 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__imp__eq])]) ).
fof(i_0_10247,plain,
! [X18058,X18059,X18060,X18061] :
( ~ class_Groups_Ocancel__semigroup__add(X18061)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18061),X18060),X18059) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18061),X18060),X18058)
| X18059 = X18058 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq])]) ).
fof(i_0_10248,plain,
! [X18050,X18051,X18052,X18053] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18053),X18052),X18051) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18053),X18052),X18050)
| X18051 = X18050
| ~ class_Groups_Ocancel__semigroup__add(X18053) )
& ( X18051 != X18050
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18053),X18052),X18051) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18053),X18052),X18050)
| ~ class_Groups_Ocancel__semigroup__add(X18053) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__cancel])])]) ).
fof(i_0_10249,plain,
! [X17538,X17539,X17540,X17541,X17542,X17543] :
( ( X17543 = X17540
| c_Com_Ocom_OLocal(X17543,X17542,X17541) != c_Com_Ocom_OLocal(X17540,X17539,X17538) )
& ( X17542 = X17539
| c_Com_Ocom_OLocal(X17543,X17542,X17541) != c_Com_Ocom_OLocal(X17540,X17539,X17538) )
& ( X17541 = X17538
| c_Com_Ocom_OLocal(X17543,X17542,X17541) != c_Com_Ocom_OLocal(X17540,X17539,X17538) )
& ( X17543 != X17540
| X17542 != X17539
| X17541 != X17538
| c_Com_Ocom_OLocal(X17543,X17542,X17541) = c_Com_Ocom_OLocal(X17540,X17539,X17538) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I2_J])])]) ).
fof(i_0_10250,plain,
! [X17532,X17533,X17534,X17535,X17536,X17537] :
( ( X17537 = X17534
| c_Com_Ocom_OCond(X17537,X17536,X17535) != c_Com_Ocom_OCond(X17534,X17533,X17532) )
& ( X17536 = X17533
| c_Com_Ocom_OCond(X17537,X17536,X17535) != c_Com_Ocom_OCond(X17534,X17533,X17532) )
& ( X17535 = X17532
| c_Com_Ocom_OCond(X17537,X17536,X17535) != c_Com_Ocom_OCond(X17534,X17533,X17532) )
& ( X17537 != X17534
| X17536 != X17533
| X17535 != X17532
| c_Com_Ocom_OCond(X17537,X17536,X17535) = c_Com_Ocom_OCond(X17534,X17533,X17532) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I4_J])])]) ).
fof(i_0_10251,plain,
! [X17207,X17208,X17209,X17210,X17211,X17212] :
( ( X17212 = X17209
| c_Com_Ocom_OCall(X17212,X17211,X17210) != c_Com_Ocom_OCall(X17209,X17208,X17207) )
& ( X17211 = X17208
| c_Com_Ocom_OCall(X17212,X17211,X17210) != c_Com_Ocom_OCall(X17209,X17208,X17207) )
& ( X17210 = X17207
| c_Com_Ocom_OCall(X17212,X17211,X17210) != c_Com_Ocom_OCall(X17209,X17208,X17207) )
& ( X17212 != X17209
| X17211 != X17208
| X17210 != X17207
| c_Com_Ocom_OCall(X17212,X17211,X17210) = c_Com_Ocom_OCall(X17209,X17208,X17207) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I7_J])])]) ).
fof(i_0_10252,plain,
! [X19666] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19666),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onat,X19666) = 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_10253,plain,
! [X19665] :
( ( hAPP(c_Int_Onat,X19665) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19665),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19665),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onat,X19665) = 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_10254,plain,
! [X21686] :
( ( ~ c_Nat__Transfer_Ois__nat(X21686)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21686)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21686))
| c_Nat__Transfer_Ois__nat(X21686) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_is__nat__def])]) ).
fof(i_0_10255,plain,
! [X18096,X18097] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18097),hAPP(c_Nat_OSuc,X18096)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18097),X18096)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
fof(i_0_10256,plain,
! [X17526,X17527,X17528,X17529,X17530,X17531] : c_Com_Ocom_OLocal(X17531,X17530,X17529) != c_Com_Ocom_OCond(X17528,X17527,X17526),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I36_J]) ).
fof(i_0_10257,plain,
! [X17623,X17624,X17625,X17626,X17627,X17628] : c_Com_Ocom_OLocal(X17628,X17627,X17626) != c_Com_Ocom_OCall(X17625,X17624,X17623),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I42_J]) ).
fof(i_0_10258,plain,
! [X17520,X17521,X17522,X17523,X17524,X17525] : c_Com_Ocom_OCond(X17525,X17524,X17523) != c_Com_Ocom_OLocal(X17522,X17521,X17520),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I37_J]) ).
fof(i_0_10259,plain,
! [X17617,X17618,X17619,X17620,X17621,X17622] : c_Com_Ocom_OCall(X17622,X17621,X17620) != c_Com_Ocom_OLocal(X17619,X17618,X17617),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I43_J]) ).
fof(i_0_10260,plain,
! [X17661,X17662,X17663,X17664,X17665,X17666] : c_Com_Ocom_OCond(X17666,X17665,X17664) != c_Com_Ocom_OCall(X17663,X17662,X17661),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I56_J]) ).
fof(i_0_10261,plain,
! [X17655,X17656,X17657,X17658,X17659,X17660] : c_Com_Ocom_OCall(X17660,X17659,X17658) != c_Com_Ocom_OCond(X17657,X17656,X17655),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I57_J]) ).
fof(i_0_10262,plain,
! [X29673,X29674] : hAPP(c_List_Olexn(X29674,X29673),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(X29674),tc_List_Olist(X29674)),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_lexn_Osimps_I1_J]) ).
fof(i_0_10263,plain,
! [X19523] : 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),X19523))),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J]) ).
fof(i_0_10264,plain,
! [X19522] : 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),X19522))),
inference(variable_rename,[status(thm)],[fact_zero__zle__int]) ).
fof(i_0_10265,plain,
! [X23310,X23311] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23311,tc_HOL_Obool)),X23310),X23310) = c_Orderings_Obot__class_Obot(tc_fun(X23311,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Diff__cancel]) ).
fof(i_0_10266,plain,
! [X29558] : c_Wellfounded_Owf(X29558,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29558,X29558),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_wf__empty]) ).
fof(i_0_10267,plain,
! [X26468,X26469,X26470] :
( ~ class_Orderings_Oorder(X26470)
| X26469 != X26468
| c_SetInterval_Oord__class_OatLeastAtMost(X26470,X26469,X26468) = hAPP(hAPP(c_Set_Oinsert(X26470),X26469),c_Orderings_Obot__class_Obot(tc_fun(X26470,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton_H])]) ).
fof(i_0_10268,plain,
! [X34171,X34172] :
( ( hAPP(c_List_Oset(X34172),c_List_Olinorder__class_Osorted__list__of__set(X34172,X34171)) = X34171
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X34172),X34171))
| ~ class_Orderings_Olinorder(X34172) )
& ( c_List_Olinorder__class_Osorted(X34172,c_List_Olinorder__class_Osorted__list__of__set(X34172,X34171))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X34172),X34171))
| ~ class_Orderings_Olinorder(X34172) )
& ( hBOOL(hAPP(c_List_Odistinct(X34172),c_List_Olinorder__class_Osorted__list__of__set(X34172,X34171)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X34172),X34171))
| ~ class_Orderings_Olinorder(X34172) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set])])]) ).
fof(i_0_10269,plain,
! [X19889,X19890,X19891] :
( ~ class_Divides_Osemiring__div(X19891)
| c_Divides_Odiv__class_Omod(X19891,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19891),X19890),X19889),X19890) = c_Groups_Ozero__class_Ozero(X19891) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self1__is__0])]) ).
fof(i_0_10270,plain,
! [X19886,X19887,X19888] :
( ~ class_Divides_Osemiring__div(X19888)
| c_Divides_Odiv__class_Omod(X19888,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19888),X19887),X19886),X19886) = c_Groups_Ozero__class_Ozero(X19888) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self2__is__0])]) ).
fof(i_0_10271,plain,
! [X33808,X33809] :
( X33809 = c_List_Olist_ONil(X33808)
| ~ hBOOL(hAPP(c_List_Odistinct(X33808),X33809))
| hBOOL(hAPP(c_List_Odistinct(X33808),c_List_Obutlast(X33808,X33809))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__butlast])]) ).
fof(i_0_10272,plain,
! [X25846,X25847] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X25847,X25846)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25846),X25847),
inference(variable_rename,[status(thm)],[fact_card__greaterThanAtMost]) ).
fof(i_0_10273,plain,
! [X32307,X32308,X32309,X32310,X32311] :
( ( X32310 = X32308
| hAPP(hAPP(c_List_Olist_OCons(X32311),X32310),X32309) != hAPP(hAPP(c_List_Olist_OCons(X32311),X32308),X32307) )
& ( X32309 = X32307
| hAPP(hAPP(c_List_Olist_OCons(X32311),X32310),X32309) != hAPP(hAPP(c_List_Olist_OCons(X32311),X32308),X32307) )
& ( X32310 != X32308
| X32309 != X32307
| hAPP(hAPP(c_List_Olist_OCons(X32311),X32310),X32309) = hAPP(hAPP(c_List_Olist_OCons(X32311),X32308),X32307) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list_Oinject])])]) ).
fof(i_0_10274,plain,
! [X33093,X33094,X33095,X33096] :
( ( hAPP(hAPP(c_List_Oappend(X33096),X33095),X33094) != hAPP(hAPP(c_List_Oappend(X33096),X33093),X33094)
| X33095 = X33093 )
& ( X33095 != X33093
| hAPP(hAPP(c_List_Oappend(X33096),X33095),X33094) = hAPP(hAPP(c_List_Oappend(X33096),X33093),X33094) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__same__eq])]) ).
fof(i_0_10275,plain,
! [X33097,X33098,X33099,X33100] :
( ( hAPP(hAPP(c_List_Oappend(X33100),X33099),X33098) != hAPP(hAPP(c_List_Oappend(X33100),X33099),X33097)
| X33098 = X33097 )
& ( X33098 != X33097
| hAPP(hAPP(c_List_Oappend(X33100),X33099),X33098) = hAPP(hAPP(c_List_Oappend(X33100),X33099),X33097) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__append__eq])]) ).
fof(i_0_10276,plain,
! [X26462,X26463] :
( ~ class_Orderings_Oorder(X26463)
| c_SetInterval_Oord__class_OatLeastAtMost(X26463,X26462,X26462) = hAPP(hAPP(c_Set_Oinsert(X26463),X26462),c_Orderings_Obot__class_Obot(tc_fun(X26463,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton])]) ).
fof(i_0_10277,plain,
! [X17355,X17356] :
( ( hBOOL(hAPP(c_Com_OWT,X17356))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X17356,X17355))) )
& ( hBOOL(hAPP(c_Com_OWT,X17355))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X17356,X17355))) )
& ( ~ hBOOL(hAPP(c_Com_OWT,X17356))
| ~ hBOOL(hAPP(c_Com_OWT,X17355))
| hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X17356,X17355))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_Oequations_I4_J])])]) ).
fof(i_0_10278,plain,
! [X17338,X17339] :
( ~ hBOOL(hAPP(c_Com_OWT,X17339))
| ~ hBOOL(hAPP(c_Com_OWT,X17338))
| hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X17339,X17338))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_OSemi])]) ).
fof(i_0_10279,plain,
! [X32770,X32771] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32771),X32770))
| c_List_Oupto(X32770,X32771) = c_List_Olist_ONil(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upto__empty])]) ).
fof(i_0_10280,plain,
! [X26992] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X26992)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X26992)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X26992)),
inference(variable_rename,[status(thm)],[fact_atMost__Suc]) ).
fof(i_0_10281,plain,
! [X23040,X23041] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X23041),X23040))
| c_Quickcheck_Obeyond(X23041,X23040) = X23040 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X23041),X23040))
| c_Quickcheck_Obeyond(X23041,X23040) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5964])]) ).
fof(i_0_10282,plain,
! [X21163] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21163) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21163),c_Int_OPls)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21163),c_Int_OPls))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21163) = 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_10283,plain,
! [X21070] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21070)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21070) = 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_10284,plain,
! [X21162] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21162)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21162),c_Int_OPls)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21162),c_Int_OPls))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21162) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__0__number__of])]) ).
cnf(i_0_10285,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_5965]) ).
fof(i_0_10286,plain,
! [X24824,X24825,X24826] :
( ~ class_Lattices_Olattice(X24826)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24826),X24825),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24826),X24825),X24824)) = X24825 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__absorb])]) ).
fof(i_0_10287,plain,
! [X24827,X24828,X24829] :
( ~ class_Lattices_Olattice(X24829)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24829),X24828),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24829),X24828),X24827)) = X24828 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__inf__absorb])]) ).
fof(i_0_10288,plain,
! [X22609,X22610,X22611] :
( ~ class_Orderings_Olinorder(X22611)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22611),X22610),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22611),X22610),X22609)) = X22610 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__inf__absorb])]) ).
fof(i_0_10289,plain,
! [X22606,X22607,X22608] :
( ~ class_Orderings_Olinorder(X22608)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22608),X22607),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22608),X22607),X22606)) = X22607 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__absorb])]) ).
fof(i_0_10290,plain,
! [X23064] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23064),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| X23064 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X23064 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23064),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_10291,plain,
! [X19263] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19263),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X19263 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X19263 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19263),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_10292,plain,
! [X33373,X33374,X33375] : hAPP(hAPP(c_List_Odrop(X33375),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X33375),X33374),X33373)) = X33373,
inference(variable_rename,[status(thm)],[fact_drop__1__Cons]) ).
fof(i_0_10293,plain,
! [X20326,X20327] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20327)),hAPP(c_Nat_OSuc,X20326)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20327),X20326),
inference(variable_rename,[status(thm)],[fact_diff__Suc__Suc]) ).
fof(i_0_10294,plain,
! [X18092,X18093] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18093)),X18092) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18093),hAPP(c_Nat_OSuc,X18092)),
inference(variable_rename,[status(thm)],[fact_add__Suc__shift]) ).
fof(i_0_10295,plain,
! [X28772,X28773,X28774] : hAPP(c_Finite__Set_Ofold1(X28774,X28773),X28772) = c_HOL_OThe(X28774,c_Finite__Set_Ofold1Set(X28774,X28773,X28772)),
inference(variable_rename,[status(thm)],[fact_fold1__def]) ).
fof(i_0_10296,plain,
! [X19910,X19911,X19913,X19914,X19915] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X19911,X19910) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X19911 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19910),esk60_2(X19910,X19911)) )
& ( X19914 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19913),X19915)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X19914,X19913) = 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_10297,plain,
! [X20062,X20063,X20065,X20066,X20067] :
( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20063,X20062) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X20063 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20062),esk66_2(X20062,X20063)) )
& ( X20066 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20065),X20067)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20066,X20065) = 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_10298,plain,
! [X24472,X24473] :
( ~ c_Nat__Transfer_Onat__set(X24473)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24472),X24473))
| c_Nat__Transfer_Ois__nat(X24472) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J])]) ).
fof(i_0_10299,plain,
! [X30395,X30396] :
( ( ~ c_Wellfounded_Oacyclic(X30396,hAPP(c_Relation_Oconverse(X30396,X30396),X30395))
| c_Wellfounded_Oacyclic(X30396,X30395) )
& ( ~ c_Wellfounded_Oacyclic(X30396,X30395)
| c_Wellfounded_Oacyclic(X30396,hAPP(c_Relation_Oconverse(X30396,X30396),X30395)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acyclic__converse])]) ).
fof(i_0_10300,plain,
! [X18305] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18305),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[i_0_5966]) ).
fof(i_0_10301,plain,
! [X18303] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18303),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[i_0_5967]) ).
fof(i_0_10302,plain,
! [X18251] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18251),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[i_0_5968]) ).
fof(i_0_10303,plain,
! [X32168,X32169] :
( ~ hBOOL(hAPP(c_List_Odistinct(X32169),X32168))
| hAPP(c_Finite__Set_Ocard(X32169),hAPP(c_List_Oset(X32169),X32168)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32169)),X32168) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__card])]) ).
fof(i_0_10304,plain,
! [X30336,X30337,X30338] : hAPP(c_Relation_ODomain(X30338,X30337),hAPP(c_Relation_Oconverse(X30337,X30338),X30336)) = hAPP(c_Relation_ORange(X30337,X30338),X30336),
inference(variable_rename,[status(thm)],[fact_Domain__converse]) ).
fof(i_0_10305,plain,
! [X30333,X30334,X30335] : hAPP(c_Relation_ORange(X30335,X30334),hAPP(c_Relation_Oconverse(X30334,X30335),X30333)) = hAPP(c_Relation_ODomain(X30334,X30335),X30333),
inference(variable_rename,[status(thm)],[fact_Range__converse]) ).
fof(i_0_10306,plain,
! [X30330,X30331] : c_Transitive__Closure_Ortrancl(X30331,hAPP(c_Relation_Oconverse(X30331,X30331),X30330)) = hAPP(c_Relation_Oconverse(X30331,X30331),c_Transitive__Closure_Ortrancl(X30331,X30330)),
inference(variable_rename,[status(thm)],[fact_rtrancl__converse]) ).
fof(i_0_10307,plain,
! [X30339,X30340,X30341] : hAPP(c_Relation_ORange(X30341,X30340),X30339) = hAPP(c_Relation_ODomain(X30340,X30341),hAPP(c_Relation_Oconverse(X30341,X30340),X30339)),
inference(variable_rename,[status(thm)],[fact_Range__def]) ).
fof(i_0_10308,plain,
! [X32799,X32800,X32801,X32802] :
( ( hAPP(hAPP(c_List_Olist__update(X32802,X32801),X32800),X32799) != c_List_Olist_ONil(X32802)
| X32801 = c_List_Olist_ONil(X32802) )
& ( X32801 != c_List_Olist_ONil(X32802)
| hAPP(hAPP(c_List_Olist__update(X32802,X32801),X32800),X32799) = c_List_Olist_ONil(X32802) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__nonempty])]) ).
fof(i_0_10309,plain,
! [X32705,X32706,X32707,X32708] :
( ( hAPP(hAPP(c_List_Omap(X32708,X32707),X32706),X32705) != c_List_Olist_ONil(X32707)
| X32705 = c_List_Olist_ONil(X32708) )
& ( X32705 != c_List_Olist_ONil(X32708)
| hAPP(hAPP(c_List_Omap(X32708,X32707),X32706),X32705) = c_List_Olist_ONil(X32707) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__is__Nil__conv])]) ).
fof(i_0_10310,plain,
! [X31888,X31889,X31890,X31891] :
( ( hAPP(hAPP(c_Option_Omap(X31891,X31890),X31889),X31888) != c_Option_Ooption_ONone(X31890)
| X31888 = c_Option_Ooption_ONone(X31891) )
& ( X31888 != c_Option_Ooption_ONone(X31891)
| hAPP(hAPP(c_Option_Omap(X31891,X31890),X31889),X31888) = c_Option_Ooption_ONone(X31890) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_option__map__is__None])]) ).
fof(i_0_10311,plain,
! [X32718,X32719,X32720,X32721] :
( ( c_List_Olist_ONil(X32721) != hAPP(hAPP(c_List_Omap(X32720,X32721),X32719),X32718)
| X32718 = c_List_Olist_ONil(X32720) )
& ( X32718 != c_List_Olist_ONil(X32720)
| c_List_Olist_ONil(X32721) = hAPP(hAPP(c_List_Omap(X32720,X32721),X32719),X32718) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nil__is__map__conv])]) ).
fof(i_0_10312,plain,
! [X23484,X23485] : c_Option_Oset(X23485,hAPP(c_Option_Ooption_OSome(X23485),X23484)) = hAPP(hAPP(c_Set_Oinsert(X23485),X23484),c_Orderings_Obot__class_Obot(tc_fun(X23485,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_Option_Oset_Osimps_I2_J]) ).
fof(i_0_10313,plain,
! [X20321,X20322] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20322),X20321) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20321),X20322) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X20322 = X20321 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diffs0__imp__equal])]) ).
fof(i_0_10314,plain,
! [X27164,X27165,X27166] :
( ~ class_Groups_Ocomm__monoid__add(X27166)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27165,X27166),X27164),c_Orderings_Obot__class_Obot(tc_fun(X27165,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X27166) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__empty])]) ).
fof(i_0_10315,plain,
! [X27161,X27162,X27163] :
( ~ class_Groups_Ocomm__monoid__add(X27163)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27162,X27163),X27161),c_Orderings_Obot__class_Obot(tc_fun(X27162,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X27163) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oempty])]) ).
fof(i_0_10316,plain,
! [X25621,X25622,X25623] :
( ~ class_Groups_Ocomm__monoid__mult(X25623)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25622,X25623),X25621),c_Orderings_Obot__class_Obot(tc_fun(X25622,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(X25623) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oempty])]) ).
fof(i_0_10317,plain,
! [X25618,X25619,X25620] :
( ~ class_Groups_Ocomm__monoid__mult(X25620)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25619,X25620),X25618),c_Orderings_Obot__class_Obot(tc_fun(X25619,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(X25620) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__empty])]) ).
fof(i_0_10318,plain,
! [X18306,X18307] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18307),X18306))
| X18306 != 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_10319,plain,
! [X28177] :
( ~ class_Finite__Set_Ofinite(X28177)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X28177),c_Orderings_Otop__class_Otop(tc_fun(X28177,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV])]) ).
fof(i_0_10320,plain,
! [X21561,X21562,X21563,X21564] :
( ( X21562 = c_Groups_Ozero__class_Ozero(X21564)
| X21563 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21564),X21561),X21562)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21564),X21563),X21562) != X21561
| ~ class_Fields_Ofield__inverse__zero(X21564) )
& ( X21562 != c_Groups_Ozero__class_Ozero(X21564)
| X21561 = c_Groups_Ozero__class_Ozero(X21564)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21564),X21563),X21562) != X21561
| ~ class_Fields_Ofield__inverse__zero(X21564) )
& ( X21562 = c_Groups_Ozero__class_Ozero(X21564)
| X21562 != c_Groups_Ozero__class_Ozero(X21564)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21564),X21563),X21562) = X21561
| ~ class_Fields_Ofield__inverse__zero(X21564) )
& ( X21561 != c_Groups_Ozero__class_Ozero(X21564)
| X21562 != c_Groups_Ozero__class_Ozero(X21564)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21564),X21563),X21562) = X21561
| ~ class_Fields_Ofield__inverse__zero(X21564) )
& ( X21562 = c_Groups_Ozero__class_Ozero(X21564)
| X21563 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21564),X21561),X21562)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21564),X21563),X21562) = X21561
| ~ class_Fields_Ofield__inverse__zero(X21564) )
& ( X21561 != c_Groups_Ozero__class_Ozero(X21564)
| X21563 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21564),X21561),X21562)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21564),X21563),X21562) = X21561
| ~ class_Fields_Ofield__inverse__zero(X21564) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__eq])])]) ).
fof(i_0_10321,plain,
! [X21557,X21558,X21559,X21560] :
( ( X21557 = c_Groups_Ozero__class_Ozero(X21560)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21560),X21559),X21557) = X21558
| X21559 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21560),X21558),X21557)
| ~ class_Fields_Ofield__inverse__zero(X21560) )
& ( X21557 != c_Groups_Ozero__class_Ozero(X21560)
| X21559 = c_Groups_Ozero__class_Ozero(X21560)
| X21559 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21560),X21558),X21557)
| ~ class_Fields_Ofield__inverse__zero(X21560) )
& ( X21557 = c_Groups_Ozero__class_Ozero(X21560)
| X21557 != c_Groups_Ozero__class_Ozero(X21560)
| X21559 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21560),X21558),X21557)
| ~ class_Fields_Ofield__inverse__zero(X21560) )
& ( X21559 != c_Groups_Ozero__class_Ozero(X21560)
| X21557 != c_Groups_Ozero__class_Ozero(X21560)
| X21559 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21560),X21558),X21557)
| ~ class_Fields_Ofield__inverse__zero(X21560) )
& ( X21557 = c_Groups_Ozero__class_Ozero(X21560)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21560),X21559),X21557) != X21558
| X21559 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21560),X21558),X21557)
| ~ class_Fields_Ofield__inverse__zero(X21560) )
& ( X21559 != c_Groups_Ozero__class_Ozero(X21560)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21560),X21559),X21557) != X21558
| X21559 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21560),X21558),X21557)
| ~ class_Fields_Ofield__inverse__zero(X21560) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__eq])])]) ).
fof(i_0_10322,plain,
! [X19006,X19007] :
( ~ class_Rings_Osemiring__1(X19007)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X19007),hAPP(c_Nat_OSuc,X19006)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19007),c_Groups_Oone__class_Oone(X19007)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X19007),X19006)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__Suc])]) ).
fof(i_0_10323,plain,
! [X18245] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X18245))),
inference(variable_rename,[status(thm)],[fact_zero__less__Suc]) ).
fof(i_0_10324,plain,
! [X18430,X18431,X18432] : hAPP(c_Nat_Osize__class_Osize(tc_sum(X18432,X18431)),hAPP(c_Sum__Type_OInl(X18432,X18431),X18430)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_sum_Osize_I3_J]) ).
fof(i_0_10325,plain,
! [X18433,X18434,X18435] : hAPP(c_Nat_Osize__class_Osize(tc_sum(X18435,X18434)),hAPP(c_Sum__Type_OInr(X18434,X18435),X18433)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_sum_Osize_I4_J]) ).
fof(i_0_10326,plain,
! [X18269,X18270] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18270),X18269))
| X18270 != X18269 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl3])]) ).
fof(i_0_10327,plain,
! [X18267,X18268] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18268),X18267))
| X18267 != X18268 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl2])]) ).
fof(i_0_10328,plain,
! [X17336,X17337] :
( ( hBOOL(hAPP(c_Com_OWT,X17337))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X17337,X17336))) )
& ( hBOOL(hAPP(c_Com_OWT,X17336))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X17337,X17336))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5969])])]) ).
fof(i_0_10329,plain,
! [X17838,X17839] :
( ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X17839,X17838)))
| hBOOL(hAPP(c_Com_OWT,X17838)) )
& ( ~ hBOOL(hAPP(c_Com_OWT,X17838))
| hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X17839,X17838))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_Oequations_I6_J])]) ).
fof(i_0_10330,plain,
! [X17759,X17760] :
( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X17760,X17759)))
| hBOOL(hAPP(c_Com_OWT,X17759)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WTs__elim__cases_I6_J])]) ).
cnf(i_0_10331,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_5970]) ).
fof(i_0_10332,plain,
! [X26845] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26845),hAPP(c_Nat_OSuc,X26845)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X26845),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_atLeastLessThan__singleton]) ).
cnf(i_0_10333,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_10334,plain,
! [X34096,X34097,X34098] :
( ~ class_Orderings_Olinorder(X34098)
| ~ c_List_Olinorder__class_Osorted(X34098,X34097)
| c_List_Olinorder__class_Osorted(X34098,c_List_Oremove1(X34098,X34096,X34097)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__remove1])]) ).
fof(i_0_10335,plain,
! [X19250,X19251,X19252] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19252),X19251) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19250),X19251)
| X19252 = X19250
| X19251 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X19252 != X19250
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19252),X19251) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19250),X19251) )
& ( X19251 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19252),X19251) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19250),X19251) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel2])])]) ).
fof(i_0_10336,plain,
! [X19756,X19757,X19758] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19758),X19757) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19758),X19756)
| X19758 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X19757 = X19756 )
& ( X19758 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19758),X19757) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19758),X19756) )
& ( X19757 != X19756
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19758),X19757) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19758),X19756) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel__disj])])]) ).
fof(i_0_10337,plain,
! [X19253,X19254,X19255] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19255),X19254) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19255),X19253)
| X19254 = X19253
| X19255 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X19254 != X19253
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19255),X19254) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19255),X19253) )
& ( X19255 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19255),X19254) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19255),X19253) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel1])])]) ).
fof(i_0_10338,plain,
! [X33445,X33446,X33447] :
( ( X33447 != c_List_Olist_ONil(X33446)
| hAPP(c_List_Ohd(X33446),hAPP(hAPP(c_List_Oappend(X33446),X33447),X33445)) = hAPP(c_List_Ohd(X33446),X33445) )
& ( X33447 = c_List_Olist_ONil(X33446)
| hAPP(c_List_Ohd(X33446),hAPP(hAPP(c_List_Oappend(X33446),X33447),X33445)) = hAPP(c_List_Ohd(X33446),X33447) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__append])]) ).
fof(i_0_10339,plain,
! [X18009] :
( ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X18009)))
| hAPP(c_Com_Obody,X18009) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),esk28_1(X18009)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WTs__elim__cases_I7_J])])]) ).
fof(i_0_10340,plain,
! [X17942,X17944,X17945] :
( ( ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X17942)))
| hAPP(c_Com_Obody,X17942) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),esk22_1(X17942)) )
& ( hAPP(c_Com_Obody,X17944) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X17945)
| hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X17944))) ) ),
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_10341,plain,
! [X17503,X17504] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X17504),X17503))
| X17503 = X17504 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc__elim__cases_I1_J])]) ).
fof(i_0_10342,plain,
! [X20823,X20824] :
( ~ class_Rings_Olinordered__idom(X20824)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20824),c_Groups_Osgn__class_Osgn(X20824,X20823)),hAPP(c_Groups_Oabs__class_Oabs(X20824),X20823)) = X20823 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__sgn__abs])]) ).
fof(i_0_10343,plain,
! [X23863] :
( ~ class_Rings_Oring__1(X23863)
| hBOOL(hAPP(hAPP(c_member(X23863),c_Groups_Oone__class_Oone(X23863)),c_Int_Oring__1__class_OInts(X23863))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__1])]) ).
fof(i_0_10344,plain,
! [X23816] :
( ~ class_Rings_Osemiring__1(X23816)
| hBOOL(hAPP(hAPP(c_member(X23816),c_Groups_Oone__class_Oone(X23816)),c_Nat_Osemiring__1__class_ONats(X23816))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__1])]) ).
fof(i_0_10345,plain,
! [X23851] :
( ~ class_Rings_Oring__1(X23851)
| hBOOL(hAPP(hAPP(c_member(X23851),c_Groups_Ozero__class_Ozero(X23851)),c_Int_Oring__1__class_OInts(X23851))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__0])]) ).
fof(i_0_10346,plain,
! [X23809] :
( ~ class_Rings_Osemiring__1(X23809)
| hBOOL(hAPP(hAPP(c_member(X23809),c_Groups_Ozero__class_Ozero(X23809)),c_Nat_Osemiring__1__class_ONats(X23809))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__0])]) ).
fof(i_0_10347,plain,
! [X19467] :
( ~ class_Rings_Olinordered__semidom(X19467)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19467),c_Groups_Ozero__class_Ozero(X19467)),c_Groups_Oone__class_Oone(X19467))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__one])]) ).
fof(i_0_10348,plain,
! [X18957] :
( ~ class_Rings_Olinordered__semidom(X18957)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18957),c_Groups_Ozero__class_Ozero(X18957)),c_Groups_Oone__class_Oone(X18957))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__one])]) ).
fof(i_0_10349,plain,
! [X21582,X21583,X21584,X21585] :
( ~ class_Rings_Odivision__ring(X21585)
| X21584 = c_Groups_Ozero__class_Ozero(X21585)
| X21583 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21585),X21582),X21584)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21585),X21583),X21584) = X21582 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__imp])]) ).
fof(i_0_10350,plain,
! [X21586,X21587,X21588,X21589] :
( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21589),X21587),X21588) != X21586
| X21587 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21589),X21586),X21588)
| X21588 = c_Groups_Ozero__class_Ozero(X21589)
| ~ class_Rings_Odivision__ring(X21589) )
& ( X21587 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21589),X21586),X21588)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21589),X21587),X21588) = X21586
| X21588 = c_Groups_Ozero__class_Ozero(X21589)
| ~ class_Rings_Odivision__ring(X21589) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__divide__eq__eq])])]) ).
fof(i_0_10351,plain,
! [X21590,X21591,X21592,X21593] :
( ( X21591 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21593),X21590),X21592)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21593),X21591),X21592) = X21590
| X21592 = c_Groups_Ozero__class_Ozero(X21593)
| ~ class_Rings_Odivision__ring(X21593) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21593),X21591),X21592) != X21590
| X21591 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21593),X21590),X21592)
| X21592 = c_Groups_Ozero__class_Ozero(X21593)
| ~ class_Rings_Odivision__ring(X21593) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__eq__divide__eq])])]) ).
fof(i_0_10352,plain,
! [X21578,X21579,X21580,X21581] :
( ~ class_Rings_Odivision__ring(X21581)
| X21580 = c_Groups_Ozero__class_Ozero(X21581)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21581),X21579),X21580) != X21578
| X21579 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21581),X21578),X21580) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__imp])]) ).
fof(i_0_10353,plain,
! [X20424,X20425,X20426] :
( ~ class_Groups_Ogroup__add(X20426)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20426),X20425),hAPP(c_Groups_Ouminus__class_Ouminus(X20426),X20424)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20426),X20425),X20424) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__minus__eq__add])]) ).
fof(i_0_10354,plain,
! [X24979,X24980,X24981] :
( ~ class_Lattices_Oboolean__algebra(X24981)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24981),X24980),X24979) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24981),X24980),hAPP(c_Groups_Ouminus__class_Ouminus(X24981),X24979)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq])]) ).
fof(i_0_10355,plain,
! [X20421,X20422,X20423] :
( ~ class_Groups_Oab__group__add(X20423)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20423),X20422),X20421) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20423),X20422),hAPP(c_Groups_Ouminus__class_Ouminus(X20423),X20421)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__diff__minus])]) ).
fof(i_0_10356,plain,
! [X20418,X20419,X20420] :
( ~ class_Groups_Ogroup__add(X20420)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20420),X20419),X20418) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20420),X20419),hAPP(c_Groups_Ouminus__class_Ouminus(X20420),X20418)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__def])]) ).
fof(i_0_10357,plain,
! [X20427,X20428,X20429] :
( ~ class_Rings_Ocomm__ring__1(X20429)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20429),X20428),X20427) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20429),X20428),hAPP(c_Groups_Ouminus__class_Ouminus(X20429),X20427)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J])]) ).
fof(i_0_10358,plain,
! [X21110,X21111] :
( ~ class_Int_Onumber__ring(X21111)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21111),hAPP(c_Int_Onumber__class_Onumber__of(X21111),c_Int_OMin)),X21110) = hAPP(c_Groups_Ouminus__class_Ouminus(X21111),X21110) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__minus1])]) ).
fof(i_0_10359,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_10360,plain,
! [X18266] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18266),X18266)),
inference(variable_rename,[status(thm)],[i_0_5971]) ).
fof(i_0_10361,plain,
! [X18261] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18261),X18261)),
inference(variable_rename,[status(thm)],[i_0_5972]) ).
fof(i_0_10362,plain,
! [X33448,X33449,X33450] :
( X33450 = c_List_Olist_ONil(X33449)
| hAPP(c_List_Ohd(X33449),hAPP(hAPP(c_List_Oappend(X33449),X33450),X33448)) = hAPP(c_List_Ohd(X33449),X33450) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__append2])]) ).
cnf(i_0_10363,plain,
( X1 = X2
| c_Int_OBit0(X1) != c_Int_OBit0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_5973]) ).
fof(i_0_10364,plain,
! [X18070,X18071,X18072] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18072),X18071) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18070),X18071)
| X18072 = X18070 )
& ( X18072 != X18070
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18072),X18071) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18070),X18071) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel])]) ).
fof(i_0_10365,plain,
! [X18073,X18074,X18075] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18075),X18074) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18075),X18073)
| X18074 = X18073 )
& ( X18074 != X18073
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18075),X18074) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18075),X18073) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel])]) ).
fof(i_0_10366,plain,
! [X29206,X29207] : hAPP(c_Set_OCollect(X29207),hAPP(c_fequal,X29206)) = hAPP(hAPP(c_Set_Oinsert(X29207),X29206),c_Orderings_Obot__class_Obot(tc_fun(X29207,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_singleton__conv2]) ).
fof(i_0_10367,plain,
! [X34074,X34075,X34076] :
( ~ class_Orderings_Olinorder(X34076)
| ~ c_List_Olinorder__class_Osorted(X34076,X34075)
| c_List_Olinorder__class_Osorted(X34076,hAPP(hAPP(c_List_Odrop(X34076),X34074),X34075)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__drop])]) ).
fof(i_0_10368,plain,
! [X34081,X34082,X34083] :
( ~ class_Orderings_Olinorder(X34083)
| ~ c_List_Olinorder__class_Osorted(X34083,X34082)
| c_List_Olinorder__class_Osorted(X34083,hAPP(hAPP(c_List_Otake(X34083),X34081),X34082)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__take])]) ).
fof(i_0_10369,plain,
! [X24550] : hBOOL(hAPP(c_Finite__Set_Ofinite(X24550),c_Orderings_Obot__class_Obot(tc_fun(X24550,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_finite_Oequations_I1_J]) ).
fof(i_0_10370,plain,
! [X24543] : hBOOL(hAPP(c_Finite__Set_Ofinite(X24543),c_Orderings_Obot__class_Obot(tc_fun(X24543,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_finite_OemptyI]) ).
fof(i_0_10371,plain,
! [X26374,X26375] : hAPP(c_Set_OPow(X26375),X26374) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X26375,tc_HOL_Obool),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Pow__not__empty]) ).
fof(i_0_10372,plain,
! [X27171,X27172,X27173,X27174] :
( ~ class_Groups_Ocomm__monoid__add(X27174)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X27173),X27172))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27173,X27174),X27171),X27172) = c_Groups_Ozero__class_Ozero(X27174) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5974])]) ).
fof(i_0_10373,plain,
! [X27167,X27168,X27169,X27170] :
( ~ class_Groups_Ocomm__monoid__add(X27170)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X27169),X27168))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27169,X27170),X27167),X27168) = c_Groups_Ozero__class_Ozero(X27170) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5975])]) ).
fof(i_0_10374,plain,
! [X25628,X25629,X25630,X25631] :
( ~ class_Groups_Ocomm__monoid__mult(X25631)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X25630),X25629))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25630,X25631),X25628),X25629) = c_Groups_Oone__class_Oone(X25631) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5976])]) ).
fof(i_0_10375,plain,
! [X25624,X25625,X25626,X25627] :
( ~ class_Groups_Ocomm__monoid__mult(X25627)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X25626),X25625))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25626,X25627),X25624),X25625) = c_Groups_Oone__class_Oone(X25627) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5977])]) ).
fof(i_0_10376,plain,
! [X28220] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28220,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X28220,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X28220,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__UNIV__eq]) ).
fof(i_0_10377,plain,
! [X28221] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28221,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X28221,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X28221,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__empty__eq]) ).
fof(i_0_10378,plain,
! [X28176] : hAPP(c_Set_OPow(X28176),c_Orderings_Otop__class_Otop(tc_fun(X28176,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X28176,tc_HOL_Obool),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Pow__UNIV]) ).
fof(i_0_10379,plain,
! [X26259] : c_Relation_OId__on(X26259,c_Orderings_Obot__class_Obot(tc_fun(X26259,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X26259,X26259),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Id__on__empty]) ).
fof(i_0_10380,plain,
! [X24940,X24941] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24941,tc_HOL_Obool)),X24940),X24940) = X24940,
inference(variable_rename,[status(thm)],[fact_Int__absorb]) ).
fof(i_0_10381,plain,
! [X24070,X24071] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24071,tc_HOL_Obool)),X24070),X24070) = X24070,
inference(variable_rename,[status(thm)],[fact_Un__absorb]) ).
fof(i_0_10382,plain,
! [X29821,X29822] :
( ~ c_Wellfounded_Owf(X29822,X29821)
| c_Wellfounded_OwfP(X29822,c_FunDef_Oin__rel(X29822,X29822,X29821)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__in__rel])]) ).
fof(i_0_10383,plain,
! [X29586,X29587,X29588] :
( ~ c_Wellfounded_Owf(X29588,X29587)
| c_Wellfounded_Owf(X29588,c_Wellfounded_Omlex__prod(X29588,X29586,X29587)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__mlex])]) ).
fof(i_0_10384,plain,
! [X21056] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21056))),
inference(variable_rename,[status(thm)],[i_0_5978]) ).
fof(i_0_10385,plain,
! [X28779,X28780] :
( ~ class_Orderings_Olinorder(X28780)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28780),X28779))
| c_Big__Operators_Olinorder__class_OMin(X28780,X28779) = hAPP(c_Finite__Set_Ofold1(X28780,c_Orderings_Oord__class_Omin(X28780)),X28779) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_OF__eq])]) ).
fof(i_0_10386,plain,
! [X28781,X28782] :
( ~ class_Orderings_Olinorder(X28782)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28782),X28781))
| c_Big__Operators_Olinorder__class_OMax(X28782,X28781) = hAPP(c_Finite__Set_Ofold1(X28782,c_Orderings_Oord__class_Omax(X28782)),X28781) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_OF__eq])]) ).
fof(i_0_10387,plain,
! [X28777,X28778] :
( ~ class_Lattices_Olattice(X28778)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28778),X28777))
| c_Big__Operators_Olattice__class_OInf__fin(X28778,X28777) = hAPP(c_Finite__Set_Ofold1(X28778,c_Lattices_Osemilattice__inf__class_Oinf(X28778)),X28777) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_OF__eq])]) ).
fof(i_0_10388,plain,
! [X28775,X28776] :
( ~ class_Lattices_Olattice(X28776)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28776),X28775))
| c_Big__Operators_Olattice__class_OSup__fin(X28776,X28775) = hAPP(c_Finite__Set_Ofold1(X28776,c_Lattices_Osemilattice__sup__class_Osup(X28776)),X28775) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_OF__eq])]) ).
fof(i_0_10389,plain,
! [X18254] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18254),hAPP(c_Nat_OSuc,X18254))),
inference(variable_rename,[status(thm)],[fact_lessI]) ).
fof(i_0_10390,plain,
! [X24977,X24978] :
( ~ class_Lattices_Oboolean__algebra(X24978)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24978),hAPP(c_Groups_Ouminus__class_Ouminus(X24978),X24977)),X24977) = c_Orderings_Obot__class_Obot(X24978) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__inf__bot])]) ).
fof(i_0_10391,plain,
! [X28258,X28259] :
( ~ class_Lattices_Oboolean__algebra(X28259)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X28259),hAPP(c_Groups_Ouminus__class_Ouminus(X28259),X28258)),X28258) = c_Orderings_Otop__class_Otop(X28259) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__sup__top])]) ).
fof(i_0_10392,plain,
! [X18888,X18889] :
( ~ class_Groups_Oab__group__add(X18889)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18889),hAPP(c_Groups_Ouminus__class_Ouminus(X18889),X18888)),X18888) = c_Groups_Ozero__class_Ozero(X18889) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__left__minus])]) ).
fof(i_0_10393,plain,
! [X18890,X18891] :
( ~ class_Groups_Ogroup__add(X18891)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18891),hAPP(c_Groups_Ouminus__class_Ouminus(X18891),X18890)),X18890) = c_Groups_Ozero__class_Ozero(X18891) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__minus])]) ).
fof(i_0_10394,plain,
! [X33745,X33746,X33747] :
( ( X33747 != c_List_Olist_ONil(X33746)
| c_List_Olast(X33746,hAPP(hAPP(c_List_Oappend(X33746),X33745),X33747)) = c_List_Olast(X33746,X33745) )
& ( X33747 = c_List_Olist_ONil(X33746)
| c_List_Olast(X33746,hAPP(hAPP(c_List_Oappend(X33746),X33745),X33747)) = c_List_Olast(X33746,X33747) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__append])]) ).
fof(i_0_10395,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,X33739) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__appendL])]) ).
fof(i_0_10396,plain,
! [X20438,X20439] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20439),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20439),X20438)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__add__0]) ).
fof(i_0_10397,plain,
! [X32656,X32657,X32658] : c_List_Osublist(X32658,X32657,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X32656)) = hAPP(hAPP(c_List_Otake(X32658),X32656),X32657),
inference(variable_rename,[status(thm)],[fact_sublist__upt__eq__take]) ).
fof(i_0_10398,plain,
! [X23137,X23138] :
( ~ class_Rings_Ocomm__semiring__1(X23138)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23138),c_Groups_Oone__class_Oone(X23138)),X23137)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__dvd])]) ).
fof(i_0_10399,plain,
! [X23324,X23325] :
( ~ class_Orderings_Obot(X23325)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23325),c_Orderings_Obot__class_Obot(X23325)),X23324)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__least])]) ).
fof(i_0_10400,plain,
! [X22224,X22225] :
( X22225 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22224,X22225),c_Divides_Odivmod__int(X22224,X22225))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__correct])]) ).
fof(i_0_10401,plain,
! [X22072,X22073] :
( ( X22073 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Opdivmod(X22072,X22073) = 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),X22072)) )
& ( X22073 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Opdivmod(X22072,X22073) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X22072),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X22073)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pdivmod__posDivAlg])]) ).
fof(i_0_10402,plain,
! [X34014,X34015] :
( ~ class_Orderings_Olinorder(X34015)
| c_List_Olinorder__class_Osorted(X34015,hAPP(hAPP(c_List_Olist_OCons(X34015),X34014),c_List_Olist_ONil(X34015))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__single])]) ).
fof(i_0_10403,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,X33744) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__appendR])]) ).
fof(i_0_10404,plain,
! [X33736,X33737,X33738] :
( ( X33738 != c_List_Olist_ONil(X33737)
| c_List_Olast(X33737,hAPP(hAPP(c_List_Olist_OCons(X33737),X33736),X33738)) = X33736 )
& ( X33738 = c_List_Olist_ONil(X33737)
| c_List_Olast(X33737,hAPP(hAPP(c_List_Olist_OCons(X33737),X33736),X33738)) = c_List_Olast(X33737,X33738) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last_Osimps])]) ).
fof(i_0_10405,plain,
! [X33733,X33734,X33735] :
( X33735 = c_List_Olist_ONil(X33734)
| c_List_Olast(X33734,hAPP(hAPP(c_List_Olist_OCons(X33734),X33733),X33735)) = c_List_Olast(X33734,X33735) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__ConsR])]) ).
fof(i_0_10406,plain,
! [X20638,X20639] :
( ( X20639 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nitpick_Onat__gcd(X20638,X20639) = X20638 )
& ( X20639 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nitpick_Onat__gcd(X20638,X20639) = c_Nitpick_Onat__gcd(X20639,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20638,X20639)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__gcd_Osimps])]) ).
fof(i_0_10407,plain,
! [X26840,X26841] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X26841)),X26840) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X26841,X26840),
inference(variable_rename,[status(thm)],[fact_atLeastSucLessThan__greaterThanLessThan]) ).
fof(i_0_10408,plain,
! [X26810,X26811] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26811),X26810)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X26810),X26811),
inference(variable_rename,[status(thm)],[fact_card__atLeastLessThan]) ).
fof(i_0_10409,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_10410,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_10411,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_10412,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_10413,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_10414,plain,
! [X32764,X32765,X32766] : hAPP(hAPP(c_List_Ozip(X32766,X32765),c_List_Olist_ONil(X32766)),X32764) = c_List_Olist_ONil(tc_prod(X32766,X32765)),
inference(variable_rename,[status(thm)],[fact_zip__Nil]) ).
fof(i_0_10415,plain,
! [X28336,X28337] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X28337,tc_HOL_Obool)),X28336)),
inference(variable_rename,[status(thm)],[fact_top1I]) ).
fof(i_0_10416,plain,
! [X29418,X29419] : hAPP(c_Set_Ovimage(X29419,X29419,c_Fun_Oid(X29419)),X29418) = X29418,
inference(variable_rename,[status(thm)],[fact_vimage__id]) ).
fof(i_0_10417,plain,
! [X28404,X28405] : hAPP(c_Set_Ovimage(X28405,X28405,c_COMBI(X28405)),X28404) = X28404,
inference(variable_rename,[status(thm)],[fact_vimage__ident]) ).
fof(i_0_10418,plain,
! [X29424,X29425] : hAPP(c_Set_Oimage(X29425,X29425,c_Fun_Oid(X29425)),X29424) = X29424,
inference(variable_rename,[status(thm)],[fact_image__id]) ).
fof(i_0_10419,plain,
! [X26600,X26601] : hAPP(c_Set_Oimage(X26601,X26601,c_COMBI(X26601)),X26600) = X26600,
inference(variable_rename,[status(thm)],[fact_image__ident]) ).
fof(i_0_10420,plain,
! [X18464,X18465,X18466] : c_Sum__Type_OProjr(X18466,X18465,hAPP(c_Sum__Type_OInr(X18465,X18466),X18464)) = X18464,
inference(variable_rename,[status(thm)],[fact_Projr_Osimps]) ).
fof(i_0_10421,plain,
! [X18461,X18462,X18463] : c_Sum__Type_OProjl(X18463,X18462,hAPP(c_Sum__Type_OInl(X18463,X18462),X18461)) = X18461,
inference(variable_rename,[status(thm)],[fact_Projl_Osimps]) ).
fof(i_0_10422,plain,
! [X30186,X30187] : c_Relation_Orefl__on(X30187,c_Orderings_Otop__class_Otop(tc_fun(X30187,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X30187,X30186)),
inference(variable_rename,[status(thm)],[fact_refl__rtrancl]) ).
cnf(i_0_10423,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_5979]) ).
cnf(i_0_10424,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_5980]) ).
fof(i_0_10425,plain,
! [X34493,X34494] :
( ~ hBOOL(hAPP(hAPP(c_fimplies,X34494),X34493))
| ~ hBOOL(X34494)
| hBOOL(X34493) ),
inference(variable_rename,[status(thm)],[i_0_5981]) ).
fof(i_0_10426,plain,
! [X27655,X27656] :
( ~ class_Orderings_Olinorder(X27656)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27656,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X27656),X27655)) = hAPP(c_SetInterval_Oord__class_OatMost(X27656),X27655) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__greaterThan])]) ).
fof(i_0_10427,plain,
! [X27611,X27612] :
( ~ class_Orderings_Olinorder(X27612)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27612,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X27612),X27611)) = hAPP(c_SetInterval_Oord__class_OlessThan(X27612),X27611) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__atLeast])]) ).
fof(i_0_10428,plain,
! [X27613,X27614] :
( ~ class_Orderings_Olinorder(X27614)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27614,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X27614),X27613)) = hAPP(c_SetInterval_Oord__class_OatLeast(X27614),X27613) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__lessThan])]) ).
fof(i_0_10429,plain,
! [X27657,X27658] :
( ~ class_Orderings_Olinorder(X27658)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27658,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X27658),X27657)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X27658),X27657) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__atMost])]) ).
fof(i_0_10430,plain,
! [X25457,X25458] :
( ( hAPP(c_Finite__Set_Ocard(X25458),X25457) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X25457 = c_Orderings_Obot__class_Obot(tc_fun(X25458,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25458),X25457)) )
& ( X25457 != c_Orderings_Obot__class_Obot(tc_fun(X25458,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(X25458),X25457) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X25458),X25457))
| hAPP(c_Finite__Set_Ocard(X25458),X25457) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5982])])]) ).
fof(i_0_10431,plain,
! [X23201,X23202] : c_Hoare__Mirabelle_Ohoare__derivs(X23202,X23201,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X23202),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_hoare__derivs_Oequations_I1_J]) ).
fof(i_0_10432,plain,
! [X23199,X23200] : c_Hoare__Mirabelle_Ohoare__derivs(X23200,X23199,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X23200),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_empty]) ).
fof(i_0_10433,plain,
! [X31418,X31419] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31419)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31419),X31418))
| X31418 = c_Orderings_Obot__class_Obot(tc_fun(X31419,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OSup__fin(X31419,X31418) = c_Complete__Lattice_OSup__class_OSup(X31419,X31418) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin__Sup])]) ).
fof(i_0_10434,plain,
! [X31423,X31424] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31424)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31424),X31423))
| X31423 = c_Orderings_Obot__class_Obot(tc_fun(X31424,tc_HOL_Obool))
| c_Big__Operators_Olattice__class_OInf__fin(X31424,X31423) = c_Complete__Lattice_OInf__class_OInf(X31424,X31423) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin__Inf])]) ).
fof(i_0_10435,plain,
! [X21151,X21152] :
( ~ class_Int_Onumber__ring(X21152)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21152),hAPP(c_Int_Onumber__class_Onumber__of(X21152),c_Int_OPls)),X21151) = X21151 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__numeral__0])]) ).
fof(i_0_10436,plain,
! [X18110,X18111] :
( ( X18111 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X18111 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18111),X18110) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X18110 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X18111 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18111),X18110) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X18111 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X18110 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18111),X18110) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X18110 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X18110 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18111),X18110) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X18111 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X18110 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18111),X18110) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X18111 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X18110 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18111),X18110) = 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_10437,plain,
! [X18108,X18109] :
( ( X18109 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X18109 = 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),X18109),X18108) )
& ( X18108 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X18109 = 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),X18109),X18108) )
& ( X18109 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X18108 = 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),X18109),X18108) )
& ( X18108 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X18108 = 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),X18109),X18108) )
& ( X18109 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X18108 != 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),X18109),X18108) )
& ( X18109 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X18108 != 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),X18109),X18108) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__is__add])])]) ).
fof(i_0_10438,plain,
! [X30003,X30004,X30005] :
( ~ hBOOL(hAPP(X30004,X30005))
| hBOOL(hAPP(X30004,c_Hilbert__Choice_OEps(X30003,X30004))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_someI__ex])])]) ).
fof(i_0_10439,plain,
! [X29990,X29991,X29992] :
( ~ hBOOL(hAPP(X29992,X29991))
| hBOOL(hAPP(X29992,c_Hilbert__Choice_OEps(X29990,X29992))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_someI])]) ).
fof(i_0_10440,plain,
! [X29987,X29988,X29989] :
( ~ hBOOL(hAPP(X29988,X29989))
| hBOOL(hAPP(X29988,c_Hilbert__Choice_OEps(X29987,X29988))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tfl__some])])]) ).
fof(i_0_10441,plain,
! [X34487,X34488] :
( ~ hBOOL(hAPP(hAPP(c_fdisj,X34488),X34487))
| hBOOL(X34488)
| hBOOL(X34487) ),
inference(variable_rename,[status(thm)],[i_0_5983]) ).
fof(i_0_10442,plain,
! [X26474,X26475] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X26475),X26474) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X26475,X26474),
inference(variable_rename,[status(thm)],[fact_atLeastSucAtMost__greaterThanAtMost]) ).
fof(i_0_10443,plain,
! [X18688,X18689] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18689),X18688),X18688) != c_Groups_Oone__class_Oone(X18689)
| X18688 = c_Groups_Oone__class_Oone(X18689)
| X18688 = hAPP(c_Groups_Ouminus__class_Ouminus(X18689),c_Groups_Oone__class_Oone(X18689))
| ~ class_Rings_Oring__1__no__zero__divisors(X18689) )
& ( X18688 != c_Groups_Oone__class_Oone(X18689)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18689),X18688),X18688) = c_Groups_Oone__class_Oone(X18689)
| ~ class_Rings_Oring__1__no__zero__divisors(X18689) )
& ( X18688 != hAPP(c_Groups_Ouminus__class_Ouminus(X18689),c_Groups_Oone__class_Oone(X18689))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18689),X18688),X18688) = c_Groups_Oone__class_Oone(X18689)
| ~ class_Rings_Oring__1__no__zero__divisors(X18689) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__1__iff])])]) ).
fof(i_0_10444,plain,
! [X18454,X18455,X18456,X18457] :
( hAPP(c_Sum__Type_OInl(X18457,X18456),X18455) != hAPP(c_Sum__Type_OInl(X18457,X18456),X18454)
| X18455 = X18454 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inl__inject])]) ).
fof(i_0_10445,plain,
! [X18450,X18451,X18452,X18453] :
( ( hAPP(c_Sum__Type_OInl(X18453,X18452),X18451) != hAPP(c_Sum__Type_OInl(X18453,X18452),X18450)
| X18451 = X18450 )
& ( X18451 != X18450
| hAPP(c_Sum__Type_OInl(X18453,X18452),X18451) = hAPP(c_Sum__Type_OInl(X18453,X18452),X18450) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum_Osimps_I1_J])]) ).
fof(i_0_10446,plain,
! [X18446,X18447,X18448,X18449] :
( hAPP(c_Sum__Type_OInr(X18449,X18448),X18447) != hAPP(c_Sum__Type_OInr(X18449,X18448),X18446)
| X18447 = X18446 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inr__inject])]) ).
fof(i_0_10447,plain,
! [X18442,X18443,X18444,X18445] :
( ( hAPP(c_Sum__Type_OInr(X18445,X18444),X18443) != hAPP(c_Sum__Type_OInr(X18445,X18444),X18442)
| X18443 = X18442 )
& ( X18443 != X18442
| hAPP(c_Sum__Type_OInr(X18445,X18444),X18443) = hAPP(c_Sum__Type_OInr(X18445,X18444),X18442) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum_Osimps_I2_J])]) ).
fof(i_0_10448,plain,
! [X17100,X17101] :
( hAPP(X17101,esk1_2(X17100,X17101)) != hAPP(X17100,esk1_2(X17100,X17101))
| X17101 = X17100 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).
fof(i_0_10449,plain,
! [X32767,X32768,X32769] : hAPP(hAPP(c_List_Ozip(X32769,X32768),X32767),c_List_Olist_ONil(X32768)) = c_List_Olist_ONil(tc_prod(X32769,X32768)),
inference(variable_rename,[status(thm)],[fact_zip_Osimps_I1_J]) ).
fof(i_0_10450,plain,
! [X17431,X17432,X17433,X17434] :
( ~ c_Groups_Ocomm__monoid(X17434,X17433,X17432)
| hAPP(hAPP(X17433,X17431),X17432) = X17431 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__monoid_Ocomm__neutral])]) ).
fof(i_0_10451,plain,
! [X27569,X27570,X27571,X27572] :
( ~ c_Finite__Set_Ofolding__one__idem(X27572,X27571,X27570)
| hAPP(hAPP(X27571,X27569),X27569) = X27569 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oidem])]) ).
fof(i_0_10452,plain,
! [X17161,X17162,X17163] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(X17163,X17162,X17161)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_com_Osize_I16_J]) ).
fof(i_0_10453,plain,
! [X23057,X23058] :
( ~ class_Rings_Ocomm__semiring__1(X23058)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23058),X23057),c_Groups_Ozero__class_Ozero(X23058))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__0__right])]) ).
fof(i_0_10454,plain,
! [X28147,X28148] :
( ~ class_Orderings_Otop(X28148)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28148),X28147),c_Orderings_Otop__class_Otop(X28148))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__greatest])]) ).
fof(i_0_10455,plain,
! [X18426,X18427,X18428,X18429] : hAPP(c_Sum__Type_OInl(X18429,X18428),X18427) != hAPP(c_Sum__Type_OInr(X18428,X18429),X18426),
inference(variable_rename,[status(thm)],[fact_Inl__not__Inr]) ).
fof(i_0_10456,plain,
! [X18422,X18423,X18424,X18425] : hAPP(c_Sum__Type_OInl(X18425,X18424),X18423) != hAPP(c_Sum__Type_OInr(X18424,X18425),X18422),
inference(variable_rename,[status(thm)],[fact_sum_Osimps_I3_J]) ).
fof(i_0_10457,plain,
! [X18418,X18419,X18420,X18421] : hAPP(c_Sum__Type_OInr(X18421,X18420),X18419) != hAPP(c_Sum__Type_OInl(X18420,X18421),X18418),
inference(variable_rename,[status(thm)],[fact_Inr__not__Inl]) ).
fof(i_0_10458,plain,
! [X18414,X18415,X18416,X18417] : hAPP(c_Sum__Type_OInr(X18417,X18416),X18415) != hAPP(c_Sum__Type_OInl(X18416,X18417),X18414),
inference(variable_rename,[status(thm)],[fact_sum_Osimps_I4_J]) ).
fof(i_0_10459,plain,
! [X33730,X33731,X33732] :
( X33732 != c_List_Olist_ONil(X33731)
| c_List_Olast(X33731,hAPP(hAPP(c_List_Olist_OCons(X33731),X33730),X33732)) = X33730 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__ConsL])]) ).
fof(i_0_10460,plain,
! [X22002,X22003,X22004] : hAPP(c_Nat_Onat_Onat__rec(X22004,X22003,X22002),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X22003,
inference(variable_rename,[status(thm)],[fact_nat__rec__0]) ).
fof(i_0_10461,plain,
! [X23098,X23099,X23100] : hAPP(hAPP(c_Set_Oinsert(X23100),X23099),X23098) != c_Orderings_Obot__class_Obot(tc_fun(X23100,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_insert__not__empty]) ).
fof(i_0_10462,plain,
! [X23101,X23102,X23103] : c_Orderings_Obot__class_Obot(tc_fun(X23103,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(X23103),X23102),X23101),
inference(variable_rename,[status(thm)],[fact_empty__not__insert]) ).
fof(i_0_10463,plain,
! [X34479,X34480] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X34480),X34479))
| hBOOL(X34480) ),
inference(variable_rename,[status(thm)],[i_0_5984]) ).
fof(i_0_10464,plain,
! [X34481,X34482] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X34482),X34481))
| hBOOL(X34481) ),
inference(variable_rename,[status(thm)],[i_0_5985]) ).
fof(i_0_10465,plain,
! [X18663] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X18663)) = 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),X18663)),
inference(variable_rename,[status(thm)],[fact_int__Suc]) ).
fof(i_0_10466,plain,
! [X20488,X20489] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20489),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20488)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20489),X20488),
inference(variable_rename,[status(thm)],[fact_diff__int__def__symmetric]) ).
fof(i_0_10467,plain,
! [X20490,X20491] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20491),X20490) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20491),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20490)),
inference(variable_rename,[status(thm)],[fact_diff__int__def]) ).
fof(i_0_10468,plain,
! [X33510,X33511,X33512] : hAPP(c_List_Otl(X33512),hAPP(hAPP(c_List_Olist_OCons(X33512),X33511),X33510)) = X33510,
inference(variable_rename,[status(thm)],[fact_tl_Osimps_I2_J]) ).
fof(i_0_10469,plain,
! [X33451,X33452,X33453] : hAPP(c_List_Ohd(X33453),hAPP(hAPP(c_List_Olist_OCons(X33453),X33452),X33451)) = X33452,
inference(variable_rename,[status(thm)],[fact_hd_Osimps]) ).
fof(i_0_10470,plain,
! [X20965,X20966,X20967] :
( ( X20966 = c_Groups_Ozero__class_Ozero(X20967)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20967),X20966),X20965) != c_Groups_Ozero__class_Ozero(X20967)
| ~ class_Power_Opower(X20967)
| ~ class_Rings_Omult__zero(X20967)
| ~ class_Rings_Ono__zero__divisors(X20967)
| ~ class_Rings_Ozero__neq__one(X20967) )
& ( X20965 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20967),X20966),X20965) != c_Groups_Ozero__class_Ozero(X20967)
| ~ class_Power_Opower(X20967)
| ~ class_Rings_Omult__zero(X20967)
| ~ class_Rings_Ono__zero__divisors(X20967)
| ~ class_Rings_Ozero__neq__one(X20967) )
& ( X20966 != c_Groups_Ozero__class_Ozero(X20967)
| X20965 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20967),X20966),X20965) = c_Groups_Ozero__class_Ozero(X20967)
| ~ class_Power_Opower(X20967)
| ~ class_Rings_Omult__zero(X20967)
| ~ class_Rings_Ono__zero__divisors(X20967)
| ~ class_Rings_Ozero__neq__one(X20967) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff])])]) ).
fof(i_0_10471,plain,
! [X21511,X21512] :
( ~ c_Nat__Transfer_Ois__nat(X21512)
| ~ c_Nat__Transfer_Ois__nat(X21511)
| c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X21512,X21511)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__int__nat__function__closures_I2_J])]) ).
fof(i_0_10472,plain,
! [X17836,X17837] :
( ~ hBOOL(hAPP(c_Com_OWT,X17837))
| hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X17836,X17837))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_While])]) ).
fof(i_0_10473,plain,
! [X29167,X29168,X29169,X29170,X29172] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X29168,tc_HOL_Obool)) != hAPP(c_Set_OCollect(X29168),X29167)
| ~ hBOOL(hAPP(X29167,X29169)) )
& ( hBOOL(hAPP(X29170,esk309_1(X29170)))
| c_Orderings_Obot__class_Obot(tc_fun(X29172,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X29172),X29170) ) ),
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_5986])])])])]) ).
fof(i_0_10474,plain,
! [X29173,X29174,X29175,X29176,X29178] :
( ( hAPP(c_Set_OCollect(X29174),X29173) != c_Orderings_Obot__class_Obot(tc_fun(X29174,tc_HOL_Obool))
| ~ hBOOL(hAPP(X29173,X29175)) )
& ( hBOOL(hAPP(X29176,esk310_1(X29176)))
| hAPP(c_Set_OCollect(X29178),X29176) = c_Orderings_Obot__class_Obot(tc_fun(X29178,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_5987])])])])]) ).
fof(i_0_10475,plain,
! [X34471,X34472] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X34472),X34471))
| X34472 = X34471 ),
inference(variable_rename,[status(thm)],[i_0_5988]) ).
fof(i_0_10476,plain,
! [X21752,X21753] :
( ~ class_Fields_Ofield__inverse__zero(X21753)
| ~ class_Int_Onumber__ring(X21753)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21753),X21752),hAPP(c_Int_Onumber__class_Onumber__of(X21753),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(X21753),X21752) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__minus1])]) ).
fof(i_0_10477,plain,
! [X29670,X29671,X29672] :
( ~ c_Wellfounded_Owf(X29672,X29671)
| c_Wellfounded_Owf(tc_List_Olist(X29672),hAPP(c_List_Olexn(X29672,X29671),X29670)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__lexn])]) ).
fof(i_0_10478,plain,
! [X32796,X32797,X32798] : hAPP(hAPP(c_List_Olist__update(X32798,c_List_Olist_ONil(X32798)),X32797),X32796) = c_List_Olist_ONil(X32798),
inference(variable_rename,[status(thm)],[fact_list__update_Osimps_I1_J]) ).
fof(i_0_10479,plain,
! [X32793,X32794,X32795] : hAPP(hAPP(c_List_Olist__update(X32795,c_List_Olist_ONil(X32795)),X32794),X32793) = c_List_Olist_ONil(X32795),
inference(variable_rename,[status(thm)],[fact_list__update__code_I1_J]) ).
fof(i_0_10480,plain,
! [X20903] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X20903) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_power__Suc__0]) ).
fof(i_0_10481,plain,
! [X31822,X31823] : hBOOL(hAPP(c_Finite__Set_Ofinite(X31823),hAPP(c_List_Oset(X31823),X31822))),
inference(variable_rename,[status(thm)],[fact_finite__set]) ).
fof(i_0_10482,plain,
! [X30361,X30362,X30363] : hAPP(c_Relation_Oconverse(X30363,X30362),hAPP(c_Relation_Oconverse(X30362,X30363),X30361)) = X30361,
inference(variable_rename,[status(thm)],[fact_converse__converse]) ).
fof(i_0_10483,plain,
! [X27076] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X27076)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X27076),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X27076)),
inference(variable_rename,[status(thm)],[fact_lessThan__Suc]) ).
fof(i_0_10484,plain,
! [X30359,X30360] : hAPP(c_Relation_OField(X30360),hAPP(c_Relation_Oconverse(X30360,X30360),X30359)) = hAPP(c_Relation_OField(X30360),X30359),
inference(variable_rename,[status(thm)],[fact_Field__converse]) ).
fof(i_0_10485,plain,
! [X20819,X20820] :
( ~ class_Int_Onumber__ring(X20820)
| hAPP(c_Int_Onumber__class_Onumber__of(X20820),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20819)) = hAPP(c_Groups_Ouminus__class_Ouminus(X20820),hAPP(c_Int_Onumber__class_Onumber__of(X20820),X20819)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__minus])]) ).
fof(i_0_10486,plain,
! [X18697,X18698] :
( ~ class_Rings_Oring__1(X18698)
| hAPP(c_Int_Oring__1__class_Oof__int(X18698),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X18697)) = hAPP(c_Groups_Ouminus__class_Ouminus(X18698),hAPP(c_Int_Oring__1__class_Oof__int(X18698),X18697)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__minus])]) ).
fof(i_0_10487,plain,
! [X20817,X20818] :
( ~ class_Int_Onumber__ring(X20818)
| hAPP(c_Groups_Ouminus__class_Ouminus(X20818),hAPP(c_Int_Onumber__class_Onumber__of(X20818),X20817)) = hAPP(c_Int_Onumber__class_Onumber__of(X20818),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20817)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__simps_I30_J])]) ).
fof(i_0_10488,plain,
! [X20901,X20902] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20902),X20901) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X20901 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X20902 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X20901 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20902),X20901) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X20902 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20902),X20901) = 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_10489,plain,
! [X19119,X19120,X19121] :
( ~ class_Orderings_Opreorder(X19121)
| X19120 != X19119
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19121),X19120),X19119)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__refl])]) ).
fof(i_0_10490,plain,
! [X18134,X18135] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(X18135,X18134)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X18134)),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_10491,plain,
! [X18885,X18886,X18887] :
( ~ class_Groups_Ogroup__add(X18887)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18887),X18886),X18885) != c_Groups_Ozero__class_Ozero(X18887)
| hAPP(c_Groups_Ouminus__class_Ouminus(X18887),X18886) = X18885 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__unique])]) ).
fof(i_0_10492,plain,
! [X18892,X18893,X18894] :
( ( X18893 != hAPP(c_Groups_Ouminus__class_Ouminus(X18894),X18892)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18894),X18893),X18892) = c_Groups_Ozero__class_Ozero(X18894)
| ~ class_Groups_Ogroup__add(X18894) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18894),X18893),X18892) != c_Groups_Ozero__class_Ozero(X18894)
| X18893 = hAPP(c_Groups_Ouminus__class_Ouminus(X18894),X18892)
| ~ class_Groups_Ogroup__add(X18894) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__neg__iff__add__eq__0])])]) ).
fof(i_0_10493,plain,
! [X29154] : c_Orderings_Otop__class_Otop(tc_fun(X29154,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X29154),hAPP(c_COMBK(tc_HOL_Obool,X29154),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(i_0_10494,plain,
! [X29179] : c_Orderings_Obot__class_Obot(tc_fun(X29179,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X29179),hAPP(c_COMBK(tc_HOL_Obool,X29179),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(i_0_10495,plain,
! [X26446,X26447] :
( ~ c_Nat__Transfer_Ois__nat(X26447)
| c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X26447,X26446)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__int__nat__set__function__closures])]) ).
fof(i_0_10496,plain,
! [X21112,X21113] :
( ~ class_Int_Onumber__ring(X21113)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21113),X21112),hAPP(c_Int_Onumber__class_Onumber__of(X21113),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(X21113),X21112) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__minus1__right])]) ).
fof(i_0_10497,plain,
! [X19477,X19478] :
( ( X19478 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19478),X19477) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X19477 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19478),X19477) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X19478 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X19477 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19478),X19477) = 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_10498,plain,
! [X18123] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X18123)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X18123)),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_10499,plain,
! [X23215,X23216] :
( ~ class_Rings_Ocomm__semiring__1(X23216)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X23216),X23215),X23215)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__refl])]) ).
fof(i_0_10500,plain,
! [X19030,X19031] :
( ~ class_Orderings_Opreorder(X19031)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19031),X19030),X19030)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])]) ).
fof(i_0_10501,plain,
! [X26918] : 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)),X26918)) = hAPP(c_Int_Onat,X26918),
inference(variable_rename,[status(thm)],[fact_card__atLeastZeroLessThan__int]) ).
fof(i_0_10502,plain,
! [X17158,X17159,X17160] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(X17160,X17159,X17158)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_com_Osize_I8_J]) ).
fof(i_0_10503,plain,
! [X18969] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X18969)),X18969) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zadd__zminus__inverse2]) ).
fof(i_0_10504,plain,
! [X26807,X26808] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26808),hAPP(c_Nat_OSuc,X26807)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26808,X26807),
inference(variable_rename,[status(thm)],[fact_atLeastLessThanSuc__atLeastAtMost]) ).
fof(i_0_10505,plain,
! [X22203,X22204] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X22204,X22203) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X22204,X22203)),
inference(variable_rename,[status(thm)],[fact_mod__int__def]) ).
fof(i_0_10506,plain,
! [X24899,X24900,X24901] :
( ~ class_Lattices_Osemilattice__inf(X24901)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24901),X24900),X24899) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24901),X24899),X24900) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__commute])]) ).
fof(i_0_10507,plain,
! [X24893,X24894,X24895] :
( ~ class_Lattices_Osemilattice__inf(X24895)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24895),X24894),X24893) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24895),X24893),X24894) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Ocommute])]) ).
fof(i_0_10508,plain,
! [X24896,X24897,X24898] :
( ~ class_Lattices_Olattice(X24898)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24898),X24897),X24896) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24898),X24896),X24897) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I1_J])]) ).
fof(i_0_10509,plain,
! [X24116,X24117,X24118] :
( ~ class_Lattices_Osemilattice__sup(X24118)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24118),X24117),X24116) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24118),X24116),X24117) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Ocommute])]) ).
fof(i_0_10510,plain,
! [X24110,X24111,X24112] :
( ~ class_Lattices_Osemilattice__sup(X24112)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24112),X24111),X24110) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24112),X24110),X24111) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__commute])]) ).
fof(i_0_10511,plain,
! [X24113,X24114,X24115] :
( ~ class_Lattices_Olattice(X24115)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24115),X24114),X24113) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24115),X24113),X24114) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I5_J])]) ).
fof(i_0_10512,plain,
! [X22627,X22628,X22629] :
( ~ class_Orderings_Olinorder(X22629)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22629),X22628),X22627) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22629),X22627),X22628) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__commute])]) ).
fof(i_0_10513,plain,
! [X22624,X22625,X22626] :
( ~ class_Orderings_Olinorder(X22626)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22626),X22625),X22624) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22626),X22624),X22625) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Ocommute])]) ).
fof(i_0_10514,plain,
! [X22535,X22536,X22537] :
( ~ class_Orderings_Olinorder(X22537)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22537),X22536),X22535) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22537),X22535),X22536) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Ocommute])]) ).
fof(i_0_10515,plain,
! [X22532,X22533,X22534] :
( ~ class_Orderings_Olinorder(X22534)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22534),X22533),X22532) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22534),X22532),X22533) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__commute])]) ).
fof(i_0_10516,plain,
! [X18708,X18709,X18710] :
( ~ class_Rings_Ocomm__semiring__1(X18710)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18710),X18709),X18708) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18710),X18708),X18709) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])]) ).
fof(i_0_10517,plain,
! [X18184,X18185,X18186] :
( ~ class_Rings_Ocomm__semiring__1(X18186)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18186),X18185),X18184) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18186),X18184),X18185) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).
fof(i_0_10518,plain,
! [X18783] : hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18783))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_nat__zminus__int]) ).
fof(i_0_10519,plain,
! [X18308] :
( X18308 = 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)),X18308)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0I])]) ).
fof(i_0_10520,plain,
! [X21513,X21514] :
( ~ c_Nat__Transfer_Ois__nat(X21514)
| ~ c_Nat__Transfer_Ois__nat(X21513)
| c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21514),X21513)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__int__nat__function__closures_I1_J])]) ).
fof(i_0_10521,plain,
! [X21509,X21510] :
( ~ c_Nat__Transfer_Ois__nat(X21510)
| ~ c_Nat__Transfer_Ois__nat(X21509)
| c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21510),X21509)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J])]) ).
fof(i_0_10522,plain,
! [X21506,X21507] :
( ~ c_Nat__Transfer_Ois__nat(X21507)
| ~ c_Nat__Transfer_Ois__nat(X21506)
| c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21507),X21506)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J])]) ).
fof(i_0_10523,plain,
! [X18970,X18971] :
( ( X18971 = 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),X18971)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18970) )
& ( X18970 = 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),X18971)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18970) )
& ( X18971 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X18970 != 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),X18971)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18970) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negative__eq__positive])])]) ).
fof(i_0_10524,plain,
! [X17882,X17883,X17884,X17885,X17886] : c_Com_Ocom_OLocal(X17886,X17885,X17884) != c_Com_Ocom_OWhile(X17883,X17882),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I38_J]) ).
fof(i_0_10525,plain,
! [X17634,X17635,X17636,X17637,X17638] : c_Com_Ocom_OLocal(X17638,X17637,X17636) != c_Com_Ocom_OSemi(X17635,X17634),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I34_J]) ).
fof(i_0_10526,plain,
! [X17612,X17613,X17614,X17615,X17616] : c_Com_Ocom_OLocal(X17616,X17615,X17614) != c_Com_Ocom_OAss(X17613,X17612),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I23_J]) ).
fof(i_0_10527,plain,
! [X17846,X17847,X17848,X17849,X17850] : c_Com_Ocom_OCond(X17850,X17849,X17848) != c_Com_Ocom_OWhile(X17847,X17846),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I52_J]) ).
fof(i_0_10528,plain,
! [X17672,X17673,X17674,X17675,X17676] : c_Com_Ocom_OCond(X17676,X17675,X17674) != c_Com_Ocom_OSemi(X17673,X17672),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I45_J]) ).
fof(i_0_10529,plain,
! [X17650,X17651,X17652,X17653,X17654] : c_Com_Ocom_OCond(X17654,X17653,X17652) != c_Com_Ocom_OAss(X17651,X17650),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I27_J]) ).
fof(i_0_10530,plain,
! [X17872,X17873,X17874,X17875,X17876] : c_Com_Ocom_OCall(X17876,X17875,X17874) != c_Com_Ocom_OWhile(X17873,X17872),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I61_J]) ).
fof(i_0_10531,plain,
! [X17387,X17388,X17389,X17390,X17391] : c_Com_Ocom_OCall(X17391,X17390,X17389) != c_Com_Ocom_OSemi(X17388,X17387),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I51_J]) ).
fof(i_0_10532,plain,
! [X17198,X17199,X17200,X17201,X17202] : c_Com_Ocom_OCall(X17202,X17201,X17200) != c_Com_Ocom_OAss(X17199,X17198),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I33_J]) ).
fof(i_0_10533,plain,
! [X17887,X17888,X17889,X17890,X17891] : c_Com_Ocom_OWhile(X17891,X17890) != c_Com_Ocom_OLocal(X17889,X17888,X17887),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I39_J]) ).
fof(i_0_10534,plain,
! [X17851,X17852,X17853,X17854,X17855] : c_Com_Ocom_OWhile(X17855,X17854) != c_Com_Ocom_OCond(X17853,X17852,X17851),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I53_J]) ).
fof(i_0_10535,plain,
! [X17877,X17878,X17879,X17880,X17881] : c_Com_Ocom_OWhile(X17881,X17880) != c_Com_Ocom_OCall(X17879,X17878,X17877),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I60_J]) ).
fof(i_0_10536,plain,
! [X17629,X17630,X17631,X17632,X17633] : c_Com_Ocom_OSemi(X17633,X17632) != c_Com_Ocom_OLocal(X17631,X17630,X17629),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I35_J]) ).
fof(i_0_10537,plain,
! [X17667,X17668,X17669,X17670,X17671] : c_Com_Ocom_OSemi(X17671,X17670) != c_Com_Ocom_OCond(X17669,X17668,X17667),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I44_J]) ).
fof(i_0_10538,plain,
! [X17392,X17393,X17394,X17395,X17396] : c_Com_Ocom_OSemi(X17396,X17395) != c_Com_Ocom_OCall(X17394,X17393,X17392),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I50_J]) ).
fof(i_0_10539,plain,
! [X17607,X17608,X17609,X17610,X17611] : c_Com_Ocom_OAss(X17611,X17610) != c_Com_Ocom_OLocal(X17609,X17608,X17607),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I22_J]) ).
fof(i_0_10540,plain,
! [X17645,X17646,X17647,X17648,X17649] : c_Com_Ocom_OAss(X17649,X17648) != c_Com_Ocom_OCond(X17647,X17646,X17645),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I26_J]) ).
fof(i_0_10541,plain,
! [X17190,X17191,X17192,X17193,X17194] : c_Com_Ocom_OAss(X17194,X17193) != c_Com_Ocom_OCall(X17192,X17191,X17190),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I32_J]) ).
cnf(i_0_10542,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_5989]) ).
fof(i_0_10543,plain,
! [X19264] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19264)),
inference(variable_rename,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).
fof(i_0_10544,plain,
! [X19032] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19032)),
inference(variable_rename,[status(thm)],[fact_le0]) ).
fof(i_0_10545,plain,
! [X30480,X30481] : c_Relation_Ototal__on(X30481,c_Orderings_Obot__class_Obot(tc_fun(X30481,tc_HOL_Obool)),X30480),
inference(variable_rename,[status(thm)],[fact_total__on__empty]) ).
fof(i_0_10546,plain,
! [X18830,X18831,X18832] :
( ~ class_Rings_Ono__zero__divisors(X18832)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18832),X18831),X18830) != c_Groups_Ozero__class_Ozero(X18832)
| X18831 = c_Groups_Ozero__class_Ozero(X18832)
| X18830 = c_Groups_Ozero__class_Ozero(X18832) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divisors__zero])]) ).
fof(i_0_10547,plain,
! [X18827,X18828,X18829] :
( ~ class_Rings_Ono__zero__divisors(X18829)
| X18828 = c_Groups_Ozero__class_Ozero(X18829)
| X18827 = c_Groups_Ozero__class_Ozero(X18829)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18829),X18828),X18827) != c_Groups_Ozero__class_Ozero(X18829) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_no__zero__divisors])]) ).
fof(i_0_10548,plain,
! [X18824,X18825,X18826] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18826),X18825),X18824) != c_Groups_Ozero__class_Ozero(X18826)
| X18825 = c_Groups_Ozero__class_Ozero(X18826)
| X18824 = c_Groups_Ozero__class_Ozero(X18826)
| ~ class_Rings_Oring__no__zero__divisors(X18826) )
& ( X18825 != c_Groups_Ozero__class_Ozero(X18826)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18826),X18825),X18824) = c_Groups_Ozero__class_Ozero(X18826)
| ~ class_Rings_Oring__no__zero__divisors(X18826) )
& ( X18824 != c_Groups_Ozero__class_Ozero(X18826)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18826),X18825),X18824) = c_Groups_Ozero__class_Ozero(X18826)
| ~ class_Rings_Oring__no__zero__divisors(X18826) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__0__iff])])]) ).
fof(i_0_10549,plain,
! [X21965] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21965) = 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_10550,plain,
! [X22328,X22329] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22329),X22328) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X22329,X22328)),
inference(variable_rename,[status(thm)],[fact_div__int__def]) ).
fof(i_0_10551,plain,
! [X20971,X20972] :
( ~ class_Power_Opower(X20972)
| ~ class_Rings_Osemiring__0(X20972)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20972),c_Groups_Ozero__class_Ozero(X20972)),hAPP(c_Nat_OSuc,X20971)) = c_Groups_Ozero__class_Ozero(X20972) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__Suc])]) ).
fof(i_0_10552,plain,
! [X21743,X21744] :
( ~ class_Fields_Ofield__inverse__zero(X21744)
| ~ class_Int_Onumber__ring(X21744)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21744),X21743),hAPP(c_Int_Onumber__class_Onumber__of(X21744),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(X21744) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__Numeral0])]) ).
fof(i_0_10553,plain,
! [X20821,X20822] :
( ~ class_Rings_Olinordered__idom(X20822)
| hAPP(c_Groups_Oabs__class_Oabs(X20822),X20821) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20822),X20821),c_Groups_Osgn__class_Osgn(X20822,X20821)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__sgn])]) ).
fof(i_0_10554,plain,
! [X17589,X17590,X17591,X17592] : c_Com_Ocom_OLocal(X17592,X17591,X17590) != hAPP(c_Com_Ocom_OBODY,X17589),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I40_J]) ).
fof(i_0_10555,plain,
! [X17603,X17604,X17605,X17606] : c_Com_Ocom_OCond(X17606,X17605,X17604) != hAPP(c_Com_Ocom_OBODY,X17603),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I54_J]) ).
fof(i_0_10556,plain,
! [X17256,X17257,X17258,X17259] : c_Com_Ocom_OCall(X17259,X17258,X17257) != hAPP(c_Com_Ocom_OBODY,X17256),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I63_J]) ).
fof(i_0_10557,plain,
! [X17585,X17586,X17587,X17588] : hAPP(c_Com_Ocom_OBODY,X17588) != c_Com_Ocom_OLocal(X17587,X17586,X17585),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I41_J]) ).
fof(i_0_10558,plain,
! [X17599,X17600,X17601,X17602] : hAPP(c_Com_Ocom_OBODY,X17602) != c_Com_Ocom_OCond(X17601,X17600,X17599),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I55_J]) ).
fof(i_0_10559,plain,
! [X17252,X17253,X17254,X17255] : hAPP(c_Com_Ocom_OBODY,X17255) != c_Com_Ocom_OCall(X17254,X17253,X17252),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I62_J]) ).
fof(i_0_10560,plain,
! [X33681] : c_List_Olists(X33681,c_Orderings_Otop__class_Otop(tc_fun(X33681,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X33681),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_lists__UNIV]) ).
fof(i_0_10561,plain,
! [X31756,X31757] : hAPP(hAPP(c_List_Omap(X31757,X31757),c_COMBI(X31757)),X31756) = X31756,
inference(variable_rename,[status(thm)],[fact_map__ident]) ).
fof(i_0_10562,plain,
! [X29763,X29764,X29765] :
( ~ c_Wellfounded_OwfP(X29765,X29764)
| hBOOL(hAPP(c_Wellfounded_Oaccp(X29765,X29764),X29763)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__wfPD])]) ).
fof(i_0_10563,plain,
! [X29333,X29334,X29335] :
( ~ c_Predicate_Oreflp(X29335,X29334)
| hBOOL(hAPP(hAPP(X29334,X29333),X29333)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reflpE])]) ).
fof(i_0_10564,plain,
! [X28351,X28352,X28353] :
( ~ c_Equiv__Relations_Oequivp(X28353,X28352)
| hBOOL(hAPP(hAPP(X28352,X28351),X28351)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__reflp])]) ).
fof(i_0_10565,plain,
! [X32737,X32738] : c_List_Osublist(X32738,X32737,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(X32738),
inference(variable_rename,[status(thm)],[fact_sublist__empty]) ).
fof(i_0_10566,plain,
! [X21594,X21595,X21596] :
( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21596),X21594),X21595) != c_Groups_Oone__class_Oone(X21596)
| X21594 = X21595
| X21595 = c_Groups_Ozero__class_Ozero(X21596)
| ~ class_Rings_Odivision__ring(X21596) )
& ( X21594 != X21595
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21596),X21594),X21595) = c_Groups_Oone__class_Oone(X21596)
| X21595 = c_Groups_Ozero__class_Ozero(X21596)
| ~ class_Rings_Odivision__ring(X21596) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__inverse__eq])])]) ).
fof(i_0_10567,plain,
! [X34276,X34277] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34277)),hAPP(c_List_Orev(X34277),X34276)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34277)),X34276),
inference(variable_rename,[status(thm)],[fact_length__rev]) ).
fof(i_0_10568,plain,
! [X33367,X33368] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33368)),hAPP(c_List_Orotate1(X33368),X33367)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33368)),X33367),
inference(variable_rename,[status(thm)],[fact_length__rotate1]) ).
fof(i_0_10569,plain,
! [X30006,X30007,X30008,X30009] :
( ~ hBOOL(hAPP(X30008,X30009))
| X30007 != c_Hilbert__Choice_OEps(X30006,X30008)
| hBOOL(hAPP(X30008,X30007)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exE__some])])]) ).
fof(i_0_10570,plain,
! [X30511,X30512] : hAPP(hAPP(c_Nat_Ocompow(X30512,X30512),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30511) = c_Fun_Oid(X30512),
inference(variable_rename,[status(thm)],[fact_funpow_Osimps_I1_J]) ).
fof(i_0_10571,plain,
! [X31892,X31893,X31894] : hAPP(hAPP(c_Option_Omap(X31894,X31893),X31892),c_Option_Ooption_ONone(X31894)) = c_Option_Ooption_ONone(X31893),
inference(variable_rename,[status(thm)],[fact_option__map__None]) ).
fof(i_0_10572,plain,
! [X32715,X32716,X32717] : hAPP(hAPP(c_List_Omap(X32717,X32716),X32715),c_List_Olist_ONil(X32717)) = c_List_Olist_ONil(X32716),
inference(variable_rename,[status(thm)],[fact_map_Osimps_I1_J]) ).
fof(i_0_10573,plain,
! [X24975,X24976] :
( ~ class_Lattices_Oboolean__algebra(X24976)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24976),X24975),hAPP(c_Groups_Ouminus__class_Ouminus(X24976),X24975)) = c_Orderings_Obot__class_Obot(X24976) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__compl__bot])]) ).
fof(i_0_10574,plain,
! [X28260,X28261] :
( ~ class_Lattices_Oboolean__algebra(X28261)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X28261),X28260),hAPP(c_Groups_Ouminus__class_Ouminus(X28261),X28260)) = c_Orderings_Otop__class_Otop(X28261) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__compl__top])]) ).
fof(i_0_10575,plain,
! [X18895,X18896] :
( ~ class_Groups_Ogroup__add(X18896)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18896),X18895),hAPP(c_Groups_Ouminus__class_Ouminus(X18896),X18895)) = c_Groups_Ozero__class_Ozero(X18896) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus])]) ).
fof(i_0_10576,plain,
! [X21515,X21516] :
( ~ c_Nat__Transfer_Ois__nat(X21516)
| c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X21516),X21515)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J])]) ).
fof(i_0_10577,plain,
! [X21120,X21121] :
( ( X21121 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| X21121 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21121),X21120) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( X21120 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| X21121 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21121),X21120) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( X21121 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| X21120 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21121),X21120) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( X21120 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| X21120 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21121),X21120) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( X21121 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X21120 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21121),X21120) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( X21121 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| X21120 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21121),X21120) = 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_10578,plain,
! [X28155,X28156,X28157] :
( ( X28156 = c_Orderings_Otop__class_Otop(X28157)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X28157),X28156),X28155) != c_Orderings_Otop__class_Otop(X28157)
| ~ class_Lattices_Obounded__lattice__top(X28157) )
& ( X28155 = c_Orderings_Otop__class_Otop(X28157)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X28157),X28156),X28155) != c_Orderings_Otop__class_Otop(X28157)
| ~ class_Lattices_Obounded__lattice__top(X28157) )
& ( X28156 != c_Orderings_Otop__class_Otop(X28157)
| X28155 != c_Orderings_Otop__class_Otop(X28157)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X28157),X28156),X28155) = c_Orderings_Otop__class_Otop(X28157)
| ~ class_Lattices_Obounded__lattice__top(X28157) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__eq__top__iff])])]) ).
fof(i_0_10579,plain,
! [X23936,X23937,X23938] :
( ( X23937 = c_Orderings_Obot__class_Obot(X23938)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23938),X23937),X23936) != c_Orderings_Obot__class_Obot(X23938)
| ~ class_Lattices_Obounded__lattice__bot(X23938) )
& ( X23936 = c_Orderings_Obot__class_Obot(X23938)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23938),X23937),X23936) != c_Orderings_Obot__class_Obot(X23938)
| ~ class_Lattices_Obounded__lattice__bot(X23938) )
& ( X23937 != c_Orderings_Obot__class_Obot(X23938)
| X23936 != c_Orderings_Obot__class_Obot(X23938)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23938),X23937),X23936) = c_Orderings_Obot__class_Obot(X23938)
| ~ class_Lattices_Obounded__lattice__bot(X23938) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__eq__bot__iff])])]) ).
fof(i_0_10580,plain,
! [X20930,X20931,X20932] :
( ~ class_Rings_Oring__1__no__zero__divisors(X20932)
| X20931 = c_Groups_Ozero__class_Ozero(X20932)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20932),X20931),X20930) != c_Groups_Ozero__class_Ozero(X20932) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__power__not__zero])]) ).
fof(i_0_10581,plain,
! [X18159,X18160] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18160),X18159),X18159) != c_Groups_Ozero__class_Ozero(X18160)
| X18159 = c_Groups_Ozero__class_Ozero(X18160)
| ~ class_Groups_Olinordered__ab__group__add(X18160) )
& ( X18159 != c_Groups_Ozero__class_Ozero(X18160)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18160),X18159),X18159) = c_Groups_Ozero__class_Ozero(X18160)
| ~ class_Groups_Olinordered__ab__group__add(X18160) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff])])]) ).
fof(i_0_10582,plain,
! [X18102,X18103] :
( ( c_Groups_Ozero__class_Ozero(X18103) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18103),X18102),X18102)
| X18102 = c_Groups_Ozero__class_Ozero(X18103)
| ~ class_Groups_Olinordered__ab__group__add(X18103) )
& ( X18102 != c_Groups_Ozero__class_Ozero(X18103)
| c_Groups_Ozero__class_Ozero(X18103) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18103),X18102),X18102)
| ~ class_Groups_Olinordered__ab__group__add(X18103) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__zero__sym])])]) ).
fof(i_0_10583,plain,
! [X27070] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X27070))),
inference(variable_rename,[status(thm)],[fact_finite__lessThan]) ).
fof(i_0_10584,plain,
! [X26940] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X26940))),
inference(variable_rename,[status(thm)],[fact_finite__atMost]) ).
cnf(i_0_10585,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_10586,plain,
! [X20900] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20900)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20900)),
inference(variable_rename,[status(thm)],[fact_minus__numeral__code_I5_J]) ).
fof(i_0_10587,plain,
! [X20282,X20283,X20284] :
( ( X20283 != X20282
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20284),X20283),X20282) = c_Groups_Ozero__class_Ozero(X20284)
| ~ class_Groups_Oab__group__add(X20284) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20284),X20283),X20282) != c_Groups_Ozero__class_Ozero(X20284)
| X20283 = X20282
| ~ class_Groups_Oab__group__add(X20284) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__iff__diff__eq__0])])]) ).
fof(i_0_10588,plain,
! [X20279,X20280,X20281] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20281),X20280),X20279) != c_Groups_Ozero__class_Ozero(X20281)
| X20280 = X20279
| ~ class_Groups_Ogroup__add(X20281) )
& ( X20280 != X20279
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20281),X20280),X20279) = c_Groups_Ozero__class_Ozero(X20281)
| ~ class_Groups_Ogroup__add(X20281) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus__eq])])]) ).
fof(i_0_10589,plain,
! [X23189,X23190] :
( X23190 != X23189
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23190),X23189)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Oeq__refl])]) ).
fof(i_0_10590,plain,
! [X19747,X19748] :
( X19748 != X19747
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19748),X19747)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__imp__le])]) ).
fof(i_0_10591,plain,
! [X32689,X32690,X32691] :
( ( hAPP(hAPP(c_List_Otake(X32691),X32690),X32689) != c_List_Olist_ONil(X32691)
| X32690 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X32689 = c_List_Olist_ONil(X32691) )
& ( X32690 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Otake(X32691),X32690),X32689) = c_List_Olist_ONil(X32691) )
& ( X32689 != c_List_Olist_ONil(X32691)
| hAPP(hAPP(c_List_Otake(X32691),X32690),X32689) = c_List_Olist_ONil(X32691) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__eq__Nil])])]) ).
fof(i_0_10592,plain,
! [X21118,X21119] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21119),X21118) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X21119 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| X21119 = 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_10593,plain,
! [X18156,X18157,X18158] :
( ( X18157 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18158),X18157),X18156)
| X18156 = c_Groups_Ozero__class_Ozero(X18158)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18158) )
& ( X18156 != c_Groups_Ozero__class_Ozero(X18158)
| X18157 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18158),X18157),X18156)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18158) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).
fof(i_0_10594,plain,
! [X20494] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20494)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X20494,
inference(variable_rename,[status(thm)],[fact_diff__Suc__1]) ).
fof(i_0_10595,plain,
! [X31994,X31995] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X31995,X31994)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X31995,X31994),
inference(variable_rename,[status(thm)],[fact_set__upto]) ).
fof(i_0_10596,plain,
! [X31996,X31997] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X31997,X31996) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X31997,X31996)),
inference(variable_rename,[status(thm)],[fact_atLeastAtMost__upto]) ).
fof(i_0_10597,plain,
! [X21149,X21150] :
( ~ class_Int_Onumber__ring(X21150)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21150),X21149),hAPP(c_Int_Onumber__class_Onumber__of(X21150),c_Int_OPls)) = X21149 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__numeral__0__right])]) ).
fof(i_0_10598,plain,
! [X23056] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X23056),X23056)),
inference(variable_rename,[status(thm)],[fact_dvd_Oorder__refl]) ).
fof(i_0_10599,plain,
! [X19070] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19070),X19070)),
inference(variable_rename,[status(thm)],[fact_zle__refl]) ).
fof(i_0_10600,plain,
! [X19751] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19751),X19751)),
inference(variable_rename,[status(thm)],[fact_le__refl]) ).
fof(i_0_10601,plain,
! [X17566] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X17566),X17566)),
inference(variable_rename,[status(thm)],[fact_evalc_Oequations_I1_J]) ).
fof(i_0_10602,plain,
! [X17505] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X17505),X17505)),
inference(variable_rename,[status(thm)],[fact_evalc_OSkip]) ).
fof(i_0_10603,plain,
! [X33146,X33147,X33148] :
( ( X33147 = c_List_Olist_ONil(X33148)
| hAPP(hAPP(c_List_Oappend(X33148),X33147),X33146) != c_List_Olist_ONil(X33148) )
& ( X33146 = c_List_Olist_ONil(X33148)
| hAPP(hAPP(c_List_Oappend(X33148),X33147),X33146) != c_List_Olist_ONil(X33148) )
& ( X33147 != c_List_Olist_ONil(X33148)
| X33146 != c_List_Olist_ONil(X33148)
| hAPP(hAPP(c_List_Oappend(X33148),X33147),X33146) = c_List_Olist_ONil(X33148) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__is__Nil__conv])])]) ).
fof(i_0_10604,plain,
! [X33135,X33136,X33137] :
( ( X33136 = c_List_Olist_ONil(X33137)
| c_List_Olist_ONil(X33137) != hAPP(hAPP(c_List_Oappend(X33137),X33136),X33135) )
& ( X33135 = c_List_Olist_ONil(X33137)
| c_List_Olist_ONil(X33137) != hAPP(hAPP(c_List_Oappend(X33137),X33136),X33135) )
& ( X33136 != c_List_Olist_ONil(X33137)
| X33135 != c_List_Olist_ONil(X33137)
| c_List_Olist_ONil(X33137) = hAPP(hAPP(c_List_Oappend(X33137),X33136),X33135) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nil__is__append__conv])])]) ).
cnf(i_0_10605,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_5990]) ).
cnf(i_0_10606,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_5991]) ).
cnf(i_0_10607,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_5992]) ).
fof(i_0_10608,plain,
! [X30245,X30246] : hAPP(c_Relation_ODomain(X30246,X30246),c_Transitive__Closure_Ortrancl(X30246,X30245)) = c_Orderings_Otop__class_Otop(tc_fun(X30246,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Domain__rtrancl]) ).
fof(i_0_10609,plain,
! [X30243,X30244] : hAPP(c_Relation_ORange(X30244,X30244),c_Transitive__Closure_Ortrancl(X30244,X30243)) = c_Orderings_Otop__class_Otop(tc_fun(X30244,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Range__rtrancl]) ).
fof(i_0_10610,plain,
! [X34449,X34450,X34451,X34452] : hAPP(hAPP(c_COMBK(X34452,X34451),X34450),X34449) = X34450,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
cnf(i_0_10611,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_5927]) ).
fof(i_0_10612,plain,
! [X21123] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21123),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21123),
inference(variable_rename,[status(thm)],[fact_zdiv__minus1__right]) ).
fof(i_0_10613,plain,
! [X18711,X18712] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18712),X18711) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18711),X18712),
inference(variable_rename,[status(thm)],[fact_zmult__commute]) ).
fof(i_0_10614,plain,
! [X19046,X19047] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19047),X19046) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19046),X19047),
inference(variable_rename,[status(thm)],[fact_nat__mult__commute]) ).
fof(i_0_10615,plain,
! [X18579,X18580] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18580),X18579) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18579),X18580),
inference(variable_rename,[status(thm)],[fact_zadd__commute]) ).
fof(i_0_10616,plain,
! [X18082,X18083] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18083),X18082) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18082),X18083),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
fof(i_0_10617,plain,
! [X22891,X22892,X22893] : hAPP(hAPP(c_Nitpick_Ofrac(X22893),X22892),X22891) = c_Nitpick_OAbs__Frac(X22893,c_Nitpick_Onorm__frac(X22892,X22891)),
inference(variable_rename,[status(thm)],[fact_Nitpick_Ofrac__def]) ).
fof(i_0_10618,plain,
! [X20416,X20417] :
( ~ class_Groups_Ogroup__add(X20417)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20417),c_Groups_Ozero__class_Ozero(X20417)),X20416) = hAPP(c_Groups_Ouminus__class_Ouminus(X20417),X20416) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0])]) ).
fof(i_0_10619,plain,
! [X34477,X34478] :
( ~ hBOOL(X34478)
| ~ hBOOL(X34477)
| hBOOL(hAPP(hAPP(c_fconj,X34478),X34477)) ),
inference(variable_rename,[status(thm)],[i_0_5993]) ).
fof(i_0_10620,plain,
! [X33152,X33153,X33154] :
( ( hAPP(hAPP(c_List_Oappend(X33154),X33153),X33152) != X33152
| X33153 = c_List_Olist_ONil(X33154) )
& ( X33153 != c_List_Olist_ONil(X33154)
| hAPP(hAPP(c_List_Oappend(X33154),X33153),X33152) = X33152 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__self__conv2])]) ).
fof(i_0_10621,plain,
! [X33149,X33150,X33151] :
( ( hAPP(hAPP(c_List_Oappend(X33151),X33150),X33149) != X33150
| X33149 = c_List_Olist_ONil(X33151) )
& ( X33149 != c_List_Olist_ONil(X33151)
| hAPP(hAPP(c_List_Oappend(X33151),X33150),X33149) = X33150 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__self__conv])]) ).
fof(i_0_10622,plain,
! [X33140,X33141,X33142] :
( ( X33142 != hAPP(hAPP(c_List_Oappend(X33141),X33142),X33140)
| X33140 = c_List_Olist_ONil(X33141) )
& ( X33140 != c_List_Olist_ONil(X33141)
| X33142 = hAPP(hAPP(c_List_Oappend(X33141),X33142),X33140) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__append__conv])]) ).
fof(i_0_10623,plain,
! [X33143,X33144,X33145] :
( ( X33145 != hAPP(hAPP(c_List_Oappend(X33144),X33143),X33145)
| X33143 = c_List_Olist_ONil(X33144) )
& ( X33143 != c_List_Olist_ONil(X33144)
| X33145 = hAPP(hAPP(c_List_Oappend(X33144),X33143),X33145) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__append__conv2])]) ).
fof(i_0_10624,plain,
! [X21010,X21011] :
( ( X21010 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21011),c_Groups_Ozero__class_Ozero(X21011)),X21010) = c_Groups_Oone__class_Oone(X21011)
| ~ class_Power_Opower(X21011)
| ~ class_Rings_Osemiring__0(X21011) )
& ( X21010 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X21011),c_Groups_Ozero__class_Ozero(X21011)),X21010) = c_Groups_Ozero__class_Ozero(X21011)
| ~ class_Power_Opower(X21011)
| ~ class_Rings_Osemiring__0(X21011) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__left])])]) ).
fof(i_0_10625,plain,
! [X32751,X32752,X32753] : hAPP(hAPP(c_List_Olist_OCons(X32753),X32752),X32751) != c_List_Olist_ONil(X32753),
inference(variable_rename,[status(thm)],[fact_list_Osimps_I3_J]) ).
fof(i_0_10626,plain,
! [X32748,X32749,X32750] : c_List_Olist_ONil(X32750) != hAPP(hAPP(c_List_Olist_OCons(X32750),X32749),X32748),
inference(variable_rename,[status(thm)],[fact_list_Osimps_I2_J]) ).
fof(i_0_10627,plain,
! [X17941] :
( hAPP(c_Com_Obody,X17941) = c_Option_Ooption_ONone(tc_Com_Ocom)
| hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X17941))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_OBody])]) ).
fof(i_0_10628,plain,
! [X31998,X31999] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X31999,X31998))),
inference(variable_rename,[status(thm)],[fact_distinct__upto]) ).
cnf(i_0_10629,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_5994]) ).
fof(i_0_10630,plain,
! [X17642,X17643,X17644] : c_Com_Ocom_OLocal(X17644,X17643,X17642) != c_Com_Ocom_OSKIP,
inference(variable_rename,[status(thm)],[fact_com_Osimps_I11_J]) ).
fof(i_0_10631,plain,
! [X17680,X17681,X17682] : c_Com_Ocom_OCond(X17682,X17681,X17680) != c_Com_Ocom_OSKIP,
inference(variable_rename,[status(thm)],[fact_com_Osimps_I15_J]) ).
fof(i_0_10632,plain,
! [X17195,X17196,X17197] : c_Com_Ocom_OCall(X17197,X17196,X17195) != c_Com_Ocom_OSKIP,
inference(variable_rename,[status(thm)],[fact_com_Osimps_I21_J]) ).
fof(i_0_10633,plain,
! [X17639,X17640,X17641] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X17641,X17640,X17639),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I10_J]) ).
fof(i_0_10634,plain,
! [X17677,X17678,X17679] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X17679,X17678,X17677),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I14_J]) ).
fof(i_0_10635,plain,
! [X17185,X17186,X17187] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(X17187,X17186,X17185),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I20_J]) ).
fof(i_0_10636,plain,
! [X33209,X33210] : c_List_Olistrel(X33210,c_Transitive__Closure_Ortrancl(X33210,X33209)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(X33210),c_List_Olistrel1(X33210,X33209)),
inference(variable_rename,[status(thm)],[fact_listrel__rtrancl__eq__rtrancl__listrel1]) ).
fof(i_0_10637,plain,
! [X29589,X29590] :
( ~ c_Wellfounded_Owf(X29590,X29589)
| c_Wellfounded_Owf(tc_fun(X29590,tc_HOL_Obool),c_Wellfounded_Omax__ext(X29590,X29589)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ext__wf])]) ).
fof(i_0_10638,plain,
! [X29607,X29608] :
( ~ c_Wellfounded_Owf(X29608,X29607)
| c_Wellfounded_Owf(tc_fun(X29608,tc_HOL_Obool),c_Wellfounded_Omin__ext(X29608,X29607)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__ext__wf])]) ).
fof(i_0_10639,plain,
! [X34278,X34279] :
( ~ class_Groups_Ocomm__monoid__add(X34279)
| hAPP(c_List_Omonoid__add__class_Olistsum(X34279),hAPP(c_List_Orev(X34279),X34278)) = hAPP(c_List_Omonoid__add__class_Olistsum(X34279),X34278) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__rev])]) ).
fof(i_0_10640,plain,
! [X20651,X20652] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20652)
| hAPP(c_Groups_Oabs__class_Oabs(X20652),hAPP(c_Groups_Oabs__class_Oabs(X20652),X20651)) = hAPP(c_Groups_Oabs__class_Oabs(X20652),X20651) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__idempotent])]) ).
fof(i_0_10641,plain,
! [X20675,X20676] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20676)
| hAPP(c_Groups_Oabs__class_Oabs(X20676),hAPP(c_Groups_Ouminus__class_Ouminus(X20676),X20675)) = hAPP(c_Groups_Oabs__class_Oabs(X20676),X20675) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__cancel])]) ).
fof(i_0_10642,plain,
! [X20681,X20682] :
( ~ class_Rings_Olinordered__idom(X20682)
| hAPP(c_Groups_Oabs__class_Oabs(X20682),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20682),X20681)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20682),X20681) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nat])]) ).
fof(i_0_10643,plain,
! [X21104] :
( ~ class_Int_Onumber__ring(X21104)
| ~ c_Int_Oiszero(X21104,hAPP(c_Int_Onumber__class_Onumber__of(X21104),c_Int_OMin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5995])]) ).
fof(i_0_10644,plain,
! [X28170] : c_Orderings_Otop__class_Otop(tc_fun(X28170,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(X28170,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_UNIV__not__empty]) ).
fof(i_0_10645,plain,
! [X21117] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X21117,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_10646,plain,
! [X20048] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20048,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_10647,plain,
! [X19256,X19257] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19257),X19256) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X19257 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X19256 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X19257 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19257),X19256) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X19256 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19257),X19256) = 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_10648,plain,
! [X32312,X32313,X32314] : hAPP(hAPP(c_List_Olist_OCons(X32314),X32313),X32312) != X32312,
inference(variable_rename,[status(thm)],[fact_not__Cons__self2]) ).
fof(i_0_10649,plain,
! [X32315,X32316,X32317] : X32317 != hAPP(hAPP(c_List_Olist_OCons(X32316),X32315),X32317),
inference(variable_rename,[status(thm)],[fact_not__Cons__self]) ).
fof(i_0_10650,plain,
! [X29109] : c_Finite__Set_Ofun__left__comm__idem(X29109,tc_fun(X29109,tc_HOL_Obool),c_Set_Oinsert(X29109)),
inference(variable_rename,[status(thm)],[fact_fun__left__comm__idem__insert]) ).
fof(i_0_10651,plain,
! [X34483,X34484] :
( ~ hBOOL(X34484)
| hBOOL(hAPP(hAPP(c_fdisj,X34484),X34483)) ),
inference(variable_rename,[status(thm)],[i_0_5996]) ).
fof(i_0_10652,plain,
! [X34485,X34486] :
( ~ hBOOL(X34486)
| hBOOL(hAPP(hAPP(c_fdisj,X34485),X34486)) ),
inference(variable_rename,[status(thm)],[i_0_5997]) ).
fof(i_0_10653,plain,
! [X34491,X34492] :
( ~ hBOOL(X34492)
| hBOOL(hAPP(hAPP(c_fimplies,X34491),X34492)) ),
inference(variable_rename,[status(thm)],[i_0_5998]) ).
fof(i_0_10654,plain,
! [X28171,X28172,X28173] :
( ~ class_Orderings_Otop(X28173)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(X28172,X28173)),X28171) = c_Orderings_Otop__class_Otop(X28173) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__apply])]) ).
fof(i_0_10655,plain,
! [X23292,X23293,X23294] :
( ~ class_Orderings_Obot(X23294)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(X23293,X23294)),X23292) = c_Orderings_Obot__class_Obot(X23294) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__fun__def])]) ).
fof(i_0_10656,plain,
! [X23217,X23218,X23219] :
( ~ class_Orderings_Obot(X23219)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(X23218,X23219)),X23217) = c_Orderings_Obot__class_Obot(X23219) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__apply])]) ).
fof(i_0_10657,plain,
! [X21850,X21851] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X21851),X21850) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,X21851),X21850),
inference(variable_rename,[status(thm)],[fact_minus__code__numeral__code]) ).
fof(i_0_10658,plain,
! [X18179,X18180] : ~ c_Option_Ois__none(X18180,hAPP(c_Option_Ooption_OSome(X18180),X18179)),
inference(variable_rename,[status(thm)],[i_0_5999]) ).
fof(i_0_10659,plain,
! [X34112,X34113] :
( ~ class_Orderings_Olinorder(X34113)
| ~ c_List_Olinorder__class_Osorted(X34113,X34112)
| c_List_Olinorder__class_Osorted(X34113,hAPP(c_List_Otl(X34113),X34112)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__tl])]) ).
cnf(i_0_10660,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]) ).
cnf(i_0_10661,plain,
c_List_Oreturn__list(X1) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),X1),
inference(split_conjunct,[status(thm)],[i_0_6000]) ).
fof(i_0_10662,plain,
! [X19035,X19036] :
( X19036 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19036),X19035)
| X19035 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X19036 = 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_10663,plain,
! [X33460,X33461] :
( X33461 = c_List_Olist_ONil(X33460)
| hAPP(c_List_Ohd(X33460),X33461) = hAPP(hAPP(c_List_Onth(X33460),X33461),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_10664,plain,
! [X34489,X34490] :
( hBOOL(X34490)
| hBOOL(hAPP(hAPP(c_fimplies,X34490),X34489)) ),
inference(variable_rename,[status(thm)],[help_c__fimplies__1]) ).
fof(i_0_10665,plain,
! [X30563,X30564] : c_Relation_Osingle__valued(X30564,X30564,c_Relation_OId__on(X30564,X30563)),
inference(variable_rename,[status(thm)],[fact_single__valued__Id__on]) ).
fof(i_0_10666,plain,
! [X29042,X29043] : c_Relation_Orefl__on(X29043,X29042,c_Relation_OId__on(X29043,X29042)),
inference(variable_rename,[status(thm)],[fact_refl__on__Id__on]) ).
fof(i_0_10667,plain,
! [X19048,X19049] :
( ( X19049 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19049),X19048) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X19048 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19049),X19048) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X19049 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X19048 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19049),X19048) = 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_10668,plain,
! [X18088,X18089] :
( ( X18089 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18089),X18088) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X18088 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18089),X18088) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X18089 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X18088 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18089),X18088) = 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_10669,plain,
! [X19043,X19044] :
( ( X19044 = 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),X19044),X19043) )
& ( X19043 = 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),X19044),X19043) )
& ( X19044 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X19043 != 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),X19044),X19043) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__1__eq__mult__iff])])]) ).
fof(i_0_10670,plain,
! [X20648,X20649,X20650] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(X20650),X20649) != hAPP(c_Int_Onumber__class_Onumber__of(X20650),X20648)
| X20649 = X20648
| ~ class_Int_Onumber__ring(X20650)
| ~ class_Int_Oring__char__0(X20650) )
& ( X20649 != X20648
| hAPP(c_Int_Onumber__class_Onumber__of(X20650),X20649) = hAPP(c_Int_Onumber__class_Onumber__of(X20650),X20648)
| ~ class_Int_Onumber__ring(X20650)
| ~ class_Int_Oring__char__0(X20650) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of])])]) ).
fof(i_0_10671,plain,
! [X30353,X30354] : hAPP(c_Relation_Oconverse(X30354,X30354),c_Relation_OId__on(X30354,X30353)) = c_Relation_OId__on(X30354,X30353),
inference(variable_rename,[status(thm)],[fact_converse__Id__on]) ).
fof(i_0_10672,plain,
! [X34473,X34474] :
( X34474 != X34473
| hBOOL(hAPP(hAPP(c_fequal,X34474),X34473)) ),
inference(variable_rename,[status(thm)],[help_c__fequal__2]) ).
fof(i_0_10673,plain,
! [X20643,X20644] :
( ~ class_Int_Onumber__ring(X20644)
| hAPP(c_Int_Oring__1__class_Oof__int(X20644),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20643)) = hAPP(c_Int_Onumber__class_Onumber__of(X20644),X20643) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__number__of__eq])]) ).
fof(i_0_10674,plain,
! [X18991,X18992] :
( ~ class_Rings_Oring__1(X18992)
| hAPP(c_Int_Oring__1__class_Oof__int(X18992),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18991)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18992),X18991) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__of__nat__eq])]) ).
fof(i_0_10675,plain,
! [X32817,X32818] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X32818,tc_HOL_Obool)) != hAPP(c_List_Oset(X32818),X32817)
| X32817 = c_List_Olist_ONil(X32818) )
& ( X32817 != c_List_Olist_ONil(X32818)
| c_Orderings_Obot__class_Obot(tc_fun(X32818,tc_HOL_Obool)) = hAPP(c_List_Oset(X32818),X32817) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__empty2])]) ).
fof(i_0_10676,plain,
! [X32815,X32816] :
( ( hAPP(c_List_Oset(X32816),X32815) != c_Orderings_Obot__class_Obot(tc_fun(X32816,tc_HOL_Obool))
| X32815 = c_List_Olist_ONil(X32816) )
& ( X32815 != c_List_Olist_ONil(X32816)
| hAPP(c_List_Oset(X32816),X32815) = c_Orderings_Obot__class_Obot(tc_fun(X32816,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__empty])]) ).
fof(i_0_10677,plain,
! [X17371,X17372] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(X17372,X17371))),
inference(variable_rename,[status(thm)],[fact_WT_OAssign]) ).
fof(i_0_10678,plain,
! [X17369,X17370] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(X17370,X17369))),
inference(variable_rename,[status(thm)],[fact_WT_Oequations_I2_J]) ).
fof(i_0_10679,plain,
! [X34298,X34299] : hAPP(c_List_Oset(X34299),hAPP(c_List_Orev(X34299),X34298)) = hAPP(c_List_Oset(X34299),X34298),
inference(variable_rename,[status(thm)],[fact_set__rev]) ).
fof(i_0_10680,plain,
! [X33338,X33339] : hAPP(c_List_Oset(X33339),hAPP(c_List_Orotate1(X33339),X33338)) = hAPP(c_List_Oset(X33339),X33338),
inference(variable_rename,[status(thm)],[fact_set__rotate1]) ).
fof(i_0_10681,plain,
! [X21049] :
( ~ class_Power_Opower(X21049)
| c_Power_Opower__class_Opower(X21049) = c_Power_Opower_Opower(X21049,c_Groups_Oone__class_Oone(X21049),c_Groups_Otimes__class_Otimes(X21049)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__power__power])]) ).
fof(i_0_10682,plain,
! [X18090,X18091] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18091),X18090) != X18091
| X18090 = 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_10683,plain,
! [X34307,X34308] :
( X34308 = c_List_Olist_ONil(X34307)
| hAPP(c_List_Ohd(X34307),hAPP(c_List_Orev(X34307),X34308)) = c_List_Olast(X34307,X34308) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__rev])]) ).
fof(i_0_10684,plain,
! [X34309,X34310] :
( X34310 = c_List_Olist_ONil(X34309)
| c_List_Olast(X34309,hAPP(c_List_Orev(X34309),X34310)) = hAPP(c_List_Ohd(X34309),X34310) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__rev])]) ).
fof(i_0_10685,plain,
! [X32763] :
( ~ class_Orderings_Olinorder(X32763)
| c_List_Olinorder__class_Osorted__list__of__set(X32763,c_Orderings_Obot__class_Obot(tc_fun(X32763,tc_HOL_Obool))) = c_List_Olist_ONil(X32763) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__empty])]) ).
fof(i_0_10686,plain,
! [X31384] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31384)
| c_Complete__Lattice_OSup__class_OSup(X31384,c_Orderings_Otop__class_Otop(tc_fun(X31384,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(X31384) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__UNIV])]) ).
fof(i_0_10687,plain,
! [X31373] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31373)
| c_Complete__Lattice_OSup__class_OSup(X31373,c_Orderings_Obot__class_Obot(tc_fun(X31373,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(X31373) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__empty])]) ).
fof(i_0_10688,plain,
! [X31388] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31388)
| c_Complete__Lattice_OInf__class_OInf(X31388,c_Orderings_Otop__class_Otop(tc_fun(X31388,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(X31388) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__UNIV])]) ).
fof(i_0_10689,plain,
! [X31387] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X31387)
| c_Complete__Lattice_OInf__class_OInf(X31387,c_Orderings_Obot__class_Obot(tc_fun(X31387,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(X31387) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__empty])]) ).
fof(i_0_10690,plain,
! [X20042] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20042),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X20042,
inference(variable_rename,[status(thm)],[fact_div__1]) ).
fof(i_0_10691,plain,
! [X31307,X31308] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X31308,tc_HOL_Obool),hAPP(c_Set_OPow(X31308),X31307)) = X31307,
inference(variable_rename,[status(thm)],[fact_Union__Pow__eq]) ).
fof(i_0_10692,plain,
! [X24810,X24811] :
( ~ class_Lattices_Obounded__lattice__bot(X24811)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24811),c_Orderings_Obot__class_Obot(X24811)),X24810) = c_Orderings_Obot__class_Obot(X24811) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__bot__left])]) ).
fof(i_0_10693,plain,
! [X28164,X28165] :
( ~ class_Lattices_Obounded__lattice__top(X28165)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X28165),c_Orderings_Otop__class_Otop(X28165)),X28164) = c_Orderings_Otop__class_Otop(X28165) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__top__left])]) ).
fof(i_0_10694,plain,
! [X21469,X21470] :
( ~ class_Rings_Odivision__ring(X21470)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21470),c_Groups_Ozero__class_Ozero(X21470)),X21469) = c_Groups_Ozero__class_Ozero(X21470) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__zero__left])]) ).
fof(i_0_10695,plain,
! [X20940,X20941] :
( ~ class_Groups_Omonoid__mult(X20941)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20941),c_Groups_Oone__class_Oone(X20941)),X20940) = c_Groups_Oone__class_Oone(X20941) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one])]) ).
fof(i_0_10696,plain,
! [X20032,X20033] :
( ~ class_Divides_Osemiring__div(X20033)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20033),c_Groups_Ozero__class_Ozero(X20033)),X20032) = c_Groups_Ozero__class_Ozero(X20033) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__0])]) ).
fof(i_0_10697,plain,
! [X18820,X18821] :
( ~ class_Rings_Omult__zero(X18821)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18821),c_Groups_Ozero__class_Ozero(X18821)),X18820) = c_Groups_Ozero__class_Ozero(X18821) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__left])]) ).
fof(i_0_10698,plain,
! [X18816,X18817] :
( ~ class_Rings_Ocomm__semiring__1(X18817)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18817),c_Groups_Ozero__class_Ozero(X18817)),X18816) = c_Groups_Ozero__class_Ozero(X18817) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J])]) ).
fof(i_0_10699,plain,
! [X34031,X34032] :
( ~ class_Orderings_Olinorder(X34032)
| X34031 = c_List_Olist_ONil(X34032)
| ~ c_List_Olinorder__class_Osorted(X34032,X34031)
| c_List_Olinorder__class_Osorted(X34032,c_List_Obutlast(X34032,X34031)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__butlast])]) ).
fof(i_0_10700,plain,
! [X18000,X18001] :
( ~ c_Com_OWT__bodies
| hAPP(c_Com_Obody,X18001) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X18000)
| hBOOL(hAPP(c_Com_OWT,X18000)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT__bodiesD])]) ).
fof(i_0_10701,plain,
! [X21122] :
( ~ class_Int_Onumber__ring(X21122)
| hAPP(c_Int_Oring__1__class_Oof__int(X21122),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(X21122),c_Int_OMin) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__m1])]) ).
fof(i_0_10702,plain,
! [X25454] : hAPP(c_Finite__Set_Ocard(X25454),c_Orderings_Obot__class_Obot(tc_fun(X25454,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_card_Oempty]) ).
cnf(i_0_10703,plain,
( c_Int_OPls = X1
| c_Int_OPls != c_Int_OBit0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6001]) ).
cnf(i_0_10704,plain,
( X1 = c_Int_OPls
| c_Int_OBit0(X1) != c_Int_OPls ),
inference(split_conjunct,[status(thm)],[i_0_6002]) ).
fof(i_0_10705,plain,
! [X21116] :
( ~ class_Int_Onumber__ring(X21116)
| ~ class_Rings_Olinordered__idom(X21116)
| hAPP(c_Groups_Oabs__class_Oabs(X21116),hAPP(c_Int_Onumber__class_Onumber__of(X21116),c_Int_OMin)) = c_Groups_Oone__class_Oone(X21116) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__one])]) ).
fof(i_0_10706,plain,
! [X18032,X18033] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X18033)),hAPP(c_Option_Ooption_OSome(X18033),X18032)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_option_Osize_I4_J]) ).
fof(i_0_10707,plain,
! [X26990] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X26990) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X26990),
inference(variable_rename,[status(thm)],[fact_atLeast0AtMost]) ).
cnf(i_0_10708,plain,
c_Int_OBit0(X1) != c_Int_OMin,
inference(split_conjunct,[status(thm)],[i_0_6003]) ).
cnf(i_0_10709,plain,
c_Int_OMin != c_Int_OBit0(X1),
inference(split_conjunct,[status(thm)],[i_0_6004]) ).
fof(i_0_10710,plain,
! [X27646,X27647,X27648] :
( ( hAPP(c_SetInterval_Oord__class_OgreaterThan(X27648),X27647) != hAPP(c_SetInterval_Oord__class_OgreaterThan(X27648),X27646)
| X27647 = X27646
| ~ class_Orderings_Olinorder(X27648) )
& ( X27647 != X27646
| hAPP(c_SetInterval_Oord__class_OgreaterThan(X27648),X27647) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X27648),X27646)
| ~ class_Orderings_Olinorder(X27648) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThan__eq__iff])])]) ).
fof(i_0_10711,plain,
! [X27602,X27603,X27604] :
( ( hAPP(c_SetInterval_Oord__class_OatLeast(X27604),X27603) != hAPP(c_SetInterval_Oord__class_OatLeast(X27604),X27602)
| X27603 = X27602
| ~ class_Orderings_Olinorder(X27604) )
& ( X27603 != X27602
| hAPP(c_SetInterval_Oord__class_OatLeast(X27604),X27603) = hAPP(c_SetInterval_Oord__class_OatLeast(X27604),X27602)
| ~ class_Orderings_Olinorder(X27604) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeast__eq__iff])])]) ).
fof(i_0_10712,plain,
! [X27072,X27073,X27074] :
( ( hAPP(c_SetInterval_Oord__class_OlessThan(X27074),X27073) != hAPP(c_SetInterval_Oord__class_OlessThan(X27074),X27072)
| X27073 = X27072
| ~ class_Orderings_Olinorder(X27074) )
& ( X27073 != X27072
| hAPP(c_SetInterval_Oord__class_OlessThan(X27074),X27073) = hAPP(c_SetInterval_Oord__class_OlessThan(X27074),X27072)
| ~ class_Orderings_Olinorder(X27074) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lessThan__eq__iff])])]) ).
fof(i_0_10713,plain,
! [X26941,X26942,X26943] :
( ( hAPP(c_SetInterval_Oord__class_OatMost(X26943),X26942) != hAPP(c_SetInterval_Oord__class_OatMost(X26943),X26941)
| X26942 = X26941
| ~ class_Orderings_Olinorder(X26943) )
& ( X26942 != X26941
| hAPP(c_SetInterval_Oord__class_OatMost(X26943),X26942) = hAPP(c_SetInterval_Oord__class_OatMost(X26943),X26941)
| ~ class_Orderings_Olinorder(X26943) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atMost__eq__iff])])]) ).
fof(i_0_10714,plain,
! [X19945,X19946,X19947] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(X19947),X19946) != hAPP(c_Groups_Ouminus__class_Ouminus(X19947),X19945)
| X19946 = X19945
| ~ class_Lattices_Oboolean__algebra(X19947) )
& ( X19946 != X19945
| hAPP(c_Groups_Ouminus__class_Ouminus(X19947),X19946) = hAPP(c_Groups_Ouminus__class_Ouminus(X19947),X19945)
| ~ class_Lattices_Oboolean__algebra(X19947) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__eq__compl__iff])])]) ).
fof(i_0_10715,plain,
! [X18770,X18771,X18772] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(X18772),X18771) != hAPP(c_Groups_Ouminus__class_Ouminus(X18772),X18770)
| X18771 = X18770
| ~ class_Groups_Ogroup__add(X18772) )
& ( X18771 != X18770
| hAPP(c_Groups_Ouminus__class_Ouminus(X18772),X18771) = hAPP(c_Groups_Ouminus__class_Ouminus(X18772),X18770)
| ~ class_Groups_Ogroup__add(X18772) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__iff__equal])])]) ).
fof(i_0_10716,plain,
! [X18723,X18724,X18725] :
( ( hAPP(c_Int_Oring__1__class_Oof__int(X18725),X18724) != hAPP(c_Int_Oring__1__class_Oof__int(X18725),X18723)
| X18724 = X18723
| ~ class_Int_Oring__char__0(X18725) )
& ( X18724 != X18723
| hAPP(c_Int_Oring__1__class_Oof__int(X18725),X18724) = hAPP(c_Int_Oring__1__class_Oof__int(X18725),X18723)
| ~ class_Int_Oring__char__0(X18725) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__eq__iff])])]) ).
fof(i_0_10717,plain,
! [X18499,X18500,X18501] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18501),X18500) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18501),X18499)
| X18500 = X18499
| ~ class_Nat_Osemiring__char__0(X18501) )
& ( X18500 != X18499
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18501),X18500) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18501),X18499)
| ~ class_Nat_Osemiring__char__0(X18501) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__eq__iff])])]) ).
fof(i_0_10718,plain,
! [X28160,X28161] :
( ~ class_Lattices_Obounded__lattice__top(X28161)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X28161),c_Orderings_Otop__class_Otop(X28161)),X28160) = X28160 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__top__left])]) ).
fof(i_0_10719,plain,
! [X23932,X23933] :
( ~ class_Lattices_Obounded__lattice__bot(X23933)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23933),c_Orderings_Obot__class_Obot(X23933)),X23932) = X23932 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__bot__left])]) ).
fof(i_0_10720,plain,
! [X18756,X18757] :
( ~ class_Groups_Ocomm__monoid__mult(X18757)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18757),c_Groups_Oone__class_Oone(X18757)),X18756) = X18756 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1])]) ).
fof(i_0_10721,plain,
! [X18754,X18755] :
( ~ class_Groups_Omonoid__mult(X18755)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18755),c_Groups_Oone__class_Oone(X18755)),X18754) = X18754 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__left])]) ).
fof(i_0_10722,plain,
! [X18702,X18703] :
( ~ class_Rings_Ocomm__semiring__1(X18703)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18703),c_Groups_Oone__class_Oone(X18703)),X18702) = X18702 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J])]) ).
fof(i_0_10723,plain,
! [X18152,X18153] :
( ~ class_Rings_Ocomm__semiring__1(X18153)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18153),c_Groups_Ozero__class_Ozero(X18153)),X18152) = X18152 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).
fof(i_0_10724,plain,
! [X18100,X18101] :
( ~ class_Groups_Ocomm__monoid__add(X18101)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18101),c_Groups_Ozero__class_Ozero(X18101)),X18100) = X18100 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])]) ).
fof(i_0_10725,plain,
! [X18098,X18099] :
( ~ class_Groups_Omonoid__add(X18099)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18099),c_Groups_Ozero__class_Ozero(X18099)),X18098) = X18098 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__left])]) ).
fof(i_0_10726,plain,
! [X21599,X21600] :
( ( X21599 != c_Groups_Ozero__class_Ozero(X21600)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21600),X21599),X21599) = c_Groups_Ozero__class_Ozero(X21600)
| ~ class_Rings_Odivision__ring__inverse__zero(X21600) )
& ( X21599 = c_Groups_Ozero__class_Ozero(X21600)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21600),X21599),X21599) = c_Groups_Oone__class_Oone(X21600)
| ~ class_Rings_Odivision__ring__inverse__zero(X21600) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__self__if])])]) ).
fof(i_0_10727,plain,
! [X19797,X19798] :
( ~ class_Divides_Osemiring__div(X19798)
| c_Divides_Odiv__class_Omod(X19798,c_Groups_Ozero__class_Ozero(X19798),X19797) = c_Groups_Ozero__class_Ozero(X19798) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__0])]) ).
fof(i_0_10728,plain,
! [X19900,X19901] :
( ~ class_Divides_Osemiring__div(X19901)
| c_Divides_Odiv__class_Omod(X19901,X19900,c_Groups_Oone__class_Oone(X19901)) = c_Groups_Ozero__class_Ozero(X19901) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__by__1])]) ).
fof(i_0_10729,plain,
! [X23556,X23557] :
( ( c_Option_Oset(X23557,X23556) != c_Orderings_Obot__class_Obot(tc_fun(X23557,tc_HOL_Obool))
| X23556 = c_Option_Ooption_ONone(X23557) )
& ( X23556 != c_Option_Ooption_ONone(X23557)
| c_Option_Oset(X23557,X23556) = c_Orderings_Obot__class_Obot(tc_fun(X23557,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__empty__eq])]) ).
fof(i_0_10730,plain,
! [X24808,X24809] :
( ~ class_Lattices_Obounded__lattice__bot(X24809)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24809),X24808),c_Orderings_Obot__class_Obot(X24809)) = c_Orderings_Obot__class_Obot(X24809) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__bot__right])]) ).
fof(i_0_10731,plain,
! [X28162,X28163] :
( ~ class_Lattices_Obounded__lattice__top(X28163)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X28163),X28162),c_Orderings_Otop__class_Otop(X28163)) = c_Orderings_Otop__class_Otop(X28163) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__top__right])]) ).
fof(i_0_10732,plain,
! [X21467,X21468] :
( ~ class_Rings_Odivision__ring__inverse__zero(X21468)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21468),X21467),c_Groups_Ozero__class_Ozero(X21468)) = c_Groups_Ozero__class_Ozero(X21468) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__zero])]) ).
fof(i_0_10733,plain,
! [X20034,X20035] :
( ~ class_Divides_Osemiring__div(X20035)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20035),X20034),c_Groups_Ozero__class_Ozero(X20035)) = c_Groups_Ozero__class_Ozero(X20035) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__by__0])]) ).
fof(i_0_10734,plain,
! [X18822,X18823] :
( ~ class_Rings_Omult__zero(X18823)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18823),X18822),c_Groups_Ozero__class_Ozero(X18823)) = c_Groups_Ozero__class_Ozero(X18823) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__right])]) ).
fof(i_0_10735,plain,
! [X18818,X18819] :
( ~ class_Rings_Ocomm__semiring__1(X18819)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18819),X18818),c_Groups_Ozero__class_Ozero(X18819)) = c_Groups_Ozero__class_Ozero(X18819) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J])]) ).
fof(i_0_10736,plain,
! [X29666,X29667] :
( ~ c_Wellfounded_Owf(X29667,X29666)
| c_Wellfounded_Owf(tc_List_Olist(X29667),c_List_Olex(X29667,X29666)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__lex])]) ).
fof(i_0_10737,plain,
! [X29659,X29660] :
( ~ c_Wellfounded_Owf(X29660,X29659)
| c_Wellfounded_Owf(tc_List_Olist(X29660),c_List_Olenlex(X29660,X29659)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__lenlex])]) ).
fof(i_0_10738,plain,
! [X33155,X33156,X33157] :
( X33157 != X33156
| X33157 = hAPP(hAPP(c_List_Oappend(X33155),c_List_Olist_ONil(X33155)),X33156) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__Nil__appendI])]) ).
fof(i_0_10739,plain,
! [X21597,X21598] :
( ~ class_Rings_Odivision__ring(X21598)
| X21597 = c_Groups_Ozero__class_Ozero(X21598)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21598),X21597),X21597) = c_Groups_Oone__class_Oone(X21598) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__self])]) ).
fof(i_0_10740,plain,
! [X20099,X20100] :
( ~ class_Divides_Osemiring__div(X20100)
| X20099 = c_Groups_Ozero__class_Ozero(X20100)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20100),X20099),X20099) = c_Groups_Oone__class_Oone(X20100) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__self])]) ).
fof(i_0_10741,plain,
! [X19799,X19800] :
( ~ class_Divides_Osemiring__div(X19800)
| c_Divides_Odiv__class_Omod(X19800,X19799,c_Groups_Ozero__class_Ozero(X19800)) = X19799 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__by__0])]) ).
fof(i_0_10742,plain,
! [X21060] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X21060))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X21060)) = X21060 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6005])]) ).
fof(i_0_10743,plain,
! [X30781] :
( ~ class_Groups_Oab__semigroup__mult(X30781)
| c_Finite__Set_Ofun__left__comm(X30781,X30781,c_Groups_Otimes__class_Otimes(X30781)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm])]) ).
fof(i_0_10744,plain,
! [X29096] :
( ~ class_Lattices_Osemilattice__inf(X29096)
| c_Finite__Set_Ofun__left__comm__idem(X29096,X29096,c_Lattices_Osemilattice__inf__class_Oinf(X29096)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__inf])]) ).
fof(i_0_10745,plain,
! [X29095] :
( ~ class_Lattices_Osemilattice__sup(X29095)
| c_Finite__Set_Ofun__left__comm__idem(X29095,X29095,c_Lattices_Osemilattice__sup__class_Osup(X29095)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__sup])]) ).
fof(i_0_10746,plain,
! [X29108] :
( ~ class_Orderings_Olinorder(X29108)
| c_Finite__Set_Ofun__left__comm__idem(X29108,X29108,c_Orderings_Oord__class_Omax(X29108)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofun__left__comm__idem__sup])]) ).
fof(i_0_10747,plain,
! [X29094] :
( ~ class_Orderings_Olinorder(X29094)
| c_Finite__Set_Ofun__left__comm__idem(X29094,X29094,c_Orderings_Oord__class_Omin(X29094)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofun__left__comm__idem__inf])]) ).
fof(i_0_10748,plain,
! [X29107] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X29107)
| c_Finite__Set_Ofun__left__comm__idem(X29107,X29107,c_Groups_Otimes__class_Otimes(X29107)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem])]) ).
fof(i_0_10749,plain,
! [X29772,X29773] : hAPP(c_Relation_ODomain(X29773,X29773),c_Relation_OId__on(X29773,X29772)) = X29772,
inference(variable_rename,[status(thm)],[fact_Domain__Id__on]) ).
fof(i_0_10750,plain,
! [X29688,X29689] : hAPP(c_Relation_ORange(X29689,X29689),c_Relation_OId__on(X29689,X29688)) = X29688,
inference(variable_rename,[status(thm)],[fact_Range__Id__on]) ).
fof(i_0_10751,plain,
! [X20983,X20984] :
( ~ class_Power_Opower(X20984)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20984),X20983),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X20984) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0])]) ).
fof(i_0_10752,plain,
! [X20778,X20779] :
( ~ class_Rings_Ocomm__semiring__1(X20779)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20779),X20778),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X20779) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J])]) ).
fof(i_0_10753,plain,
! [X28158,X28159] :
( ~ class_Lattices_Obounded__lattice__top(X28159)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X28159),X28158),c_Orderings_Otop__class_Otop(X28159)) = X28158 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__top__right])]) ).
fof(i_0_10754,plain,
! [X23934,X23935] :
( ~ class_Lattices_Obounded__lattice__bot(X23935)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23935),X23934),c_Orderings_Obot__class_Obot(X23935)) = X23934 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__bot__right])]) ).
fof(i_0_10755,plain,
! [X21488,X21489] :
( ~ class_Rings_Odivision__ring(X21489)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21489),X21488),c_Groups_Oone__class_Oone(X21489)) = X21488 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__1])]) ).
fof(i_0_10756,plain,
! [X20287,X20288] :
( ~ class_Groups_Ogroup__add(X20288)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20288),X20287),c_Groups_Ozero__class_Ozero(X20288)) = X20287 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0__right])]) ).
fof(i_0_10757,plain,
! [X20036,X20037] :
( ~ class_Divides_Osemiring__div(X20037)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20037),X20036),c_Groups_Oone__class_Oone(X20037)) = X20036 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__by__1])]) ).
fof(i_0_10758,plain,
! [X18762,X18763] :
( ~ class_Groups_Ocomm__monoid__mult(X18763)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18763),X18762),c_Groups_Oone__class_Oone(X18763)) = X18762 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ocomm__neutral])]) ).
fof(i_0_10759,plain,
! [X18760,X18761] :
( ~ class_Groups_Omonoid__mult(X18761)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18761),X18760),c_Groups_Oone__class_Oone(X18761)) = X18760 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__right])]) ).
fof(i_0_10760,plain,
! [X18705,X18706] :
( ~ class_Rings_Ocomm__semiring__1(X18706)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18706),X18705),c_Groups_Oone__class_Oone(X18706)) = X18705 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J])]) ).
fof(i_0_10761,plain,
! [X18154,X18155] :
( ~ class_Rings_Ocomm__semiring__1(X18155)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18155),X18154),c_Groups_Ozero__class_Ozero(X18155)) = X18154 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])]) ).
fof(i_0_10762,plain,
! [X18106,X18107] :
( ~ class_Groups_Ocomm__monoid__add(X18107)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18107),X18106),c_Groups_Ozero__class_Ozero(X18107)) = X18106 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral])]) ).
fof(i_0_10763,plain,
! [X18104,X18105] :
( ~ class_Groups_Omonoid__add(X18105)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18105),X18104),c_Groups_Ozero__class_Ozero(X18105)) = X18104 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])]) ).
fof(i_0_10764,plain,
! [X19939,X19940] :
( ~ class_Lattices_Oboolean__algebra(X19940)
| hAPP(c_Groups_Ouminus__class_Ouminus(X19940),hAPP(c_Groups_Ouminus__class_Ouminus(X19940),X19939)) = X19939 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__compl])]) ).
fof(i_0_10765,plain,
! [X18752,X18753] :
( ~ class_Groups_Ogroup__add(X18753)
| hAPP(c_Groups_Ouminus__class_Ouminus(X18753),hAPP(c_Groups_Ouminus__class_Ouminus(X18753),X18752)) = X18752 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__minus])]) ).
fof(i_0_10766,plain,
! [X20683] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20683)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20683),
inference(variable_rename,[status(thm)],[fact_abs__int__eq]) ).
fof(i_0_10767,plain,
! [X18875] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18875)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18875),
inference(variable_rename,[status(thm)],[fact_of__int__int__eq]) ).
fof(i_0_10768,plain,
! [X19801,X19802] :
( ~ class_Divides_Osemiring__div(X19802)
| c_Divides_Odiv__class_Omod(X19802,X19801,X19801) = c_Groups_Ozero__class_Ozero(X19802) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__self])]) ).
fof(i_0_10769,plain,
! [X34285,X34286,X34287] :
( ( hAPP(c_List_Orev(X34287),X34286) != hAPP(c_List_Orev(X34287),X34285)
| X34286 = X34285 )
& ( X34286 != X34285
| hAPP(c_List_Orev(X34287),X34286) = hAPP(c_List_Orev(X34287),X34285) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__is__rev__conv])]) ).
fof(i_0_10770,plain,
! [X18027,X18028,X18029] :
( ( hAPP(c_Option_Ooption_OSome(X18029),X18028) != hAPP(c_Option_Ooption_OSome(X18029),X18027)
| X18028 = X18027 )
& ( X18028 != X18027
| hAPP(c_Option_Ooption_OSome(X18029),X18028) = hAPP(c_Option_Ooption_OSome(X18029),X18027) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_option_Oinject])]) ).
fof(i_0_10771,plain,
! [X25455,X25456] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X25456),X25455))
| hAPP(c_Finite__Set_Ocard(X25456),X25455) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6006])]) ).
fof(i_0_10772,plain,
! [X21846,X21847] :
( ( X21847 != X21846
| c_Random_Oinc__shift(X21847,X21846) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
& ( X21847 = X21846
| c_Random_Oinc__shift(X21847,X21846) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X21846),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_10773,plain,
! [X33133,X33134] : hAPP(hAPP(c_List_Oappend(X33134),c_List_Olist_ONil(X33134)),X33133) = X33133,
inference(variable_rename,[status(thm)],[fact_append__Nil]) ).
fof(i_0_10774,plain,
! [X19519] : hAPP(c_Nat_OSuc,X19519) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X19519),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left]) ).
fof(i_0_10775,plain,
! [X32735,X32736] : c_List_Osublist(X32736,c_List_Olist_ONil(X32736),X32735) = c_List_Olist_ONil(X32736),
inference(variable_rename,[status(thm)],[fact_sublist__nil]) ).
fof(i_0_10776,plain,
! [X32803,X32804] : c_List_Oremove1(X32804,X32803,c_List_Olist_ONil(X32804)) = c_List_Olist_ONil(X32804),
inference(variable_rename,[status(thm)],[fact_remove1_Osimps_I1_J]) ).
fof(i_0_10777,plain,
! [X26809] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26809),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_10778,plain,
! [X20953,X20954] :
( ~ class_Groups_Omonoid__mult(X20954)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20954),X20953),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X20953 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one__right])]) ).
fof(i_0_10779,plain,
! [X20691,X20692] :
( ~ class_Rings_Ocomm__semiring__1(X20692)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20692),X20691),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X20691 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J])]) ).
fof(i_0_10780,plain,
! [X20285,X20286] :
( ~ class_Groups_Ogroup__add(X20286)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20286),X20285),X20285) = c_Groups_Ozero__class_Ozero(X20286) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__self])]) ).
fof(i_0_10781,plain,
! [X33607,X33608] : c_List_Olist_Olist__size(X33608,X33607,c_List_Olist_ONil(X33608)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_list_Osize_I1_J]) ).
fof(i_0_10782,plain,
! [X18007,X18008] : c_Option_Ooption_Ooption__size(X18008,X18007,c_Option_Ooption_ONone(X18008)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_option_Osize_I1_J]) ).
fof(i_0_10783,plain,
! [X32692,X32693] : hAPP(hAPP(c_List_Otake(X32693),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32692) = c_List_Olist_ONil(X32693),
inference(variable_rename,[status(thm)],[fact_take__0]) ).
fof(i_0_10784,plain,
! [X33318,X33319] : hAPP(hAPP(c_List_Odrop(X33319),X33318),c_List_Olist_ONil(X33319)) = c_List_Olist_ONil(X33319),
inference(variable_rename,[status(thm)],[fact_drop__Nil]) ).
fof(i_0_10785,plain,
! [X32687,X32688] : hAPP(hAPP(c_List_Otake(X32688),X32687),c_List_Olist_ONil(X32688)) = c_List_Olist_ONil(X32688),
inference(variable_rename,[status(thm)],[fact_take__Nil]) ).
fof(i_0_10786,plain,
! [X18767,X18768,X18769] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(X18769),X18768) != X18767
| hAPP(c_Groups_Ouminus__class_Ouminus(X18769),X18767) = X18768
| ~ class_Groups_Ogroup__add(X18769) )
& ( hAPP(c_Groups_Ouminus__class_Ouminus(X18769),X18767) != X18768
| hAPP(c_Groups_Ouminus__class_Ouminus(X18769),X18768) = X18767
| ~ class_Groups_Ogroup__add(X18769) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__equation__iff])])]) ).
fof(i_0_10787,plain,
! [X18764,X18765,X18766] :
( ( X18765 != hAPP(c_Groups_Ouminus__class_Ouminus(X18766),X18764)
| X18764 = hAPP(c_Groups_Ouminus__class_Ouminus(X18766),X18765)
| ~ class_Groups_Ogroup__add(X18766) )
& ( X18764 != hAPP(c_Groups_Ouminus__class_Ouminus(X18766),X18765)
| X18765 = hAPP(c_Groups_Ouminus__class_Ouminus(X18766),X18764)
| ~ class_Groups_Ogroup__add(X18766) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equation__minus__iff])])]) ).
fof(i_0_10788,plain,
! [X32004] :
( ( ~ c_List_Onat__list(X32004)
| c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X32004)) )
& ( ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X32004))
| c_List_Onat__list(X32004) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__list__def])]) ).
fof(i_0_10789,plain,
! [X26991] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X26991)) = hAPP(c_Nat_OSuc,X26991),
inference(variable_rename,[status(thm)],[fact_card__atMost]) ).
fof(i_0_10790,plain,
! [X22782] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X22782)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X22782),
inference(variable_rename,[status(thm)],[fact_nat__of__number]) ).
fof(i_0_10791,plain,
! [X20913] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20913)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20913),
inference(variable_rename,[status(thm)],[fact_nat__number__of]) ).
fof(i_0_10792,plain,
! [X20912] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20912) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20912)),
inference(variable_rename,[status(thm)],[fact_nat__number__of__def]) ).
fof(i_0_10793,plain,
! [X19518] : hAPP(c_Nat_OSuc,X19518) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19518),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).
fof(i_0_10794,plain,
! [X19071,X19072] :
( ~ class_Rings_Olinordered__idom(X19072)
| c_Groups_Osgn__class_Osgn(X19072,c_Groups_Osgn__class_Osgn(X19072,X19071)) = c_Groups_Osgn__class_Osgn(X19072,X19071) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__sgn])]) ).
fof(i_0_10795,plain,
! [X24891,X24892] :
( ~ class_Lattices_Osemilattice__inf(X24892)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24892),X24891),X24891) = X24891 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__idem])]) ).
fof(i_0_10796,plain,
! [X24889,X24890] :
( ~ class_Lattices_Osemilattice__inf(X24890)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24890),X24889),X24889) = X24889 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oidem])]) ).
fof(i_0_10797,plain,
! [X24866,X24867] :
( ~ class_Lattices_Olattice(X24867)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24867),X24866),X24866) = X24866 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oidem])]) ).
fof(i_0_10798,plain,
! [X24121,X24122] :
( ~ class_Lattices_Osemilattice__sup(X24122)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24122),X24121),X24121) = X24121 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Oidem])]) ).
fof(i_0_10799,plain,
! [X24119,X24120] :
( ~ class_Lattices_Osemilattice__sup(X24120)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24120),X24119),X24119) = X24119 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__idem])]) ).
fof(i_0_10800,plain,
! [X24146,X24147] :
( ~ class_Lattices_Olattice(X24147)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24147),X24146),X24146) = X24146 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oidem])]) ).
fof(i_0_10801,plain,
! [X22790,X22791] :
( ~ class_Orderings_Olinorder(X22791)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22791),X22790),X22790) = X22790 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oidem])]) ).
fof(i_0_10802,plain,
! [X22622,X22623] :
( ~ class_Orderings_Olinorder(X22623)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X22623),X22622),X22622) = X22622 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oidem])]) ).
fof(i_0_10803,plain,
! [X22788,X22789] :
( ~ class_Orderings_Olinorder(X22789)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22789),X22788),X22788) = X22788 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oidem])]) ).
fof(i_0_10804,plain,
! [X22538,X22539] :
( ~ class_Orderings_Olinorder(X22539)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X22539),X22538),X22538) = X22538 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oidem])]) ).
fof(i_0_10805,plain,
! [X19934,X19935] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X19935)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19935),X19934),X19934) = X19934 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__idem])]) ).
fof(i_0_10806,plain,
! [X19932,X19933] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X19933)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19933),X19932),X19932) = X19932 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times_Oidem])]) ).
fof(i_0_10807,plain,
! [X32695,X32696] :
( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32696)),X32695) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X32695 = c_List_Olist_ONil(X32696) )
& ( X32695 != c_List_Olist_ONil(X32696)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32696)),X32695) = 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_10808,plain,
! [X21109] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X21109) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21109),
inference(variable_rename,[status(thm)],[fact_mult__Min]) ).
fof(i_0_10809,plain,
! [X27075] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27075) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X27075),
inference(variable_rename,[status(thm)],[fact_atLeast0LessThan]) ).
fof(i_0_10810,plain,
! [X33352,X33353] : hAPP(hAPP(c_List_Odrop(X33353),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33352) = X33352,
inference(variable_rename,[status(thm)],[fact_drop__0]) ).
fof(i_0_10811,plain,
! [X33138,X33139] : hAPP(hAPP(c_List_Oappend(X33139),X33138),c_List_Olist_ONil(X33139)) = X33138,
inference(variable_rename,[status(thm)],[fact_append__Nil2]) ).
fof(i_0_10812,plain,
! [X34280,X34281] : hAPP(c_List_Orev(X34281),hAPP(c_List_Orev(X34281),X34280)) = X34280,
inference(variable_rename,[status(thm)],[fact_rev__rev__ident]) ).
fof(i_0_10813,plain,
! [X18011,X18012] : hAPP(c_Option_Othe(X18012),hAPP(c_Option_Ooption_OSome(X18012),X18011)) = X18011,
inference(variable_rename,[status(thm)],[fact_the_Osimps]) ).
fof(i_0_10814,plain,
! [X19872] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X19872) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zmod__zero]) ).
fof(i_0_10815,plain,
! [X21059] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X21059))
| hAPP(c_Int_Onat,X21059) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__nat])]) ).
fof(i_0_10816,plain,
! [X27645] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X27645)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X27645),
inference(variable_rename,[status(thm)],[fact_atLeast__Suc__greaterThan]) ).
fof(i_0_10817,plain,
! [X27077] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X27077)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X27077),
inference(variable_rename,[status(thm)],[fact_lessThan__Suc__atMost]) ).
fof(i_0_10818,plain,
! [X21885] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21885) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21885)),
inference(variable_rename,[status(thm)],[fact_less__eq__Suc__le__raw]) ).
fof(i_0_10819,plain,
! [X20068] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20068),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
& c_Divides_Odiv__class_Omod(tc_Int_Oint,X20068,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X20068 ),
inference(variable_rename,[status(thm)],[fact_DIVISION__BY__ZERO]) ).
fof(i_0_10820,plain,
! [X21155] :
( ~ class_Int_Onumber__ring(X21155)
| c_Int_Oiszero(X21155,hAPP(c_Int_Onumber__class_Onumber__of(X21155),c_Int_OPls)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__Numeral0])]) ).
fof(i_0_10821,plain,
! [X31865] : hAPP(c_Option_Omap(X31865,X31865),c_Fun_Oid(X31865)) = c_Fun_Oid(tc_Option_Ooption(X31865)),
inference(variable_rename,[status(thm)],[fact_Option_Omap_Oid]) ).
fof(i_0_10822,plain,
! [X31864] : hAPP(c_Option_Omap(X31864,X31864),c_COMBI(X31864)) = c_Fun_Oid(tc_Option_Ooption(X31864)),
inference(variable_rename,[status(thm)],[fact_Option_Omap_Oidentity]) ).
fof(i_0_10823,plain,
! [X31759] : hAPP(c_List_Omap(X31759,X31759),c_Fun_Oid(X31759)) = c_Fun_Oid(tc_List_Olist(X31759)),
inference(variable_rename,[status(thm)],[fact_List_Omap_Oid]) ).
fof(i_0_10824,plain,
! [X31758] : hAPP(c_List_Omap(X31758,X31758),c_COMBI(X31758)) = c_Fun_Oid(tc_List_Olist(X31758)),
inference(variable_rename,[status(thm)],[fact_List_Omap_Oidentity]) ).
fof(i_0_10825,plain,
! [X18577,X18578] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18578) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18577)
| X18578 = X18577 )
& ( X18578 != X18577
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18578) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18577) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I1_J])]) ).
fof(i_0_10826,plain,
! [X18575,X18576] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18576) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18575)
| X18576 = X18575 )
& ( X18576 != X18575
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18576) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18575) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__int__eq])]) ).
fof(i_0_10827,plain,
! [X19873] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X19873,X19873) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zmod__self]) ).
fof(i_0_10828,plain,
! [X34282,X34283,X34284] :
( ( hAPP(c_List_Orev(X34284),X34283) != X34282
| X34283 = hAPP(c_List_Orev(X34284),X34282) )
& ( X34283 != hAPP(c_List_Orev(X34284),X34282)
| hAPP(c_List_Orev(X34284),X34283) = X34282 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__swap])]) ).
fof(i_0_10829,plain,
! [X22544] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22544) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_min__0L]) ).
fof(i_0_10830,plain,
! [X20325] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20325) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__0__eq__0]) ).
fof(i_0_10831,plain,
! [X20012] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20012) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zdiv__zero]) ).
fof(i_0_10832,plain,
! [X19259] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19259) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_mult__0]) ).
fof(i_0_10833,plain,
! [X32805] : hBOOL(hAPP(c_List_Odistinct(X32805),c_List_Olist_ONil(X32805))),
inference(variable_rename,[status(thm)],[fact_distinct_Osimps_I1_J]) ).
fof(i_0_10834,plain,
! [X29884,X29885,X29886] : hAPP(c_New__DSequence_Opos__single(X29886,X29885),X29884) = c_Lazy__Sequence_Osingle(X29886,X29885),
inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__single__def]) ).
fof(i_0_10835,plain,
! [X29876,X29877,X29878] : hAPP(c_New__DSequence_Oneg__single(X29878,X29877),X29876) = c_Lazy__Sequence_Ohb__single(X29878,X29877),
inference(variable_rename,[status(thm)],[fact_New__DSequence_Oneg__single__def]) ).
fof(i_0_10836,plain,
! [X30188,X30189] : c_Transitive__Closure_Ortrancl(X30189,c_Transitive__Closure_Ortrancl(X30189,X30188)) = c_Transitive__Closure_Ortrancl(X30189,X30188),
inference(variable_rename,[status(thm)],[fact_rtrancl__idemp]) ).
fof(i_0_10837,plain,
! [X32819] : hAPP(c_List_Oset(X32819),c_List_Olist_ONil(X32819)) = c_Orderings_Obot__class_Obot(tc_fun(X32819,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_List_Oset_Osimps_I1_J]) ).
fof(i_0_10838,plain,
! [X22617] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22617) = X22617,
inference(variable_rename,[status(thm)],[fact_max__0L]) ).
fof(i_0_10839,plain,
! [X18704] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X18704) = X18704,
inference(variable_rename,[status(thm)],[fact_zmult__1]) ).
fof(i_0_10840,plain,
! [X19042] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X19042) = X19042,
inference(variable_rename,[status(thm)],[fact_nat__mult__1]) ).
fof(i_0_10841,plain,
! [X18588] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18588) = X18588,
inference(variable_rename,[status(thm)],[fact_zadd__0]) ).
fof(i_0_10842,plain,
! [X18086] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18086) = X18086,
inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).
fof(i_0_10843,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_10844,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_10845,plain,
! [X20061] :
( X20061 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20061),X20061) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__self])]) ).
fof(i_0_10846,plain,
! [X18242,X18243] :
( X18243 = c_Option_Ooption_ONone(X18242)
| X18243 = hAPP(c_Option_Ooption_OSome(X18242),esk33_2(X18242,X18243)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_option_Oexhaust])])]) ).
fof(i_0_10847,plain,
! [X18019,X18020,X18022,X18023,X18024] :
( ( X18020 = hAPP(c_Option_Ooption_OSome(X18019),esk30_2(X18019,X18020))
| X18020 = c_Option_Ooption_ONone(X18019) )
& ( X18023 != c_Option_Ooption_ONone(X18022)
| X18023 != hAPP(c_Option_Ooption_OSome(X18022),X18024) ) ),
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_10848,plain,
! [X18013,X18014,X18016,X18017,X18018] :
( ( X18014 = c_Option_Ooption_ONone(X18013)
| X18014 = hAPP(c_Option_Ooption_OSome(X18013),esk29_2(X18013,X18014)) )
& ( X18017 != hAPP(c_Option_Ooption_OSome(X18016),X18018)
| X18017 != c_Option_Ooption_ONone(X18016) ) ),
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_10849,plain,
! [X21115] :
( ~ class_Int_Onumber__ring(X21115)
| hAPP(c_Groups_Ouminus__class_Ouminus(X21115),c_Groups_Oone__class_Oone(X21115)) = hAPP(c_Int_Onumber__class_Onumber__of(X21115),c_Int_OMin) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__simps_I31_J])]) ).
fof(i_0_10850,plain,
! [X21114] :
( ~ class_Int_Onumber__ring(X21114)
| hAPP(c_Int_Onumber__class_Onumber__of(X21114),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(X21114),c_Groups_Oone__class_Oone(X21114)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Min])]) ).
fof(i_0_10851,plain,
! [X22545] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X22545),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_10852,plain,
! [X19258] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19258),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_10853,plain,
! [X18787,X18788] :
( ( c_Groups_Ozero__class_Ozero(X18788) != hAPP(c_Groups_Ouminus__class_Ouminus(X18788),X18787)
| c_Groups_Ozero__class_Ozero(X18788) = X18787
| ~ class_Groups_Ogroup__add(X18788) )
& ( c_Groups_Ozero__class_Ozero(X18788) != X18787
| c_Groups_Ozero__class_Ozero(X18788) = hAPP(c_Groups_Ouminus__class_Ouminus(X18788),X18787)
| ~ class_Groups_Ogroup__add(X18788) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__equal__iff__equal])])]) ).
fof(i_0_10854,plain,
! [X20661,X20662] :
( ( hAPP(c_Groups_Oabs__class_Oabs(X20662),X20661) != c_Groups_Ozero__class_Ozero(X20662)
| X20661 = c_Groups_Ozero__class_Ozero(X20662)
| ~ class_Groups_Oordered__ab__group__add__abs(X20662) )
& ( X20661 != c_Groups_Ozero__class_Ozero(X20662)
| hAPP(c_Groups_Oabs__class_Oabs(X20662),X20661) = c_Groups_Ozero__class_Ozero(X20662)
| ~ class_Groups_Oordered__ab__group__add__abs(X20662) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__eq__0])])]) ).
fof(i_0_10855,plain,
! [X18791,X18792] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(X18792),X18791) != c_Groups_Ozero__class_Ozero(X18792)
| X18791 = c_Groups_Ozero__class_Ozero(X18792)
| ~ class_Groups_Ogroup__add(X18792) )
& ( X18791 != c_Groups_Ozero__class_Ozero(X18792)
| hAPP(c_Groups_Ouminus__class_Ouminus(X18792),X18791) = c_Groups_Ozero__class_Ozero(X18792)
| ~ class_Groups_Ogroup__add(X18792) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__0__iff__equal])])]) ).
fof(i_0_10856,plain,
! [X34475] :
( ~ hBOOL(hAPP(c_fNot,X34475))
| ~ hBOOL(X34475) ),
inference(variable_rename,[status(thm)],[i_0_6007]) ).
fof(i_0_10857,plain,
! [X22616] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X22616),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X22616,
inference(variable_rename,[status(thm)],[fact_max__0R]) ).
fof(i_0_10858,plain,
! [X20324] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20324),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X20324,
inference(variable_rename,[status(thm)],[fact_minus__nat_Odiff__0]) ).
fof(i_0_10859,plain,
! [X18707] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18707),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X18707,
inference(variable_rename,[status(thm)],[fact_zmult__1__right]) ).
fof(i_0_10860,plain,
! [X19045] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19045),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X19045,
inference(variable_rename,[status(thm)],[fact_nat__mult__1__right]) ).
fof(i_0_10861,plain,
! [X18587] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18587),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X18587,
inference(variable_rename,[status(thm)],[fact_zadd__0__right]) ).
fof(i_0_10862,plain,
! [X18087] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18087),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X18087,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(i_0_10863,plain,
! [X27071] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X27071)) = X27071,
inference(variable_rename,[status(thm)],[fact_card__lessThan]) ).
fof(i_0_10864,plain,
! [X18696] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X18696)) = X18696,
inference(variable_rename,[status(thm)],[fact_zminus__zminus]) ).
fof(i_0_10865,plain,
! [X33861,X33862] : hAPP(c_List_Ofilter(X33862,X33861),c_List_Olist_ONil(X33862)) = c_List_Olist_ONil(X33862),
inference(variable_rename,[status(thm)],[fact_filter_Osimps_I1_J]) ).
fof(i_0_10866,plain,
! [X24548,X24549] :
( ~ class_Finite__Set_Ofinite(X24549)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24549),X24548)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite])]) ).
fof(i_0_10867,plain,
! [X24546,X24547] :
( ~ class_Finite__Set_Ofinite(X24547)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X24547),X24546)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__code])]) ).
fof(i_0_10868,plain,
! [X18983,X18984] :
( ( hAPP(c_Int_Oring__1__class_Oof__int(X18984),X18983) != c_Groups_Ozero__class_Ozero(X18984)
| X18983 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ class_Int_Oring__char__0(X18984) )
& ( X18983 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(c_Int_Oring__1__class_Oof__int(X18984),X18983) = c_Groups_Ozero__class_Ozero(X18984)
| ~ class_Int_Oring__char__0(X18984) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__eq__0__iff])])]) ).
fof(i_0_10869,plain,
! [X18981,X18982] :
( ( c_Groups_Ozero__class_Ozero(X18982) != hAPP(c_Int_Oring__1__class_Oof__int(X18982),X18981)
| X18981 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ class_Int_Oring__char__0(X18982) )
& ( X18981 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Groups_Ozero__class_Ozero(X18982) = hAPP(c_Int_Oring__1__class_Oof__int(X18982),X18981)
| ~ class_Int_Oring__char__0(X18982) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__0__eq__iff])])]) ).
cnf(i_0_10870,plain,
( c_Int_OBit0(X1) = c_Int_OPls
| X1 != c_Int_OPls ),
inference(split_conjunct,[status(thm)],[i_0_6002]) ).
cnf(i_0_10871,plain,
( c_Int_OPls = c_Int_OBit0(X1)
| c_Int_OPls != X1 ),
inference(split_conjunct,[status(thm)],[i_0_6001]) ).
fof(i_0_10872,plain,
! [X20323] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20323),X20323) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__self__eq__0]) ).
fof(i_0_10873,plain,
! [X20698,X20699] :
( ~ class_Int_Onumber__ring(X20699)
| hAPP(c_Int_Onumber__class_Onumber__of(X20699),X20698) = hAPP(c_Int_Oring__1__class_Oof__int(X20699),X20698) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__eq])]) ).
fof(i_0_10874,plain,
! [X23555] : c_Option_Oset(X23555,c_Option_Ooption_ONone(X23555)) = c_Orderings_Obot__class_Obot(tc_fun(X23555,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Option_Oset_Osimps_I1_J]) ).
fof(i_0_10875,plain,
! [X17790,X17791,X17792,X17793] :
( ( X17793 = X17791
| c_Com_Ocom_OWhile(X17793,X17792) != c_Com_Ocom_OWhile(X17791,X17790) )
& ( X17792 = X17790
| c_Com_Ocom_OWhile(X17793,X17792) != c_Com_Ocom_OWhile(X17791,X17790) )
& ( X17793 != X17791
| X17792 != X17790
| c_Com_Ocom_OWhile(X17793,X17792) = c_Com_Ocom_OWhile(X17791,X17790) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I5_J])])]) ).
fof(i_0_10876,plain,
! [X17351,X17352,X17353,X17354] :
( ( X17354 = X17352
| c_Com_Ocom_OSemi(X17354,X17353) != c_Com_Ocom_OSemi(X17352,X17351) )
& ( X17353 = X17351
| c_Com_Ocom_OSemi(X17354,X17353) != c_Com_Ocom_OSemi(X17352,X17351) )
& ( X17354 != X17352
| X17353 != X17351
| c_Com_Ocom_OSemi(X17354,X17353) = c_Com_Ocom_OSemi(X17352,X17351) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I3_J])])]) ).
fof(i_0_10877,plain,
! [X17203,X17204,X17205,X17206] :
( ( X17206 = X17204
| c_Com_Ocom_OAss(X17206,X17205) != c_Com_Ocom_OAss(X17204,X17203) )
& ( X17205 = X17203
| c_Com_Ocom_OAss(X17206,X17205) != c_Com_Ocom_OAss(X17204,X17203) )
& ( X17206 != X17204
| X17205 != X17203
| c_Com_Ocom_OAss(X17206,X17205) = c_Com_Ocom_OAss(X17204,X17203) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I1_J])])]) ).
fof(i_0_10878,plain,
! [X18793,X18794] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(X18794),X18793) != X18793
| X18793 = c_Groups_Ozero__class_Ozero(X18794)
| ~ class_Groups_Olinordered__ab__group__add(X18794) )
& ( X18793 != c_Groups_Ozero__class_Ozero(X18794)
| hAPP(c_Groups_Ouminus__class_Ouminus(X18794),X18793) = X18793
| ~ class_Groups_Olinordered__ab__group__add(X18794) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__zero])])]) ).
fof(i_0_10879,plain,
! [X18789,X18790] :
( ( X18789 != hAPP(c_Groups_Ouminus__class_Ouminus(X18790),X18789)
| X18789 = c_Groups_Ozero__class_Ozero(X18790)
| ~ class_Groups_Olinordered__ab__group__add(X18790) )
& ( X18789 != c_Groups_Ozero__class_Ozero(X18790)
| X18789 = hAPP(c_Groups_Ouminus__class_Ouminus(X18790),X18789)
| ~ class_Groups_Olinordered__ab__group__add(X18790) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equal__neg__zero])])]) ).
fof(i_0_10880,plain,
! [X17166,X17167] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(X17167,X17166)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_com_Osize_I10_J]) ).
fof(i_0_10881,plain,
! [X21145] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X21145),c_Int_OPls) = X21145,
inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I1_J]) ).
fof(i_0_10882,plain,
! [X21142] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21142),c_Int_OPls) = X21142,
inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).
fof(i_0_10883,plain,
! [X18835] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18835)) = X18835,
inference(variable_rename,[status(thm)],[fact_nat__int]) ).
fof(i_0_10884,plain,
! [X34445,X34446] :
( ~ class_Smallcheck_Osmall(X34446)
| ~ class_Smallcheck_Osmall(X34445)
| class_Smallcheck_Osmall(tc_prod(X34446,X34445)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod__Smallcheck_Osmall])]) ).
fof(i_0_10885,plain,
! [X34443,X34444] :
( ~ class_Finite__Set_Ofinite(X34444)
| ~ class_Finite__Set_Ofinite(X34443)
| class_Finite__Set_Ofinite(tc_prod(X34444,X34443)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod__Finite__Set_Ofinite])]) ).
fof(i_0_10886,plain,
! [X34424,X34425] :
( ~ class_Finite__Set_Ofinite(X34425)
| ~ class_Finite__Set_Ofinite(X34424)
| class_Finite__Set_Ofinite(tc_fun(X34425,X34424)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Finite__Set_Ofinite])]) ).
fof(i_0_10887,plain,
! [X34440,X34441] :
( ~ class_Finite__Set_Ofinite(X34441)
| ~ class_Finite__Set_Ofinite(X34440)
| class_Finite__Set_Ofinite(tc_sum(X34441,X34440)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_sum__Finite__Set_Ofinite])]) ).
fof(i_0_10888,plain,
! [X21617,X21618] :
( ~ c_Nat__Transfer_Ois__nat(X21618)
| ~ c_Nat__Transfer_Ois__nat(X21617)
| c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X21618,X21617)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J])]) ).
fof(i_0_10889,plain,
! [X17864,X17865,X17866,X17867] : c_Com_Ocom_OWhile(X17867,X17866) != c_Com_Ocom_OSemi(X17865,X17864),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I47_J]) ).
fof(i_0_10890,plain,
! [X17856,X17857,X17858,X17859] : c_Com_Ocom_OWhile(X17859,X17858) != c_Com_Ocom_OAss(X17857,X17856),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I29_J]) ).
fof(i_0_10891,plain,
! [X17868,X17869,X17870,X17871] : c_Com_Ocom_OSemi(X17871,X17870) != c_Com_Ocom_OWhile(X17869,X17868),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I46_J]) ).
fof(i_0_10892,plain,
! [X17860,X17861,X17862,X17863] : c_Com_Ocom_OAss(X17863,X17862) != c_Com_Ocom_OWhile(X17861,X17860),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I28_J]) ).
fof(i_0_10893,plain,
! [X17379,X17380,X17381,X17382] : c_Com_Ocom_OSemi(X17382,X17381) != c_Com_Ocom_OAss(X17380,X17379),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I25_J]) ).
fof(i_0_10894,plain,
! [X17383,X17384,X17385,X17386] : c_Com_Ocom_OAss(X17386,X17385) != c_Com_Ocom_OSemi(X17384,X17383),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I24_J]) ).
fof(i_0_10895,plain,
! [X21143] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X21143) = X21143,
inference(variable_rename,[status(thm)],[fact_add__Pls]) ).
fof(i_0_10896,plain,
! [X34222,X34223] :
( ( hAPP(c_List_Orev(X34223),X34222) != c_List_Olist_ONil(X34223)
| X34222 = c_List_Olist_ONil(X34223) )
& ( X34222 != c_List_Olist_ONil(X34223)
| hAPP(c_List_Orev(X34223),X34222) = c_List_Olist_ONil(X34223) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__is__Nil__conv])]) ).
fof(i_0_10897,plain,
! [X33316,X33317] :
( ( hAPP(c_List_Orotate1(X33317),X33316) != c_List_Olist_ONil(X33317)
| X33316 = c_List_Olist_ONil(X33317) )
& ( X33316 != c_List_Olist_ONil(X33317)
| hAPP(c_List_Orotate1(X33317),X33316) = c_List_Olist_ONil(X33317) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate1__is__Nil__conv])]) ).
fof(i_0_10898,plain,
! [X34224,X34225] :
( ( c_List_Olist_ONil(X34225) != hAPP(c_List_Orev(X34225),X34224)
| X34224 = c_List_Olist_ONil(X34225) )
& ( X34224 != c_List_Olist_ONil(X34225)
| c_List_Olist_ONil(X34225) = hAPP(c_List_Orev(X34225),X34224) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nil__is__rev__conv])]) ).
fof(i_0_10899,plain,
! [X21144] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X21144) = c_Int_OPls,
inference(variable_rename,[status(thm)],[fact_mult__Pls]) ).
fof(i_0_10900,plain,
! [X29609] : c_Wellfounded_Owf(tc_fun(X29609,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X29609)),
inference(variable_rename,[status(thm)],[fact_wf__finite__psubset]) ).
fof(i_0_10901,plain,
! [X17152] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,X17152)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_com_Osize_I15_J]) ).
fof(i_0_10902,plain,
! [X33983] : c_List_Otranspose(X33983,c_List_Olist_ONil(tc_List_Olist(X33983))) = c_List_Olist_ONil(tc_List_Olist(X33983)),
inference(variable_rename,[status(thm)],[fact_transpose_Osimps_I1_J]) ).
fof(i_0_10903,plain,
! [X17843,X17844,X17845] : hAPP(c_Com_Ocom_OBODY,X17845) != c_Com_Ocom_OWhile(X17844,X17843),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I59_J]) ).
fof(i_0_10904,plain,
! [X17376,X17377,X17378] : hAPP(c_Com_Ocom_OBODY,X17378) != c_Com_Ocom_OSemi(X17377,X17376),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I49_J]) ).
fof(i_0_10905,plain,
! [X17246,X17247,X17248] : hAPP(c_Com_Ocom_OBODY,X17248) != c_Com_Ocom_OAss(X17247,X17246),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I31_J]) ).
fof(i_0_10906,plain,
! [X17840,X17841,X17842] : c_Com_Ocom_OWhile(X17842,X17841) != hAPP(c_Com_Ocom_OBODY,X17840),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I58_J]) ).
fof(i_0_10907,plain,
! [X17373,X17374,X17375] : c_Com_Ocom_OSemi(X17375,X17374) != hAPP(c_Com_Ocom_OBODY,X17373),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I48_J]) ).
fof(i_0_10908,plain,
! [X17249,X17250,X17251] : c_Com_Ocom_OAss(X17251,X17250) != hAPP(c_Com_Ocom_OBODY,X17249),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I30_J]) ).
cnf(i_0_10909,plain,
c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
inference(split_conjunct,[status(thm)],[fact_succ__Min]) ).
cnf(i_0_10910,plain,
c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
inference(split_conjunct,[status(thm)],[fact_Bit0__Pls]) ).
cnf(i_0_10911,plain,
c_Int_Opred(c_Int_OPls) = c_Int_OMin,
inference(split_conjunct,[status(thm)],[fact_pred__Pls]) ).
fof(i_0_10912,plain,
! [X26169,X26170] :
( ( hAPP(c_Int_ORep__Integ,X26170) != hAPP(c_Int_ORep__Integ,X26169)
| X26170 = X26169 )
& ( X26170 != X26169
| hAPP(c_Int_ORep__Integ,X26170) = hAPP(c_Int_ORep__Integ,X26169) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Rep__Integ__inject])]) ).
fof(i_0_10913,plain,
! [X22746,X22747] :
( ( hAPP(c_Code__Numeral_Onat__of,X22747) != hAPP(c_Code__Numeral_Onat__of,X22746)
| X22747 = X22746 )
& ( X22747 != X22746
| hAPP(c_Code__Numeral_Onat__of,X22747) = hAPP(c_Code__Numeral_Onat__of,X22746) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Code__Numeral_Onat__of__inject])]) ).
fof(i_0_10914,plain,
! [X22744,X22745] :
( ( hAPP(c_Code__Numeral_Onat__of,X22745) != hAPP(c_Code__Numeral_Onat__of,X22744)
| X22745 = X22744 )
& ( X22745 != X22744
| hAPP(c_Code__Numeral_Onat__of,X22745) = hAPP(c_Code__Numeral_Onat__of,X22744) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral_Onat__of__inject])]) ).
fof(i_0_10915,plain,
! [X21872,X21873] :
( ( hAPP(c_Code__Numeral_Oof__nat,X21873) != hAPP(c_Code__Numeral_Oof__nat,X21872)
| X21873 = X21872 )
& ( X21873 != X21872
| hAPP(c_Code__Numeral_Oof__nat,X21873) = hAPP(c_Code__Numeral_Oof__nat,X21872) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Code__Numeral_Oof__nat__inject])]) ).
fof(i_0_10916,plain,
! [X18118,X18119] :
( ( hAPP(c_Nat_OSuc,X18119) != hAPP(c_Nat_OSuc,X18118)
| X18119 = X18118 )
& ( X18119 != X18118
| hAPP(c_Nat_OSuc,X18119) = hAPP(c_Nat_OSuc,X18118) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat_Oinject])]) ).
fof(i_0_10917,plain,
! [X18116,X18117] :
( hAPP(c_Nat_OSuc,X18117) != hAPP(c_Nat_OSuc,X18116)
| X18117 = X18116 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__inject])]) ).
fof(i_0_10918,plain,
! [X17131,X17132] :
( ( hAPP(c_Com_Ocom_OBODY,X17132) != hAPP(c_Com_Ocom_OBODY,X17131)
| X17132 = X17131 )
& ( X17132 != X17131
| hAPP(c_Com_Ocom_OBODY,X17132) = hAPP(c_Com_Ocom_OBODY,X17131) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I6_J])]) ).
fof(i_0_10919,plain,
! [X19369,X19370] :
( ( c_Groups_Osgn__class_Osgn(X19370,X19369) != c_Groups_Ozero__class_Ozero(X19370)
| X19369 = c_Groups_Ozero__class_Ozero(X19370)
| ~ class_Rings_Olinordered__idom(X19370) )
& ( X19369 != c_Groups_Ozero__class_Ozero(X19370)
| c_Groups_Osgn__class_Osgn(X19370,X19369) = c_Groups_Ozero__class_Ozero(X19370)
| ~ class_Rings_Olinordered__idom(X19370) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__0__0])])]) ).
fof(i_0_10920,plain,
! [X32694] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32694)),c_List_Olist_ONil(X32694)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_list_Osize_I3_J]) ).
fof(i_0_10921,plain,
! [X18034] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X18034)),c_Option_Ooption_ONone(X18034)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_option_Osize_I3_J]) ).
fof(i_0_10922,plain,
! [X21108] :
( ~ class_Rings_Osemiring__1(X21108)
| ~ c_Int_Oiszero(X21108,c_Groups_Oone__class_Oone(X21108)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6008])]) ).
fof(i_0_10923,plain,
! [X34101,X34102] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X34102,X34101)),
inference(variable_rename,[status(thm)],[fact_sorted__upto]) ).
fof(i_0_10924,plain,
! [X18025,X18026] : hAPP(c_Option_Ooption_OSome(X18026),X18025) != c_Option_Ooption_ONone(X18026),
inference(variable_rename,[status(thm)],[fact_option_Osimps_I3_J]) ).
fof(i_0_10925,plain,
! [X18030,X18031] : c_Option_Ooption_ONone(X18031) != hAPP(c_Option_Ooption_OSome(X18031),X18030),
inference(variable_rename,[status(thm)],[fact_option_Osimps_I2_J]) ).
fof(i_0_10926,plain,
! [X29993,X29994] : c_Hilbert__Choice_OEps(X29994,hAPP(c_fequal,X29993)) = X29993,
inference(variable_rename,[status(thm)],[fact_some__sym__eq__trivial]) ).
fof(i_0_10927,plain,
! [X23019,X23020] : c_HOL_OThe(X23020,hAPP(c_fequal,X23019)) = X23019,
inference(variable_rename,[status(thm)],[fact_the__sym__eq__trivial]) ).
fof(i_0_10928,plain,
! [X32820] :
( ~ class_Groups_Omonoid__add(X32820)
| hAPP(c_List_Omonoid__add__class_Olistsum(X32820),c_List_Olist_ONil(X32820)) = c_Groups_Ozero__class_Ozero(X32820) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__simps_I1_J])]) ).
fof(i_0_10929,plain,
! [X20674] :
( ~ class_Rings_Olinordered__idom(X20674)
| hAPP(c_Groups_Oabs__class_Oabs(X20674),c_Groups_Oone__class_Oone(X20674)) = c_Groups_Oone__class_Oone(X20674) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__one])]) ).
fof(i_0_10930,plain,
! [X20660] :
( ~ class_Groups_Oordered__ab__group__add__abs(X20660)
| hAPP(c_Groups_Oabs__class_Oabs(X20660),c_Groups_Ozero__class_Ozero(X20660)) = c_Groups_Ozero__class_Ozero(X20660) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__zero])]) ).
fof(i_0_10931,plain,
! [X28257] :
( ~ class_Lattices_Oboolean__algebra(X28257)
| hAPP(c_Groups_Ouminus__class_Ouminus(X28257),c_Orderings_Otop__class_Otop(X28257)) = c_Orderings_Obot__class_Obot(X28257) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__top__eq])]) ).
fof(i_0_10932,plain,
! [X28256] :
( ~ class_Lattices_Oboolean__algebra(X28256)
| hAPP(c_Groups_Ouminus__class_Ouminus(X28256),c_Orderings_Obot__class_Obot(X28256)) = c_Orderings_Otop__class_Otop(X28256) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__bot__eq])]) ).
fof(i_0_10933,plain,
! [X18786] :
( ~ class_Groups_Ogroup__add(X18786)
| hAPP(c_Groups_Ouminus__class_Ouminus(X18786),c_Groups_Ozero__class_Ozero(X18786)) = c_Groups_Ozero__class_Ozero(X18786) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__zero])]) ).
fof(i_0_10934,plain,
! [X34406,X34407] :
( ~ class_Lattices_Obounded__lattice(X34407)
| class_Lattices_Obounded__lattice(tc_fun(X34406,X34407)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice])]) ).
fof(i_0_10935,plain,
! [X34410,X34411] :
( ~ class_Lattices_Obounded__lattice(X34411)
| class_Lattices_Obounded__lattice__top(tc_fun(X34410,X34411)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice__top])]) ).
fof(i_0_10936,plain,
! [X34430,X34431] :
( ~ class_Orderings_Otop(X34431)
| class_Orderings_Otop(tc_fun(X34430,X34431)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Otop])]) ).
fof(i_0_10937,plain,
! [X34408,X34409] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X34409)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X34408,X34409)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Complete__Lattice_Ocomplete__lattice])]) ).
fof(i_0_10938,plain,
! [X34418,X34419] :
( ~ class_Lattices_Odistrib__lattice(X34419)
| class_Lattices_Odistrib__lattice(tc_fun(X34418,X34419)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Odistrib__lattice])]) ).
fof(i_0_10939,plain,
! [X34416,X34417] :
( ~ class_Lattices_Olattice(X34417)
| class_Lattices_Osemilattice__inf(tc_fun(X34416,X34417)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Osemilattice__inf])]) ).
fof(i_0_10940,plain,
! [X34414,X34415] :
( ~ class_Lattices_Olattice(X34415)
| class_Lattices_Osemilattice__sup(tc_fun(X34414,X34415)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Osemilattice__sup])]) ).
fof(i_0_10941,plain,
! [X34426,X34427] :
( ~ class_Lattices_Olattice(X34427)
| class_Lattices_Olattice(tc_fun(X34426,X34427)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Olattice])]) ).
fof(i_0_10942,plain,
! [X34412,X34413] :
( ~ class_Lattices_Obounded__lattice(X34413)
| class_Lattices_Obounded__lattice__bot(tc_fun(X34412,X34413)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice__bot])]) ).
fof(i_0_10943,plain,
! [X34434,X34435] :
( ~ class_Orderings_Obot(X34435)
| class_Orderings_Obot(tc_fun(X34434,X34435)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Obot])]) ).
fof(i_0_10944,plain,
! [X34438,X34439] :
( ~ class_Groups_Ominus(X34439)
| class_Groups_Ominus(tc_fun(X34438,X34439)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ominus])]) ).
fof(i_0_10945,plain,
! [X34436,X34437] :
( ~ class_Groups_Ouminus(X34437)
| class_Groups_Ouminus(tc_fun(X34436,X34437)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ouminus])]) ).
fof(i_0_10946,plain,
! [X34420,X34421] :
( ~ class_Lattices_Oboolean__algebra(X34421)
| class_Lattices_Oboolean__algebra(tc_fun(X34420,X34421)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Oboolean__algebra])]) ).
fof(i_0_10947,plain,
! [X34432,X34433] :
( ~ class_Orderings_Oord(X34433)
| class_Orderings_Oord(tc_fun(X34432,X34433)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])]) ).
fof(i_0_10948,plain,
! [X34422,X34423] :
( ~ class_Orderings_Opreorder(X34423)
| class_Orderings_Opreorder(tc_fun(X34422,X34423)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder])]) ).
fof(i_0_10949,plain,
! [X34428,X34429] :
( ~ class_Orderings_Oorder(X34429)
| class_Orderings_Oorder(tc_fun(X34428,X34429)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder])]) ).
fof(i_0_10950,plain,
! [X29858,X29859] :
( ~ c_Wellfounded_Owf(X29859,X29858)
| c_Wellfounded_Oacyclic(X29859,X29858) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__acyclic])]) ).
fof(i_0_10951,plain,
! [X21508] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21508)),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J]) ).
fof(i_0_10952,plain,
! [X26171] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X26171)) = X26171,
inference(variable_rename,[status(thm)],[fact_Rep__Integ__inverse]) ).
fof(i_0_10953,plain,
! [X22750] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X22750)) = X22750,
inference(variable_rename,[status(thm)],[fact_nat__of__of__nat]) ).
fof(i_0_10954,plain,
! [X22749] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X22749)) = X22749,
inference(variable_rename,[status(thm)],[fact_of__nat__nat__of]) ).
fof(i_0_10955,plain,
! [X22748] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X22748)) = X22748,
inference(variable_rename,[status(thm)],[fact_nat__of__inverse]) ).
fof(i_0_10956,plain,
! [X21105,X21106] :
( ( ~ c_Int_Oiszero(X21106,X21105)
| X21105 = c_Groups_Ozero__class_Ozero(X21106)
| ~ class_Rings_Osemiring__1(X21106) )
& ( X21105 != c_Groups_Ozero__class_Ozero(X21106)
| c_Int_Oiszero(X21106,X21105)
| ~ class_Rings_Osemiring__1(X21106) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__def])])]) ).
fof(i_0_10957,plain,
! [X18512] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18512) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X18512 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X18512 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18512) = 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_10958,plain,
! [X18693] :
( ~ class_Rings_Oring__1(X18693)
| hAPP(c_Int_Oring__1__class_Oof__int(X18693),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(X18693) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__1])]) ).
fof(i_0_10959,plain,
! [X18980] :
( ~ class_Rings_Oring__1(X18980)
| hAPP(c_Int_Oring__1__class_Oof__int(X18980),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(X18980) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__0])]) ).
fof(i_0_10960,plain,
! [X18780] :
( ~ class_Rings_Osemiring__1(X18780)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18780),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X18780) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__1])]) ).
fof(i_0_10961,plain,
! [X18529] :
( ~ class_Rings_Osemiring__1(X18529)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18529),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X18529) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__0])]) ).
fof(i_0_10962,plain,
! [X20909] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20909) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X20909),
inference(variable_rename,[status(thm)],[fact_int__number__of__def]) ).
fof(i_0_10963,plain,
! [X17164,X17165] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(X17165,X17164)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_com_Osize_I2_J]) ).
fof(i_0_10964,plain,
! [X34476] :
( hBOOL(X34476)
| hBOOL(hAPP(c_fNot,X34476)) ),
inference(variable_rename,[status(thm)],[i_0_6009]) ).
fof(i_0_10965,plain,
! [X19371] :
( ~ class_Groups_Osgn__if(X19371)
| c_Groups_Osgn__class_Osgn(X19371,c_Groups_Ozero__class_Ozero(X19371)) = c_Groups_Ozero__class_Ozero(X19371) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn0])]) ).
fof(i_0_10966,plain,
! [X22728] :
( ~ class_Orderings_Oord(X22728)
| c_Orderings_Oord__class_Omax(X22728) = c_Orderings_Oord_Omax(X22728,c_Orderings_Oord__class_Oless__eq(X22728)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ord__max])]) ).
fof(i_0_10967,plain,
! [X22563] :
( ~ class_Orderings_Oord(X22563)
| c_Orderings_Oord__class_Omin(X22563) = c_Orderings_Oord_Omin(X22563,c_Orderings_Oord__class_Oless__eq(X22563)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__ord__min])]) ).
fof(i_0_10968,plain,
! [X34227] : hAPP(c_List_Orev(X34227),c_List_Olist_ONil(X34227)) = c_List_Olist_ONil(X34227),
inference(variable_rename,[status(thm)],[fact_rev_Osimps_I1_J]) ).
fof(i_0_10969,plain,
! [X33479] : hAPP(c_List_Otl(X33479),c_List_Olist_ONil(X33479)) = c_List_Olist_ONil(X33479),
inference(variable_rename,[status(thm)],[fact_tl_Osimps_I1_J]) ).
fof(i_0_10970,plain,
! [X21148] :
( ~ class_Int_Onumber__ring(X21148)
| hAPP(c_Int_Onumber__class_Onumber__of(X21148),c_Int_OPls) = c_Groups_Ozero__class_Ozero(X21148) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Pls])]) ).
fof(i_0_10971,plain,
! [X21147] :
( ~ class_Int_Onumber__ring(X21147)
| c_Groups_Ozero__class_Ozero(X21147) = hAPP(c_Int_Onumber__class_Onumber__of(X21147),c_Int_OPls) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__norm_I112_J])]) ).
fof(i_0_10972,plain,
! [X17151] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,X17151)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_com_Osize_I7_J]) ).
fof(i_0_10973,plain,
! [X18181,X18182] :
( ( ~ c_Option_Ois__none(X18182,X18181)
| X18181 = c_Option_Ooption_ONone(X18182) )
& ( X18181 != c_Option_Ooption_ONone(X18182)
| c_Option_Ois__none(X18182,X18181) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_is__none__def])]) ).
fof(i_0_10974,plain,
! [X34080] :
( ~ class_Orderings_Olinorder(X34080)
| c_List_Olinorder__class_Osorted(X34080,c_List_Olist_ONil(X34080)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted_Oequations_I1_J])]) ).
fof(i_0_10975,plain,
! [X34013] :
( ~ class_Orderings_Olinorder(X34013)
| c_List_Olinorder__class_Osorted(X34013,c_List_Olist_ONil(X34013)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted_ONil])]) ).
fof(i_0_10976,plain,
! [X21107] :
( ~ class_Rings_Osemiring__1(X21107)
| c_Int_Oiszero(X21107,c_Groups_Ozero__class_Ozero(X21107)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__0])]) ).
fof(i_0_10977,plain,
! [X18042] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OGlb(X18042)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_vname_Osize_I3_J]) ).
fof(i_0_10978,plain,
! [X17924] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OLoc(X17924)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_vname_Osize_I4_J]) ).
fof(i_0_10979,plain,
! [X22971,X22972] : hAPP(c_New__DSequence_Opos__empty(X22972),X22971) = c_Lazy__Sequence_Oempty(X22972),
inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__empty__def]) ).
fof(i_0_10980,plain,
! [X33810] : c_List_Obutlast(X33810,c_List_Olist_ONil(X33810)) = c_List_Olist_ONil(X33810),
inference(variable_rename,[status(thm)],[fact_butlast_Osimps_I1_J]) ).
fof(i_0_10981,plain,
! [X18038] : hAPP(c_Nat_OSuc,X18038) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_Suc__not__Zero]) ).
fof(i_0_10982,plain,
! [X18037] : hAPP(c_Nat_OSuc,X18037) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_nat_Osimps_I3_J]) ).
fof(i_0_10983,plain,
! [X18035] : hAPP(c_Nat_OSuc,X18035) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_Suc__neq__Zero]) ).
fof(i_0_10984,plain,
! [X18040] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X18040),
inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).
fof(i_0_10985,plain,
! [X18039] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X18039),
inference(variable_rename,[status(thm)],[fact_nat_Osimps_I2_J]) ).
fof(i_0_10986,plain,
! [X18036] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X18036),
inference(variable_rename,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(i_0_10987,plain,
! [X18246] :
( X18246 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X18246 = hAPP(c_Nat_OSuc,esk34_1(X18246)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat_Oexhaust])])]) ).
fof(i_0_10988,plain,
! [X17892,X17893] : c_Com_Ocom_OWhile(X17893,X17892) != c_Com_Ocom_OSKIP,
inference(variable_rename,[status(thm)],[fact_com_Osimps_I17_J]) ).
fof(i_0_10989,plain,
! [X17397,X17398] : c_Com_Ocom_OSemi(X17398,X17397) != c_Com_Ocom_OSKIP,
inference(variable_rename,[status(thm)],[fact_com_Osimps_I13_J]) ).
fof(i_0_10990,plain,
! [X17188,X17189] : c_Com_Ocom_OAss(X17189,X17188) != c_Com_Ocom_OSKIP,
inference(variable_rename,[status(thm)],[fact_com_Osimps_I9_J]) ).
fof(i_0_10991,plain,
! [X17894,X17895] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X17895,X17894),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I16_J]) ).
fof(i_0_10992,plain,
! [X17399,X17400] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X17400,X17399),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I12_J]) ).
fof(i_0_10993,plain,
! [X17183,X17184] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(X17184,X17183),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I8_J]) ).
fof(i_0_10994,plain,
! [X24956] :
( ~ class_Lattices_Osemilattice__inf(X24956)
| ~ class_Orderings_Olinorder(X24956)
| c_Lattices_Osemilattice__inf__class_Oinf(X24956) = c_Orderings_Oord__class_Omin(X24956) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__min])]) ).
fof(i_0_10995,plain,
! [X24148] :
( ~ class_Lattices_Osemilattice__sup(X24148)
| ~ class_Orderings_Olinorder(X24148)
| c_Lattices_Osemilattice__sup__class_Osup(X24148) = c_Orderings_Oord__class_Omax(X24148) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__max])]) ).
fof(i_0_10996,plain,
! [X18120] : hAPP(c_Nat_OSuc,X18120) != X18120,
inference(variable_rename,[status(thm)],[fact_Suc__n__not__n]) ).
fof(i_0_10997,plain,
! [X18121] : X18121 != hAPP(c_Nat_OSuc,X18121),
inference(variable_rename,[status(thm)],[fact_n__not__Suc__n]) ).
fof(i_0_10998,plain,
! [X29412,X29413] : hAPP(c_Fun_Oid(X29413),X29412) = X29412,
inference(variable_rename,[status(thm)],[fact_id__def]) ).
fof(i_0_10999,plain,
! [X29410,X29411] : hAPP(c_Fun_Oid(X29411),X29410) = X29410,
inference(variable_rename,[status(thm)],[fact_id__apply]) ).
fof(i_0_11000,plain,
! [X29180,X29181] : hAPP(c_Set_OCollect(X29181),X29180) = X29180,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(i_0_11001,plain,
! [X34447,X34448] : hAPP(c_COMBI(X34448),X34447) = X34447,
inference(variable_rename,[status(thm)],[help_c__COMBI__1]) ).
fof(i_0_11002,plain,
! [X18183] : c_Option_Ois__none(X18183,c_Option_Ooption_ONone(X18183)),
inference(variable_rename,[status(thm)],[fact_is__none__code_I1_J]) ).
fof(i_0_11003,plain,
! [X18834] :
( ~ class_Rings_Ozero__neq__one(X18834)
| c_Groups_Ozero__class_Ozero(X18834) != c_Groups_Oone__class_Oone(X18834) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__neq__one])]) ).
fof(i_0_11004,plain,
! [X18833] :
( ~ class_Rings_Ozero__neq__one(X18833)
| c_Groups_Oone__class_Oone(X18833) != c_Groups_Ozero__class_Ozero(X18833) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__neq__zero])]) ).
fof(i_0_11005,plain,
! [X17261] : hAPP(c_Com_Ocom_OBODY,X17261) != c_Com_Ocom_OSKIP,
inference(variable_rename,[status(thm)],[fact_com_Osimps_I19_J]) ).
fof(i_0_11006,plain,
! [X17260] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,X17260),
inference(variable_rename,[status(thm)],[fact_com_Osimps_I18_J]) ).
fof(i_0_11007,plain,
! [X23383] : c_Quickcheck_Obeyond(X23383,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_11008,plain,
! [X29633] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X29633)),
inference(variable_rename,[status(thm)],[fact_wf__int__ge__less__than]) ).
fof(i_0_11009,plain,
! [X29576] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X29576)),
inference(variable_rename,[status(thm)],[fact_wf__int__ge__less__than2]) ).
fof(i_0_11010,plain,
! [X20891] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20891) = X20891,
inference(variable_rename,[status(thm)],[fact_number__of__is__id]) ).
fof(i_0_11011,plain,
! [X17245] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X17245) = X17245,
inference(variable_rename,[status(thm)],[fact_nat__size]) ).
fof(i_0_11012,plain,
! [X34442] :
( ~ class_Finite__Set_Ofinite(X34442)
| class_Finite__Set_Ofinite(tc_Option_Ooption(X34442)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Option__Ooption__Finite__Set_Ofinite])]) ).
fof(i_0_11013,plain,
! [X18084,X18085] :
( ( c_Com_Ovname_OGlb(X18085) != c_Com_Ovname_OGlb(X18084)
| X18085 = X18084 )
& ( X18085 != X18084
| c_Com_Ovname_OGlb(X18085) = c_Com_Ovname_OGlb(X18084) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vname_Osimps_I1_J])]) ).
fof(i_0_11014,plain,
! [X17794,X17795] :
( ( c_Com_Ovname_OLoc(X17795) != c_Com_Ovname_OLoc(X17794)
| X17795 = X17794 )
& ( X17795 != X17794
| c_Com_Ovname_OLoc(X17795) = c_Com_Ovname_OLoc(X17794) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vname_Osimps_I2_J])]) ).
fof(i_0_11015,plain,
! [X18112,X18113] : c_Com_Ovname_OGlb(X18113) != c_Com_Ovname_OLoc(X18112),
inference(variable_rename,[status(thm)],[fact_vname_Osimps_I3_J]) ).
fof(i_0_11016,plain,
! [X18114,X18115] : c_Com_Ovname_OLoc(X18115) != c_Com_Ovname_OGlb(X18114),
inference(variable_rename,[status(thm)],[fact_vname_Osimps_I4_J]) ).
fof(i_0_11017,plain,
! [X18041] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(X18041)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_vname_Osize_I1_J]) ).
fof(i_0_11018,plain,
! [X17910] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(X17910)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_vname_Osize_I2_J]) ).
fof(i_0_11019,plain,
! [X28364] : c_Equiv__Relations_Oequivp(X28364,c_fequal),
inference(variable_rename,[status(thm)],[fact_identity__equivp]) ).
fof(i_0_11020,plain,
~ hBOOL(c_fFalse),
inference(fof_simplification,[status(thm)],[help_c__fFalse__1]) ).
cnf(i_0_11021,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,esk171_11(X3,X4,X5,X2,X1,X6,X7,X8,X9,X10,X11)),esk172_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_11022,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk172_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_11023,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk171_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_11024,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_11025,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_11026,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_11027,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_11028,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_11029,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_11030,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_11031,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_11032,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_11033,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_11034,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_11035,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_11036,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk299_8(X3,X4,X5,X2,X1,X6,X7,X8)),esk300_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_11037,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_11038,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_11039,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_11040,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,esk404_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_11041,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_11042,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_11043,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_11044,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_11045,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_11046,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_11047,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_11048,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_11049,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_11050,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_11051,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_11052,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_11053,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_11054,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_11055,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_11056,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_11057,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_11058,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_11059,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_11060,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_11061,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_11062,plain,
( X3 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk169_7(X2,X3,X4,X5,X6,X7,X1)),esk170_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_11063,plain,
( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),hAPP(X4,esk299_8(X5,X6,X4,X7,X8,X1,X3,X2))),hAPP(X6,esk300_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_11064,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_11065,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_11066,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_11067,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_11068,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_11069,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_11070,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_11071,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_11072,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_11073,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_11074,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk404_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_11075,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_11076,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk265_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_11077,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk365_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_11078,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_11079,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X6,X5,X3),X2),X4)))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(X2,esk98_7(X3,X2,X1,X4,X5,X6,X7)),esk99_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_11080,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_11081,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_11082,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_11083,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_11084,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,esk265_8(X2,X1,X3,X4,X5,X6,X7,X8)) != hAPP(hAPP(c_Fun_Ocomp(X6,X8,X7,X2),X5),esk265_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_11085,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,esk365_8(X2,X1,X3,X4,X5,X6,X7,X8)) != hAPP(X2,esk365_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_11086,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_11087,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_11088,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_11089,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,esk173_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_11090,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,esk398_7(X2,X3,X1,X4,X5,X6,X7)),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6077]),
[final] ).
cnf(i_0_11091,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_11092,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_11093,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_11094,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_11095,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_11096,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_11097,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_11098,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)),esk443_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_11099,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_11100,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_11101,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_11102,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk365_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_11103,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_11104,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),esk109_7(X6,X7,X5,X4,X3,X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),esk110_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_11105,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),esk109_7(X6,X7,X5,X4,X3,X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),esk110_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_11106,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_11107,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_11108,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_11109,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_11110,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_11111,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_11112,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_11113,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_11114,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_11115,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_11116,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_11117,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_11118,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_11119,plain,
( hBOOL(hAPP(hAPP(X1,esk99_7(X2,X3,X4,X5,X6,X7,X1)),esk98_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_11120,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_11121,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_11122,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_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_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),esk313_6(X5,X4,X6,X3,X2,X1))))) != hAPP(X5,esk313_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_11124,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_11125,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_11126,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_11127,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),esk311_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_11128,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_11129,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,esk367_5(X3,X4,X5,X2,X1)))),hAPP(X2,esk367_5(X3,X4,X5,X2,X1)))),c_Transitive__Closure_Ortrancl(X1,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_6109]),
[final] ).
cnf(i_0_11130,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk430_6(X3,X4,X1,X5,X2,X6)),esk431_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_11131,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk429_6(X3,X4,X2,X5,X6,X1)),esk430_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_11132,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_11133,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_11134,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,esk288_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_11135,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_11136,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_11137,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_11138,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_11139,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk308_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_11140,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk109_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_11141,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk109_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_11142,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_11143,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_11144,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,esk23_6(X1,X4,X2,X5,X6,X3)),hAPP(c_Natural_Ogetlocs,X2))),X3),hAPP(hAPP(c_Natural_Ogetlocs,esk23_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_11145,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk398_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_11146,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk173_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_11147,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk170_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_11148,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk169_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_11149,plain,
( X1 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,esk26_6(X1,X2,X3,X4,X5,X6)),hAPP(c_Natural_Ogetlocs,X3))),X6),hAPP(hAPP(c_Natural_Ogetlocs,esk26_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_11150,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk83_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),esk82_4(X1,X2,X3,X4)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk82_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_11151,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk83_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),esk82_4(X2,X3,X4,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X3,esk82_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_11152,plain,
( hAPP(X1,esk83_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),esk82_4(X2,X1,X3,X4)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X1,esk82_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_11153,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk288_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_11154,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_11155,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_11156,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,esk345_6(X3,X2,X1,X4,X5,X6)),esk346_6(X3,X2,X1,X4,X5,X6)))) ),
inference(split_conjunct,[status(thm)],[i_0_6125]),
[final] ).
cnf(i_0_11157,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_11158,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_11159,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_11160,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_11161,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_11162,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_11163,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_11164,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_11165,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_11166,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk313_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_11167,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk311_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_11168,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_11169,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_11170,plain,
( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,esk109_7(X3,X2,X4,X5,X1,X6,X7)),esk110_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_11171,plain,
( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,esk109_7(X3,X2,X4,X5,X1,X6,X7)),esk110_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_11172,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_11173,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_11174,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_11175,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),esk331_3(X2,X3,X1)),esk331_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))),esk330_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_6138]),
[final] ).
cnf(i_0_11176,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_11177,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk331_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))),esk330_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_6138]),
[final] ).
cnf(i_0_11178,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_11179,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_11180,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_11181,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_11182,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_11183,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_11184,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_11185,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_11186,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_11187,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_11188,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(X3,esk347_6(X4,X3,X5,X6,X2,X1)),esk348_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_11189,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_11190,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))))),esk390_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_11191,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),esk414_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_11192,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_11193,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_11194,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_11195,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_11196,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_11197,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_11198,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_11199,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_11200,plain,
( hAPP(X1,esk169_7(X2,X3,X1,X4,X5,X6,X7)) = hAPP(X1,esk170_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_11201,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,esk329_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_11202,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,esk320_4(X3,X2,X1,X4)))),hAPP(X1,esk320_4(X3,X2,X1,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_6161]),
[final] ).
cnf(i_0_11203,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_11204,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_11205,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_11206,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)))),esk495_3(X3,X2,X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6165,c_0_6100]),c_0_6100]),
[final] ).
cnf(i_0_11207,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)))),esk494_3(X2,X3,X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6166,c_0_6100]),c_0_6100]),
[final] ).
cnf(i_0_11208,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_11209,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_11210,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_11211,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_11212,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_11213,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_11214,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,esk308_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_11215,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_11216,plain,
( hBOOL(hAPP(X1,esk320_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_11217,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_11218,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_11219,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_11220,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_11221,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_11222,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_11223,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_11224,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_11225,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_11226,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_11227,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_11228,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_11229,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_11230,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_11231,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)),esk333_4(X3,X4,X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_6184]),
[final] ).
cnf(i_0_11232,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_11233,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,esk290_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_6186]),
[final] ).
cnf(i_0_11234,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,esk289_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_6187]),
[final] ).
cnf(i_0_11235,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_11236,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_11237,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_11238,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_11239,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_11240,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)),esk270_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),esk270_4(X2,X3,X4,X1)),X3))),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_6190]),
[final] ).
cnf(i_0_11241,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_11242,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_11243,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_11244,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_11245,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_11246,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_11247,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_11248,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_11249,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_11250,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_11251,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,esk253_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_11252,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_11253,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_6203]),
[final] ).
cnf(i_0_11254,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_6204]),
[final] ).
cnf(i_0_11255,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_11256,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_6203]),
[final] ).
cnf(i_0_11257,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_6204]),
[final] ).
cnf(i_0_11258,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_11259,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_11260,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_11261,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_11262,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_11263,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_11264,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_11265,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),esk312_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_11266,plain,
( X1 = hAPP(hAPP(X2,X3),esk414_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_11267,plain,
( X1 = hAPP(hAPP(X2,X3),esk390_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_11268,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk463_5(X5,X4,X3,X2,X1)),esk463_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_11269,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_11270,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)),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_11271,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)),esk378_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_11272,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_11273,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_11274,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_11275,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_11276,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk81_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),esk80_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk80_3(X1,X2,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_6221]),
[final] ).
cnf(i_0_11277,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk79_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),esk78_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk78_3(X1,X2,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_6222]),
[final] ).
cnf(i_0_11278,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk372_5(X2,X3,X4,X5,X1)),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk373_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_11279,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk372_5(X2,X3,X4,X5,X1)),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk373_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_11280,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_11281,plain,
( hAPP(X1,esk81_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),esk80_3(X2,X1,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X1,esk80_3(X2,X1,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_6221]),
[final] ).
cnf(i_0_11282,plain,
( hAPP(X1,esk79_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),esk78_3(X2,X1,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X1,esk78_3(X2,X1,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_6222]),
[final] ).
cnf(i_0_11283,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_11284,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk290_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_6186]),
[final] ).
cnf(i_0_11285,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk289_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_6187]),
[final] ).
cnf(i_0_11286,plain,
( hAPP(X1,esk435_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_11287,plain,
( hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),esk435_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_11288,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_11289,plain,
( hBOOL(hAPP(X1,esk312_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_11290,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_11291,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_11292,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,esk24_5(X1,X2,X4,X5,X3)),hAPP(c_Natural_Ogetlocs,X2))),X3),hAPP(hAPP(c_Natural_Ogetlocs,esk24_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_11293,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_11294,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_11295,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_11296,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_11297,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_11298,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_11299,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_11300,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_11301,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_11302,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_11303,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_11304,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk264_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_11305,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk263_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_11306,plain,
( X1 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,esk25_5(X1,X2,X3,X4,X5)),hAPP(c_Natural_Ogetlocs,X2))),X5),hAPP(hAPP(c_Natural_Ogetlocs,esk25_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_11307,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_11308,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_11309,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_11310,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_11311,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_11312,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_11313,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,esk15_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_11314,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_11315,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_11316,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_11317,plain,
( hBOOL(hAPP(hAPP(X1,esk317_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_11318,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_11319,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk413_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_11320,plain,
( X1 = hAPP(hAPP(hAPP(c_Natural_Oupdate,esk21_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_11321,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk253_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_11322,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,esk474_5(X3,X2,X4,X5,X1))),hAPP(X3,esk474_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_11323,plain,
( hBOOL(hAPP(hAPP(X1,X2),esk317_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_11324,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,esk260_5(X3,X2,X4,X5,X1))),hAPP(X3,esk260_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_11325,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_11326,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk382_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_6215]),
[final] ).
cnf(i_0_11327,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_11328,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_11329,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,esk304_5(X5,X4,X3,X2,X1)),esk305_5(X5,X4,X3,X2,X1))) != hAPP(hAPP(X2,hAPP(X4,esk304_5(X5,X4,X3,X2,X1))),hAPP(X4,esk305_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_11330,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),esk491_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_11331,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),esk491_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_11332,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),esk491_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_11333,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),esk491_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_11334,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_11335,plain,
( hBOOL(hAPP(hAPP(X1,X3),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk88_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),esk87_3(X1,X2,X3)),esk88_3(X1,X2,X3))))
| hBOOL(hAPP(hAPP(X1,esk87_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)))),esk88_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_11336,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_6268]),
[final] ).
cnf(i_0_11337,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_6269]),
[final] ).
cnf(i_0_11338,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_6268]),
[final] ).
cnf(i_0_11339,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_6269]),
[final] ).
cnf(i_0_11340,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_11341,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_11342,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),esk455_4(X3,X4,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X4),esk455_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_11343,plain,
( hBOOL(hAPP(hAPP(X1,X3),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk93_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk92_3(X1,X2,X3)),esk93_3(X1,X2,X3)))
| hBOOL(hAPP(hAPP(X1,esk92_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)))),esk93_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_11344,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)),esk445_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_11345,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_11346,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk444_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_11347,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk386_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_11348,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_11349,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_11350,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk374_5(X3,X4,X5,X2,X1))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk375_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_11351,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk374_5(X3,X4,X5,X2,X1))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk375_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_11352,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)),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_11353,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_11354,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_11355,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk374_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_11356,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk374_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_11357,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_11358,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_11359,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_11360,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_11361,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_11362,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_11363,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_11364,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_11365,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_11366,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_11367,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_11368,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_11369,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_11370,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_11371,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_11372,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_11373,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_11374,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_11375,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_11376,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk123_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_11377,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk119_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_11378,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_11379,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,esk263_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_11380,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,esk143_4(X4,X3,X2,X1)),esk144_4(X4,X3,X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk143_4(X4,X3,X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk144_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_11381,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_11382,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_11383,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_11384,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_11385,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,esk413_6(X4,X3,X2,X1,X5,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_6254]),
[final] ).
cnf(i_0_11386,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_11387,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_11388,plain,
( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk347_6(X1,X4,X3,X2,X5,X6)),esk348_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_11389,plain,
( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk429_6(X4,X5,X6,X1,X3,X2)),esk431_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_11390,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_11391,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_11392,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_11393,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_11394,plain,
( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk345_6(X4,X5,X6,X3,X2,X1)),esk346_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_11395,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_11396,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_11397,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_11398,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_11399,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_11400,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_11401,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_11402,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_11403,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_11404,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_11405,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_11406,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_11407,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_11408,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_11409,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_11410,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_11411,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_11412,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,esk102_2(X2,X1))),hAPP(X2,esk103_2(X2,X1))))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6324]),
[final] ).
cnf(i_0_11413,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),esk103_2(X1,X2)),esk102_2(X1,X2)))
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[i_0_6324]),
[final] ).
cnf(i_0_11414,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_11415,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_11416,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),esk102_2(X1,X2)),esk103_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_11417,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_11418,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_11419,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_11420,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_11421,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_11422,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_11423,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,esk168_5(X3,X2,X4,X5,X1))),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_6331]),
[final] ).
cnf(i_0_11424,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,esk243_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_11425,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_11426,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_11427,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_11428,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,esk163_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_11429,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_11430,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_11431,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_11432,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),esk456_4(X3,X4,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X4),esk456_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_11433,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_11434,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_11435,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),esk456_4(X3,X4,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X4),esk456_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_11436,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_11437,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_11438,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_11439,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_11440,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_11441,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_11442,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_11443,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_11444,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_11445,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_11446,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_11447,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_11448,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_11449,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_11450,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_11451,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk377_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_6216]),
[final] ).
cnf(i_0_11452,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_11453,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_11454,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_11455,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_11456,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_11457,plain,
( hAPP(X1,esk263_6(X2,X3,X1,X4,X5,X6)) = hAPP(X1,esk264_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_11458,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),esk447_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_11459,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_11460,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_11461,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_11462,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_11463,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk446_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_11464,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_11465,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_11466,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_11467,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_11468,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,esk280_5(X3,X4,X5,X2,X1),esk281_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_11469,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,esk278_5(X3,X4,X5,X2,X1),esk279_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_11470,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),esk465_4(X3,X4,X2,X1))),esk464_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_11471,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_11472,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_11473,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_11474,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_11475,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_11476,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))),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_11477,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_11478,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_11479,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_11480,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_11481,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_11482,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_11483,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_11484,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),esk280_5(X2,X3,X4,X5,X1)),esk281_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_11485,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),esk278_5(X2,X3,X4,X5,X1)),esk279_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_11486,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),esk476_4(X2,X3,X4,X1)),esk475_4(X2,X3,X4,X1))),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6386]),
[final] ).
cnf(i_0_11487,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),esk475_4(X2,X3,X4,X1)),esk476_4(X2,X3,X4,X1))),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_6386]),
[final] ).
cnf(i_0_11488,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk386_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_11489,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_11490,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_11491,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_11492,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)),esk432_4(X1,X2,X3,X4)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk433_4(X1,X2,X3,X4)),esk434_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_11493,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),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_6223]),
[final] ).
cnf(i_0_11494,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),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_6223]),
[final] ).
cnf(i_0_11495,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_11496,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_11497,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_11498,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_11499,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_11500,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_11501,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)
| esk263_6(X1,X2,X3,X4,X5,X6) != esk264_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_11502,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_11503,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_11504,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_11505,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_11506,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_11507,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_11508,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_11509,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_11510,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_11511,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_11512,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_11513,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,esk391_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_11514,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk162_5(X2,X3,X4,X5,X1)),hAPP(X3,esk161_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_11515,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_11516,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_11517,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk298_5(X2,X3,X4,X1,X5)),hAPP(X2,esk297_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_11518,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_11519,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_11520,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_11521,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_11522,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_11523,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_11524,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk433_4(X1,X2,X3,X4)),esk434_4(X1,X2,X3,X4)))
| hBOOL(hAPP(hAPP(hAPP(X1,esk432_4(X1,X2,X3,X4)),esk433_4(X1,X2,X3,X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk434_4(X1,X2,X3,X4)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| hBOOL(hAPP(hAPP(hAPP(X1,X4),X3),X2))
| hAPP(esk432_4(X1,X2,X3,X4),esk434_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_11525,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_11526,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_11527,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_11528,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_11529,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_11530,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_11531,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_11532,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_11533,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)),esk271_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),esk271_4(X2,X3,X4,X1)),X3))),X2) ),
inference(split_conjunct,[status(thm)],[i_0_6424]),
[final] ).
cnf(i_0_11534,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_11535,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),esk277_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_11536,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_11537,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_11538,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,esk318_3(X2,X1,X3)))),hAPP(X3,esk318_3(X2,X1,X3)))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6428]),
[final] ).
cnf(i_0_11539,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_11540,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_11541,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_11542,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_11543,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,esk252_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_11544,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,esk242_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_11545,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_11546,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_11547,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_11548,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_11549,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_11550,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_11551,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_11552,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_11553,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_11554,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,esk396_5(X3,X4,X5,X2,X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_6441]),
[final] ).
cnf(i_0_11555,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_11556,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_11557,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,esk394_5(X3,X4,X5,X2,X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_6444]),
[final] ).
cnf(i_0_11558,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_11559,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_11560,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_11561,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,esk397_5(X2,X1,X3,X4,X5)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6447]),
[final] ).
cnf(i_0_11562,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_11563,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_11564,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,esk395_5(X3,X4,X5,X2,X1))))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6450]),
[final] ).
cnf(i_0_11565,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,esk254_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_11566,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_11567,plain,
( hBOOL(hAPP(hAPP(hAPP(X1,X4),X3),X2))
| ~ hBOOL(hAPP(hAPP(hAPP(X1,esk432_4(X1,X2,X3,X4)),esk433_4(X1,X2,X3,X4)),esk434_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_11568,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_11569,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_11570,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,esk23_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_11571,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk466_4(X2,X3,X4,X1)),esk467_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_11572,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_11573,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_11574,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_11575,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_11576,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_11577,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_11578,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_11579,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_11580,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_11581,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_11582,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_11583,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_11584,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_11585,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_11586,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk177_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_11587,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_11588,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_11589,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_11590,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_11591,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_11592,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_11593,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_11594,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk154_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_11595,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_11596,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_6475]),
[final] ).
cnf(i_0_11597,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_6476]),
[final] ).
cnf(i_0_11598,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_11599,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_11600,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))),esk24_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_11601,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk427_4(X3,X4,X1,X2)),esk428_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_11602,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,esk26_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_11603,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_11604,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,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_11605,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_11606,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,esk44_4(X4,X3,X2,X1))),hAPP(X2,hAPP(c_Nat_OSuc,esk44_4(X4,X3,X2,X1)))))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6480]),
[final] ).
cnf(i_0_11607,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,esk43_4(X3,X4,X2,X1))),hAPP(X2,hAPP(c_Nat_OSuc,esk43_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_11608,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,esk44_4(X2,X1,X4,X3))),hAPP(X4,hAPP(c_Nat_OSuc,esk44_4(X2,X1,X4,X3)))))
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_6480]),
[final] ).
cnf(i_0_11609,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk266_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_11610,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_11611,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_11612,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_11613,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),esk287_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_11614,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_11615,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_11616,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_11617,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_11618,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_11619,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_11620,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_11621,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_11622,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_11623,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_11624,plain,
( c_Natural_Oevaln(X1,hAPP(hAPP(hAPP(c_Natural_Oupdate,X2),c_Com_Ovname_OLoc(X3)),hAPP(X4,X2)),X5,esk21_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_11625,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_11626,plain,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),esk436_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_11627,plain,
( hAPP(X3,X2) = c_Option_Ooption_ONone(X6)
| hAPP(X1,esk436_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_11628,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_11629,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_11630,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk425_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_11631,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_11632,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)),esk272_3(X2,X3,X1))),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6502]),
[final] ).
cnf(i_0_11633,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_11634,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_11635,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_11636,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,esk14_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_11637,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk446_5(X3,X1,X4,X5,X2)),esk447_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_11638,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_11639,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_11640,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk474_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_11641,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk388_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_11642,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_11643,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_11644,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_11645,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_11646,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_11647,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_11648,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk252_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_11649,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk242_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_11650,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_11651,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_11652,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_11653,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk240_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_6513]),
[final] ).
cnf(i_0_11654,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk230_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_6514]),
[final] ).
cnf(i_0_11655,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_11656,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk241_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_6513]),
[final] ).
cnf(i_0_11657,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk231_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_6514]),
[final] ).
cnf(i_0_11658,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk243_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_11659,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk238_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_11660,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk236_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_11661,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk168_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_11662,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_11663,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__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_6519]),
[final] ).
cnf(i_0_11664,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk244_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_6520]),
[final] ).
cnf(i_0_11665,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk156_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_6521]),
[final] ).
cnf(i_0_11666,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk155_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_6522]),
[final] ).
cnf(i_0_11667,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_11668,plain,
( X1 = hAPP(hAPP(hAPP(c_Natural_Oupdate,esk20_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_11669,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk239_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_11670,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk237_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_11671,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_11672,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk444_5(X3,X4,X5,X1,X2)),esk445_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_11673,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_11674,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_11675,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),esk117_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_11676,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X3,esk165_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_11677,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_11678,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk161_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_11679,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_11680,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk391_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_11681,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk165_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_11682,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk260_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_11683,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_11684,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk257_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_6532]),
[final] ).
cnf(i_0_11685,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk256_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_6533]),
[final] ).
cnf(i_0_11686,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk190_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_6534]),
[final] ).
cnf(i_0_11687,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk189_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_6535]),
[final] ).
cnf(i_0_11688,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)))
| esk383_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_11689,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) != esk378_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_11690,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_11691,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_11692,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk159_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_11693,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk160_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_11694,plain,
( hBOOL(hAPP(hAPP(X1,esk159_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_11695,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_11696,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk297_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_11697,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk396_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_11698,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_11699,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_11700,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_11701,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_11702,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk123_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_11703,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk119_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_11704,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_11705,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_11706,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk163_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_11707,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk394_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_11708,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(X3,esk164_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_11709,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,esk425_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_11710,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_11711,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_11712,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk397_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_11713,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk164_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_11714,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_11715,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_11716,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_11717,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_11718,plain,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),esk258_4(X1,X3,X4,X2)),esk259_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_11719,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,esk480_4(X2,X1,X3,X4))),hAPP(X2,esk480_4(X2,X1,X3,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_6551]),
[final] ).
cnf(i_0_11720,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_11721,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_11722,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_11723,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_11724,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_11725,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_11726,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk275_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_11727,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_11728,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_11729,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_11730,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk395_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_11731,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_11732,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk254_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_11733,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_11734,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_11735,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_11736,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_11737,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_11738,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_11739,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,esk48_4(X3,X2,X4,X1))),hAPP(X3,esk48_4(X3,X2,X4,X1))))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_6567]),
[final] ).
cnf(i_0_11740,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_11741,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_11742,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk437_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_11743,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_11744,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_11745,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),esk462_5(X3,X4,X1,X5,X2)),X3)
| hAPP(hAPP(c_List_Oappend(X2),esk461_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_11746,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_11747,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,esk193_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_11748,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_11749,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))),esk25_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_11750,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_11751,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_11752,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_11753,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_11754,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_11755,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_11756,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_11757,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_11758,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_11759,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_11760,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_11761,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,esk255_3(X2,X3,X1))),hAPP(X3,esk255_3(X2,X3,X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_6584]),
[final] ).
cnf(i_0_11762,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,esk197_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_11763,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_6586]),
[final] ).
cnf(i_0_11764,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),esk322_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_11765,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_11766,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_11767,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_11768,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_11769,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_11770,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_11771,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_11772,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_11773,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_11774,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_11775,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_11776,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_11777,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_11778,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_11779,plain,
( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk231_5(X2,X3,X4,X5,X1)),esk230_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_6514]),
[final] ).
cnf(i_0_11780,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk241_5(X2,X3,X4,X5,X1)),esk240_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_6513]),
[final] ).
cnf(i_0_11781,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_11782,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_11783,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_11784,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_11785,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_11786,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_11787,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_11788,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_11789,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_11790,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_11791,plain,
( hBOOL(hAPP(X1,X6))
| ~ hBOOL(hAPP(X1,esk162_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_11792,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_11793,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_11794,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_11795,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_11796,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_11797,plain,
( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk239_5(X2,X3,X4,X5,X1)),esk238_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_11798,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk237_5(X2,X3,X4,X5,X1)),esk236_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_11799,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_11800,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_11801,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_11802,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_11803,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_11804,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_11805,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_11806,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_11807,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_11808,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),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_11809,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_11810,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_11811,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_11812,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),esk302_3(X2,X3,X1)),esk302_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_11813,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),esk301_3(X2,X3,X1)),esk301_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_11814,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_11815,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_11816,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_11817,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk388_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_11818,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_11819,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_11820,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_11821,plain,
( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk297_5(X4,X5,X1,X3,X2)),esk298_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_11822,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_11823,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_11824,plain,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = hAPP(hAPP(c_Set_Oinsert(X1),esk280_5(X4,X3,X2,X5,X1)),esk281_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_11825,plain,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = hAPP(hAPP(c_Set_Oinsert(X1),esk278_5(X4,X3,X2,X5,X1)),esk279_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_11826,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,esk177_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_11827,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_11828,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_11829,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_11830,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_11831,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_11832,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_11833,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_11834,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_11835,plain,
( hBOOL(hAPP(X1,X7))
| ~ hBOOL(hAPP(X1,esk160_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_11836,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_11837,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_11838,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_11839,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_11840,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_11841,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_11842,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_11843,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,esk267_5(X2,X1,X3,X4,X5)) != hAPP(X2,esk267_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_11844,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,esk261_5(X2,X1,X3,X4,X5)) != hAPP(X2,esk261_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_11845,plain,
( hAPP(hAPP(c_List_Omap(X5,X4),X1),X3) = hAPP(hAPP(c_List_Omap(X5,X4),X2),X3)
| hAPP(X1,esk437_5(X2,X3,X1,X4,X5)) != hAPP(X2,esk437_5(X2,X3,X1,X4,X5)) ),
inference(split_conjunct,[status(thm)],[i_0_6570]),
[final] ).
cnf(i_0_11846,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_11847,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_11848,plain,
( hBOOL(hAPP(X1,esk425_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_11849,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_11850,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_11851,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_11852,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_11853,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_11854,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_6653]),
[final] ).
cnf(i_0_11855,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_6654]),
[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)),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_6655]),
[final] ).
cnf(i_0_11857,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_11858,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_11859,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_11860,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_6659]),
[final] ).
cnf(i_0_11861,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_6660]),
[final] ).
cnf(i_0_11862,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_6661]),
[final] ).
cnf(i_0_11863,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_11864,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_11865,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_11866,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_11867,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_11868,plain,
( hAPP(hAPP(c_List_Oappend(X1),X2),esk462_5(X3,X4,X5,X2,X1)) = X4
| hAPP(hAPP(c_List_Oappend(X1),esk461_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_11869,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),esk462_5(X3,X4,X1,X5,X2)),X3)
| X5 = hAPP(hAPP(c_List_Oappend(X2),X4),esk461_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_11870,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_11871,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_11872,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_11873,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),hAPP(hAPP(hAPP(c_Natural_Oupdate,X2),c_Com_Ovname_OLoc(X3)),hAPP(X4,X2))),esk20_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_11874,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_11875,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_11876,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_11877,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_11878,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_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),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_11880,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_11881,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_11882,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_11883,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_11884,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_11885,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_11886,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_11887,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_11888,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_11889,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_11890,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_11891,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_11892,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_11893,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_11894,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_11895,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_11896,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,esk424_2(X2,X1)))
| ~ hBOOL(hAPP(X2,esk424_2(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_6689]),
[final] ).
cnf(i_0_11897,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_11898,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_11899,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_11900,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_11901,plain,
( hBOOL(hAPP(X1,esk424_2(X2,X1)))
| hBOOL(hAPP(X2,esk424_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_11902,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk424_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_11903,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_11904,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_11905,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_11906,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_11907,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_11908,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_11909,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_11910,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_11911,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),esk468_4(X3,X1,X4,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),esk467_4(X3,X1,X4,X2)),esk469_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_11912,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),esk468_4(X3,X4,X1,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),esk466_4(X3,X4,X1,X2)),esk469_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_11913,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_11914,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_11915,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_11916,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_11917,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_11918,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_11919,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)),esk192_3(X1,X3,X2)),hAPP(hAPP(c_Set_Oinsert(X2),esk191_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_11920,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_11921,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_11922,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_11923,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk330_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),esk331_3(X2,X3,X1)),esk331_3(X2,X3,X1))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6138]),
[final] ).
cnf(i_0_11924,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_11925,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_11926,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_11927,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_11928,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_11929,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_11930,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_11931,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_11932,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_11933,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_11934,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_11935,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_11936,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_11937,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_11938,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk477_3(X2,X3,X1)),esk477_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_11939,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_11940,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_11941,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_11942,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_11943,plain,
( hAPP(X1,esk154_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_11944,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_11945,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk456_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_11946,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_11947,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_11948,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_11949,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_11950,plain,
( hAPP(X1,esk266_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_11951,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_11952,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_11953,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_11954,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_11955,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_11956,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_11957,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_11958,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_11959,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_11960,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_11961,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_11962,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_11963,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_11964,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_11965,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_11966,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_11967,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_11968,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_11969,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_11970,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_11971,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_11972,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_11973,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),esk419_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_11974,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),esk415_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_11975,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk456_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_11976,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_11977,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_11978,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_11979,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_11980,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_11981,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_11982,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_11983,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_11984,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_11985,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_11986,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_11987,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_11988,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),esk371_3(X2,X3,X1)),esk370_3(X2,X3,X1))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6756]),
[final] ).
cnf(i_0_11989,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)),esk371_3(X2,X3,X1))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_6756]),
[final] ).
cnf(i_0_11990,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_11991,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_11992,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_11993,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_11994,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_11995,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_11996,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_11997,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_11998,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_11999,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_12000,plain,
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),esk258_4(X2,X3,X4,X1)),esk259_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_12001,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_12002,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_12003,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk277_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_12004,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_12005,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_12006,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_12007,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_12008,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_12009,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_12010,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_12011,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_12012,plain,
( hBOOL(hAPP(hAPP(X1,X2),esk275_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_12013,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_12014,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_12015,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_12016,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_12017,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_12018,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_12019,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_6775]),
[final] ).
cnf(i_0_12020,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X2),esk326_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_12021,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_12022,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_12023,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_12024,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_12025,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_12026,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_12027,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_12028,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_12029,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_12030,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_12031,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk115_4(X2,X3,X4,X1)),X3))
| hBOOL(hAPP(hAPP(c_member(X1),esk114_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_12032,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_12033,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk113_4(X2,X3,X4,X1)),X3))
| hBOOL(hAPP(hAPP(c_member(X1),esk112_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_12034,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_12035,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_12036,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_12037,plain,
( X1 = hAPP(c_Nat_OSuc,esk375_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_12038,plain,
( X1 = hAPP(c_Nat_OSuc,esk373_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_12039,plain,
( X1 = hAPP(c_Nat_OSuc,esk375_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_12040,plain,
( X1 = hAPP(c_Nat_OSuc,esk373_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_12041,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_12042,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_12043,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_12044,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_12045,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_12046,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_12047,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_12048,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_12049,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_12050,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_12051,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_12052,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_12053,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_12054,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_12055,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_12056,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_12057,plain,
( hAPP(hAPP(c_List_Otake(X1),esk456_4(X2,X3,X4,X1)),X4) = hAPP(hAPP(c_List_Otake(X1),esk456_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_12058,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_12059,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_12060,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_12061,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_12062,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_12063,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_12064,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_12065,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk267_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_6644]),
[final] ).
cnf(i_0_12066,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk261_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_6645]),
[final] ).
cnf(i_0_12067,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_12068,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_12069,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_12070,plain,
( hAPP(hAPP(c_List_Oappend(X1),X2),esk462_5(X3,X4,X5,X2,X1)) = X4
| X2 = hAPP(hAPP(c_List_Oappend(X1),X4),esk461_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_12071,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),esk460_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_12072,plain,
( hAPP(hAPP(c_List_Oappend(X1),esk459_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_12073,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk443_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_12074,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),esk145_2(X2,X1)),esk146_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk145_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk146_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_12075,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),esk135_2(X2,X1)),esk136_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk135_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk136_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_12076,plain,
( c_Hoare__Mirabelle_Otriple__valid(X5,X4,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X3),X2),X1))
| ~ hBOOL(hAPP(hAPP(X1,esk2_4(X1,X2,X3,X4)),esk4_4(X1,X2,X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_6809]),
[final] ).
cnf(i_0_12077,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_12078,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,esk291_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_12079,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_12080,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_12081,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_12082,plain,
( hAPP(hAPP(c_List_Oappend(X1),esk459_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_12083,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),esk460_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_12084,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),esk292_2(X2,X1)),esk293_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk292_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk293_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_12085,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_12086,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_12087,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_12088,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_12089,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_12090,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,esk251_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_6519]),
[final] ).
cnf(i_0_12091,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,esk244_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_6520]),
[final] ).
cnf(i_0_12092,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,esk156_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_6521]),
[final] ).
cnf(i_0_12093,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,esk155_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_6522]),
[final] ).
cnf(i_0_12094,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_12095,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_12096,plain,
( hAPP(hAPP(c_List_Otake(X1),esk456_4(X2,X3,X4,X1)),X4) = hAPP(hAPP(c_List_Otake(X1),esk456_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_12097,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_12098,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_12099,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_12100,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_12101,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_12102,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_12103,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk465_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_12104,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk83_4(X1,X2,X3,X4)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk82_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_12105,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_12106,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_12107,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_12108,plain,
( hBOOL(hAPP(hAPP(c_member(X4),esk112_4(X1,X2,X3,X4)),X3))
| hBOOL(hAPP(X1,X5))
| ~ hBOOL(hAPP(X1,esk113_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_12109,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk113_4(X2,X3,X4,X1)),X3))
| hBOOL(hAPP(X2,X5))
| ~ hBOOL(hAPP(X2,esk112_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_12110,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_12111,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_12112,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_12113,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_12114,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_12115,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),esk139_2(X2,X1)),esk140_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk139_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk140_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_12116,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),esk137_2(X2,X1)),esk138_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk137_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk138_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_12117,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),esk141_2(X2,X1)),esk142_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk141_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk142_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_12118,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),esk133_2(X2,X1)),esk134_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk133_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk134_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_12119,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_12120,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_12121,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk419_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_12122,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_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_12123,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_12124,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_12125,plain,
( hAPP(c_Map_Omap__of(X1,X2,X5),X3) = hAPP(c_Option_Ooption_OSome(X2),esk440_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_12126,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_12127,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_12128,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_12129,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_12130,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_12131,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_12132,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_12133,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,esk257_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_6532]),
[final] ).
cnf(i_0_12134,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,esk256_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_6533]),
[final] ).
cnf(i_0_12135,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,esk190_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_6534]),
[final] ).
cnf(i_0_12136,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,esk189_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_6535]),
[final] ).
cnf(i_0_12137,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_12138,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_12139,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_12140,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_12141,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_12142,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_12143,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_12144,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_12145,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk495_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_6857,c_0_6100]),c_0_6100]),
[final] ).
cnf(i_0_12146,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk494_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_6858,c_0_6100]),c_0_6100]),
[final] ).
cnf(i_0_12147,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_12148,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_12149,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_12150,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_12151,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_12152,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_12153,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_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_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_12155,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_12156,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_12157,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_12158,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_12159,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_12160,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_12161,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,esk342_3(X3,X2,X1)))),c_Predicate_ORangeP(X1,X1,hAPP(X2,esk343_3(X3,X2,X1)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ c_Wellfounded_OwfP(X1,hAPP(X2,esk341_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_6872]),
[final] ).
cnf(i_0_12162,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_12163,plain,
( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk457_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Int_Oint))),esk458_3(X1,X2,X3)))
| hBOOL(hAPP(hAPP(X1,X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk457_3(X1,X2,X3)),esk458_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_12164,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_12165,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_12166,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_12167,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_12168,plain,
( hBOOL(hAPP(X1,X5))
| ~ hBOOL(hAPP(X1,esk113_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(X1,esk112_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_12169,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_12170,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_12171,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_12172,plain,
( X1 = hAPP(hAPP(c_List_Olist__update(X2,X3),esk465_4(X4,X1,X3,X2)),esk464_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_12173,plain,
( hBOOL(hAPP(X1,esk115_4(X1,X2,X3,X4)))
| hBOOL(hAPP(hAPP(c_member(X4),esk114_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_12174,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk115_4(X2,X3,X4,X1)),X3))
| hBOOL(hAPP(X2,esk114_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_12175,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_12176,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_12177,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk369_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_12178,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)))
| esk475_4(X1,X2,X3,X4) != esk476_4(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_6386]),
[final] ).
cnf(i_0_12179,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_12180,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_12181,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_12182,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_12183,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,esk339_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_12184,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,esk158_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_12185,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_12186,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_12187,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_12188,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_12189,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_12190,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_12191,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_12192,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_12193,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_12194,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_12195,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk455_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_12196,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_12197,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_12198,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_12199,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk291_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_12200,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_12201,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_12202,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_12203,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_12204,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_12205,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_12206,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_12207,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_12208,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk83_4(X2,X3,X4,X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk82_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_12209,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk83_4(X1,X2,X3,X4)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),esk82_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_12210,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,esk294_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_12211,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_12212,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_12213,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk202_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_12214,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,esk276_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_12215,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_12216,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_12217,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_12218,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_12219,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_12220,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_12221,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_12222,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_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_12223,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk416_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_12224,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_12225,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_12226,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_12227,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_12228,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_12229,plain,
( X1 = hAPP(c_Set_Oimage(X2,X3,X4),esk117_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_12230,plain,
( X1 = hAPP(X2,esk269_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_12231,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_12232,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_12233,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),esk150_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_12234,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_12235,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_12236,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_12237,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_12238,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_12239,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk379_3(X3,X2,X1)),esk381_3(X3,X2,X1))),X3))
| c_Relation_Osingle__valued(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_6930]),
[final] ).
cnf(i_0_12240,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk379_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_12241,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(esk319_2(X2,X1),hAPP(c_Nat_OSuc,X3))),hAPP(esk319_2(X2,X1),X3))),X2))
| c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_6428]),
[final] ).
cnf(i_0_12242,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_12243,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_12244,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_12245,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_12246,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk204_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_12247,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_12248,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_12249,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_12250,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),esk72_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_12251,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_12252,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_12253,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_12254,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_12255,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk203_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_12256,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_12257,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_12258,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_12259,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_12260,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_12261,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_12262,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_12263,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_12264,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_12265,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_12266,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_12267,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_12268,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_12269,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_12270,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_12271,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_12272,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_12273,plain,
( hAPP(c_Set_Oimage(X2,X1,esk196_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_12274,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_12275,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_12276,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_12277,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_12278,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_12279,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_12280,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_12281,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_12282,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_12283,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_12284,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_12285,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_12286,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),esk418_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_12287,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),esk416_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_12288,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_12289,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk205_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_12290,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_12291,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_12292,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_12293,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_12294,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_12295,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_12296,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_12297,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_12298,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_12299,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_12300,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_12301,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_12302,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_12303,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_12304,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_12305,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_12306,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_12307,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_12308,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_12309,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_12310,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_12311,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_12312,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk420_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_12313,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_12314,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_12315,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_12316,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_12317,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_12318,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_12319,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk302_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_12320,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk301_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_12321,plain,
( hBOOL(hAPP(hAPP(X1,esk2_4(X2,X3,X1,X4)),esk3_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_12322,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_12323,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_12324,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_12325,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_12326,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_12327,plain,
( hAPP(c_Map_Omap__of(X1,X4,hAPP(hAPP(c_List_Ozip(X1,X4),X3),X5)),X2) = hAPP(c_Option_Ooption_OSome(X4),esk442_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_12328,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_12329,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_12330,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_12331,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_12332,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_12333,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_12334,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_12335,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_12336,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_12337,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_12338,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_12339,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_12340,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_12341,plain,
( hAPP(X1,esk83_4(X2,X1,X3,X4)) = X2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk82_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_12342,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_12343,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_12344,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_12345,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_12346,plain,
( hBOOL(hAPP(hAPP(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk94_3(X1,X2,X3))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk95_3(X1,X2,X3))))
| hBOOL(hAPP(hAPP(X1,X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk95_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_12347,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk216_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_12348,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_12349,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)))))
| esk269_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_12350,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_12351,plain,
( X2 = hAPP(hAPP(c_List_Olist_OCons(X1),esk472_3(X3,X2,X1)),esk473_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_12352,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_12353,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_12354,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_12355,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_12356,plain,
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),esk32_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_12357,plain,
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),esk17_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_12358,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_12359,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_12360,plain,
( hBOOL(hAPP(X1,esk115_4(X1,X2,X3,X4)))
| hBOOL(hAPP(X1,esk114_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_12361,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_12362,plain,
( c_Natural_Oevaln(X1,X2,X3,esk32_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_12363,plain,
( c_Natural_Oevaln(X1,X2,X3,esk17_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_12364,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_12365,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_12366,plain,
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),esk32_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_12367,plain,
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),esk17_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_12368,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_12369,plain,
( c_Natural_Oevaln(X1,X2,X3,esk32_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_12370,plain,
( c_Natural_Oevaln(X1,X2,X3,esk17_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_12371,plain,
( c_Natural_Oevaln(X1,esk9_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_12372,plain,
( c_Natural_Oevaln(X1,esk8_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_12373,plain,
( c_Natural_Oevaln(X1,X2,X3,esk9_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_12374,plain,
( c_Natural_Oevaln(X1,X2,X3,esk8_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_12375,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_12376,plain,
( X1 = hAPP(c_Relation_OImage(X2,X2,X3),hAPP(hAPP(c_Set_Oinsert(X2),esk132_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_12377,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_12378,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_12379,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_12380,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_12381,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_12382,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk218_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_12383,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk226_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_12384,plain,
( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk203_4(X2,X3,X4,X1)),esk202_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_12385,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_12386,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_12387,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_12388,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_12389,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_12390,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_12391,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_12392,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_12393,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_12394,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_12395,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_12396,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_12397,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk212_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_12398,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_12399,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_12400,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_12401,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_12402,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_12403,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk423_3(X2,X1,X3)),X3)),X2))
| c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),esk421_2(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_6982]),
[final] ).
cnf(i_0_12404,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_12405,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),esk121_1(X1)),esk122_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_12406,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk118_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_12407,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk217_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_12408,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_12409,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_12410,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_12411,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_12412,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_12413,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_12414,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk329_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_12415,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),esk179_3(X3,X2,X1)),esk180_3(X3,X2,X1))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(X2,esk179_3(X3,X2,X1))),hAPP(X2,esk180_3(X3,X2,X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7055]),
[final] ).
cnf(i_0_12416,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),esk175_3(X3,X2,X1)),esk176_3(X3,X2,X1))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(X2,esk175_3(X3,X2,X1))),hAPP(X2,esk176_3(X3,X2,X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7056]),
[final] ).
cnf(i_0_12417,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_12418,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_12419,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_12420,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_12421,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_12422,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_12423,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_12424,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_12425,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_12426,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_12427,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_12428,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk339_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_12429,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk158_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_12430,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_12431,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_12432,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_12433,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_12434,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_12435,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_12436,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_12437,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),esk295_3(X3,X2,X1)),esk296_3(X3,X2,X1))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X2,esk295_3(X3,X2,X1))),hAPP(X2,esk296_3(X3,X2,X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7072]),
[final] ).
cnf(i_0_12438,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_7073]),
[final] ).
cnf(i_0_12439,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_7074]),
[final] ).
cnf(i_0_12440,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_12441,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_12442,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk125_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_12443,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_12444,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_12445,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk480_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_12446,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_12447,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk220_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_12448,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk228_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_12449,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk205_4(X2,X3,X4,X1)),esk204_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_12450,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_12451,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk116_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_12452,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk116_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_12453,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk481_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_12454,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_12455,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_12456,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_12457,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_12458,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_12459,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk132_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_12460,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_12461,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk83_4(X2,X3,X4,X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk82_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_12462,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_12463,plain,
( hBOOL(hAPP(X4,X2))
| hBOOL(hAPP(hAPP(c_member(X1),esk111_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_12464,plain,
( hBOOL(hAPP(X4,X2))
| hBOOL(hAPP(hAPP(c_member(X1),esk111_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_12465,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_7090]),
[final] ).
cnf(i_0_12466,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_7091]),
[final] ).
cnf(i_0_12467,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_12468,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_12469,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk258_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_12470,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk227_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_12471,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk219_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_12472,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_12473,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_12474,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_12475,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_12476,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_12477,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_12478,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2)),esk31_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_12479,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2)),esk18_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_12480,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_12481,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_12482,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_12483,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk213_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_12484,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_12485,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_12486,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),esk183_3(X3,X2,X1)),esk184_3(X3,X2,X1))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(X2,esk183_3(X3,X2,X1))),hAPP(X2,esk184_3(X3,X2,X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7102]),
[final] ).
cnf(i_0_12487,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),esk181_3(X3,X2,X1)),esk182_3(X3,X2,X1))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(X2,esk181_3(X3,X2,X1))),hAPP(X2,esk182_3(X3,X2,X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7103]),
[final] ).
cnf(i_0_12488,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),esk185_3(X3,X2,X1)),esk186_3(X3,X2,X1))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(X2,esk185_3(X3,X2,X1))),hAPP(X2,esk186_3(X3,X2,X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7104]),
[final] ).
cnf(i_0_12489,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),esk187_3(X3,X2,X1)),esk188_3(X3,X2,X1))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(X2,esk187_3(X3,X2,X1))),hAPP(X2,esk188_3(X3,X2,X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7105]),
[final] ).
cnf(i_0_12490,plain,
( hBOOL(hAPP(X3,esk225_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,esk222_2(X3,X2)))
| ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk222_2(X3,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk223_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_12491,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_12492,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_12493,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_12494,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_12495,plain,
( c_Wellfounded_Oacyclic(X1,X2)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk376_2(X2,X1)),esk376_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_12496,plain,
( c_Wellfounded_Oacyclic(X1,X2)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk366_2(X2,X1)),esk366_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_12497,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_12498,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_12499,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk150_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_12500,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_12501,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_12502,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_12503,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2)),esk31_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_12504,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2)),esk18_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_12505,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_12506,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_12507,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_12508,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_12509,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_12510,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_12511,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_12512,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_12513,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_12514,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_12515,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_12516,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_12517,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_12518,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_12519,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_12520,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_12521,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_12522,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_12523,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_12524,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_12525,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_12526,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_12527,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_12528,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_12529,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_12530,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_12531,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_12532,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_12533,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk250_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_7139]),
[final] ).
cnf(i_0_12534,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk157_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_7140]),
[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_Olistrel1(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7141]),
[final] ).
cnf(i_0_12536,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_12537,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_12538,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_12539,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_12540,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_12541,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_12542,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_12543,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_12544,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_12545,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_12546,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_12547,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_12548,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk210_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_12549,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk208_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_12550,plain,
( hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk460_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_12551,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk459_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_12552,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_12553,plain,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk90_3(X3,X2,X1)),esk91_3(X3,X2,X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_7149]),
[final] ).
cnf(i_0_12554,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_12555,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_12556,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk229_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_12557,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk221_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_12558,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk294_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_12559,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_12560,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk411_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_12561,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_12562,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_12563,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk224_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,esk222_2(X1,X2)))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk222_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk223_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_12564,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_12565,plain,
( c_Nitpick_Orefl_H(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk108_2(X2,X1)),esk108_2(X2,X1))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7156]),
[final] ).
cnf(i_0_12566,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),esk75_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_12567,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),esk71_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_12568,plain,
( hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk460_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_12569,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk459_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_12570,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_12571,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_12572,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_12573,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_12574,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_12575,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_12576,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_12577,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_12578,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_12579,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_12580,plain,
( X1 = hAPP(c_Option_Ooption_OSome(X2),esk438_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_12581,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_12582,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_12583,plain,
( hAPP(X1,esk438_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_12584,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_12585,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_12586,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_12587,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_12588,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_12589,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),esk457_3(X1,X2,X3)),esk458_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_12590,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),esk94_3(X1,X2,X3)),esk95_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_12591,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),esk92_3(X1,X2,X3)),esk93_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_12592,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),esk87_3(X1,X2,X3)),esk88_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_12593,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),esk96_3(X1,X2,X3)),esk97_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_12594,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_12595,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),esk12_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_12596,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),esk11_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_12597,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_12598,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_12599,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_12600,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_12601,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk369_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_12602,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,esk250_3(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7139]),
[final] ).
cnf(i_0_12603,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,esk157_3(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7140]),
[final] ).
cnf(i_0_12604,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_12605,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_12606,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_12607,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_12608,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_12609,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_12610,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_12611,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk333_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_12612,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_12613,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_12614,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_12615,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_12616,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_12617,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_12618,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),esk336_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_12619,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_12620,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_12621,plain,
( hAPP(hAPP(c_List_Otake(X1),X4),X2) = hAPP(hAPP(c_List_Otake(X1),X4),X3)
| hAPP(hAPP(c_List_Onth(X1),X2),esk481_4(X3,X2,X1,X4)) != hAPP(hAPP(c_List_Onth(X1),X3),esk481_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_12622,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_12623,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_12624,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_12625,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_Ortrancl(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7199]),
[final] ).
cnf(i_0_12626,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_12627,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_12628,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_12629,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk276_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_12630,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_12631,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_12632,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_12633,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_12634,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk247_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_12635,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_12636,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk211_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_12637,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk209_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_12638,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_12639,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_12640,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_12641,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_12642,plain,
( esk97_3(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(X1,esk97_3(X1,X2,X3)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,esk96_3(X1,X2,X3),esk97_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_12643,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_12644,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_12645,plain,
( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk217_4(X2,X3,X4,X1)),esk216_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_12646,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_12647,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk249_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_12648,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_12649,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_12650,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_12651,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_12652,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_12653,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_12654,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_12655,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_12656,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_12657,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_12658,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_12659,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_12660,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_12661,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_12662,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_12663,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_12664,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_12665,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_12666,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_12667,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_12668,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_12669,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_12670,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_12671,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_12672,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_12673,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_12674,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_12675,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_12676,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_12677,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_12678,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_12679,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_12680,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_12681,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_12682,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_12683,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_12684,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_12685,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_12686,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk195_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_12687,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk194_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_12688,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_12689,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_12690,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_12691,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_12692,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_12693,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_12694,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_12695,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk151_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_12696,plain,
( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk428_4(X4,X1,X3,X2)),esk427_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_12697,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_12698,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_12699,plain,
( hBOOL(hAPP(X1,esk224_2(X1,X2)))
| ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,esk222_2(X1,X2)))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk222_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk223_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_12700,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_12701,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk227_4(X2,X3,X4,X1)),esk226_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_12702,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk219_4(X2,X3,X4,X1)),esk218_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_12703,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk393_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_12704,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk167_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_12705,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk392_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_7253]),
[final] ).
cnf(i_0_12706,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk166_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_7254]),
[final] ).
cnf(i_0_12707,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X1,esk349_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_12708,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_12709,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_12710,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_12711,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_12712,plain,
( hAPP(X1,esk83_4(X2,X1,X3,X4)) = X2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),esk82_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_12713,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_12714,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_12715,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_12716,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk213_4(X2,X3,X4,X1)),esk212_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_12717,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_12718,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_12719,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)),esk405_3(X2,X3,X1)),X3))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),esk406_3(X2,X3,X1)),esk407_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_12720,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_12721,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_12722,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_12723,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_12724,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_12725,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_12726,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_12727,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_7272]),
[final] ).
cnf(i_0_12728,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_7273]),
[final] ).
cnf(i_0_12729,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk349_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_12730,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_12731,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_12732,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_12733,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_12734,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_12735,plain,
( X1 = hAPP(X2,esk268_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_12736,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_12737,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_12738,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_12739,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_12740,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_12741,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_12742,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_12743,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_12744,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_12745,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_12746,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_12747,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_12748,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_12749,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_12750,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk407_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)),esk405_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_12751,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)),esk405_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_12752,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_12753,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_12754,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_12755,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_12756,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_12757,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_12758,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_12759,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_12760,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_12761,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_12762,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_12763,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_12764,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_12765,plain,
( c_Wellfounded_Owf(tc_prod(X3,X1),c_Recdef_Osame__fst(X3,X1,X4,X2))
| ~ c_Wellfounded_Owf(X1,hAPP(X2,esk321_4(X3,X2,X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_7301]),
[final] ).
cnf(i_0_12766,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_12767,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_12768,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_12769,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_12770,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_12771,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_12772,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_12773,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_12774,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_12775,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_12776,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_12777,plain,
( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk229_4(X2,X3,X4,X1)),esk228_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_12778,plain,
( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk221_4(X2,X3,X4,X1)),esk220_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_12779,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_12780,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_12781,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_12782,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_12783,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_12784,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_12785,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_12786,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_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))
| 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_12788,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_7319]),
[final] ).
cnf(i_0_12789,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_7320]),
[final] ).
cnf(i_0_12790,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_7321]),
[final] ).
cnf(i_0_12791,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_12792,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_12793,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_12794,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_12795,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_12796,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_12797,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_12798,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_12799,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,esk77_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_12800,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_12801,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_12802,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_12803,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_12804,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_12805,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_12806,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_12807,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_12808,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_12809,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_12810,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_12811,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_12812,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_12813,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_12814,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_12815,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_12816,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_12817,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_12818,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_12819,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_12820,plain,
( hBOOL(hAPP(X3,esk225_2(X3,X2)))
| hBOOL(hAPP(X3,esk222_2(X3,X2)))
| hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk222_2(X3,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk223_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_12821,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_12822,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_12823,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_12824,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_12825,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_12826,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_12827,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_12828,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_12829,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_12830,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_12831,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_12832,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_12833,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_12834,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_7353]),
[final] ).
cnf(i_0_12835,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_7354]),
[final] ).
cnf(i_0_12836,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_7355]),
[final] ).
cnf(i_0_12837,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_12838,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_12839,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_12840,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_12841,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_12842,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_12843,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_12844,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_12845,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_12846,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_12847,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_12848,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_12849,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_12850,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_12851,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_12852,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_12853,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_12854,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_12855,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_12856,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_7371]),
[final] ).
cnf(i_0_12857,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_12858,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_7373]),
[final] ).
cnf(i_0_12859,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_12860,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_12861,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_12862,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_12863,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_12864,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_12865,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_12866,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_12867,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_12868,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_12869,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_12870,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_12871,plain,
( X3 = esk268_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_12872,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_12873,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_12874,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_12875,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),esk262_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_12876,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_12877,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_12878,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_12879,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_12880,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_12881,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_12882,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_12883,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_12884,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_12885,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_12886,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_12887,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_12888,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_12889,plain,
( hBOOL(hAPP(hAPP(X1,X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,esk457_3(X1,X2,X3)),esk458_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_12890,plain,
( hBOOL(hAPP(hAPP(X1,X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,esk96_3(X1,X2,X3)),esk97_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_12891,plain,
( hBOOL(hAPP(hAPP(X1,X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,esk94_3(X1,X2,X3)),esk95_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_12892,plain,
( hBOOL(hAPP(hAPP(X1,X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,esk92_3(X1,X2,X3)),esk93_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_12893,plain,
( hBOOL(hAPP(hAPP(X1,X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,esk87_3(X1,X2,X3)),esk88_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_12894,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_12895,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_12896,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,esk61_3(X2,X1,X3)),esk62_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_12897,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_12898,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_12899,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_7401]),
[final] ).
cnf(i_0_12900,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_7402]),
[final] ).
cnf(i_0_12901,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_12902,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_12903,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,esk63_3(X2,X1,X3)),esk64_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_12904,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_12905,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_12906,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_12907,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_12908,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_12909,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_12910,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_12911,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_12912,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_12913,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_12914,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_12915,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_12916,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_12917,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_12918,plain,
( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk209_4(X2,X3,X4,X1)),esk208_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_12919,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk211_4(X2,X3,X4,X1)),esk210_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_12920,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_12921,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_12922,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_12923,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk224_2(X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))
| hBOOL(hAPP(X1,esk222_2(X1,X2)))
| hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk222_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk223_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_12924,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_12925,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_12926,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_12927,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_12928,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_12929,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_12930,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_12931,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_12932,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_12933,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_12934,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_12935,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_12936,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_12937,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_12938,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_12939,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_12940,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_12941,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_12942,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_12943,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_12944,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_12945,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk441_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_12946,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_12947,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_12948,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_12949,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_12950,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_12951,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_12952,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_12953,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_12954,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_12955,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_12956,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_12957,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_12958,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_12959,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_12960,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_12961,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_12962,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_12963,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_12964,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_12965,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_12966,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_12967,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_12968,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_12969,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_12970,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_12971,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_12972,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_12973,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_12974,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_12975,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_12976,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_12977,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_12978,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk410_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_12979,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_12980,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_12981,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_12982,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_12983,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_12984,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_12985,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_12986,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_12987,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_12988,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_12989,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_12990,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_12991,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_12992,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_12993,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_7462]),
[final] ).
cnf(i_0_12994,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_7463]),
[final] ).
cnf(i_0_12995,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_7462]),
[final] ).
cnf(i_0_12996,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_7463]),
[final] ).
cnf(i_0_12997,plain,
( hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(X4,esk111_4(X4,X3,X5,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_6786]),
[final] ).
cnf(i_0_12998,plain,
( hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(X4,esk111_4(X4,X5,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_6786]),
[final] ).
cnf(i_0_12999,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_13000,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk259_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_13001,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_13002,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_13003,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_13004,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_13005,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_13006,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_13007,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_13008,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_13009,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_13010,plain,
( hBOOL(hAPP(X1,esk259_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_13011,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_13012,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_13013,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_13014,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)),esk412_3(X2,X3,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7475]),
[final] ).
cnf(i_0_13015,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_13016,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_13017,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_13018,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_13019,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_13020,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_13021,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_13022,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_13023,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,esk342_3(X2,X1,X3)) != hAPP(X1,esk343_3(X2,X1,X3))
| ~ c_Wellfounded_OwfP(X3,hAPP(X1,esk341_3(X2,X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_6872]),
[final] ).
cnf(i_0_13024,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_13025,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_13026,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_13027,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_13028,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_13029,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)),esk406_3(X2,X3,X1)),esk407_3(X2,X3,X1)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(X1),esk405_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_13030,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_13031,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_13032,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_13033,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_13034,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_13035,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_13036,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_13037,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_13038,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_13039,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_13040,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_13041,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_13042,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_13043,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_13044,plain,
hAPP(hAPP(c_List_Ozip(X1,X2),c_List_OtakeWhile(X1,X3,X4)),X5) = c_List_OtakeWhile(tc_prod(X1,X2),hAPP(c_Fun_Ocomp(X1,tc_HOL_Obool,tc_prod(X1,X2),X3),c_Product__Type_Ofst(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5)),
inference(split_conjunct,[status(thm)],[i_0_7496]),
[final] ).
cnf(i_0_13045,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_7497,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13046,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_7498,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13047,plain,
( X2 = hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk389_2(X2,X1)),esk389_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_7499,c_0_6053]),
[final] ).
cnf(i_0_13048,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_13049,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_13050,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_7502]),
[final] ).
cnf(i_0_13051,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_7503,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_13052,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_7504]),
[final] ).
cnf(i_0_13053,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_13054,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_7505,c_0_6053]),
[final] ).
cnf(i_0_13055,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_7506,c_0_6053]),
[final] ).
cnf(i_0_13056,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_7507]),
[final] ).
cnf(i_0_13057,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_7508]),
[final] ).
cnf(i_0_13058,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_7509]),
[final] ).
cnf(i_0_13059,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_7510]),
[final] ).
cnf(i_0_13060,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_7511]),
[final] ).
cnf(i_0_13061,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk206_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_7512]),
[final] ).
cnf(i_0_13062,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk214_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_7513]),
[final] ).
cnf(i_0_13063,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_7514]),
[final] ).
cnf(i_0_13064,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk147_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_7515]),
[final] ).
cnf(i_0_13065,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_7516,c_0_6100]),
[final] ).
cnf(i_0_13066,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_13067,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_7517,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_13068,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_7518]),
[final] ).
cnf(i_0_13069,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_7519]),
[final] ).
cnf(i_0_13070,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_13071,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_13072,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_7520]),
[final] ).
cnf(i_0_13073,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_7521]),
[final] ).
cnf(i_0_13074,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_7522]),
[final] ).
cnf(i_0_13075,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk407_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),esk405_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_13076,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),esk405_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_13077,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_7523]),
[final] ).
cnf(i_0_13078,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_13079,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_13080,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_7524]),
[final] ).
cnf(i_0_13081,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk120_2(X2,X1)),esk120_2(X2,X1))),X2))
| c_Relation_Oirrefl(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7525]),
[final] ).
cnf(i_0_13082,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_7526]),
[final] ).
cnf(i_0_13083,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk65_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_7527]),
[final] ).
cnf(i_0_13084,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_7528]),
[final] ).
cnf(i_0_13085,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_13086,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_7530]),
[final] ).
cnf(i_0_13087,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_7531]),
[final] ).
cnf(i_0_13088,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_13089,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_13090,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)),esk439_0)) ),
inference(split_conjunct,[status(thm)],[i_0_7436]),
[final] ).
cnf(i_0_13091,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_7532]),
[final] ).
cnf(i_0_13092,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_13093,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_13094,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_7502]),
[final] ).
cnf(i_0_13095,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_13096,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_13097,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_7533]),
[final] ).
cnf(i_0_13098,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_7534]),
[final] ).
cnf(i_0_13099,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_13100,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)),esk405_3(X1,X2,X3)),X2))
| esk406_3(X1,X2,X3) != esk407_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_13101,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_7535]),
[final] ).
cnf(i_0_13102,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_7536]),
[final] ).
cnf(i_0_13103,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_13104,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_7538]),
[final] ).
cnf(i_0_13105,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_7525]),
[final] ).
cnf(i_0_13106,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_7539]),
[final] ).
cnf(i_0_13107,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_7540]),
[final] ).
cnf(i_0_13108,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_7541]),
[final] ).
cnf(i_0_13109,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_13110,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_13111,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_13112,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_13113,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_7542,c_0_6053]),
[final] ).
cnf(i_0_13114,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_7543]),
[final] ).
cnf(i_0_13115,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_13116,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_13117,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_7502]),
[final] ).
cnf(i_0_13118,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_7544]),
[final] ).
cnf(i_0_13119,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_7545]),
[final] ).
cnf(i_0_13120,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_13121,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_13122,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_13123,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk65_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_7527]),
[final] ).
cnf(i_0_13124,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),esk490_2(X2,X1))),hAPP(hAPP(c_List_Onth(X1),X2),esk489_2(X2,X1))))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7546]),
[final] ).
cnf(i_0_13125,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_13126,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_13127,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_7548]),
[final] ).
cnf(i_0_13128,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_7549]),
[final] ).
cnf(i_0_13129,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_7550]),
[final] ).
cnf(i_0_13130,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_7551]),
[final] ).
cnf(i_0_13131,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk503_3(X2,X1,X3))),esk504_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),esk501_3(X2,X1,X3))),esk502_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_7552]),
[final] ).
cnf(i_0_13132,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_7553]),
[final] ).
cnf(i_0_13133,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),esk31_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_13134,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),esk18_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_13135,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_7554,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13136,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_7555,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13137,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_7556,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13138,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_7557,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13139,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_7558]),
[final] ).
cnf(i_0_13140,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_7559]),
[final] ).
cnf(i_0_13141,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_7560]),
[final] ).
cnf(i_0_13142,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_7561]),
[final] ).
cnf(i_0_13143,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk499_3(X2,X1,X3))),esk500_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),esk497_3(X2,X1,X3))),esk498_3(X2,X1,X3))
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_7562]),
[final] ).
cnf(i_0_13144,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_7563]),
[final] ).
cnf(i_0_13145,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_7564]),
[final] ).
cnf(i_0_13146,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk81_3(X1,X2,X3)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk80_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_13147,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk79_3(X1,X2,X3)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk78_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_13148,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_7565]),
[final] ).
cnf(i_0_13149,plain,
hAPP(hAPP(c_List_Ozip(X1,X2),X3),c_List_OtakeWhile(X2,X4,X5)) = c_List_OtakeWhile(tc_prod(X1,X2),hAPP(c_Fun_Ocomp(X2,tc_HOL_Obool,tc_prod(X1,X2),X4),c_Product__Type_Osnd(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X5)),
inference(split_conjunct,[status(thm)],[i_0_7566]),
[final] ).
cnf(i_0_13150,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_7567,c_0_6015]),
[final] ).
cnf(i_0_13151,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_7568]),
[final] ).
cnf(i_0_13152,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_7569]),
[final] ).
cnf(i_0_13153,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_7570]),
[final] ).
cnf(i_0_13154,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_7571]),
[final] ).
cnf(i_0_13155,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_7572]),
[final] ).
cnf(i_0_13156,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_7573]),
[final] ).
cnf(i_0_13157,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_7574]),
[final] ).
cnf(i_0_13158,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_7575]),
[final] ).
cnf(i_0_13159,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_13160,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_13161,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_7576]),
[final] ).
cnf(i_0_13162,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_7577]),
[final] ).
cnf(i_0_13163,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_7578]),
[final] ).
cnf(i_0_13164,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_13165,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_13166,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_7579,c_0_6070]),
[final] ).
cnf(i_0_13167,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_13168,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_7580]),
[final] ).
cnf(i_0_13169,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_7581,c_0_6135]),
[final] ).
cnf(i_0_13170,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),esk31_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_13171,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),esk18_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_13172,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,esk65_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_7527]),
[final] ).
cnf(i_0_13173,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_7582]),
[final] ).
cnf(i_0_13174,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),esk12_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_13175,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),esk11_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_13176,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_7583]),
[final] ).
cnf(i_0_13177,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk503_3(X2,X1,X3))),esk504_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),esk501_3(X2,X1,X3))),esk502_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_7552]),
[final] ).
cnf(i_0_13178,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk499_3(X2,X1,X3))),esk500_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),esk497_3(X2,X1,X3))),esk498_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_7562]),
[final] ).
cnf(i_0_13179,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_7584]),
[final] ).
cnf(i_0_13180,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_7585,c_0_6670]),c_0_6670]),c_0_6670]),
[final] ).
cnf(i_0_13181,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk61_3(X1,X3,X2))),esk62_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_13182,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_13183,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_13184,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_13185,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_7586,c_0_6070]),
[final] ).
cnf(i_0_13186,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),esk100_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_7587]),
[final] ).
cnf(i_0_13187,plain,
( hBOOL(hAPP(X1,esk224_2(X1,X2)))
| hBOOL(hAPP(X1,esk222_2(X1,X2)))
| hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk222_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk223_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_13188,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_7588]),
[final] ).
cnf(i_0_13189,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_7589]),
[final] ).
cnf(i_0_13190,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk63_3(X1,X3,X2))),esk64_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_13191,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_7590]),
[final] ).
cnf(i_0_13192,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_7591]),
[final] ).
cnf(i_0_13193,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_7592]),
[final] ).
cnf(i_0_13194,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_7593]),
[final] ).
cnf(i_0_13195,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_7594]),
[final] ).
cnf(i_0_13196,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_7595]),
[final] ).
cnf(i_0_13197,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,esk411_4(X3,X2,X1,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_7153]),
[final] ).
cnf(i_0_13198,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_7596]),
[final] ).
cnf(i_0_13199,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_7596]),
[final] ).
cnf(i_0_13200,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,esk65_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_7527]),
[final] ).
cnf(i_0_13201,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_7597]),
[final] ).
cnf(i_0_13202,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_7598]),
[final] ).
cnf(i_0_13203,plain,
( hBOOL(hAPP(X1,esk321_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_13204,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_7527]),
[final] ).
cnf(i_0_13205,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_7599]),
[final] ).
cnf(i_0_13206,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_7600]),
[final] ).
cnf(i_0_13207,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_7601]),
[final] ).
cnf(i_0_13208,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_13209,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_7602]),
[final] ).
cnf(i_0_13210,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_7603]),
[final] ).
cnf(i_0_13211,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_7604]),
[final] ).
cnf(i_0_13212,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_7605]),
[final] ).
cnf(i_0_13213,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_7606]),
[final] ).
cnf(i_0_13214,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_7607]),
[final] ).
cnf(i_0_13215,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_7608,c_0_6670]),c_0_6670]),
[final] ).
cnf(i_0_13216,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_7609]),
[final] ).
cnf(i_0_13217,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_13218,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_7610]),
[final] ).
cnf(i_0_13219,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_7611]),
[final] ).
cnf(i_0_13220,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_7612]),
[final] ).
cnf(i_0_13221,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_7613]),
[final] ).
cnf(i_0_13222,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_13223,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_13224,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_13225,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_7614]),
[final] ).
cnf(i_0_13226,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_7614]),
[final] ).
cnf(i_0_13227,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_7615]),
[final] ).
cnf(i_0_13228,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_7615]),
[final] ).
cnf(i_0_13229,plain,
( c_Natural_Oevaln(X1,esk3_4(X2,X1,X3,X4),X4,esk4_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_13230,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_7616]),
[final] ).
cnf(i_0_13231,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_7617,c_0_6053]),
[final] ).
cnf(i_0_13232,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_7618]),
[final] ).
cnf(i_0_13233,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_13234,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_7619]),
[final] ).
cnf(i_0_13235,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_7620]),
[final] ).
cnf(i_0_13236,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_7621]),
[final] ).
cnf(i_0_13237,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_7622]),
[final] ).
cnf(i_0_13238,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_7623,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13239,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_7624]),
[final] ).
cnf(i_0_13240,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_7625]),
[final] ).
cnf(i_0_13241,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_7626,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13242,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_7627,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13243,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_7628,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13244,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_7629,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13245,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_7630]),
[final] ).
cnf(i_0_13246,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_7631,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_13247,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_7632]),
[final] ).
cnf(i_0_13248,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_7633]),
[final] ).
cnf(i_0_13249,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_7634,c_0_6062]),
[final] ).
cnf(i_0_13250,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk207_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_7512]),
[final] ).
cnf(i_0_13251,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk215_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_7513]),
[final] ).
cnf(i_0_13252,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_7578]),
[final] ).
cnf(i_0_13253,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_7635]),
[final] ).
cnf(i_0_13254,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_7636]),
[final] ).
cnf(i_0_13255,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_7637]),
[final] ).
cnf(i_0_13256,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_7638]),
[final] ).
cnf(i_0_13257,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_7639,c_0_6053]),
[final] ).
cnf(i_0_13258,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_7640]),
[final] ).
cnf(i_0_13259,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_7641]),
[final] ).
cnf(i_0_13260,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_7642]),
[final] ).
cnf(i_0_13261,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_7643]),
[final] ).
cnf(i_0_13262,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_7644]),
[final] ).
cnf(i_0_13263,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_7645]),
[final] ).
cnf(i_0_13264,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_7646]),
[final] ).
cnf(i_0_13265,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_7647]),
[final] ).
cnf(i_0_13266,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_7648]),
[final] ).
cnf(i_0_13267,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_7649]),
[final] ).
cnf(i_0_13268,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_7650]),
[final] ).
cnf(i_0_13269,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_7651]),
[final] ).
cnf(i_0_13270,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_7652]),
[final] ).
cnf(i_0_13271,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_7653]),
[final] ).
cnf(i_0_13272,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_7654]),
[final] ).
cnf(i_0_13273,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_7655,c_0_6100]),
[final] ).
cnf(i_0_13274,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_7656]),
[final] ).
cnf(i_0_13275,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_13276,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_7637]),
[final] ).
cnf(i_0_13277,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_7657]),
[final] ).
cnf(i_0_13278,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_7658]),
[final] ).
cnf(i_0_13279,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_7659]),
[final] ).
cnf(i_0_13280,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_7660]),
[final] ).
cnf(i_0_13281,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_7661]),
[final] ).
cnf(i_0_13282,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_7662]),
[final] ).
cnf(i_0_13283,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_7663]),
[final] ).
cnf(i_0_13284,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_7664]),
[final] ).
cnf(i_0_13285,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_7665]),
[final] ).
cnf(i_0_13286,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_7666]),
[final] ).
cnf(i_0_13287,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_7667]),
[final] ).
cnf(i_0_13288,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_7668]),
[final] ).
cnf(i_0_13289,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_7669,c_0_6100]),
[final] ).
cnf(i_0_13290,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_7670]),
[final] ).
cnf(i_0_13291,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_7637]),
[final] ).
cnf(i_0_13292,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk286_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_7671]),
[final] ).
cnf(i_0_13293,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk283_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_7672]),
[final] ).
cnf(i_0_13294,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk283_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_7672]),
[final] ).
cnf(i_0_13295,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk286_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_7671]),
[final] ).
cnf(i_0_13296,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_13297,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_7673]),
[final] ).
cnf(i_0_13298,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_7674]),
[final] ).
cnf(i_0_13299,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_7675]),
[final] ).
cnf(i_0_13300,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_7676]),
[final] ).
cnf(i_0_13301,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_7677]),
[final] ).
cnf(i_0_13302,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_7678]),
[final] ).
cnf(i_0_13303,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_7679]),
[final] ).
cnf(i_0_13304,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_7680]),
[final] ).
cnf(i_0_13305,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_7681]),
[final] ).
cnf(i_0_13306,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_7682]),
[final] ).
cnf(i_0_13307,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_13308,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_13309,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_7683]),
[final] ).
cnf(i_0_13310,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_13311,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_7684]),
[final] ).
cnf(i_0_13312,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,esk303_3(X1,X2,X3))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7685]),
[final] ).
cnf(i_0_13313,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,esk153_3(X1,X2,X3))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7686]),
[final] ).
cnf(i_0_13314,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_7687]),
[final] ).
cnf(i_0_13315,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_7688]),
[final] ).
cnf(i_0_13316,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_7689]),
[final] ).
cnf(i_0_13317,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_7690]),
[final] ).
cnf(i_0_13318,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_7691]),
[final] ).
cnf(i_0_13319,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_7692]),
[final] ).
cnf(i_0_13320,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_7693]),
[final] ).
cnf(i_0_13321,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_13322,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_13323,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_7694]),
[final] ).
cnf(i_0_13324,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_7695]),
[final] ).
cnf(i_0_13325,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_7696]),
[final] ).
cnf(i_0_13326,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_7697]),
[final] ).
cnf(i_0_13327,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_7698]),
[final] ).
cnf(i_0_13328,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_7699]),
[final] ).
cnf(i_0_13329,plain,
( X1 = hAPP(X2,esk118_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_13330,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_7700]),
[final] ).
cnf(i_0_13331,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_7518]),
[final] ).
cnf(i_0_13332,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_7701]),
[final] ).
cnf(i_0_13333,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_13334,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_7702]),
[final] ).
cnf(i_0_13335,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_7703]),
[final] ).
cnf(i_0_13336,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_7704,c_0_6070]),
[final] ).
cnf(i_0_13337,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_7705]),
[final] ).
cnf(i_0_13338,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_7706]),
[final] ).
cnf(i_0_13339,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_7707]),
[final] ).
cnf(i_0_13340,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_7707]),
[final] ).
cnf(i_0_13341,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_7708]),
[final] ).
cnf(i_0_13342,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_7709]),
[final] ).
cnf(i_0_13343,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_7710]),
[final] ).
cnf(i_0_13344,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_7711,c_0_6053]),
[final] ).
cnf(i_0_13345,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_7712,c_0_6053]),
[final] ).
cnf(i_0_13346,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_13347,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_13348,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk504_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),esk501_3(X1,X2,X3))),esk502_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_7552]),
[final] ).
cnf(i_0_13349,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_7601]),
[final] ).
cnf(i_0_13350,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_7713]),
[final] ).
cnf(i_0_13351,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk503_3(X2,X1,X3))),esk504_3(X2,X1,X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk502_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_7552]),
[final] ).
cnf(i_0_13352,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_13353,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk500_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),esk497_3(X1,X2,X3))),esk498_3(X1,X2,X3))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7562]),
[final] ).
cnf(i_0_13354,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_7714]),
[final] ).
cnf(i_0_13355,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_7715]),
[final] ).
cnf(i_0_13356,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_7716,c_0_6053]),
[final] ).
cnf(i_0_13357,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_7717]),
[final] ).
cnf(i_0_13358,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_7718]),
[final] ).
cnf(i_0_13359,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_7719]),
[final] ).
cnf(i_0_13360,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_7720]),
[final] ).
cnf(i_0_13361,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_7721]),
[final] ).
cnf(i_0_13362,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk499_3(X2,X1,X3))),esk500_3(X2,X1,X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk498_3(X2,X1,X3)),X2))
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_7562]),
[final] ).
cnf(i_0_13363,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_7722]),
[final] ).
cnf(i_0_13364,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_13365,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_7724]),
[final] ).
cnf(i_0_13366,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_7725]),
[final] ).
cnf(i_0_13367,plain,
( c_Fun_Oinj__on(X1,X2,esk193_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_13368,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_7726]),
[final] ).
cnf(i_0_13369,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_7727]),
[final] ).
cnf(i_0_13370,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_7728,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13371,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_7729]),
[final] ).
cnf(i_0_13372,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_7730]),
[final] ).
cnf(i_0_13373,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_7731]),
[final] ).
cnf(i_0_13374,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_7718]),
[final] ).
cnf(i_0_13375,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_7717]),
[final] ).
cnf(i_0_13376,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_7732]),
[final] ).
cnf(i_0_13377,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_7733]),
[final] ).
cnf(i_0_13378,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_7734]),
[final] ).
cnf(i_0_13379,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_7735]),
[final] ).
cnf(i_0_13380,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_7736]),
[final] ).
cnf(i_0_13381,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_7737]),
[final] ).
cnf(i_0_13382,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk412_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_13383,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_7738,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13384,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_7717]),
[final] ).
cnf(i_0_13385,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_7718]),
[final] ).
cnf(i_0_13386,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_7739]),
[final] ).
cnf(i_0_13387,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_7740]),
[final] ).
cnf(i_0_13388,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_7578]),
[final] ).
cnf(i_0_13389,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_7741]),
[final] ).
cnf(i_0_13390,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_7742]),
[final] ).
cnf(i_0_13391,plain,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk450_3(X1,X3,X2))))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7743]),
[final] ).
cnf(i_0_13392,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_7744]),
[final] ).
cnf(i_0_13393,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_13394,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_7745,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13395,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_7746,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13396,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_7718]),
[final] ).
cnf(i_0_13397,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_7717]),
[final] ).
cnf(i_0_13398,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_7462]),
[final] ).
cnf(i_0_13399,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_7463]),
[final] ).
cnf(i_0_13400,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_7747,c_0_6062]),
[final] ).
cnf(i_0_13401,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk504_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),esk501_3(X1,X2,X3))),esk502_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_7552]),
[final] ).
cnf(i_0_13402,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk500_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),esk497_3(X1,X2,X3))),esk498_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_7562]),
[final] ).
cnf(i_0_13403,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_13404,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),esk485_3(X2,X3,X1)),esk486_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_7748]),
[final] ).
cnf(i_0_13405,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_7749]),
[final] ).
cnf(i_0_13406,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk503_3(X2,X1,X3))),esk504_3(X2,X1,X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk502_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_7552]),
[final] ).
cnf(i_0_13407,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk499_3(X2,X1,X3))),esk500_3(X2,X1,X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk498_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_7562]),
[final] ).
cnf(i_0_13408,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_13409,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_13410,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_7750]),
[final] ).
cnf(i_0_13411,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_7751]),
[final] ).
cnf(i_0_13412,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk62_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_13413,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_7752]),
[final] ).
cnf(i_0_13414,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_13415,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_13416,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_7753]),
[final] ).
cnf(i_0_13417,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_7754]),
[final] ).
cnf(i_0_13418,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk64_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_13419,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk207_3(X2,X1,X3)),esk206_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_7512]),
[final] ).
cnf(i_0_13420,plain,
( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk215_3(X2,X1,X3)),esk214_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_7513]),
[final] ).
cnf(i_0_13421,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_7755]),
[final] ).
cnf(i_0_13422,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_7756]),
[final] ).
cnf(i_0_13423,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_7757]),
[final] ).
cnf(i_0_13424,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_13425,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_13426,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_7758]),
[final] ).
cnf(i_0_13427,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_7759]),
[final] ).
cnf(i_0_13428,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_7760]),
[final] ).
cnf(i_0_13429,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_13430,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_13431,plain,
( X2 = hAPP(c_Set_Oimage(tc_Nat_Onat,X1,esk315_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)),esk314_2(X2,X1))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7467]),
[final] ).
cnf(i_0_13432,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_7761]),
[final] ).
cnf(i_0_13433,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_7705]),
[final] ).
cnf(i_0_13434,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_13435,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_13436,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk331_3(X2,X3,X1)),X3))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk330_3(X2,X3,X1)),X2))
| c_Relation_Orefl__on(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_6138]),
[final] ).
cnf(i_0_13437,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_7762]),
[final] ).
cnf(i_0_13438,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_7763]),
[final] ).
cnf(i_0_13439,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_7534]),
[final] ).
cnf(i_0_13440,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_7764,c_0_6670]),
[final] ).
cnf(i_0_13441,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_7765,c_0_6100]),
[final] ).
cnf(i_0_13442,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_7766,c_0_6100]),
[final] ).
cnf(i_0_13443,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_7767]),
[final] ).
cnf(i_0_13444,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_7768]),
[final] ).
cnf(i_0_13445,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),
inference(split_conjunct,[status(thm)],[i_0_7769]),
[final] ).
cnf(i_0_13446,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_13447,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_7770]),
[final] ).
cnf(i_0_13448,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_7771]),
[final] ).
cnf(i_0_13449,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_7772]),
[final] ).
cnf(i_0_13450,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_7719]),
[final] ).
cnf(i_0_13451,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_7773]),
[final] ).
cnf(i_0_13452,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_7774]),
[final] ).
cnf(i_0_13453,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_7775]),
[final] ).
cnf(i_0_13454,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_7776]),
[final] ).
cnf(i_0_13455,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_7777]),
[final] ).
cnf(i_0_13456,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_7778,c_0_6135]),c_0_6135]),c_0_6135]),
[final] ).
cnf(i_0_13457,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_7779]),
[final] ).
cnf(i_0_13458,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_13459,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_13460,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_7780]),
[final] ).
cnf(i_0_13461,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_7781]),
[final] ).
cnf(i_0_13462,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)),esk409_3(X2,X3,X1)),esk410_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_13463,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_7782]),
[final] ).
cnf(i_0_13464,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_7783]),
[final] ).
cnf(i_0_13465,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_7784]),
[final] ).
cnf(i_0_13466,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_13467,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_13468,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_7785]),
[final] ).
cnf(i_0_13469,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_7786]),
[final] ).
cnf(i_0_13470,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_7787]),
[final] ).
cnf(i_0_13471,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2)),esk19_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_7788]),
[final] ).
cnf(i_0_13472,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_7789]),
[final] ).
cnf(i_0_13473,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_7790]),
[final] ).
cnf(i_0_13474,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_13475,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_7540]),
[final] ).
cnf(i_0_13476,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_7791]),
[final] ).
cnf(i_0_13477,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_7792]),
[final] ).
cnf(i_0_13478,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_7793]),
[final] ).
cnf(i_0_13479,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),esk84_3(X3,X2,X1))))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7794]),
[final] ).
cnf(i_0_13480,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_13481,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_7795]),
[final] ).
cnf(i_0_13482,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_7796]),
[final] ).
cnf(i_0_13483,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_7797]),
[final] ).
cnf(i_0_13484,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_7798]),
[final] ).
cnf(i_0_13485,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_7799]),
[final] ).
cnf(i_0_13486,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_7800]),
[final] ).
cnf(i_0_13487,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_7801]),
[final] ).
cnf(i_0_13488,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_7802]),
[final] ).
cnf(i_0_13489,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_7803]),
[final] ).
cnf(i_0_13490,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_7804]),
[final] ).
cnf(i_0_13491,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_7805]),
[final] ).
cnf(i_0_13492,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_7806]),
[final] ).
cnf(i_0_13493,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_7807]),
[final] ).
cnf(i_0_13494,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_7808]),
[final] ).
cnf(i_0_13495,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_13496,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_7809]),
[final] ).
cnf(i_0_13497,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_13498,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_13499,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_7810]),
[final] ).
cnf(i_0_13500,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_7811]),
[final] ).
cnf(i_0_13501,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_13502,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,esk307_2(X2,X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_7812]),
[final] ).
cnf(i_0_13503,plain,
( hAPP(X1,esk194_4(X2,X1,X3,X4)) = hAPP(X1,esk195_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_13504,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_13505,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_7813]),
[final] ).
cnf(i_0_13506,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_13507,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_7814]),
[final] ).
cnf(i_0_13508,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_7815]),
[final] ).
cnf(i_0_13509,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_7816]),
[final] ).
cnf(i_0_13510,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_7817]),
[final] ).
cnf(i_0_13511,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_7818]),
[final] ).
cnf(i_0_13512,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_7819]),
[final] ).
cnf(i_0_13513,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_7820]),
[final] ).
cnf(i_0_13514,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_7821]),
[final] ).
cnf(i_0_13515,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_7822]),
[final] ).
cnf(i_0_13516,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_7823]),
[final] ).
cnf(i_0_13517,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_7824]),
[final] ).
cnf(i_0_13518,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk503_3(X2,X1,X3))),esk504_3(X2,X1,X3))
| epred2_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,esk501_3(X2,X1,X3)))
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7552]),
[final] ).
cnf(i_0_13519,plain,
( X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk501_3(X2,X3,X1))),esk502_3(X2,X3,X1))
| epred2_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk503_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7552]),
[final] ).
cnf(i_0_13520,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_7825]),
[final] ).
cnf(i_0_13521,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_7826]),
[final] ).
cnf(i_0_13522,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_7827]),
[final] ).
cnf(i_0_13523,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_7828]),
[final] ).
cnf(i_0_13524,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_7829]),
[final] ).
cnf(i_0_13525,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_7830]),
[final] ).
cnf(i_0_13526,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_13527,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_7831]),
[final] ).
cnf(i_0_13528,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_7832]),
[final] ).
cnf(i_0_13529,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_7833]),
[final] ).
cnf(i_0_13530,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_7834]),
[final] ).
cnf(i_0_13531,plain,
( hBOOL(hAPP(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),esk101_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_7587]),
[final] ).
cnf(i_0_13532,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_7835]),
[final] ).
cnf(i_0_13533,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_7836]),
[final] ).
cnf(i_0_13534,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_7837]),
[final] ).
cnf(i_0_13535,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk499_3(X2,X1,X3))),esk500_3(X2,X1,X3))
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,esk498_3(X2,X1,X3)))
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_7562]),
[final] ).
cnf(i_0_13536,plain,
( X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk497_3(X2,X3,X1))),esk498_3(X2,X3,X1))
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk500_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7562]),
[final] ).
cnf(i_0_13537,plain,
( c_Hoare__Mirabelle_Otriple__valid(X1,X2,X5)
| ~ c_Hoare__Mirabelle_Otriple__valid(X1,X2,esk336_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_13538,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_7838,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_13539,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_7839]),
[final] ).
cnf(i_0_13540,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_7840]),
[final] ).
cnf(i_0_13541,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_7841]),
[final] ).
cnf(i_0_13542,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_7842]),
[final] ).
cnf(i_0_13543,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_7843]),
[final] ).
cnf(i_0_13544,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_7844]),
[final] ).
cnf(i_0_13545,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_7845]),
[final] ).
cnf(i_0_13546,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_7846]),
[final] ).
cnf(i_0_13547,plain,
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),esk16_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_7847]),
[final] ).
cnf(i_0_13548,plain,
( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)),X2,esk27_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_7848]),
[final] ).
cnf(i_0_13549,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_7849]),
[final] ).
cnf(i_0_13550,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_7546]),
[final] ).
cnf(i_0_13551,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_13552,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_7850]),
[final] ).
cnf(i_0_13553,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_7851]),
[final] ).
cnf(i_0_13554,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_7852]),
[final] ).
cnf(i_0_13555,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_7853]),
[final] ).
cnf(i_0_13556,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_7730]),
[final] ).
cnf(i_0_13557,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_7854,c_0_6015]),
[final] ).
cnf(i_0_13558,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_7855,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13559,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_7856]),
[final] ).
cnf(i_0_13560,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_13561,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_7857]),
[final] ).
cnf(i_0_13562,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_7858]),
[final] ).
cnf(i_0_13563,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_7859]),
[final] ).
cnf(i_0_13564,plain,
( hBOOL(hAPP(X1,esk116_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_13565,plain,
( hBOOL(hAPP(X1,esk116_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_13566,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_7584]),
[final] ).
cnf(i_0_13567,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),esk148_3(X2,X3,X1)),esk149_3(X2,X3,X1)))
| hAPP(c_Finite__Set_Ocard(X1),X3) != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7860]),
[final] ).
cnf(i_0_13568,plain,
( hAPP(X1,esk81_3(X2,X1,X3)) = X2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk80_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_13569,plain,
( hAPP(X1,esk79_3(X2,X1,X3)) = X2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk78_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_13570,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_7861]),
[final] ).
cnf(i_0_13571,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_7862]),
[final] ).
cnf(i_0_13572,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_7863]),
[final] ).
cnf(i_0_13573,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_7864]),
[final] ).
cnf(i_0_13574,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_7865]),
[final] ).
cnf(i_0_13575,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_7866]),
[final] ).
cnf(i_0_13576,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_7867]),
[final] ).
cnf(i_0_13577,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_7868]),
[final] ).
cnf(i_0_13578,plain,
( c_Natural_Oevaln(X1,X2,X3,esk16_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_7847]),
[final] ).
cnf(i_0_13579,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_7756]),
[final] ).
cnf(i_0_13580,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_7869]),
[final] ).
cnf(i_0_13581,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_13582,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_7755]),
[final] ).
cnf(i_0_13583,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_13584,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_7759]),
[final] ).
cnf(i_0_13585,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_7870]),
[final] ).
cnf(i_0_13586,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_13587,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_7758]),
[final] ).
cnf(i_0_13588,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_13589,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_7871]),
[final] ).
cnf(i_0_13590,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_7872]),
[final] ).
cnf(i_0_13591,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_13592,plain,
( X3 = X2
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_fequal),esk441_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_13593,plain,
c_Map_Omap__upds(X1,X2,X3,c_List_Olist_ONil(X1),X4) = X3,
inference(split_conjunct,[status(thm)],[i_0_7873]),
[final] ).
cnf(i_0_13594,plain,
c_Map_Omap__upds(X1,X2,X3,X4,c_List_Olist_ONil(X2)) = X3,
inference(split_conjunct,[status(thm)],[i_0_7874]),
[final] ).
cnf(i_0_13595,plain,
c_Option_Ooption_Ooption__rec(X1,X2,X3,X4,c_Option_Ooption_ONone(X2)) = X3,
inference(split_conjunct,[status(thm)],[i_0_7875]),
[final] ).
cnf(i_0_13596,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_7876]),
[final] ).
cnf(i_0_13597,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_7877]),
[final] ).
cnf(i_0_13598,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_7719]),
[final] ).
cnf(i_0_13599,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk503_3(X2,X1,X3))),esk504_3(X2,X1,X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,esk501_3(X2,X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7552]),
[final] ).
cnf(i_0_13600,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk499_3(X2,X1,X3))),esk500_3(X2,X1,X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,esk498_3(X2,X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7562]),
[final] ).
cnf(i_0_13601,plain,
( X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk501_3(X2,X3,X1))),esk502_3(X2,X3,X1))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk503_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7552]),
[final] ).
cnf(i_0_13602,plain,
( X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk497_3(X2,X3,X1))),esk498_3(X2,X3,X1))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk500_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7562]),
[final] ).
cnf(i_0_13603,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_7878]),
[final] ).
cnf(i_0_13604,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_7879]),
[final] ).
cnf(i_0_13605,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_7880]),
[final] ).
cnf(i_0_13606,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_7881]),
[final] ).
cnf(i_0_13607,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_13608,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_13609,plain,
( hBOOL(hAPP(X1,esk75_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_13610,plain,
( hBOOL(hAPP(X1,esk71_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_13611,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_7882]),
[final] ).
cnf(i_0_13612,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_7883]),
[final] ).
cnf(i_0_13613,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk503_3(X2,X1,X3))),esk504_3(X2,X1,X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk502_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_7552]),
[final] ).
cnf(i_0_13614,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_7884,c_0_6135]),c_0_6135]),
[final] ).
cnf(i_0_13615,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk449_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_7743]),
[final] ).
cnf(i_0_13616,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_7885]),
[final] ).
cnf(i_0_13617,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_7886]),
[final] ).
cnf(i_0_13618,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_7887,c_0_6670]),c_0_6670]),
[final] ).
cnf(i_0_13619,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_7888,c_0_6062]),c_0_6062]),
[final] ).
cnf(i_0_13620,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_7681]),
[final] ).
cnf(i_0_13621,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_7889]),
[final] ).
cnf(i_0_13622,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk499_3(X2,X1,X3))),esk500_3(X2,X1,X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk498_3(X2,X1,X3)))
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_7562]),
[final] ).
cnf(i_0_13623,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,esk247_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_13624,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_7890]),
[final] ).
cnf(i_0_13625,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_7891]),
[final] ).
cnf(i_0_13626,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_7892]),
[final] ).
cnf(i_0_13627,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_13628,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_13629,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk504_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),esk501_3(X1,X2,X3))),esk502_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_7552]),
[final] ).
cnf(i_0_13630,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_7893]),
[final] ).
cnf(i_0_13631,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_7894]),
[final] ).
cnf(i_0_13632,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_13633,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_7501]),
[final] ).
cnf(i_0_13634,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_7895]),
[final] ).
cnf(i_0_13635,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_7896]),
[final] ).
cnf(i_0_13636,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_7806]),
[final] ).
cnf(i_0_13637,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_7806]),
[final] ).
cnf(i_0_13638,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_7897]),
[final] ).
cnf(i_0_13639,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_13640,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_7898]),
[final] ).
cnf(i_0_13641,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk500_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),esk497_3(X1,X2,X3))),esk498_3(X1,X2,X3))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7562]),
[final] ).
cnf(i_0_13642,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_7899]),
[final] ).
cnf(i_0_13643,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_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_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_13645,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_7902]),
[final] ).
cnf(i_0_13646,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_7901]),
[final] ).
cnf(i_0_13647,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_7902]),
[final] ).
cnf(i_0_13648,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_7857]),
[final] ).
cnf(i_0_13649,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_7903]),
[final] ).
cnf(i_0_13650,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_7858]),
[final] ).
cnf(i_0_13651,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_7904]),
[final] ).
cnf(i_0_13652,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_7730]),
[final] ).
cnf(i_0_13653,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_7905]),
[final] ).
cnf(i_0_13654,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_7906]),
[final] ).
cnf(i_0_13655,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_13656,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_13657,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_7907]),
[final] ).
cnf(i_0_13658,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk504_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk502_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_7552]),
[final] ).
cnf(i_0_13659,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_7908]),
[final] ).
cnf(i_0_13660,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_7909,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13661,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_13662,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_7501]),
[final] ).
cnf(i_0_13663,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_7910]),
[final] ).
cnf(i_0_13664,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_13665,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,esk104_2(X2,X1))),hAPP(X2,esk105_2(X2,X1))))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_7911]),
[final] ).
cnf(i_0_13666,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_7912]),
[final] ).
cnf(i_0_13667,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_7913]),
[final] ).
cnf(i_0_13668,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_7914]),
[final] ).
cnf(i_0_13669,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_13670,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_13671,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_7915]),
[final] ).
cnf(i_0_13672,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_7916]),
[final] ).
cnf(i_0_13673,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk500_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk498_3(X1,X2,X3)),X1))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7562]),
[final] ).
cnf(i_0_13674,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,esk249_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_13675,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_7917,c_0_6070]),
[final] ).
cnf(i_0_13676,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_7918]),
[final] ).
cnf(i_0_13677,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_7919,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13678,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_7920]),
[final] ).
cnf(i_0_13679,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_7921]),
[final] ).
cnf(i_0_13680,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_7922]),
[final] ).
cnf(i_0_13681,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_7923]),
[final] ).
cnf(i_0_13682,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_13683,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_13684,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))
| esk406_3(X1,X2,X3) != esk407_3(X1,X2,X3)
| hAPP(c_Finite__Set_Ocard(X3),esk405_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_13685,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_7924]),
[final] ).
cnf(i_0_13686,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_7925]),
[final] ).
cnf(i_0_13687,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_7926]),
[final] ).
cnf(i_0_13688,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_7927]),
[final] ).
cnf(i_0_13689,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_OtakeWhile(X1,X4,X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_7928]),
[final] ).
cnf(i_0_13690,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_7929]),
[final] ).
cnf(i_0_13691,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_7930]),
[final] ).
cnf(i_0_13692,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_7931]),
[final] ).
cnf(i_0_13693,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_13694,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_7932]),
[final] ).
cnf(i_0_13695,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_7933]),
[final] ).
cnf(i_0_13696,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk503_3(X2,X1,X3))),esk504_3(X2,X1,X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk502_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_7552]),
[final] ).
cnf(i_0_13697,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk499_3(X2,X1,X3))),esk500_3(X2,X1,X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk498_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_7562]),
[final] ).
cnf(i_0_13698,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_7934]),
[final] ).
cnf(i_0_13699,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_7935]),
[final] ).
cnf(i_0_13700,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_7936,c_0_6135]),
[final] ).
cnf(i_0_13701,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_7937]),
[final] ).
cnf(i_0_13702,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_13703,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk62_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_13704,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_7938]),
[final] ).
cnf(i_0_13705,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_7939,c_0_6015]),
[final] ).
cnf(i_0_13706,plain,
c_Fun_Oinj__on(X1,tc_prod(X2,X1),esk287_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_13707,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_7940]),
[final] ).
cnf(i_0_13708,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_7941]),
[final] ).
cnf(i_0_13709,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_7942]),
[final] ).
cnf(i_0_13710,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk504_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),esk501_3(X1,X2,X3))),esk502_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_7552]),
[final] ).
cnf(i_0_13711,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk500_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),esk497_3(X1,X2,X3))),esk498_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_7562]),
[final] ).
cnf(i_0_13712,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_13713,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_13714,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_13715,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_13716,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_13717,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_13718,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_13719,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_7943]),
[final] ).
cnf(i_0_13720,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_7944]),
[final] ).
cnf(i_0_13721,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_7945]),
[final] ).
cnf(i_0_13722,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_7946]),
[final] ).
cnf(i_0_13723,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_7947,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13724,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_7948,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13725,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_7949,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13726,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_7950,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13727,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_7951]),
[final] ).
cnf(i_0_13728,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_7952]),
[final] ).
cnf(i_0_13729,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_13730,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_7953]),
[final] ).
cnf(i_0_13731,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_7954]),
[final] ).
cnf(i_0_13732,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_7955]),
[final] ).
cnf(i_0_13733,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk64_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_13734,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_7956]),
[final] ).
cnf(i_0_13735,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_7957]),
[final] ).
cnf(i_0_13736,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_7958]),
[final] ).
cnf(i_0_13737,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_7959]),
[final] ).
cnf(i_0_13738,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_7960]),
[final] ).
cnf(i_0_13739,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_7961]),
[final] ).
cnf(i_0_13740,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_7962]),
[final] ).
cnf(i_0_13741,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_7897]),
[final] ).
cnf(i_0_13742,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk426_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_7963]),
[final] ).
cnf(i_0_13743,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_7964]),
[final] ).
cnf(i_0_13744,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk178_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_7965]),
[final] ).
cnf(i_0_13745,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_7966]),
[final] ).
cnf(i_0_13746,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk504_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk502_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_7552]),
[final] ).
cnf(i_0_13747,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk500_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk498_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_7562]),
[final] ).
cnf(i_0_13748,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_7967]),
[final] ).
cnf(i_0_13749,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_7968]),
[final] ).
cnf(i_0_13750,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_7969]),
[final] ).
cnf(i_0_13751,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_7970]),
[final] ).
cnf(i_0_13752,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_7971]),
[final] ).
cnf(i_0_13753,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_7972]),
[final] ).
cnf(i_0_13754,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_7973]),
[final] ).
cnf(i_0_13755,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_7974]),
[final] ).
cnf(i_0_13756,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_7975]),
[final] ).
cnf(i_0_13757,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_7976]),
[final] ).
cnf(i_0_13758,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_7662]),
[final] ).
cnf(i_0_13759,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_7977]),
[final] ).
cnf(i_0_13760,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_7717]),
[final] ).
cnf(i_0_13761,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_7978]),
[final] ).
cnf(i_0_13762,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_7718]),
[final] ).
cnf(i_0_13763,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_7979]),
[final] ).
cnf(i_0_13764,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_7980]),
[final] ).
cnf(i_0_13765,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_7668]),
[final] ).
cnf(i_0_13766,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_7981]),
[final] ).
cnf(i_0_13767,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_7982]),
[final] ).
cnf(i_0_13768,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_7983]),
[final] ).
cnf(i_0_13769,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_7984]),
[final] ).
cnf(i_0_13770,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_7985]),
[final] ).
cnf(i_0_13771,plain,
( c_Big__Operators_Olinorder__class_OMax(X1,X3) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk361_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_7986]),
[final] ).
cnf(i_0_13772,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_13773,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_7987]),
[final] ).
cnf(i_0_13774,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_7988]),
[final] ).
cnf(i_0_13775,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_7989]),
[final] ).
cnf(i_0_13776,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_7847]),
[final] ).
cnf(i_0_13777,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_7686]),
[final] ).
cnf(i_0_13778,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_7990]),
[final] ).
cnf(i_0_13779,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_7991]),
[final] ).
cnf(i_0_13780,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_7992]),
[final] ).
cnf(i_0_13781,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_7993]),
[final] ).
cnf(i_0_13782,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_7994,c_0_6015]),c_0_6015]),
[final] ).
cnf(i_0_13783,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_7995,c_0_6015]),c_0_6015]),
[final] ).
cnf(i_0_13784,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_7996]),
[final] ).
cnf(i_0_13785,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_7997,c_0_6015]),c_0_6015]),
[final] ).
cnf(i_0_13786,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_7998,c_0_6015]),c_0_6015]),
[final] ).
cnf(i_0_13787,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_7971]),
[final] ).
cnf(i_0_13788,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_7970]),
[final] ).
cnf(i_0_13789,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_7999]),
[final] ).
cnf(i_0_13790,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_8000]),
[final] ).
cnf(i_0_13791,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_8001]),
[final] ).
cnf(i_0_13792,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_7797]),
[final] ).
cnf(i_0_13793,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_8002]),
[final] ).
cnf(i_0_13794,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_8003]),
[final] ).
cnf(i_0_13795,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_13796,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_8004]),
[final] ).
cnf(i_0_13797,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_7982]),
[final] ).
cnf(i_0_13798,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_7982]),
[final] ).
cnf(i_0_13799,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_7983]),
[final] ).
cnf(i_0_13800,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_7983]),
[final] ).
cnf(i_0_13801,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_7984]),
[final] ).
cnf(i_0_13802,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_7984]),
[final] ).
cnf(i_0_13803,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_13804,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_13805,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_7591]),
[final] ).
cnf(i_0_13806,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_8005]),
[final] ).
cnf(i_0_13807,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_7675]),
[final] ).
cnf(i_0_13808,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_8006]),
[final] ).
cnf(i_0_13809,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_7678]),
[final] ).
cnf(i_0_13810,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_8007]),
[final] ).
cnf(i_0_13811,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_8008]),
[final] ).
cnf(i_0_13812,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_8009]),
[final] ).
cnf(i_0_13813,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_7688]),
[final] ).
cnf(i_0_13814,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_8010]),
[final] ).
cnf(i_0_13815,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_7717]),
[final] ).
cnf(i_0_13816,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_8011]),
[final] ).
cnf(i_0_13817,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_7718]),
[final] ).
cnf(i_0_13818,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_8012]),
[final] ).
cnf(i_0_13819,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_7689]),
[final] ).
cnf(i_0_13820,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_13821,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_7714]),
[final] ).
cnf(i_0_13822,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_7715]),
[final] ).
cnf(i_0_13823,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_7633]),
[final] ).
cnf(i_0_13824,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_13825,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_13826,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),esk125_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7077]),
[final] ).
cnf(i_0_13827,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_8013]),
[final] ).
cnf(i_0_13828,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_8014]),
[final] ).
cnf(i_0_13829,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_13830,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_7897]),
[final] ).
cnf(i_0_13831,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_7982]),
[final] ).
cnf(i_0_13832,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_7983]),
[final] ).
cnf(i_0_13833,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_7984]),
[final] ).
cnf(i_0_13834,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_8015]),
[final] ).
cnf(i_0_13835,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_8016,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13836,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_13837,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_7523]),
[final] ).
cnf(i_0_13838,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_8017]),
[final] ).
cnf(i_0_13839,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_8018]),
[final] ).
cnf(i_0_13840,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_8019]),
[final] ).
cnf(i_0_13841,plain,
hAPP(hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[i_0_8020]),
[final] ).
cnf(i_0_13842,plain,
hAPP(hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[i_0_8021]),
[final] ).
cnf(i_0_13843,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_13844,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_8022]),
[final] ).
cnf(i_0_13845,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_8023]),
[final] ).
cnf(i_0_13846,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_8024]),
[final] ).
cnf(i_0_13847,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_8025]),
[final] ).
cnf(i_0_13848,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_8026]),
[final] ).
cnf(i_0_13849,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_8027]),
[final] ).
cnf(i_0_13850,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_8028]),
[final] ).
cnf(i_0_13851,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_8029]),
[final] ).
cnf(i_0_13852,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_8030]),
[final] ).
cnf(i_0_13853,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_7651]),
[final] ).
cnf(i_0_13854,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_8031]),
[final] ).
cnf(i_0_13855,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_8032]),
[final] ).
cnf(i_0_13856,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_8033]),
[final] ).
cnf(i_0_13857,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_8034]),
[final] ).
cnf(i_0_13858,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_8035]),
[final] ).
cnf(i_0_13859,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_8036]),
[final] ).
cnf(i_0_13860,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_8037]),
[final] ).
cnf(i_0_13861,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_8038]),
[final] ).
cnf(i_0_13862,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_8039]),
[final] ).
cnf(i_0_13863,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_8040]),
[final] ).
cnf(i_0_13864,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_8041]),
[final] ).
cnf(i_0_13865,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_13866,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_8042]),
[final] ).
cnf(i_0_13867,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_8043]),
[final] ).
cnf(i_0_13868,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_13869,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_7898]),
[final] ).
cnf(i_0_13870,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_8044]),
[final] ).
cnf(i_0_13871,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_8045]),
[final] ).
cnf(i_0_13872,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_8046]),
[final] ).
cnf(i_0_13873,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_8047]),
[final] ).
cnf(i_0_13874,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_8048]),
[final] ).
cnf(i_0_13875,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_13876,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_8049]),
[final] ).
cnf(i_0_13877,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_8050]),
[final] ).
cnf(i_0_13878,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_8051]),
[final] ).
cnf(i_0_13879,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_8052]),
[final] ).
cnf(i_0_13880,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_13881,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,esk393_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_13882,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,esk167_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_13883,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,esk392_4(X1,X2,X3,X4)) != c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7253]),
[final] ).
cnf(i_0_13884,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,esk166_4(X1,X2,X3,X4)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7254]),
[final] ).
cnf(i_0_13885,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_8053]),
[final] ).
cnf(i_0_13886,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_8054]),
[final] ).
cnf(i_0_13887,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk69_3(X2,X1,X3))),esk70_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_8055]),
[final] ).
cnf(i_0_13888,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk303_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_7685]),
[final] ).
cnf(i_0_13889,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk153_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_7686]),
[final] ).
cnf(i_0_13890,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),esk471_3(X2,X3,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8056]),
[final] ).
cnf(i_0_13891,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_8057]),
[final] ).
cnf(i_0_13892,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_7705]),
[final] ).
cnf(i_0_13893,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_13894,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_8058]),
[final] ).
cnf(i_0_13895,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_8059]),
[final] ).
cnf(i_0_13896,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_8060]),
[final] ).
cnf(i_0_13897,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_7630]),
[final] ).
cnf(i_0_13898,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_8061]),
[final] ).
cnf(i_0_13899,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_8062]),
[final] ).
cnf(i_0_13900,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_8063,c_0_6070]),
[final] ).
cnf(i_0_13901,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_7938]),
[final] ).
cnf(i_0_13902,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_8064]),
[final] ).
cnf(i_0_13903,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_8065]),
[final] ).
cnf(i_0_13904,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_8066]),
[final] ).
cnf(i_0_13905,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_8067]),
[final] ).
cnf(i_0_13906,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_8068]),
[final] ).
cnf(i_0_13907,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk399_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_7951]),
[final] ).
cnf(i_0_13908,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_8069]),
[final] ).
cnf(i_0_13909,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_8070]),
[final] ).
cnf(i_0_13910,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk67_3(X2,X1,X3))),esk68_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_8071]),
[final] ).
cnf(i_0_13911,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_8072]),
[final] ).
cnf(i_0_13912,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_8073]),
[final] ).
cnf(i_0_13913,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_8074,c_0_6670]),c_0_6670]),
[final] ).
cnf(i_0_13914,plain,
( c_Fun_Oinj__on(X4,X3,X2,X1)
| esk194_4(X1,X2,X3,X4) != esk195_4(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_7242]),
[final] ).
cnf(i_0_13915,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_8075]),
[final] ).
cnf(i_0_13916,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_8076]),
[final] ).
cnf(i_0_13917,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_13918,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_8077]),
[final] ).
cnf(i_0_13919,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk504_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred2_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk501_3(X1,X2,X3)))
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7552]),
[final] ).
cnf(i_0_13920,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_7946]),
[final] ).
cnf(i_0_13921,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_8078,c_0_6135]),c_0_6135]),
[final] ).
cnf(i_0_13922,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_8079]),
[final] ).
cnf(i_0_13923,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk502_3(X2,X3,X1)),X2))
| epred2_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk503_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7552]),
[final] ).
cnf(i_0_13924,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_8080]),
[final] ).
cnf(i_0_13925,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk500_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk498_3(X1,X2,X3)))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7562]),
[final] ).
cnf(i_0_13926,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_7901]),
[final] ).
cnf(i_0_13927,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_8081]),
[final] ).
cnf(i_0_13928,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_8082]),
[final] ).
cnf(i_0_13929,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_8083]),
[final] ).
cnf(i_0_13930,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk498_3(X2,X3,X1)),X2))
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk500_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7562]),
[final] ).
cnf(i_0_13931,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_8084]),
[final] ).
cnf(i_0_13932,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_8084]),
[final] ).
cnf(i_0_13933,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_8085]),
[final] ).
cnf(i_0_13934,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_8086]),
[final] ).
cnf(i_0_13935,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_8087]),
[final] ).
cnf(i_0_13936,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_8087]),
[final] ).
cnf(i_0_13937,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_8088]),
[final] ).
cnf(i_0_13938,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk69_3(X2,X1,X3))),esk70_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_8055]),
[final] ).
cnf(i_0_13939,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_8089]),
[final] ).
cnf(i_0_13940,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_8090]),
[final] ).
cnf(i_0_13941,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk191_3(X2,X3,X1)),esk192_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_13942,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_13943,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_7942]),
[final] ).
cnf(i_0_13944,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_8091]),
[final] ).
cnf(i_0_13945,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_8091]),
[final] ).
cnf(i_0_13946,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_8092]),
[final] ).
cnf(i_0_13947,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_8092]),
[final] ).
cnf(i_0_13948,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_8093]),
[final] ).
cnf(i_0_13949,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_8094]),
[final] ).
cnf(i_0_13950,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_8095]),
[final] ).
cnf(i_0_13951,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_8096]),
[final] ).
cnf(i_0_13952,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),esk350_2(X2,X1)),hAPP(c_Relation_OImage(X1,X1,X2),esk350_2(X2,X1))))
| c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_8097]),
[final] ).
cnf(i_0_13953,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_8098]),
[final] ).
cnf(i_0_13954,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_8099]),
[final] ).
cnf(i_0_13955,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),c_List_OtakeWhile(X3,X1,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_7928]),
[final] ).
cnf(i_0_13956,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_8100]),
[final] ).
cnf(i_0_13957,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_8101]),
[final] ).
cnf(i_0_13958,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_8102]),
[final] ).
cnf(i_0_13959,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_13960,plain,
( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X2),esk178_3(X3,X1,X2)),esk178_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_7965]),
[final] ).
cnf(i_0_13961,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_8103]),
[final] ).
cnf(i_0_13962,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_8104]),
[final] ).
cnf(i_0_13963,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_13964,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_8105,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6169]),c_0_6016]),
[final] ).
cnf(i_0_13965,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_8106]),
[final] ).
cnf(i_0_13966,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_8107,c_0_6062]),
[final] ).
cnf(i_0_13967,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk503_3(X2,X1,X3))),esk504_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_7552]),
[final] ).
cnf(i_0_13968,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_8108,c_0_6135]),c_0_6135]),
[final] ).
cnf(i_0_13969,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_8109,c_0_6135]),c_0_6135]),
[final] ).
cnf(i_0_13970,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_13971,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_13972,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_8110]),
[final] ).
cnf(i_0_13973,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_8111]),
[final] ).
cnf(i_0_13974,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_7788]),
[final] ).
cnf(i_0_13975,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk67_3(X2,X1,X3))),esk68_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_8071]),
[final] ).
cnf(i_0_13976,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_7740]),
[final] ).
cnf(i_0_13977,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_8112]),
[final] ).
cnf(i_0_13978,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_8112]),
[final] ).
cnf(i_0_13979,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_8113]),
[final] ).
cnf(i_0_13980,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_8113]),
[final] ).
cnf(i_0_13981,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_8114]),
[final] ).
cnf(i_0_13982,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_8115]),
[final] ).
cnf(i_0_13983,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),esk501_3(X1,X2,X3))),esk502_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_7552]),
[final] ).
cnf(i_0_13984,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_8116,c_0_6670]),c_0_6670]),
[final] ).
cnf(i_0_13985,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_8117]),
[final] ).
cnf(i_0_13986,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_8118]),
[final] ).
cnf(i_0_13987,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk499_3(X2,X1,X3))),esk500_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_7562]),
[final] ).
cnf(i_0_13988,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_8119,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_13989,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk504_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,esk501_3(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7552]),
[final] ).
cnf(i_0_13990,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk500_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,esk498_3(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7562]),
[final] ).
cnf(i_0_13991,plain,
( X1 = hAPP(c_Int_ORep__Integ,esk306_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_8120]),
[final] ).
cnf(i_0_13992,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk417_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_8121]),
[final] ).
cnf(i_0_13993,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk479_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_8122]),
[final] ).
cnf(i_0_13994,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk450_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_7743]),
[final] ).
cnf(i_0_13995,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),esk497_3(X1,X2,X3))),esk498_3(X1,X2,X3))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7562]),
[final] ).
cnf(i_0_13996,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk502_3(X2,X3,X1)),X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk503_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7552]),
[final] ).
cnf(i_0_13997,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk498_3(X2,X3,X1)),X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk500_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7562]),
[final] ).
cnf(i_0_13998,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X3),X2),X4)))
| ~ hBOOL(hAPP(X1,esk449_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_7743]),
[final] ).
cnf(i_0_13999,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_8123]),
[final] ).
cnf(i_0_14000,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_8124]),
[final] ).
cnf(i_0_14001,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_8125]),
[final] ).
cnf(i_0_14002,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_8126]),
[final] ).
cnf(i_0_14003,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk504_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)),esk502_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_7552]),
[final] ).
cnf(i_0_14004,plain,
( c_Fun_Oinj__on(X1,X2,esk197_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_14005,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_8117]),
[final] ).
cnf(i_0_14006,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_8127]),
[final] ).
cnf(i_0_14007,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_7562]),
[final] ).
cnf(i_0_14008,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_7552]),
[final] ).
cnf(i_0_14009,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_8128]),
[final] ).
cnf(i_0_14010,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_8129]),
[final] ).
cnf(i_0_14011,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_8130]),
[final] ).
cnf(i_0_14012,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_8131]),
[final] ).
cnf(i_0_14013,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),esk340_2(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_8132]),
[final] ).
cnf(i_0_14014,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_8133]),
[final] ).
cnf(i_0_14015,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_8134]),
[final] ).
cnf(i_0_14016,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_7672]),
[final] ).
cnf(i_0_14017,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_7671]),
[final] ).
cnf(i_0_14018,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_8135]),
[final] ).
cnf(i_0_14019,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_8136]),
[final] ).
cnf(i_0_14020,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_8137]),
[final] ).
cnf(i_0_14021,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_8138]),
[final] ).
cnf(i_0_14022,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_7857]),
[final] ).
cnf(i_0_14023,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_8139]),
[final] ).
cnf(i_0_14024,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_7814]),
[final] ).
cnf(i_0_14025,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_8140]),
[final] ).
cnf(i_0_14026,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_8141]),
[final] ).
cnf(i_0_14027,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_7818]),
[final] ).
cnf(i_0_14028,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_8142]),
[final] ).
cnf(i_0_14029,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_7970]),
[final] ).
cnf(i_0_14030,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_8143]),
[final] ).
cnf(i_0_14031,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_7971]),
[final] ).
cnf(i_0_14032,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_7821]),
[final] ).
cnf(i_0_14033,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_8144]),
[final] ).
cnf(i_0_14034,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk500_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)),esk498_3(X1,X2,X3)))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7562]),
[final] ).
cnf(i_0_14035,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_8145]),
[final] ).
cnf(i_0_14036,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_8146]),
[final] ).
cnf(i_0_14037,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_8147]),
[final] ).
cnf(i_0_14038,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_8148]),
[final] ).
cnf(i_0_14039,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_8149]),
[final] ).
cnf(i_0_14040,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_14041,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_14042,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk285_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_8150]),
[final] ).
cnf(i_0_14043,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk284_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_8151]),
[final] ).
cnf(i_0_14044,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk282_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_8152]),
[final] ).
cnf(i_0_14045,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_14046,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_8112]),
[final] ).
cnf(i_0_14047,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)),esk492_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2))) ),
inference(rw,[status(thm)],[i_0_8153,c_0_6100]),
[final] ).
cnf(i_0_14048,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)),esk493_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2))) ),
inference(rw,[status(thm)],[i_0_8154,c_0_6100]),
[final] ).
cnf(i_0_14049,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_8155]),
[final] ).
cnf(i_0_14050,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_8156]),
[final] ).
cnf(i_0_14051,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk504_3(X1,X2,X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk502_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_7552]),
[final] ).
cnf(i_0_14052,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_8157]),
[final] ).
cnf(i_0_14053,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_8158,c_0_8159]),
[final] ).
cnf(i_0_14054,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_7562]),
[final] ).
cnf(i_0_14055,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_7552]),
[final] ).
cnf(i_0_14056,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_8160]),
[final] ).
cnf(i_0_14057,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_8161]),
[final] ).
cnf(i_0_14058,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_8162]),
[final] ).
cnf(i_0_14059,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_8163]),
[final] ).
cnf(i_0_14060,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_8164]),
[final] ).
cnf(i_0_14061,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_8165]),
[final] ).
cnf(i_0_14062,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_8166]),
[final] ).
cnf(i_0_14063,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_8167]),
[final] ).
cnf(i_0_14064,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk454_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_8168]),
[final] ).
cnf(i_0_14065,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk500_3(X1,X2,X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk498_3(X1,X2,X3)),X1))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7562]),
[final] ).
cnf(i_0_14066,plain,
( X1 = hAPP(c_Nat_OSuc,esk27_4(X2,X1,X3,X4))
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X4),X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7848]),
[final] ).
cnf(i_0_14067,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_8169]),
[final] ).
cnf(i_0_14068,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_8170]),
[final] ).
cnf(i_0_14069,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_8171]),
[final] ).
cnf(i_0_14070,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_8172]),
[final] ).
cnf(i_0_14071,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_8173]),
[final] ).
cnf(i_0_14072,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_8174]),
[final] ).
cnf(i_0_14073,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_7892]),
[final] ).
cnf(i_0_14074,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_8175]),
[final] ).
cnf(i_0_14075,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_8176]),
[final] ).
cnf(i_0_14076,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_8177]),
[final] ).
cnf(i_0_14077,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_8178]),
[final] ).
cnf(i_0_14078,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_8179]),
[final] ).
cnf(i_0_14079,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_8180]),
[final] ).
cnf(i_0_14080,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_8181,c_0_6053]),
[final] ).
cnf(i_0_14081,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_14082,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_8182]),
[final] ).
cnf(i_0_14083,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_8183]),
[final] ).
cnf(i_0_14084,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_7982]),
[final] ).
cnf(i_0_14085,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_7982]),
[final] ).
cnf(i_0_14086,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_8184]),
[final] ).
cnf(i_0_14087,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_8185]),
[final] ).
cnf(i_0_14088,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_8186]),
[final] ).
cnf(i_0_14089,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_8185]),
[final] ).
cnf(i_0_14090,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_7983]),
[final] ).
cnf(i_0_14091,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_7983]),
[final] ).
cnf(i_0_14092,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_8187]),
[final] ).
cnf(i_0_14093,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_8188]),
[final] ).
cnf(i_0_14094,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_8189]),
[final] ).
cnf(i_0_14095,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_7984]),
[final] ).
cnf(i_0_14096,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_7984]),
[final] ).
cnf(i_0_14097,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_8190]),
[final] ).
cnf(i_0_14098,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_8191]),
[final] ).
cnf(i_0_14099,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_8192]),
[final] ).
cnf(i_0_14100,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_8193]),
[final] ).
cnf(i_0_14101,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk503_3(X2,X1,X3))),esk504_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_7552]),
[final] ).
cnf(i_0_14102,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk499_3(X2,X1,X3))),esk500_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_7562]),
[final] ).
cnf(i_0_14103,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_8194]),
[final] ).
cnf(i_0_14104,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_8195,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_14105,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_8196,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_14106,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_8197]),
[final] ).
cnf(i_0_14107,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_8198]),
[final] ).
cnf(i_0_14108,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_8199]),
[final] ).
cnf(i_0_14109,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_8200]),
[final] ).
cnf(i_0_14110,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_8199]),
[final] ).
cnf(i_0_14111,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_8200]),
[final] ).
cnf(i_0_14112,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_8201]),
[final] ).
cnf(i_0_14113,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_8202]),
[final] ).
cnf(i_0_14114,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_8201]),
[final] ).
cnf(i_0_14115,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_8202]),
[final] ).
cnf(i_0_14116,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_8203]),
[final] ).
cnf(i_0_14117,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_8203]),
[final] ).
cnf(i_0_14118,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_8204]),
[final] ).
cnf(i_0_14119,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_8205]),
[final] ).
cnf(i_0_14120,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_8206]),
[final] ).
cnf(i_0_14121,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk340_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_8132]),
[final] ).
cnf(i_0_14122,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_8207]),
[final] ).
cnf(i_0_14123,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_8208]),
[final] ).
cnf(i_0_14124,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_8206]),
[final] ).
cnf(i_0_14125,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),esk501_3(X1,X2,X3))),esk502_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_7552]),
[final] ).
cnf(i_0_14126,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),esk497_3(X1,X2,X3))),esk498_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_7562]),
[final] ).
cnf(i_0_14127,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_8209,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_14128,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_8210]),
[final] ).
cnf(i_0_14129,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_14130,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_14131,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)),esk399_3(X2,X3,X1)),X2) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_7951]),
[final] ).
cnf(i_0_14132,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_8211]),
[final] ).
cnf(i_0_14133,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_8212]),
[final] ).
cnf(i_0_14134,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_8213]),
[final] ).
cnf(i_0_14135,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_8214]),
[final] ).
cnf(i_0_14136,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),esk282_3(X2,X3,X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8152]),
[final] ).
cnf(i_0_14137,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),esk284_3(X2,X3,X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8151]),
[final] ).
cnf(i_0_14138,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),esk285_3(X2,X3,X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8150]),
[final] ).
cnf(i_0_14139,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_8215]),
[final] ).
cnf(i_0_14140,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_7941]),
[final] ).
cnf(i_0_14141,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_8216,c_0_6670]),
[final] ).
cnf(i_0_14142,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_14143,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_8217]),
[final] ).
cnf(i_0_14144,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_8055]),
[final] ).
cnf(i_0_14145,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_8218]),
[final] ).
cnf(i_0_14146,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_8219]),
[final] ).
cnf(i_0_14147,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_8220]),
[final] ).
cnf(i_0_14148,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_8221]),
[final] ).
cnf(i_0_14149,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_8014]),
[final] ).
cnf(i_0_14150,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_8222]),
[final] ).
cnf(i_0_14151,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_8223]),
[final] ).
cnf(i_0_14152,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_8224]),
[final] ).
cnf(i_0_14153,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_8225]),
[final] ).
cnf(i_0_14154,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_8226]),
[final] ).
cnf(i_0_14155,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_8227]),
[final] ).
cnf(i_0_14156,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_8228]),
[final] ).
cnf(i_0_14157,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_8229]),
[final] ).
cnf(i_0_14158,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_8230]),
[final] ).
cnf(i_0_14159,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_8231]),
[final] ).
cnf(i_0_14160,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_8232]),
[final] ).
cnf(i_0_14161,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_8233]),
[final] ).
cnf(i_0_14162,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_8234]),
[final] ).
cnf(i_0_14163,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk504_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)),esk502_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_7552]),
[final] ).
cnf(i_0_14164,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk500_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)),esk498_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_7562]),
[final] ).
cnf(i_0_14165,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_8235]),
[final] ).
cnf(i_0_14166,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_8236]),
[final] ).
cnf(i_0_14167,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_8237]),
[final] ).
cnf(i_0_14168,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_14169,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_8238]),
[final] ).
cnf(i_0_14170,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_7923]),
[final] ).
cnf(i_0_14171,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_7637]),
[final] ).
cnf(i_0_14172,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_8061]),
[final] ).
cnf(i_0_14173,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_8239]),
[final] ).
cnf(i_0_14174,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_8240]),
[final] ).
cnf(i_0_14175,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_8241]),
[final] ).
cnf(i_0_14176,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_8242]),
[final] ).
cnf(i_0_14177,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_8243]),
[final] ).
cnf(i_0_14178,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_8244]),
[final] ).
cnf(i_0_14179,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_8245]),
[final] ).
cnf(i_0_14180,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_14181,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_14182,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_8246]),
[final] ).
cnf(i_0_14183,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_8247]),
[final] ).
cnf(i_0_14184,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_8248]),
[final] ).
cnf(i_0_14185,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_8249]),
[final] ).
cnf(i_0_14186,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_8250]),
[final] ).
cnf(i_0_14187,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_7836]),
[final] ).
cnf(i_0_14188,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_7835]),
[final] ).
cnf(i_0_14189,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_8251]),
[final] ).
cnf(i_0_14190,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_7839]),
[final] ).
cnf(i_0_14191,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_8252]),
[final] ).
cnf(i_0_14192,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_7841]),
[final] ).
cnf(i_0_14193,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_8253]),
[final] ).
cnf(i_0_14194,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_7844]),
[final] ).
cnf(i_0_14195,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_8254]),
[final] ).
cnf(i_0_14196,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_7846]),
[final] ).
cnf(i_0_14197,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_8255]),
[final] ).
cnf(i_0_14198,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_8256]),
[final] ).
cnf(i_0_14199,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_8257]),
[final] ).
cnf(i_0_14200,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_8068]),
[final] ).
cnf(i_0_14201,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_8258]),
[final] ).
cnf(i_0_14202,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_8259]),
[final] ).
cnf(i_0_14203,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_8260]),
[final] ).
cnf(i_0_14204,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_8261]),
[final] ).
cnf(i_0_14205,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_8262]),
[final] ).
cnf(i_0_14206,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_8263]),
[final] ).
cnf(i_0_14207,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk504_3(X1,X2,X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk502_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_7552]),
[final] ).
cnf(i_0_14208,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk500_3(X1,X2,X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk498_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_7562]),
[final] ).
cnf(i_0_14209,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_8264]),
[final] ).
cnf(i_0_14210,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_8265]),
[final] ).
cnf(i_0_14211,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_8266]),
[final] ).
cnf(i_0_14212,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_8101]),
[final] ).
cnf(i_0_14213,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_8102]),
[final] ).
cnf(i_0_14214,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_8267]),
[final] ).
cnf(i_0_14215,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_8268]),
[final] ).
cnf(i_0_14216,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_8269]),
[final] ).
cnf(i_0_14217,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_8146]),
[final] ).
cnf(i_0_14218,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_8270]),
[final] ).
cnf(i_0_14219,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_8271]),
[final] ).
cnf(i_0_14220,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_8272]),
[final] ).
cnf(i_0_14221,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_8273]),
[final] ).
cnf(i_0_14222,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_8274]),
[final] ).
cnf(i_0_14223,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_8244]),
[final] ).
cnf(i_0_14224,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_8245]),
[final] ).
cnf(i_0_14225,plain,
( epred2_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk503_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,esk501_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7552]),
[final] ).
cnf(i_0_14226,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk403_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_8275]),
[final] ).
cnf(i_0_14227,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk403_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_8275]),
[final] ).
cnf(i_0_14228,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_8276]),
[final] ).
cnf(i_0_14229,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_8277]),
[final] ).
cnf(i_0_14230,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_8278]),
[final] ).
cnf(i_0_14231,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_8279]),
[final] ).
cnf(i_0_14232,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_8280]),
[final] ).
cnf(i_0_14233,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_8281]),
[final] ).
cnf(i_0_14234,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_8282]),
[final] ).
cnf(i_0_14235,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_8283]),
[final] ).
cnf(i_0_14236,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_8284]),
[final] ).
cnf(i_0_14237,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_7748]),
[final] ).
cnf(i_0_14238,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_8285]),
[final] ).
cnf(i_0_14239,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_8286]),
[final] ).
cnf(i_0_14240,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_8071]),
[final] ).
cnf(i_0_14241,plain,
( epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk500_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,esk498_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7562]),
[final] ).
cnf(i_0_14242,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_8287]),
[final] ).
cnf(i_0_14243,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_8288]),
[final] ).
cnf(i_0_14244,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_8152]),
[final] ).
cnf(i_0_14245,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_8151]),
[final] ).
cnf(i_0_14246,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_8150]),
[final] ).
cnf(i_0_14247,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_8289]),
[final] ).
cnf(i_0_14248,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_8213]),
[final] ).
cnf(i_0_14249,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_8213]),
[final] ).
cnf(i_0_14250,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_8290]),
[final] ).
cnf(i_0_14251,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_14252,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_14253,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk478_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_8122]),
[final] ).
cnf(i_0_14254,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_8291]),
[final] ).
cnf(i_0_14255,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_8292]),
[final] ).
cnf(i_0_14256,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_8293]),
[final] ).
cnf(i_0_14257,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_14258,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),esk19_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_7788]),
[final] ).
cnf(i_0_14259,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_8294]),
[final] ).
cnf(i_0_14260,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_8295]),
[final] ).
cnf(i_0_14261,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_8296]),
[final] ).
cnf(i_0_14262,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_8297]),
[final] ).
cnf(i_0_14263,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_8298]),
[final] ).
cnf(i_0_14264,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_8299]),
[final] ).
cnf(i_0_14265,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_14266,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_8300]),
[final] ).
cnf(i_0_14267,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_8301]),
[final] ).
cnf(i_0_14268,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_8302]),
[final] ).
cnf(i_0_14269,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_8303]),
[final] ).
cnf(i_0_14270,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_8304]),
[final] ).
cnf(i_0_14271,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_8200]),
[final] ).
cnf(i_0_14272,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_8201]),
[final] ).
cnf(i_0_14273,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_8305]),
[final] ).
cnf(i_0_14274,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_8306]),
[final] ).
cnf(i_0_14275,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_8203]),
[final] ).
cnf(i_0_14276,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_8307]),
[final] ).
cnf(i_0_14277,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_8308]),
[final] ).
cnf(i_0_14278,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_8309]),
[final] ).
cnf(i_0_14279,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_8310]),
[final] ).
cnf(i_0_14280,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_8311,c_0_6670]),
[final] ).
cnf(i_0_14281,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_8312]),
[final] ).
cnf(i_0_14282,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_8313]),
[final] ).
cnf(i_0_14283,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_8314]),
[final] ).
cnf(i_0_14284,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_8315]),
[final] ).
cnf(i_0_14285,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_8316]),
[final] ).
cnf(i_0_14286,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_8317]),
[final] ).
cnf(i_0_14287,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_8318]),
[final] ).
cnf(i_0_14288,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_8319]),
[final] ).
cnf(i_0_14289,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_8046]),
[final] ).
cnf(i_0_14290,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_8047]),
[final] ).
cnf(i_0_14291,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_8048]),
[final] ).
cnf(i_0_14292,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_8320]),
[final] ).
cnf(i_0_14293,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_8321]),
[final] ).
cnf(i_0_14294,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_7882]),
[final] ).
cnf(i_0_14295,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_7906]),
[final] ).
cnf(i_0_14296,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk423_3(X2,X1,X3)),esk421_2(X2,X1)))
| c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),esk421_2(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_6982]),
[final] ).
cnf(i_0_14297,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_7319]),
[final] ).
cnf(i_0_14298,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_7320]),
[final] ).
cnf(i_0_14299,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_7321]),
[final] ).
cnf(i_0_14300,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_14301,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_8322]),
[final] ).
cnf(i_0_14302,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_8041]),
[final] ).
cnf(i_0_14303,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_8323]),
[final] ).
cnf(i_0_14304,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_8324]),
[final] ).
cnf(i_0_14305,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_8325]),
[final] ).
cnf(i_0_14306,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_8326]),
[final] ).
cnf(i_0_14307,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_8327]),
[final] ).
cnf(i_0_14308,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_8328]),
[final] ).
cnf(i_0_14309,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_8329]),
[final] ).
cnf(i_0_14310,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_7792]),
[final] ).
cnf(i_0_14311,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_8330]),
[final] ).
cnf(i_0_14312,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_8331]),
[final] ).
cnf(i_0_14313,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_7792]),
[final] ).
cnf(i_0_14314,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_8332]),
[final] ).
cnf(i_0_14315,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_8331]),
[final] ).
cnf(i_0_14316,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_8333]),
[final] ).
cnf(i_0_14317,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_8334]),
[final] ).
cnf(i_0_14318,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_8335]),
[final] ).
cnf(i_0_14319,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_8336]),
[final] ).
cnf(i_0_14320,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_8337]),
[final] ).
cnf(i_0_14321,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_8338]),
[final] ).
cnf(i_0_14322,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_8339]),
[final] ).
cnf(i_0_14323,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_8340]),
[final] ).
cnf(i_0_14324,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_8046]),
[final] ).
cnf(i_0_14325,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_8047]),
[final] ).
cnf(i_0_14326,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_8048]),
[final] ).
cnf(i_0_14327,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_8341]),
[final] ).
cnf(i_0_14328,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_8342]),
[final] ).
cnf(i_0_14329,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_8343]),
[final] ).
cnf(i_0_14330,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_8344]),
[final] ).
cnf(i_0_14331,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_8345]),
[final] ).
cnf(i_0_14332,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_8346]),
[final] ).
cnf(i_0_14333,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_8347]),
[final] ).
cnf(i_0_14334,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_8273]),
[final] ).
cnf(i_0_14335,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_8348]),
[final] ).
cnf(i_0_14336,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_8349]),
[final] ).
cnf(i_0_14337,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_14338,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_14339,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_8350]),
[final] ).
cnf(i_0_14340,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_8351]),
[final] ).
cnf(i_0_14341,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_8352]),
[final] ).
cnf(i_0_14342,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_8061]),
[final] ).
cnf(i_0_14343,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_8353]),
[final] ).
cnf(i_0_14344,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_8354]),
[final] ).
cnf(i_0_14345,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_8355]),
[final] ).
cnf(i_0_14346,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_8356]),
[final] ).
cnf(i_0_14347,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk503_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,esk501_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7552]),
[final] ).
cnf(i_0_14348,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk500_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,esk498_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7562]),
[final] ).
cnf(i_0_14349,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_8357]),
[final] ).
cnf(i_0_14350,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_8358]),
[final] ).
cnf(i_0_14351,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_8359]),
[final] ).
cnf(i_0_14352,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_8360]),
[final] ).
cnf(i_0_14353,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_8361,c_0_6015]),
[final] ).
cnf(i_0_14354,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_8362,c_0_6015]),c_0_6015]),
[final] ).
cnf(i_0_14355,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_8050]),
[final] ).
cnf(i_0_14356,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_8050]),
[final] ).
cnf(i_0_14357,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_8363]),
[final] ).
cnf(i_0_14358,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_8364]),
[final] ).
cnf(i_0_14359,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_8365]),
[final] ).
cnf(i_0_14360,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_8366]),
[final] ).
cnf(i_0_14361,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_8068]),
[final] ).
cnf(i_0_14362,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_8291]),
[final] ).
cnf(i_0_14363,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_8367]),
[final] ).
cnf(i_0_14364,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_8368]),
[final] ).
cnf(i_0_14365,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_8369]),
[final] ).
cnf(i_0_14366,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_8369]),
[final] ).
cnf(i_0_14367,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_8370]),
[final] ).
cnf(i_0_14368,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_8371]),
[final] ).
cnf(i_0_14369,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_8372]),
[final] ).
cnf(i_0_14370,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_8064]),
[final] ).
cnf(i_0_14371,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk471_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_8056]),
[final] ).
cnf(i_0_14372,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_8373]),
[final] ).
cnf(i_0_14373,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_8374]),
[final] ).
cnf(i_0_14374,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_8375]),
[final] ).
cnf(i_0_14375,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk502_3(X2,X3,X1)))
| epred2_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk503_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7552]),
[final] ).
cnf(i_0_14376,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_8376]),
[final] ).
cnf(i_0_14377,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_8377]),
[final] ).
cnf(i_0_14378,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_8378]),
[final] ).
cnf(i_0_14379,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_8378]),
[final] ).
cnf(i_0_14380,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_8378]),
[final] ).
cnf(i_0_14381,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_8378]),
[final] ).
cnf(i_0_14382,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_8379]),
[final] ).
cnf(i_0_14383,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_7942]),
[final] ).
cnf(i_0_14384,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_8380]),
[final] ).
cnf(i_0_14385,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_14386,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_8381]),
[final] ).
cnf(i_0_14387,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_8382]),
[final] ).
cnf(i_0_14388,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_8382]),
[final] ).
cnf(i_0_14389,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_8383]),
[final] ).
cnf(i_0_14390,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_8384]),
[final] ).
cnf(i_0_14391,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_8385]),
[final] ).
cnf(i_0_14392,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk70_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_8055]),
[final] ).
cnf(i_0_14393,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk498_3(X2,X3,X1)))
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk500_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7562]),
[final] ).
cnf(i_0_14394,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_8386]),
[final] ).
cnf(i_0_14395,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_8387]),
[final] ).
cnf(i_0_14396,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_8388]),
[final] ).
cnf(i_0_14397,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_8389]),
[final] ).
cnf(i_0_14398,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_8045]),
[final] ).
cnf(i_0_14399,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk504_3(X1,X2,X3)))
| epred2_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk501_3(X1,X2,X3)))
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7552]),
[final] ).
cnf(i_0_14400,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_8390]),
[final] ).
cnf(i_0_14401,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_8391]),
[final] ).
cnf(i_0_14402,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_8392]),
[final] ).
cnf(i_0_14403,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_8393,c_0_6015]),
[final] ).
cnf(i_0_14404,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_8394,c_0_6015]),
[final] ).
cnf(i_0_14405,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_8395,c_0_6015]),
[final] ).
cnf(i_0_14406,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_8396,c_0_6015]),
[final] ).
cnf(i_0_14407,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_8397,c_0_6015]),
[final] ).
cnf(i_0_14408,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_8398,c_0_6015]),
[final] ).
cnf(i_0_14409,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_8399]),
[final] ).
cnf(i_0_14410,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_8400]),
[final] ).
cnf(i_0_14411,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_14412,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk402_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_8401]),
[final] ).
cnf(i_0_14413,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_8402]),
[final] ).
cnf(i_0_14414,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_8403,c_0_6053]),
[final] ).
cnf(i_0_14415,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_8404]),
[final] ).
cnf(i_0_14416,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_8405]),
[final] ).
cnf(i_0_14417,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_8406]),
[final] ).
cnf(i_0_14418,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk500_3(X1,X2,X3)))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk498_3(X1,X2,X3)))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7562]),
[final] ).
cnf(i_0_14419,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_8117]),
[final] ).
cnf(i_0_14420,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_8407]),
[final] ).
cnf(i_0_14421,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_8408]),
[final] ).
cnf(i_0_14422,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_8046]),
[final] ).
cnf(i_0_14423,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_8047]),
[final] ).
cnf(i_0_14424,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_8409]),
[final] ).
cnf(i_0_14425,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_7985]),
[final] ).
cnf(i_0_14426,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk362_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_8410]),
[final] ).
cnf(i_0_14427,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk361_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_7986]),
[final] ).
cnf(i_0_14428,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_8411]),
[final] ).
cnf(i_0_14429,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk408_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_8412]),
[final] ).
cnf(i_0_14430,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_8413]),
[final] ).
cnf(i_0_14431,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_8414]),
[final] ).
cnf(i_0_14432,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_8415]),
[final] ).
cnf(i_0_14433,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_8416]),
[final] ).
cnf(i_0_14434,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_8417,c_0_6226]),
[final] ).
cnf(i_0_14435,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_8418,c_0_6226]),
[final] ).
cnf(i_0_14436,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk68_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_8071]),
[final] ).
cnf(i_0_14437,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_8419,c_0_6169]),
[final] ).
cnf(i_0_14438,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_8420,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_14439,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_8421]),
[final] ).
cnf(i_0_14440,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_8387]),
[final] ).
cnf(i_0_14441,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_7987]),
[final] ).
cnf(i_0_14442,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_8422]),
[final] ).
cnf(i_0_14443,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_8423]),
[final] ).
cnf(i_0_14444,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_8424]),
[final] ).
cnf(i_0_14445,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_8094]),
[final] ).
cnf(i_0_14446,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_8100]),
[final] ).
cnf(i_0_14447,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_8425]),
[final] ).
cnf(i_0_14448,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_8122]),
[final] ).
cnf(i_0_14449,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_8426]),
[final] ).
cnf(i_0_14450,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_8427]),
[final] ).
cnf(i_0_14451,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_8428]),
[final] ).
cnf(i_0_14452,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_8429]),
[final] ).
cnf(i_0_14453,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_8429]),
[final] ).
cnf(i_0_14454,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_8430]),
[final] ).
cnf(i_0_14455,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_8430]),
[final] ).
cnf(i_0_14456,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_8429]),
[final] ).
cnf(i_0_14457,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_8429]),
[final] ).
cnf(i_0_14458,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_8430]),
[final] ).
cnf(i_0_14459,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_8430]),
[final] ).
cnf(i_0_14460,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_8431]),
[final] ).
cnf(i_0_14461,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_8431]),
[final] ).
cnf(i_0_14462,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_8431]),
[final] ).
cnf(i_0_14463,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_8431]),
[final] ).
cnf(i_0_14464,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_7353]),
[final] ).
cnf(i_0_14465,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_7354]),
[final] ).
cnf(i_0_14466,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_7355]),
[final] ).
cnf(i_0_14467,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_14468,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_7989]),
[final] ).
cnf(i_0_14469,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_8432,c_0_6015]),c_0_6015]),
[final] ).
cnf(i_0_14470,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_8433,c_0_6015]),c_0_6015]),
[final] ).
cnf(i_0_14471,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_8434]),
[final] ).
cnf(i_0_14472,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_8435]),
[final] ).
cnf(i_0_14473,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_8436]),
[final] ).
cnf(i_0_14474,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_8437]),
[final] ).
cnf(i_0_14475,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_7816]),
[final] ).
cnf(i_0_14476,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_8438]),
[final] ).
cnf(i_0_14477,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_7819]),
[final] ).
cnf(i_0_14478,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_8439]),
[final] ).
cnf(i_0_14479,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_8440]),
[final] ).
cnf(i_0_14480,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_7996]),
[final] ).
cnf(i_0_14481,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_8441,c_0_6015]),c_0_6015]),
[final] ).
cnf(i_0_14482,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_8442,c_0_6015]),c_0_6015]),
[final] ).
cnf(i_0_14483,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_8443]),
[final] ).
cnf(i_0_14484,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_8444]),
[final] ).
cnf(i_0_14485,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_7999]),
[final] ).
cnf(i_0_14486,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_8000]),
[final] ).
cnf(i_0_14487,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_8445]),
[final] ).
cnf(i_0_14488,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_8446]),
[final] ).
cnf(i_0_14489,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_8447]),
[final] ).
cnf(i_0_14490,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_8448]),
[final] ).
cnf(i_0_14491,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_8449]),
[final] ).
cnf(i_0_14492,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_8450]),
[final] ).
cnf(i_0_14493,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_8451,c_0_6016]),
[final] ).
cnf(i_0_14494,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_8452]),
[final] ).
cnf(i_0_14495,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_8453]),
[final] ).
cnf(i_0_14496,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_8453]),
[final] ).
cnf(i_0_14497,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_8454]),
[final] ).
cnf(i_0_14498,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_8455]),
[final] ).
cnf(i_0_14499,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk486_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_7748]),
[final] ).
cnf(i_0_14500,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk485_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_7748]),
[final] ).
cnf(i_0_14501,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk470_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_8045]),
[final] ).
cnf(i_0_14502,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_8456]),
[final] ).
cnf(i_0_14503,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_8457]),
[final] ).
cnf(i_0_14504,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_14505,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_8458]),
[final] ).
cnf(i_0_14506,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X3,X2),X4),X5)))
| ~ hBOOL(hAPP(X1,esk89_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7149]),
[final] ).
cnf(i_0_14507,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_14508,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_8046]),
[final] ).
cnf(i_0_14509,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_8047]),
[final] ).
cnf(i_0_14510,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_8459]),
[final] ).
cnf(i_0_14511,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_8376]),
[final] ).
cnf(i_0_14512,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_8377]),
[final] ).
cnf(i_0_14513,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 != esk247_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_14514,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_7913]),
[final] ).
cnf(i_0_14515,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_8460]),
[final] ).
cnf(i_0_14516,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_8461]),
[final] ).
cnf(i_0_14517,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_8462]),
[final] ).
cnf(i_0_14518,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_14519,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_8463]),
[final] ).
cnf(i_0_14520,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_8464]),
[final] ).
cnf(i_0_14521,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_8465]),
[final] ).
cnf(i_0_14522,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_8466]),
[final] ).
cnf(i_0_14523,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_8380]),
[final] ).
cnf(i_0_14524,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_8467]),
[final] ).
cnf(i_0_14525,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk70_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_8055]),
[final] ).
cnf(i_0_14526,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_8468]),
[final] ).
cnf(i_0_14527,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_8469]),
[final] ).
cnf(i_0_14528,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_8470]),
[final] ).
cnf(i_0_14529,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_14530,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk502_3(X2,X3,X1)))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk503_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7552]),
[final] ).
cnf(i_0_14531,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk498_3(X2,X3,X1)))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk500_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7562]),
[final] ).
cnf(i_0_14532,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_8471]),
[final] ).
cnf(i_0_14533,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_8472]),
[final] ).
cnf(i_0_14534,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_8473]),
[final] ).
cnf(i_0_14535,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_8474]),
[final] ).
cnf(i_0_14536,plain,
( c_Big__Operators_Olinorder__class_OMin(X1,X3) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk362_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_8410]),
[final] ).
cnf(i_0_14537,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk246_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_14538,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_8475]),
[final] ).
cnf(i_0_14539,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_8283]),
[final] ).
cnf(i_0_14540,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_8476]),
[final] ).
cnf(i_0_14541,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_8477]),
[final] ).
cnf(i_0_14542,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_8478]),
[final] ).
cnf(i_0_14543,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_8479]),
[final] ).
cnf(i_0_14544,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk488_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_8480]),
[final] ).
cnf(i_0_14545,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk487_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_8481]),
[final] ).
cnf(i_0_14546,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_8482]),
[final] ).
cnf(i_0_14547,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_8483]),
[final] ).
cnf(i_0_14548,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_8484]),
[final] ).
cnf(i_0_14549,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_14550,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_14551,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_8485]),
[final] ).
cnf(i_0_14552,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_8429]),
[final] ).
cnf(i_0_14553,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_8486]),
[final] ).
cnf(i_0_14554,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_8487]),
[final] ).
cnf(i_0_14555,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_8430]),
[final] ).
cnf(i_0_14556,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_8488]),
[final] ).
cnf(i_0_14557,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_8489]),
[final] ).
cnf(i_0_14558,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_8490]),
[final] ).
cnf(i_0_14559,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_8431]),
[final] ).
cnf(i_0_14560,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_8491]),
[final] ).
cnf(i_0_14561,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_8492]),
[final] ).
cnf(i_0_14562,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_8493]),
[final] ).
cnf(i_0_14563,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_8494]),
[final] ).
cnf(i_0_14564,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk77_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_14565,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_8495]),
[final] ).
cnf(i_0_14566,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_8496]),
[final] ).
cnf(i_0_14567,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_8497]),
[final] ).
cnf(i_0_14568,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_8498,c_0_6053]),
[final] ).
cnf(i_0_14569,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_8499]),
[final] ).
cnf(i_0_14570,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),esk417_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8121]),
[final] ).
cnf(i_0_14571,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_8500,c_0_6135]),c_0_6135]),
[final] ).
cnf(i_0_14572,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_8501,c_0_6135]),c_0_6135]),
[final] ).
cnf(i_0_14573,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_8502]),
[final] ).
cnf(i_0_14574,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_8043]),
[final] ).
cnf(i_0_14575,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_8503]),
[final] ).
cnf(i_0_14576,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_8504]),
[final] ).
cnf(i_0_14577,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk451_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_8505]),
[final] ).
cnf(i_0_14578,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk504_3(X1,X2,X3)))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred2_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk501_3(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7552]),
[final] ).
cnf(i_0_14579,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk500_3(X1,X2,X3)))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk498_3(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_7562]),
[final] ).
cnf(i_0_14580,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_8506]),
[final] ).
cnf(i_0_14581,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_8507]),
[final] ).
cnf(i_0_14582,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_8508]),
[final] ).
cnf(i_0_14583,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_8509]),
[final] ).
cnf(i_0_14584,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_8510]),
[final] ).
cnf(i_0_14585,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_8511]),
[final] ).
cnf(i_0_14586,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_8512]),
[final] ).
cnf(i_0_14587,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_8513]),
[final] ).
cnf(i_0_14588,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_8514]),
[final] ).
cnf(i_0_14589,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_8515]),
[final] ).
cnf(i_0_14590,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_8087]),
[final] ).
cnf(i_0_14591,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_8516]),
[final] ).
cnf(i_0_14592,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_8015]),
[final] ).
cnf(i_0_14593,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk504_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_7552]),
[final] ).
cnf(i_0_14594,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_8517]),
[final] ).
cnf(i_0_14595,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_8518]),
[final] ).
cnf(i_0_14596,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_8519]),
[final] ).
cnf(i_0_14597,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_8520]),
[final] ).
cnf(i_0_14598,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_8521]),
[final] ).
cnf(i_0_14599,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_8522]),
[final] ).
cnf(i_0_14600,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_8514]),
[final] ).
cnf(i_0_14601,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_8515]),
[final] ).
cnf(i_0_14602,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_8523]),
[final] ).
cnf(i_0_14603,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_8524]),
[final] ).
cnf(i_0_14604,plain,
( hAPP(X1,esk151_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_14605,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_8525]),
[final] ).
cnf(i_0_14606,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_8526]),
[final] ).
cnf(i_0_14607,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_8527]),
[final] ).
cnf(i_0_14608,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_7819]),
[final] ).
cnf(i_0_14609,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_7816]),
[final] ).
cnf(i_0_14610,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk504_3(X1,X2,X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk502_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_7552]),
[final] ).
cnf(i_0_14611,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 != esk249_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_14612,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk199_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_8528]),
[final] ).
cnf(i_0_14613,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk248_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_14614,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_8529]),
[final] ).
cnf(i_0_14615,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_8530]),
[final] ).
cnf(i_0_14616,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk334_2(X1,X2)),c_Int_OInteg))
| hBOOL(hAPP(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_8531]),
[final] ).
cnf(i_0_14617,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_7937]),
[final] ).
cnf(i_0_14618,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_8532]),
[final] ).
cnf(i_0_14619,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_8533,c_0_6015]),
[final] ).
cnf(i_0_14620,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk500_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_7562]),
[final] ).
cnf(i_0_14621,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_8534]),
[final] ).
cnf(i_0_14622,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_8535]),
[final] ).
cnf(i_0_14623,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_8536]),
[final] ).
cnf(i_0_14624,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_8496]),
[final] ).
cnf(i_0_14625,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_8537]),
[final] ).
cnf(i_0_14626,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk68_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_8071]),
[final] ).
cnf(i_0_14627,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_8538]),
[final] ).
cnf(i_0_14628,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_8539]),
[final] ).
cnf(i_0_14629,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_7835]),
[final] ).
cnf(i_0_14630,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_7836]),
[final] ).
cnf(i_0_14631,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_8540]),
[final] ).
cnf(i_0_14632,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),esk502_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_7552]),
[final] ).
cnf(i_0_14633,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_8541]),
[final] ).
cnf(i_0_14634,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_8542]),
[final] ).
cnf(i_0_14635,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_8543]),
[final] ).
cnf(i_0_14636,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk500_3(X1,X2,X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk498_3(X1,X2,X3)))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7562]),
[final] ).
cnf(i_0_14637,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_8544]),
[final] ).
cnf(i_0_14638,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_8545]),
[final] ).
cnf(i_0_14639,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_8546]),
[final] ).
cnf(i_0_14640,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_8547]),
[final] ).
cnf(i_0_14641,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_8548]),
[final] ).
cnf(i_0_14642,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_8549]),
[final] ).
cnf(i_0_14643,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_8550]),
[final] ).
cnf(i_0_14644,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_8551]),
[final] ).
cnf(i_0_14645,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_8552]),
[final] ).
cnf(i_0_14646,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_8553]),
[final] ).
cnf(i_0_14647,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_8554]),
[final] ).
cnf(i_0_14648,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_8555]),
[final] ).
cnf(i_0_14649,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_7934]),
[final] ).
cnf(i_0_14650,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_7935]),
[final] ).
cnf(i_0_14651,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_8556]),
[final] ).
cnf(i_0_14652,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_8557]),
[final] ).
cnf(i_0_14653,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_8558]),
[final] ).
cnf(i_0_14654,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_8465]),
[final] ).
cnf(i_0_14655,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),esk498_3(X1,X2,X3)),X1))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7562]),
[final] ).
cnf(i_0_14656,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_8559]),
[final] ).
cnf(i_0_14657,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_8560]),
[final] ).
cnf(i_0_14658,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_8561]),
[final] ).
cnf(i_0_14659,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_8562]),
[final] ).
cnf(i_0_14660,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_8563]),
[final] ).
cnf(i_0_14661,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk420_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_14662,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_8564]),
[final] ).
cnf(i_0_14663,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_8565]),
[final] ).
cnf(i_0_14664,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk200_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_8566]),
[final] ).
cnf(i_0_14665,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_8567]),
[final] ).
cnf(i_0_14666,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_8129]),
[final] ).
cnf(i_0_14667,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_8130]),
[final] ).
cnf(i_0_14668,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_8131]),
[final] ).
cnf(i_0_14669,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_8568]),
[final] ).
cnf(i_0_14670,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_8569]),
[final] ).
cnf(i_0_14671,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_8056]),
[final] ).
cnf(i_0_14672,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_8570]),
[final] ).
cnf(i_0_14673,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_8571]),
[final] ).
cnf(i_0_14674,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_8572]),
[final] ).
cnf(i_0_14675,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_8429]),
[final] ).
cnf(i_0_14676,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_8573]),
[final] ).
cnf(i_0_14677,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_8486]),
[final] ).
cnf(i_0_14678,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_8430]),
[final] ).
cnf(i_0_14679,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_8574]),
[final] ).
cnf(i_0_14680,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_8431]),
[final] ).
cnf(i_0_14681,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_8575]),
[final] ).
cnf(i_0_14682,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_8404]),
[final] ).
cnf(i_0_14683,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_8405]),
[final] ).
cnf(i_0_14684,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_8406]),
[final] ).
cnf(i_0_14685,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_8576]),
[final] ).
cnf(i_0_14686,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_8577]),
[final] ).
cnf(i_0_14687,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_8578]),
[final] ).
cnf(i_0_14688,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_8579]),
[final] ).
cnf(i_0_14689,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),esk426_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_7963]),
[final] ).
cnf(i_0_14690,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_8580]),
[final] ).
cnf(i_0_14691,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_8465]),
[final] ).
cnf(i_0_14692,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_8581]),
[final] ).
cnf(i_0_14693,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_14694,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_8582]),
[final] ).
cnf(i_0_14695,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_8583]),
[final] ).
cnf(i_0_14696,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_8584,c_0_6169]),
[final] ).
cnf(i_0_14697,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_8585]),
[final] ).
cnf(i_0_14698,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_8586]),
[final] ).
cnf(i_0_14699,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_8587]),
[final] ).
cnf(i_0_14700,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_8588]),
[final] ).
cnf(i_0_14701,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_8589]),
[final] ).
cnf(i_0_14702,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_8590]),
[final] ).
cnf(i_0_14703,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_8591]),
[final] ).
cnf(i_0_14704,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_8592,c_0_6014]),c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_14705,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_8593]),
[final] ).
cnf(i_0_14706,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_7961]),
[final] ).
cnf(i_0_14707,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk478_3(X3,X1,X2)),esk479_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_8122]),
[final] ).
cnf(i_0_14708,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_8594]),
[final] ).
cnf(i_0_14709,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk131_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_8595]),
[final] ).
cnf(i_0_14710,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk130_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_8595]),
[final] ).
cnf(i_0_14711,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))
| esk409_3(X1,X2,X3) != esk410_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_7452]),
[final] ).
cnf(i_0_14712,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_8596]),
[final] ).
cnf(i_0_14713,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_8597]),
[final] ).
cnf(i_0_14714,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_8155]),
[final] ).
cnf(i_0_14715,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_8156]),
[final] ).
cnf(i_0_14716,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_8598]),
[final] ).
cnf(i_0_14717,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_8599]),
[final] ).
cnf(i_0_14718,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_8600]),
[final] ).
cnf(i_0_14719,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_8601]),
[final] ).
cnf(i_0_14720,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_8602]),
[final] ).
cnf(i_0_14721,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_8603]),
[final] ).
cnf(i_0_14722,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_8604]),
[final] ).
cnf(i_0_14723,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_8605]),
[final] ).
cnf(i_0_14724,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_8606]),
[final] ).
cnf(i_0_14725,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_7621]),
[final] ).
cnf(i_0_14726,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_8607]),
[final] ).
cnf(i_0_14727,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_8608]),
[final] ).
cnf(i_0_14728,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_8178]),
[final] ).
cnf(i_0_14729,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_8179]),
[final] ).
cnf(i_0_14730,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_8176]),
[final] ).
cnf(i_0_14731,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_8177]),
[final] ).
cnf(i_0_14732,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_8180]),
[final] ).
cnf(i_0_14733,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk504_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_7552]),
[final] ).
cnf(i_0_14734,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk500_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_7562]),
[final] ).
cnf(i_0_14735,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_14736,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_8609]),
[final] ).
cnf(i_0_14737,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_8610]),
[final] ).
cnf(i_0_14738,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_8611]),
[final] ).
cnf(i_0_14739,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_8612]),
[final] ).
cnf(i_0_14740,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_8613]),
[final] ).
cnf(i_0_14741,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_8314]),
[final] ).
cnf(i_0_14742,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_8614]),
[final] ).
cnf(i_0_14743,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_8615]),
[final] ).
cnf(i_0_14744,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_8616]),
[final] ).
cnf(i_0_14745,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_8069]),
[final] ).
cnf(i_0_14746,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_8617]),
[final] ).
cnf(i_0_14747,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_8069]),
[final] ).
cnf(i_0_14748,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_8618]),
[final] ).
cnf(i_0_14749,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_8619]),
[final] ).
cnf(i_0_14750,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_8620]),
[final] ).
cnf(i_0_14751,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_8621]),
[final] ).
cnf(i_0_14752,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_8070]),
[final] ).
cnf(i_0_14753,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_8622]),
[final] ).
cnf(i_0_14754,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_8070]),
[final] ).
cnf(i_0_14755,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_8623]),
[final] ).
cnf(i_0_14756,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk245_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_8624]),
[final] ).
cnf(i_0_14757,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk152_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_8625]),
[final] ).
cnf(i_0_14758,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_8591]),
[final] ).
cnf(i_0_14759,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_8591]),
[final] ).
cnf(i_0_14760,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_8626]),
[final] ).
cnf(i_0_14761,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_8627]),
[final] ).
cnf(i_0_14762,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,esk74_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8628]),
[final] ).
cnf(i_0_14763,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,esk73_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8629]),
[final] ).
cnf(i_0_14764,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_8630]),
[final] ).
cnf(i_0_14765,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_8631]),
[final] ).
cnf(i_0_14766,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_8632]),
[final] ).
cnf(i_0_14767,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk504_3(X1,X2,X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk502_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_7552]),
[final] ).
cnf(i_0_14768,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk500_3(X1,X2,X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk498_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_7562]),
[final] ).
cnf(i_0_14769,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_8273]),
[final] ).
cnf(i_0_14770,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_8633]),
[final] ).
cnf(i_0_14771,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_8017]),
[final] ).
cnf(i_0_14772,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_8634,c_0_6226]),
[final] ).
cnf(i_0_14773,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_8635]),
[final] ).
cnf(i_0_14774,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_8636]),
[final] ).
cnf(i_0_14775,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_8637]),
[final] ).
cnf(i_0_14776,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_8638]),
[final] ).
cnf(i_0_14777,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),esk502_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_7552]),
[final] ).
cnf(i_0_14778,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),esk498_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_7562]),
[final] ).
cnf(i_0_14779,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_8639]),
[final] ).
cnf(i_0_14780,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_8640]),
[final] ).
cnf(i_0_14781,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_8641]),
[final] ).
cnf(i_0_14782,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_8641]),
[final] ).
cnf(i_0_14783,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_8642]),
[final] ).
cnf(i_0_14784,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_8206]),
[final] ).
cnf(i_0_14785,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_8643]),
[final] ).
cnf(i_0_14786,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_8644]),
[final] ).
cnf(i_0_14787,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_8645]),
[final] ).
cnf(i_0_14788,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_8646]),
[final] ).
cnf(i_0_14789,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_8647]),
[final] ).
cnf(i_0_14790,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_8648]),
[final] ).
cnf(i_0_14791,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_8649]),
[final] ).
cnf(i_0_14792,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_8650]),
[final] ).
cnf(i_0_14793,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_8651]),
[final] ).
cnf(i_0_14794,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_8652]),
[final] ).
cnf(i_0_14795,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_8653]),
[final] ).
cnf(i_0_14796,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_8654]),
[final] ).
cnf(i_0_14797,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_8655]),
[final] ).
cnf(i_0_14798,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_14799,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_8656,c_0_6135]),c_0_6135]),
[final] ).
cnf(i_0_14800,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_8657]),
[final] ).
cnf(i_0_14801,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_8658]),
[final] ).
cnf(i_0_14802,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
| hAPP(X3,esk344_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_8659]),
[final] ).
cnf(i_0_14803,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_8334]),
[final] ).
cnf(i_0_14804,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_8660]),
[final] ).
cnf(i_0_14805,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_8661]),
[final] ).
cnf(i_0_14806,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_8661]),
[final] ).
cnf(i_0_14807,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_8336]),
[final] ).
cnf(i_0_14808,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_8662]),
[final] ).
cnf(i_0_14809,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_8662]),
[final] ).
cnf(i_0_14810,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_8106]),
[final] ).
cnf(i_0_14811,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_8663]),
[final] ).
cnf(i_0_14812,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_8664]),
[final] ).
cnf(i_0_14813,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_8350]),
[final] ).
cnf(i_0_14814,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_8665,c_0_6670]),
[final] ).
cnf(i_0_14815,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_8666]),
[final] ).
cnf(i_0_14816,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_8667]),
[final] ).
cnf(i_0_14817,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_8591]),
[final] ).
cnf(i_0_14818,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2)))
| ~ hBOOL(hAPP(X1,esk70_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8055]),
[final] ).
cnf(i_0_14819,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_8668]),
[final] ).
cnf(i_0_14820,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_8604]),
[final] ).
cnf(i_0_14821,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_8669]),
[final] ).
cnf(i_0_14822,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_8670]),
[final] ).
cnf(i_0_14823,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk76_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_8671]),
[final] ).
cnf(i_0_14824,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk496_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
| c_List_OtakeWhile(X1,X3,X2) = X2 ),
inference(split_conjunct,[status(thm)],[i_0_8672]),
[final] ).
cnf(i_0_14825,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_8673]),
[final] ).
cnf(i_0_14826,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_8674]),
[final] ).
cnf(i_0_14827,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_8675]),
[final] ).
cnf(i_0_14828,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_8676]),
[final] ).
cnf(i_0_14829,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_8677]),
[final] ).
cnf(i_0_14830,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_8678]),
[final] ).
cnf(i_0_14831,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_8679]),
[final] ).
cnf(i_0_14832,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_8680]),
[final] ).
cnf(i_0_14833,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_8427]),
[final] ).
cnf(i_0_14834,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_8681]),
[final] ).
cnf(i_0_14835,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_8682]),
[final] ).
cnf(i_0_14836,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_8683]),
[final] ).
cnf(i_0_14837,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_8684]),
[final] ).
cnf(i_0_14838,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_8685]),
[final] ).
cnf(i_0_14839,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_8686]),
[final] ).
cnf(i_0_14840,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_8687]),
[final] ).
cnf(i_0_14841,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_8688]),
[final] ).
cnf(i_0_14842,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk72_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_14843,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_8408]),
[final] ).
cnf(i_0_14844,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_8689]),
[final] ).
cnf(i_0_14845,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_8690]),
[final] ).
cnf(i_0_14846,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_8691]),
[final] ).
cnf(i_0_14847,plain,
c_List_OtakeWhile(X1,X2,X3) = hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3),
inference(split_conjunct,[status(thm)],[i_0_8692]),
[final] ).
cnf(i_0_14848,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk235_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_8693]),
[final] ).
cnf(i_0_14849,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_8694]),
[final] ).
cnf(i_0_14850,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_14851,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_8695]),
[final] ).
cnf(i_0_14852,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_8696,c_0_6135]),c_0_6135]),
[final] ).
cnf(i_0_14853,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_8697]),
[final] ).
cnf(i_0_14854,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_8697]),
[final] ).
cnf(i_0_14855,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_8698]),
[final] ).
cnf(i_0_14856,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk482_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_8699]),
[final] ).
cnf(i_0_14857,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_8524]),
[final] ).
cnf(i_0_14858,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_8700]),
[final] ).
cnf(i_0_14859,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_8701]),
[final] ).
cnf(i_0_14860,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_8702]),
[final] ).
cnf(i_0_14861,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_8703]),
[final] ).
cnf(i_0_14862,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_8704]),
[final] ).
cnf(i_0_14863,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_8705]),
[final] ).
cnf(i_0_14864,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_8706]),
[final] ).
cnf(i_0_14865,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_8707]),
[final] ).
cnf(i_0_14866,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_8708]),
[final] ).
cnf(i_0_14867,plain,
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,esk200_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_8566]),
[final] ).
cnf(i_0_14868,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_8112]),
[final] ).
cnf(i_0_14869,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_8709]),
[final] ).
cnf(i_0_14870,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_8710]),
[final] ).
cnf(i_0_14871,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(X1,esk74_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_8628]),
[final] ).
cnf(i_0_14872,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(X1,esk73_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_8629]),
[final] ).
cnf(i_0_14873,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(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_8071]),
[final] ).
cnf(i_0_14874,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk483_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_8711]),
[final] ).
cnf(i_0_14875,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),esk488_3(X3,X2,X1)))
| ~ c_List_Olinorder__class_Osorted(X1,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8480]),
[final] ).
cnf(i_0_14876,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),esk487_3(X3,X2,X1)))
| ~ c_List_Olinorder__class_Osorted(X1,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_8481]),
[final] ).
cnf(i_0_14877,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_8712]),
[final] ).
cnf(i_0_14878,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_14879,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_8713]),
[final] ).
cnf(i_0_14880,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_8714]),
[final] ).
cnf(i_0_14881,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_8715,c_0_6670]),
[final] ).
cnf(i_0_14882,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_8716]),
[final] ).
cnf(i_0_14883,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_8717]),
[final] ).
cnf(i_0_14884,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_8718]),
[final] ).
cnf(i_0_14885,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_8719]),
[final] ).
cnf(i_0_14886,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_8718]),
[final] ).
cnf(i_0_14887,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_8720]),
[final] ).
cnf(i_0_14888,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_8721]),
[final] ).
cnf(i_0_14889,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_8722]),
[final] ).
cnf(i_0_14890,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_8723]),
[final] ).
cnf(i_0_14891,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_8093]),
[final] ).
cnf(i_0_14892,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_8724]),
[final] ).
cnf(i_0_14893,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_8725,c_0_6226]),
[final] ).
cnf(i_0_14894,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_7637]),
[final] ).
cnf(i_0_14895,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_8726]),
[final] ).
cnf(i_0_14896,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_8727]),
[final] ).
cnf(i_0_14897,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_8728]),
[final] ).
cnf(i_0_14898,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_8729]),
[final] ).
cnf(i_0_14899,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_8730]),
[final] ).
cnf(i_0_14900,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_8731]),
[final] ).
cnf(i_0_14901,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_14902,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk232_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_8732]),
[final] ).
cnf(i_0_14903,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_7989]),
[final] ).
cnf(i_0_14904,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_8733]),
[final] ).
cnf(i_0_14905,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_8734]),
[final] ).
cnf(i_0_14906,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_8274]),
[final] ).
cnf(i_0_14907,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),esk338_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_14908,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_8735,c_0_6062]),
[final] ).
cnf(i_0_14909,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_8736,c_0_6062]),
[final] ).
cnf(i_0_14910,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_8737]),
[final] ).
cnf(i_0_14911,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_8738]),
[final] ).
cnf(i_0_14912,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_8739]),
[final] ).
cnf(i_0_14913,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_8740]),
[final] ).
cnf(i_0_14914,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_8741]),
[final] ).
cnf(i_0_14915,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_8742]),
[final] ).
cnf(i_0_14916,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_8743]),
[final] ).
cnf(i_0_14917,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_8744]),
[final] ).
cnf(i_0_14918,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_8745]),
[final] ).
cnf(i_0_14919,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_8746,c_0_6015]),c_0_6015]),c_0_6015]),
[final] ).
cnf(i_0_14920,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_8747,c_0_6015]),c_0_6015]),c_0_6015]),
[final] ).
cnf(i_0_14921,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_8748]),
[final] ).
cnf(i_0_14922,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_8749]),
[final] ).
cnf(i_0_14923,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_8750]),
[final] ).
cnf(i_0_14924,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_8751]),
[final] ).
cnf(i_0_14925,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_8752]),
[final] ).
cnf(i_0_14926,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_8753]),
[final] ).
cnf(i_0_14927,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_8754]),
[final] ).
cnf(i_0_14928,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_8755]),
[final] ).
cnf(i_0_14929,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_8756]),
[final] ).
cnf(i_0_14930,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_8643]),
[final] ).
cnf(i_0_14931,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_8757]),
[final] ).
cnf(i_0_14932,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_8267]),
[final] ).
cnf(i_0_14933,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_8268]),
[final] ).
cnf(i_0_14934,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_8758,c_0_6135]),c_0_6135]),
[final] ).
cnf(i_0_14935,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_8759,c_0_6135]),c_0_6135]),
[final] ).
cnf(i_0_14936,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_8760]),
[final] ).
cnf(i_0_14937,plain,
( hBOOL(hAPP(X1,esk100_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_7587]),
[final] ).
cnf(i_0_14938,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_8761]),
[final] ).
cnf(i_0_14939,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_8324]),
[final] ).
cnf(i_0_14940,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_8762]),
[final] ).
cnf(i_0_14941,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_8763]),
[final] ).
cnf(i_0_14942,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_8764]),
[final] ).
cnf(i_0_14943,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_8765]),
[final] ).
cnf(i_0_14944,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_8766]),
[final] ).
cnf(i_0_14945,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_8767]),
[final] ).
cnf(i_0_14946,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_8767]),
[final] ).
cnf(i_0_14947,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_8768]),
[final] ).
cnf(i_0_14948,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_8769]),
[final] ).
cnf(i_0_14949,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,esk70_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8055]),
[final] ).
cnf(i_0_14950,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_8770,c_0_6226]),
[final] ).
cnf(i_0_14951,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_8728]),
[final] ).
cnf(i_0_14952,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_8771]),
[final] ).
cnf(i_0_14953,plain,
( hBOOL(hAPP(X1,esk199_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_8528]),
[final] ).
cnf(i_0_14954,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_8772]),
[final] ).
cnf(i_0_14955,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_8773]),
[final] ).
cnf(i_0_14956,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_8774]),
[final] ).
cnf(i_0_14957,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_8775]),
[final] ).
cnf(i_0_14958,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_8776]),
[final] ).
cnf(i_0_14959,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_8777]),
[final] ).
cnf(i_0_14960,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_8778]),
[final] ).
cnf(i_0_14961,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_8779]),
[final] ).
cnf(i_0_14962,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_8780]),
[final] ).
cnf(i_0_14963,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_8781]),
[final] ).
cnf(i_0_14964,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_8782]),
[final] ).
cnf(i_0_14965,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_8783]),
[final] ).
cnf(i_0_14966,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_8784]),
[final] ).
cnf(i_0_14967,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_8785]),
[final] ).
cnf(i_0_14968,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_8786]),
[final] ).
cnf(i_0_14969,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_8787]),
[final] ).
cnf(i_0_14970,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_8788]),
[final] ).
cnf(i_0_14971,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_8789]),
[final] ).
cnf(i_0_14972,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_8790]),
[final] ).
cnf(i_0_14973,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_8558]),
[final] ).
cnf(i_0_14974,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_8791]),
[final] ).
cnf(i_0_14975,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_8792]),
[final] ).
cnf(i_0_14976,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_8793]),
[final] ).
cnf(i_0_14977,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_8794]),
[final] ).
cnf(i_0_14978,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_8794]),
[final] ).
cnf(i_0_14979,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_8795]),
[final] ).
cnf(i_0_14980,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_8796]),
[final] ).
cnf(i_0_14981,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_8797]),
[final] ).
cnf(i_0_14982,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_8798]),
[final] ).
cnf(i_0_14983,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_8799]),
[final] ).
cnf(i_0_14984,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_8800]),
[final] ).
cnf(i_0_14985,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_8801]),
[final] ).
cnf(i_0_14986,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_8802]),
[final] ).
cnf(i_0_14987,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_8803]),
[final] ).
cnf(i_0_14988,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_8804]),
[final] ).
cnf(i_0_14989,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_8805]),
[final] ).
cnf(i_0_14990,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_8806,c_0_6015]),
[final] ).
cnf(i_0_14991,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_8643]),
[final] ).
cnf(i_0_14992,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_8807]),
[final] ).
cnf(i_0_14993,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_8724]),
[final] ).
cnf(i_0_14994,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_8626]),
[final] ).
cnf(i_0_14995,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_8808]),
[final] ).
cnf(i_0_14996,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_8809]),
[final] ).
cnf(i_0_14997,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk332_3(X2,X3,X1)),X2))
| hBOOL(hAPP(c_Predicate_OPowp(X1,X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8810]),
[final] ).
cnf(i_0_14998,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_8811]),
[final] ).
cnf(i_0_14999,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_8812]),
[final] ).
cnf(i_0_15000,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk198_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_8528]),
[final] ).
cnf(i_0_15001,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_8813]),
[final] ).
cnf(i_0_15002,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_8814]),
[final] ).
cnf(i_0_15003,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_8815]),
[final] ).
cnf(i_0_15004,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_8816,c_0_6015]),
[final] ).
cnf(i_0_15005,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_8043]),
[final] ).
cnf(i_0_15006,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_8168]),
[final] ).
cnf(i_0_15007,plain,
( hBOOL(hAPP(X1,esk65_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_7527]),
[final] ).
cnf(i_0_15008,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_8817]),
[final] ).
cnf(i_0_15009,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_8818]),
[final] ).
cnf(i_0_15010,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_8819,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_15011,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_8302]),
[final] ).
cnf(i_0_15012,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_8302]),
[final] ).
cnf(i_0_15013,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_8245]),
[final] ).
cnf(i_0_15014,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_8372]),
[final] ).
cnf(i_0_15015,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_7515]),
[final] ).
cnf(i_0_15016,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_7621]),
[final] ).
cnf(i_0_15017,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_8820]),
[final] ).
cnf(i_0_15018,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_8595]),
[final] ).
cnf(i_0_15019,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_7637]),
[final] ).
cnf(i_0_15020,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_8821]),
[final] ).
cnf(i_0_15021,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_15022,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_8112]),
[final] ).
cnf(i_0_15023,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_8822,c_0_6135]),
[final] ).
cnf(i_0_15024,plain,
( X2 = X3
| hAPP(hAPP(c_List_Onth(X1),X2),esk451_3(X1,X3,X2)) != hAPP(hAPP(c_List_Onth(X1),X3),esk451_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_8505]),
[final] ).
cnf(i_0_15025,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_8588]),
[final] ).
cnf(i_0_15026,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_8581]),
[final] ).
cnf(i_0_15027,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_8804]),
[final] ).
cnf(i_0_15028,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_8805]),
[final] ).
cnf(i_0_15029,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_8823]),
[final] ).
cnf(i_0_15030,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_15031,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_8824]),
[final] ).
cnf(i_0_15032,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_8704]),
[final] ).
cnf(i_0_15033,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_8824]),
[final] ).
cnf(i_0_15034,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_8704]),
[final] ).
cnf(i_0_15035,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_8825]),
[final] ).
cnf(i_0_15036,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_8707]),
[final] ).
cnf(i_0_15037,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_8825]),
[final] ).
cnf(i_0_15038,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_8707]),
[final] ).
cnf(i_0_15039,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_8708]),
[final] ).
cnf(i_0_15040,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_8708]),
[final] ).
cnf(i_0_15041,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,esk503_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7552]),
[final] ).
cnf(i_0_15042,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_8826]),
[final] ).
cnf(i_0_15043,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_8827]),
[final] ).
cnf(i_0_15044,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_8828]),
[final] ).
cnf(i_0_15045,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_8829]),
[final] ).
cnf(i_0_15046,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_8830]),
[final] ).
cnf(i_0_15047,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_8831]),
[final] ).
cnf(i_0_15048,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_8832]),
[final] ).
cnf(i_0_15049,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_8833]),
[final] ).
cnf(i_0_15050,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_8834]),
[final] ).
cnf(i_0_15051,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_8631]),
[final] ).
cnf(i_0_15052,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_8835]),
[final] ).
cnf(i_0_15053,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_8318]),
[final] ).
cnf(i_0_15054,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_8836]),
[final] ).
cnf(i_0_15055,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_8837]),
[final] ).
cnf(i_0_15056,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_8838]),
[final] ).
cnf(i_0_15057,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_8217]),
[final] ).
cnf(i_0_15058,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_8839]),
[final] ).
cnf(i_0_15059,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_8840]),
[final] ).
cnf(i_0_15060,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_8841]),
[final] ).
cnf(i_0_15061,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_8842]),
[final] ).
cnf(i_0_15062,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,esk67_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8071]),
[final] ).
cnf(i_0_15063,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk201_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_8566]),
[final] ).
cnf(i_0_15064,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,esk501_3(X1,X3,X2)))
| ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_7552]),
[final] ).
cnf(i_0_15065,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_8843,c_0_6015]),
[final] ).
cnf(i_0_15066,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_8844,c_0_6015]),
[final] ).
cnf(i_0_15067,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_8845,c_0_6015]),
[final] ).
cnf(i_0_15068,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_8846,c_0_6015]),
[final] ).
cnf(i_0_15069,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_8847,c_0_6015]),
[final] ).
cnf(i_0_15070,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_8848]),
[final] ).
cnf(i_0_15071,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_8849,c_0_8850]),c_0_8850]),
[final] ).
cnf(i_0_15072,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_8851,c_0_6062]),
[final] ).
cnf(i_0_15073,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_8259]),
[final] ).
cnf(i_0_15074,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,esk500_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7562]),
[final] ).
cnf(i_0_15075,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_8852]),
[final] ).
cnf(i_0_15076,plain,
( hBOOL(hAPP(hAPP(X1,esk86_3(X2,X1,X3)),X2))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X3,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8853]),
[final] ).
cnf(i_0_15077,plain,
( hBOOL(hAPP(hAPP(X1,esk85_3(X2,X1,X3)),X2))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X3,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8854]),
[final] ).
cnf(i_0_15078,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_8855,c_0_6053]),
[final] ).
cnf(i_0_15079,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_8856]),
[final] ).
cnf(i_0_15080,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_8857,c_0_6169]),
[final] ).
cnf(i_0_15081,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_8858]),
[final] ).
cnf(i_0_15082,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_8859]),
[final] ).
cnf(i_0_15083,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_8860]),
[final] ).
cnf(i_0_15084,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_8861]),
[final] ).
cnf(i_0_15085,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_8862]),
[final] ).
cnf(i_0_15086,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_8863,c_0_6226]),
[final] ).
cnf(i_0_15087,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_8864,c_0_6226]),
[final] ).
cnf(i_0_15088,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_8865]),
[final] ).
cnf(i_0_15089,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_8866]),
[final] ).
cnf(i_0_15090,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk371_3(X2,X3,X1)),X3))
| c_Relation_Ototal__on(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_6756]),
[final] ).
cnf(i_0_15091,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_15092,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)
| esk492_2(X1,X2) != c_List_Olist_ONil(X2) ),
inference(rw,[status(thm)],[i_0_8867,c_0_6100]),
[final] ).
cnf(i_0_15093,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)
| esk493_2(X1,X2) != c_List_Olist_ONil(X2) ),
inference(rw,[status(thm)],[i_0_8868,c_0_6100]),
[final] ).
cnf(i_0_15094,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_8869]),
[final] ).
cnf(i_0_15095,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_8870]),
[final] ).
cnf(i_0_15096,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_8871]),
[final] ).
cnf(i_0_15097,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_8872]),
[final] ).
cnf(i_0_15098,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,esk498_3(X1,X3,X2)))
| ~ hBOOL(hAPP(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_7562]),
[final] ).
cnf(i_0_15099,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_8873]),
[final] ).
cnf(i_0_15100,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_8874]),
[final] ).
cnf(i_0_15101,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_8875]),
[final] ).
cnf(i_0_15102,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_8876]),
[final] ).
cnf(i_0_15103,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_8877]),
[final] ).
cnf(i_0_15104,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_8878]),
[final] ).
cnf(i_0_15105,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_8480]),
[final] ).
cnf(i_0_15106,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_8481]),
[final] ).
cnf(i_0_15107,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_8879]),
[final] ).
cnf(i_0_15108,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_15109,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_8880]),
[final] ).
cnf(i_0_15110,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_8881,c_0_6062]),
[final] ).
cnf(i_0_15111,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_8882]),
[final] ).
cnf(i_0_15112,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_8883,c_0_6062]),
[final] ).
cnf(i_0_15113,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),esk402_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_8401]),
[final] ).
cnf(i_0_15114,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_8884]),
[final] ).
cnf(i_0_15115,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_8885]),
[final] ).
cnf(i_0_15116,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_8886]),
[final] ).
cnf(i_0_15117,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_8886]),
[final] ).
cnf(i_0_15118,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_8106]),
[final] ).
cnf(i_0_15119,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_8741]),
[final] ).
cnf(i_0_15120,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_8887]),
[final] ).
cnf(i_0_15121,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_8245]),
[final] ).
cnf(i_0_15122,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_8888]),
[final] ).
cnf(i_0_15123,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_8889]),
[final] ).
cnf(i_0_15124,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_8890]),
[final] ).
cnf(i_0_15125,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_8891]),
[final] ).
cnf(i_0_15126,plain,
( hBOOL(hAPP(X1,esk65_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_7527]),
[final] ).
cnf(i_0_15127,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_8892,c_0_6100]),
[final] ).
cnf(i_0_15128,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_8893]),
[final] ).
cnf(i_0_15129,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_8894]),
[final] ).
cnf(i_0_15130,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_8895]),
[final] ).
cnf(i_0_15131,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_8896]),
[final] ).
cnf(i_0_15132,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_8897]),
[final] ).
cnf(i_0_15133,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_8898]),
[final] ).
cnf(i_0_15134,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_8899]),
[final] ).
cnf(i_0_15135,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_8900]),
[final] ).
cnf(i_0_15136,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_8632]),
[final] ).
cnf(i_0_15137,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_8901]),
[final] ).
cnf(i_0_15138,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_8902]),
[final] ).
cnf(i_0_15139,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_8903]),
[final] ).
cnf(i_0_15140,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_8326]),
[final] ).
cnf(i_0_15141,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_8904]),
[final] ).
cnf(i_0_15142,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_8905]),
[final] ).
cnf(i_0_15143,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_8906]),
[final] ).
cnf(i_0_15144,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_8907]),
[final] ).
cnf(i_0_15145,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_8908]),
[final] ).
cnf(i_0_15146,plain,
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,esk232_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_8732]),
[final] ).
cnf(i_0_15147,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_8909]),
[final] ).
cnf(i_0_15148,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_8910]),
[final] ).
cnf(i_0_15149,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_8911]),
[final] ).
cnf(i_0_15150,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_8912]),
[final] ).
cnf(i_0_15151,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_8913]),
[final] ).
cnf(i_0_15152,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_8914]),
[final] ).
cnf(i_0_15153,plain,
( hBOOL(hAPP(hAPP(X3,esk324_2(X4,X3)),X4))
| ~ hBOOL(hAPP(c_Predicate_ORangeP(X1,X2,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_8915]),
[final] ).
cnf(i_0_15154,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_8916]),
[final] ).
cnf(i_0_15155,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_8369]),
[final] ).
cnf(i_0_15156,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_8917]),
[final] ).
cnf(i_0_15157,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_8918]),
[final] ).
cnf(i_0_15158,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_8919]),
[final] ).
cnf(i_0_15159,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_8920]),
[final] ).
cnf(i_0_15160,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_8921,c_0_6135]),
[final] ).
cnf(i_0_15161,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_8922]),
[final] ).
cnf(i_0_15162,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_8923]),
[final] ).
cnf(i_0_15163,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_7541]),
[final] ).
cnf(i_0_15164,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_8924]),
[final] ).
cnf(i_0_15165,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_8925]),
[final] ).
cnf(i_0_15166,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk234_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_8693]),
[final] ).
cnf(i_0_15167,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_8652]),
[final] ).
cnf(i_0_15168,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_8926]),
[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))
| 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_8927]),
[final] ).
cnf(i_0_15170,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_8275]),
[final] ).
cnf(i_0_15171,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_8928]),
[final] ).
cnf(i_0_15172,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_8929]),
[final] ).
cnf(i_0_15173,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_8930]),
[final] ).
cnf(i_0_15174,plain,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
inference(split_conjunct,[status(thm)],[i_0_8931]),
[final] ).
cnf(i_0_15175,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[i_0_8932]),
[final] ).
cnf(i_0_15176,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_8933]),
[final] ).
cnf(i_0_15177,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_8934]),
[final] ).
cnf(i_0_15178,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_8793]),
[final] ).
cnf(i_0_15179,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_8793]),
[final] ).
cnf(i_0_15180,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_8935]),
[final] ).
cnf(i_0_15181,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_8936]),
[final] ).
cnf(i_0_15182,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_15183,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_15184,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_15185,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_8937]),
[final] ).
cnf(i_0_15186,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_8938]),
[final] ).
cnf(i_0_15187,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_8939]),
[final] ).
cnf(i_0_15188,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_8940]),
[final] ).
cnf(i_0_15189,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_15190,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_8941]),
[final] ).
cnf(i_0_15191,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_8942]),
[final] ).
cnf(i_0_15192,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_8943]),
[final] ).
cnf(i_0_15193,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_8944]),
[final] ).
cnf(i_0_15194,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_8945]),
[final] ).
cnf(i_0_15195,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_8946]),
[final] ).
cnf(i_0_15196,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_8947]),
[final] ).
cnf(i_0_15197,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_8948]),
[final] ).
cnf(i_0_15198,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_8949]),
[final] ).
cnf(i_0_15199,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_8950]),
[final] ).
cnf(i_0_15200,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,esk503_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7552]),
[final] ).
cnf(i_0_15201,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,esk500_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_7562]),
[final] ).
cnf(i_0_15202,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_8293]),
[final] ).
cnf(i_0_15203,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_8951]),
[final] ).
cnf(i_0_15204,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_8952]),
[final] ).
cnf(i_0_15205,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_8673]),
[final] ).
cnf(i_0_15206,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_8953]),
[final] ).
cnf(i_0_15207,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_8674]),
[final] ).
cnf(i_0_15208,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_8954]),
[final] ).
cnf(i_0_15209,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_8767]),
[final] ).
cnf(i_0_15210,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_8767]),
[final] ).
cnf(i_0_15211,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_8768]),
[final] ).
cnf(i_0_15212,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_8769]),
[final] ).
cnf(i_0_15213,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_8955]),
[final] ).
cnf(i_0_15214,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_8956]),
[final] ).
cnf(i_0_15215,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_8957]),
[final] ).
cnf(i_0_15216,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk86_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8853]),
[final] ).
cnf(i_0_15217,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk85_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_8854]),
[final] ).
cnf(i_0_15218,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_8293]),
[final] ).
cnf(i_0_15219,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_8958,c_0_6053]),c_0_6053]),
[final] ).
cnf(i_0_15220,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_8959]),
[final] ).
cnf(i_0_15221,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_8960]),
[final] ).
cnf(i_0_15222,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),esk408_2(X2,X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8412]),
[final] ).
cnf(i_0_15223,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_8961]),
[final] ).
cnf(i_0_15224,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk233_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_8732]),
[final] ).
cnf(i_0_15225,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_8962]),
[final] ).
cnf(i_0_15226,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_8963]),
[final] ).
cnf(i_0_15227,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_8964]),
[final] ).
cnf(i_0_15228,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_8965]),
[final] ).
cnf(i_0_15229,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_8966]),
[final] ).
cnf(i_0_15230,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_8967]),
[final] ).
cnf(i_0_15231,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_8632]),
[final] ).
cnf(i_0_15232,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_8968]),
[final] ).
cnf(i_0_15233,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_8969]),
[final] ).
cnf(i_0_15234,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_8970]),
[final] ).
cnf(i_0_15235,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_8971]),
[final] ).
cnf(i_0_15236,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_8972]),
[final] ).
cnf(i_0_15237,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_8973]),
[final] ).
cnf(i_0_15238,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_8974]),
[final] ).
cnf(i_0_15239,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_8975]),
[final] ).
cnf(i_0_15240,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_8976]),
[final] ).
cnf(i_0_15241,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_8402]),
[final] ).
cnf(i_0_15242,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_8977]),
[final] ).
cnf(i_0_15243,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_8978]),
[final] ).
cnf(i_0_15244,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_8979]),
[final] ).
cnf(i_0_15245,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_8980]),
[final] ).
cnf(i_0_15246,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_8981]),
[final] ).
cnf(i_0_15247,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,esk501_3(X1,X3,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7552]),
[final] ).
cnf(i_0_15248,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,esk498_3(X1,X3,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_7562]),
[final] ).
cnf(i_0_15249,plain,
( hBOOL(hAPP(X1,esk235_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_8693]),
[final] ).
cnf(i_0_15250,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_8982]),
[final] ).
cnf(i_0_15251,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_8983]),
[final] ).
cnf(i_0_15252,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_8984,c_0_6015]),c_0_6015]),
[final] ).
cnf(i_0_15253,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_8985]),
[final] ).
cnf(i_0_15254,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_8986]),
[final] ).
cnf(i_0_15255,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_8987]),
[final] ).
cnf(i_0_15256,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_8988]),
[final] ).
cnf(i_0_15257,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_8348]),
[final] ).
cnf(i_0_15258,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)
| esk470_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_8045]),
[final] ).
cnf(i_0_15259,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_8989]),
[final] ).
cnf(i_0_15260,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_8989]),
[final] ).
cnf(i_0_15261,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_8990]),
[final] ).
cnf(i_0_15262,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_8991]),
[final] ).
cnf(i_0_15263,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_15264,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_15265,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_7253]),
[final] ).
cnf(i_0_15266,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_7254]),
[final] ).
cnf(i_0_15267,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_7781]),
[final] ).
cnf(i_0_15268,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_15269,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_8992]),
[final] ).
cnf(i_0_15270,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_8992]),
[final] ).
cnf(i_0_15271,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_8916]),
[final] ).
cnf(i_0_15272,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_8993]),
[final] ).
cnf(i_0_15273,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_8994]),
[final] ).
cnf(i_0_15274,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_8995]),
[final] ).
cnf(i_0_15275,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_8996]),
[final] ).
cnf(i_0_15276,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_8997]),
[final] ).
cnf(i_0_15277,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_8554]),
[final] ).
cnf(i_0_15278,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_8555]),
[final] ).
cnf(i_0_15279,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_8998]),
[final] ).
cnf(i_0_15280,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_8999]),
[final] ).
cnf(i_0_15281,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_9000]),
[final] ).
cnf(i_0_15282,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_9001]),
[final] ).
cnf(i_0_15283,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_9002]),
[final] ).
cnf(i_0_15284,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_9003]),
[final] ).
cnf(i_0_15285,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_9004]),
[final] ).
cnf(i_0_15286,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_9005]),
[final] ).
cnf(i_0_15287,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_9006]),
[final] ).
cnf(i_0_15288,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_9007]),
[final] ).
cnf(i_0_15289,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_9008]),
[final] ).
cnf(i_0_15290,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)),esk502_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_7552]),
[final] ).
cnf(i_0_15291,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_9009]),
[final] ).
cnf(i_0_15292,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_9010]),
[final] ).
cnf(i_0_15293,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_9011]),
[final] ).
cnf(i_0_15294,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_9012]),
[final] ).
cnf(i_0_15295,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_8798]),
[final] ).
cnf(i_0_15296,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_9013]),
[final] ).
cnf(i_0_15297,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_9014]),
[final] ).
cnf(i_0_15298,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_9015]),
[final] ).
cnf(i_0_15299,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_9016]),
[final] ).
cnf(i_0_15300,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_9017]),
[final] ).
cnf(i_0_15301,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_9018]),
[final] ).
cnf(i_0_15302,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_8604]),
[final] ).
cnf(i_0_15303,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_9019]),
[final] ).
cnf(i_0_15304,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_9020]),
[final] ).
cnf(i_0_15305,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_9021]),
[final] ).
cnf(i_0_15306,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_9022]),
[final] ).
cnf(i_0_15307,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_9023]),
[final] ).
cnf(i_0_15308,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk504_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_7552]),
[final] ).
cnf(i_0_15309,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_9024]),
[final] ).
cnf(i_0_15310,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_9025]),
[final] ).
cnf(i_0_15311,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_9026]),
[final] ).
cnf(i_0_15312,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_15313,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_15314,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_9027]),
[final] ).
cnf(i_0_15315,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_9027]),
[final] ).
cnf(i_0_15316,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_9028]),
[final] ).
cnf(i_0_15317,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_9029]),
[final] ).
cnf(i_0_15318,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_9030]),
[final] ).
cnf(i_0_15319,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)),esk498_3(X1,X2,X3)))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_7562]),
[final] ).
cnf(i_0_15320,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_8378]),
[final] ).
cnf(i_0_15321,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_9031]),
[final] ).
cnf(i_0_15322,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_9032]),
[final] ).
cnf(i_0_15323,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_9033]),
[final] ).
cnf(i_0_15324,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_9034]),
[final] ).
cnf(i_0_15325,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_9035]),
[final] ).
cnf(i_0_15326,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_9036]),
[final] ).
cnf(i_0_15327,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_9037]),
[final] ).
cnf(i_0_15328,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_9038]),
[final] ).
cnf(i_0_15329,plain,
( c_Natural_Oevaln(X1,X2,esk13_3(X3,X2,X1),X3)
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9039]),
[final] ).
cnf(i_0_15330,plain,
( c_Natural_Oevaln(X1,X2,esk10_3(X3,X2,X1),X3)
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9040]),
[final] ).
cnf(i_0_15331,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_8373]),
[final] ).
cnf(i_0_15332,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_8975]),
[final] ).
cnf(i_0_15333,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_9041]),
[final] ).
cnf(i_0_15334,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_9042]),
[final] ).
cnf(i_0_15335,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_9043]),
[final] ).
cnf(i_0_15336,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_9044]),
[final] ).
cnf(i_0_15337,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_9045]),
[final] ).
cnf(i_0_15338,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_8334]),
[final] ).
cnf(i_0_15339,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_9046]),
[final] ).
cnf(i_0_15340,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_8336]),
[final] ).
cnf(i_0_15341,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_9047]),
[final] ).
cnf(i_0_15342,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_9048]),
[final] ).
cnf(i_0_15343,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_9049]),
[final] ).
cnf(i_0_15344,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_9050]),
[final] ).
cnf(i_0_15345,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_9051]),
[final] ).
cnf(i_0_15346,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_9052]),
[final] ).
cnf(i_0_15347,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_9053]),
[final] ).
cnf(i_0_15348,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_9054]),
[final] ).
cnf(i_0_15349,plain,
hAPP(c_Fun_Ocomp(X1,X1,X2,c_Fun_Oid(X1)),X3) = X3,
inference(split_conjunct,[status(thm)],[i_0_9055]),
[final] ).
cnf(i_0_15350,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_9056]),
[final] ).
cnf(i_0_15351,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_9057]),
[final] ).
cnf(i_0_15352,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_9058]),
[final] ).
cnf(i_0_15353,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_9059]),
[final] ).
cnf(i_0_15354,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk500_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_7562]),
[final] ).
cnf(i_0_15355,plain,
( hBOOL(hAPP(hAPP(X3,X4),esk328_2(X4,X3)))
| ~ hBOOL(hAPP(c_Predicate_ODomainP(X1,X2,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_9060]),
[final] ).
cnf(i_0_15356,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_9061]),
[final] ).
cnf(i_0_15357,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_9062]),
[final] ).
cnf(i_0_15358,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_8831]),
[final] ).
cnf(i_0_15359,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_7616]),
[final] ).
cnf(i_0_15360,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_7569]),
[final] ).
cnf(i_0_15361,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_9063]),
[final] ).
cnf(i_0_15362,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_8628]),
[final] ).
cnf(i_0_15363,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_8629]),
[final] ).
cnf(i_0_15364,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_9064]),
[final] ).
cnf(i_0_15365,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_9065]),
[final] ).
cnf(i_0_15366,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_9066,c_0_6169]),
[final] ).
cnf(i_0_15367,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk59_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_9067]),
[final] ).
cnf(i_0_15368,plain,
hAPP(c_List_Ofoldl(X1,X2,X3,X4),c_List_Olist_ONil(X2)) = X4,
inference(split_conjunct,[status(thm)],[i_0_9068]),
[final] ).
cnf(i_0_15369,plain,
hAPP(c_List_Olist_Olist__case(X1,X2,X3,X4),c_List_Olist_ONil(X2)) = X3,
inference(split_conjunct,[status(thm)],[i_0_9069]),
[final] ).
cnf(i_0_15370,plain,
hAPP(c_Fun_Ocomp(X1,X2,X1,X3),c_Fun_Oid(X1)) = X3,
inference(split_conjunct,[status(thm)],[i_0_9070]),
[final] ).
cnf(i_0_15371,plain,
hAPP(c_Option_Ooption_Ooption__case(X1,X2,X3,X4),c_Option_Ooption_ONone(X2)) = X3,
inference(split_conjunct,[status(thm)],[i_0_9071]),
[final] ).
cnf(i_0_15372,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_9072]),
[final] ).
cnf(i_0_15373,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_9072]),
[final] ).
cnf(i_0_15374,negated_conjecture,
~ c_Hoare__Mirabelle_Otriple__valid(t_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),
inference(split_conjunct,[status(thm)],[i_0_9073]),
[final] ).
cnf(i_0_15375,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_9074,c_0_6135]),
[final] ).
cnf(i_0_15376,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_9075]),
[final] ).
cnf(i_0_15377,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_9076]),
[final] ).
cnf(i_0_15378,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_9077]),
[final] ).
cnf(i_0_15379,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_8729]),
[final] ).
cnf(i_0_15380,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_9078]),
[final] ).
cnf(i_0_15381,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_8730]),
[final] ).
cnf(i_0_15382,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_9079]),
[final] ).
cnf(i_0_15383,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_8731]),
[final] ).
cnf(i_0_15384,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_9080,c_0_6015]),
[final] ).
cnf(i_0_15385,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_9081,c_0_6015]),
[final] ).
cnf(i_0_15386,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_9082,c_0_6015]),
[final] ).
cnf(i_0_15387,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_9083,c_0_6015]),
[final] ).
cnf(i_0_15388,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_9084]),
[final] ).
cnf(i_0_15389,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_9085]),
[final] ).
cnf(i_0_15390,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_9086]),
[final] ).
cnf(i_0_15391,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_8401]),
[final] ).
cnf(i_0_15392,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_9087]),
[final] ).
cnf(i_0_15393,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_9088]),
[final] ).
cnf(i_0_15394,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_9089]),
[final] ).
cnf(i_0_15395,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),esk104_2(X1,X2)),esk105_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_7911]),
[final] ).
cnf(i_0_15396,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk192_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_15397,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_9090]),
[final] ).
cnf(i_0_15398,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_15399,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_9091]),
[final] ).
cnf(i_0_15400,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_9092]),
[final] ).
cnf(i_0_15401,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_9093]),
[final] ).
cnf(i_0_15402,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_9094]),
[final] ).
cnf(i_0_15403,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_9095]),
[final] ).
cnf(i_0_15404,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_8583]),
[final] ).
cnf(i_0_15405,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_8738]),
[final] ).
cnf(i_0_15406,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_8739]),
[final] ).
cnf(i_0_15407,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_9096]),
[final] ).
cnf(i_0_15408,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_9097]),
[final] ).
cnf(i_0_15409,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_9098]),
[final] ).
cnf(i_0_15410,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_9099]),
[final] ).
cnf(i_0_15411,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_9100]),
[final] ).
cnf(i_0_15412,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_8654]),
[final] ).
cnf(i_0_15413,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_9101]),
[final] ).
cnf(i_0_15414,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_8111]),
[final] ).
cnf(i_0_15415,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_8111]),
[final] ).
cnf(i_0_15416,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_9102]),
[final] ).
cnf(i_0_15417,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_9103]),
[final] ).
cnf(i_0_15418,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_8504]),
[final] ).
cnf(i_0_15419,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X4))
| ~ c_Natural_Oevaln(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_9040]),
[final] ).
cnf(i_0_15420,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X4))
| ~ c_Natural_Oevaln(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_9104]),
[final] ).
cnf(i_0_15421,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_15422,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_9105]),
[final] ).
cnf(i_0_15423,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_9106]),
[final] ).
cnf(i_0_15424,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_9107]),
[final] ).
cnf(i_0_15425,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_9108]),
[final] ).
cnf(i_0_15426,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_9109]),
[final] ).
cnf(i_0_15427,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_9110]),
[final] ).
cnf(i_0_15428,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_9111]),
[final] ).
cnf(i_0_15429,plain,
( hBOOL(hAPP(X1,esk192_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_15430,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_9112]),
[final] ).
cnf(i_0_15431,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_9072]),
[final] ).
cnf(i_0_15432,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_9113,c_0_6670]),
[final] ).
cnf(i_0_15433,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_9114]),
[final] ).
cnf(i_0_15434,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_9115,c_0_6670]),
[final] ).
cnf(i_0_15435,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_9116]),
[final] ).
cnf(i_0_15436,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_8752]),
[final] ).
cnf(i_0_15437,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_8753]),
[final] ).
cnf(i_0_15438,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_9117]),
[final] ).
cnf(i_0_15439,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_8754]),
[final] ).
cnf(i_0_15440,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_8756]),
[final] ).
cnf(i_0_15441,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_9118]),
[final] ).
cnf(i_0_15442,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_9119]),
[final] ).
cnf(i_0_15443,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_9120]),
[final] ).
cnf(i_0_15444,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_9121]),
[final] ).
cnf(i_0_15445,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_8532]),
[final] ).
cnf(i_0_15446,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_9122]),
[final] ).
cnf(i_0_15447,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),esk439_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_15448,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_9123]),
[final] ).
cnf(i_0_15449,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_9124]),
[final] ).
cnf(i_0_15450,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_9125]),
[final] ).
cnf(i_0_15451,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_9126]),
[final] ).
cnf(i_0_15452,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_9127]),
[final] ).
cnf(i_0_15453,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_8990]),
[final] ).
cnf(i_0_15454,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_8991]),
[final] ).
cnf(i_0_15455,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_9128]),
[final] ).
cnf(i_0_15456,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_9129]),
[final] ).
cnf(i_0_15457,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_9130]),
[final] ).
cnf(i_0_15458,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_9131]),
[final] ).
cnf(i_0_15459,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_9132]),
[final] ).
cnf(i_0_15460,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_9133]),
[final] ).
cnf(i_0_15461,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_8585]),
[final] ).
cnf(i_0_15462,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_9134]),
[final] ).
cnf(i_0_15463,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_8585]),
[final] ).
cnf(i_0_15464,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_9135]),
[final] ).
cnf(i_0_15465,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_9136]),
[final] ).
cnf(i_0_15466,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_9137]),
[final] ).
cnf(i_0_15467,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_8586]),
[final] ).
cnf(i_0_15468,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_9138]),
[final] ).
cnf(i_0_15469,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_8586]),
[final] ).
cnf(i_0_15470,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_9139,c_0_6015]),
[final] ).
cnf(i_0_15471,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_8919]),
[final] ).
cnf(i_0_15472,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_9140]),
[final] ).
cnf(i_0_15473,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_8924]),
[final] ).
cnf(i_0_15474,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_8925]),
[final] ).
cnf(i_0_15475,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_9141]),
[final] ).
cnf(i_0_15476,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_9142]),
[final] ).
cnf(i_0_15477,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_9143]),
[final] ).
cnf(i_0_15478,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_9144]),
[final] ).
cnf(i_0_15479,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_9145]),
[final] ).
cnf(i_0_15480,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_8648]),
[final] ).
cnf(i_0_15481,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_9146]),
[final] ).
cnf(i_0_15482,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_9147]),
[final] ).
cnf(i_0_15483,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)),esk502_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_7552]),
[final] ).
cnf(i_0_15484,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)),esk498_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_7562]),
[final] ).
cnf(i_0_15485,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_9148]),
[final] ).
cnf(i_0_15486,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_9149]),
[final] ).
cnf(i_0_15487,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_9150]),
[final] ).
cnf(i_0_15488,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_8841]),
[final] ).
cnf(i_0_15489,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_9151]),
[final] ).
cnf(i_0_15490,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_9152]),
[final] ).
cnf(i_0_15491,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_9153]),
[final] ).
cnf(i_0_15492,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_9153]),
[final] ).
cnf(i_0_15493,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_9154]),
[final] ).
cnf(i_0_15494,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_9154]),
[final] ).
cnf(i_0_15495,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_9155]),
[final] ).
cnf(i_0_15496,plain,
( hBOOL(hAPP(X1,esk77_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_15497,plain,
( c_Hoare__Mirabelle_Ohoare__valids(X1,X3,X2)
| ~ c_Hoare__Mirabelle_Otriple__valid(X1,esk337_3(X2,X3,X1),esk338_3(X2,X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_7194]),
[final] ).
cnf(i_0_15498,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_9156]),
[final] ).
cnf(i_0_15499,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_9157]),
[final] ).
cnf(i_0_15500,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_9158]),
[final] ).
cnf(i_0_15501,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_9159,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_15502,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_9160,c_0_9161]),
[final] ).
cnf(i_0_15503,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_9162]),
[final] ).
cnf(i_0_15504,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_9163]),
[final] ).
cnf(i_0_15505,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_8912]),
[final] ).
cnf(i_0_15506,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_8261]),
[final] ).
cnf(i_0_15507,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_9164]),
[final] ).
cnf(i_0_15508,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_9165]),
[final] ).
cnf(i_0_15509,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk504_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_7552]),
[final] ).
cnf(i_0_15510,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk500_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_7562]),
[final] ).
cnf(i_0_15511,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_8525]),
[final] ).
cnf(i_0_15512,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_9166]),
[final] ).
cnf(i_0_15513,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_8959]),
[final] ).
cnf(i_0_15514,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_8960]),
[final] ).
cnf(i_0_15515,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_9167]),
[final] ).
cnf(i_0_15516,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_8955]),
[final] ).
cnf(i_0_15517,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_9168]),
[final] ).
cnf(i_0_15518,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_9168]),
[final] ).
cnf(i_0_15519,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_9169]),
[final] ).
cnf(i_0_15520,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_9170]),
[final] ).
cnf(i_0_15521,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_9171]),
[final] ).
cnf(i_0_15522,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_9172,c_0_6169]),
[final] ).
cnf(i_0_15523,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_9173]),
[final] ).
cnf(i_0_15524,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_9174]),
[final] ).
cnf(i_0_15525,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_9175]),
[final] ).
cnf(i_0_15526,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_9176]),
[final] ).
cnf(i_0_15527,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_9177]),
[final] ).
cnf(i_0_15528,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_9178]),
[final] ).
cnf(i_0_15529,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_9179]),
[final] ).
cnf(i_0_15530,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_9180]),
[final] ).
cnf(i_0_15531,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_9181]),
[final] ).
cnf(i_0_15532,plain,
( esk246_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_15533,plain,
( hBOOL(hAPP(c_Predicate_OPowp(X3,X1),X2))
| ~ hBOOL(hAPP(X1,esk332_3(X2,X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8810]),
[final] ).
cnf(i_0_15534,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_15535,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_9182]),
[final] ).
cnf(i_0_15536,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_9183]),
[final] ).
cnf(i_0_15537,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_9184]),
[final] ).
cnf(i_0_15538,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_9185]),
[final] ).
cnf(i_0_15539,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_9186,c_0_6135]),c_0_6135]),
[final] ).
cnf(i_0_15540,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_9187]),
[final] ).
cnf(i_0_15541,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_9188]),
[final] ).
cnf(i_0_15542,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_15543,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_15544,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_9189]),
[final] ).
cnf(i_0_15545,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_8869]),
[final] ).
cnf(i_0_15546,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_8870]),
[final] ).
cnf(i_0_15547,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_9190]),
[final] ).
cnf(i_0_15548,plain,
( c_Hoare__Mirabelle_Otriple__valid(X1,esk337_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_15549,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_9191]),
[final] ).
cnf(i_0_15550,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_9192]),
[final] ).
cnf(i_0_15551,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_9193]),
[final] ).
cnf(i_0_15552,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_9194]),
[final] ).
cnf(i_0_15553,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_9195]),
[final] ).
cnf(i_0_15554,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_9196]),
[final] ).
cnf(i_0_15555,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_9197]),
[final] ).
cnf(i_0_15556,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_8663]),
[final] ).
cnf(i_0_15557,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_9198]),
[final] ).
cnf(i_0_15558,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_9199]),
[final] ).
cnf(i_0_15559,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_9200]),
[final] ).
cnf(i_0_15560,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk74_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_8628]),
[final] ).
cnf(i_0_15561,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk73_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_8629]),
[final] ).
cnf(i_0_15562,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_8515]),
[final] ).
cnf(i_0_15563,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_9201]),
[final] ).
cnf(i_0_15564,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_9202]),
[final] ).
cnf(i_0_15565,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_9203]),
[final] ).
cnf(i_0_15566,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_9204]),
[final] ).
cnf(i_0_15567,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_8955]),
[final] ).
cnf(i_0_15568,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_9205]),
[final] ).
cnf(i_0_15569,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_9206]),
[final] ).
cnf(i_0_15570,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_9207]),
[final] ).
cnf(i_0_15571,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),esk84_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_7794]),
[final] ).
cnf(i_0_15572,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),esk72_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_15573,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_9208]),
[final] ).
cnf(i_0_15574,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_9209]),
[final] ).
cnf(i_0_15575,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_9210]),
[final] ).
cnf(i_0_15576,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_9211]),
[final] ).
cnf(i_0_15577,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_8927]),
[final] ).
cnf(i_0_15578,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_8675]),
[final] ).
cnf(i_0_15579,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_8675]),
[final] ).
cnf(i_0_15580,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_9212]),
[final] ).
cnf(i_0_15581,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_9213]),
[final] ).
cnf(i_0_15582,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_9214]),
[final] ).
cnf(i_0_15583,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_9215]),
[final] ).
cnf(i_0_15584,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_9216]),
[final] ).
cnf(i_0_15585,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_9217]),
[final] ).
cnf(i_0_15586,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_9218]),
[final] ).
cnf(i_0_15587,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_9219]),
[final] ).
cnf(i_0_15588,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_9220]),
[final] ).
cnf(i_0_15589,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_9221]),
[final] ).
cnf(i_0_15590,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_9222]),
[final] ).
cnf(i_0_15591,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_9223]),
[final] ).
cnf(i_0_15592,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_9224]),
[final] ).
cnf(i_0_15593,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_9225]),
[final] ).
cnf(i_0_15594,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_9116]),
[final] ).
cnf(i_0_15595,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_8874]),
[final] ).
cnf(i_0_15596,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_8875]),
[final] ).
cnf(i_0_15597,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_8876]),
[final] ).
cnf(i_0_15598,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_8877]),
[final] ).
cnf(i_0_15599,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_9226]),
[final] ).
cnf(i_0_15600,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_9227]),
[final] ).
cnf(i_0_15601,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_9228]),
[final] ).
cnf(i_0_15602,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_9229]),
[final] ).
cnf(i_0_15603,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_9230]),
[final] ).
cnf(i_0_15604,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_9231]),
[final] ).
cnf(i_0_15605,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_9232]),
[final] ).
cnf(i_0_15606,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_9233]),
[final] ).
cnf(i_0_15607,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_9234]),
[final] ).
cnf(i_0_15608,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_9235]),
[final] ).
cnf(i_0_15609,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_9236]),
[final] ).
cnf(i_0_15610,plain,
( hAPP(hAPP(c_List_Onth(X1),X2),esk454_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_8168]),
[final] ).
cnf(i_0_15611,plain,
( esk248_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_15612,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_9237]),
[final] ).
cnf(i_0_15613,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_9237]),
[final] ).
cnf(i_0_15614,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_9238]),
[final] ).
cnf(i_0_15615,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_9238]),
[final] ).
cnf(i_0_15616,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_9239]),
[final] ).
cnf(i_0_15617,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_9240]),
[final] ).
cnf(i_0_15618,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_9241]),
[final] ).
cnf(i_0_15619,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_9242,c_0_6053]),
[final] ).
cnf(i_0_15620,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_9120]),
[final] ).
cnf(i_0_15621,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_9243,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_15622,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_9244]),
[final] ).
cnf(i_0_15623,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_9245,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_15624,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_9246,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_15625,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_9247]),
[final] ).
cnf(i_0_15626,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_8804]),
[final] ).
cnf(i_0_15627,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_8995]),
[final] ).
cnf(i_0_15628,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_9248]),
[final] ).
cnf(i_0_15629,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_9249]),
[final] ).
cnf(i_0_15630,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_9250]),
[final] ).
cnf(i_0_15631,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_9251]),
[final] ).
cnf(i_0_15632,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_9252]),
[final] ).
cnf(i_0_15633,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_9253]),
[final] ).
cnf(i_0_15634,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_9254]),
[final] ).
cnf(i_0_15635,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_9255]),
[final] ).
cnf(i_0_15636,plain,
( c_List_OtakeWhile(X3,X1,X2) = X2
| ~ hBOOL(hAPP(X1,esk496_3(X2,X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8672]),
[final] ).
cnf(i_0_15637,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_9256]),
[final] ).
cnf(i_0_15638,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_8722]),
[final] ).
cnf(i_0_15639,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_9000]),
[final] ).
cnf(i_0_15640,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_9001]),
[final] ).
cnf(i_0_15641,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_9257]),
[final] ).
cnf(i_0_15642,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_9258]),
[final] ).
cnf(i_0_15643,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_8628]),
[final] ).
cnf(i_0_15644,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_8629]),
[final] ).
cnf(i_0_15645,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_8962]),
[final] ).
cnf(i_0_15646,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_8963]),
[final] ).
cnf(i_0_15647,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_8964]),
[final] ).
cnf(i_0_15648,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_8965]),
[final] ).
cnf(i_0_15649,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_8966]),
[final] ).
cnf(i_0_15650,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_8737]),
[final] ).
cnf(i_0_15651,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_8967]),
[final] ).
cnf(i_0_15652,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_8968]),
[final] ).
cnf(i_0_15653,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_8969]),
[final] ).
cnf(i_0_15654,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_8970]),
[final] ).
cnf(i_0_15655,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_8972]),
[final] ).
cnf(i_0_15656,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_8971]),
[final] ).
cnf(i_0_15657,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_8957]),
[final] ).
cnf(i_0_15658,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_9045]),
[final] ).
cnf(i_0_15659,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_9044]),
[final] ).
cnf(i_0_15660,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_9259]),
[final] ).
cnf(i_0_15661,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_9260]),
[final] ).
cnf(i_0_15662,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_15663,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_8840]),
[final] ).
cnf(i_0_15664,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_9261]),
[final] ).
cnf(i_0_15665,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_9262]),
[final] ).
cnf(i_0_15666,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_9263,c_0_6015]),
[final] ).
cnf(i_0_15667,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_9264]),
[final] ).
cnf(i_0_15668,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_9265]),
[final] ).
cnf(i_0_15669,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_15670,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_15671,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_9266]),
[final] ).
cnf(i_0_15672,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_8813]),
[final] ).
cnf(i_0_15673,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_8350]),
[final] ).
cnf(i_0_15674,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_8350]),
[final] ).
cnf(i_0_15675,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_8654]),
[final] ).
cnf(i_0_15676,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_9267]),
[final] ).
cnf(i_0_15677,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_9268,c_0_6015]),c_0_6015]),
[final] ).
cnf(i_0_15678,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_8737]),
[final] ).
cnf(i_0_15679,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_9269]),
[final] ).
cnf(i_0_15680,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_9270]),
[final] ).
cnf(i_0_15681,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_9271,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_15682,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_9272,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_15683,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_9273,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_15684,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_9274,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_15685,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_9275]),
[final] ).
cnf(i_0_15686,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_9276]),
[final] ).
cnf(i_0_15687,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_9277]),
[final] ).
cnf(i_0_15688,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_9010]),
[final] ).
cnf(i_0_15689,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_9011]),
[final] ).
cnf(i_0_15690,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_9278]),
[final] ).
cnf(i_0_15691,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_9279]),
[final] ).
cnf(i_0_15692,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_9280]),
[final] ).
cnf(i_0_15693,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_9281]),
[final] ).
cnf(i_0_15694,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_9282]),
[final] ).
cnf(i_0_15695,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_9283]),
[final] ).
cnf(i_0_15696,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_9284]),
[final] ).
cnf(i_0_15697,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_9285]),
[final] ).
cnf(i_0_15698,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_9286]),
[final] ).
cnf(i_0_15699,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_9287]),
[final] ).
cnf(i_0_15700,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_9288]),
[final] ).
cnf(i_0_15701,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_9289]),
[final] ).
cnf(i_0_15702,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_9290]),
[final] ).
cnf(i_0_15703,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_9291]),
[final] ).
cnf(i_0_15704,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_9292]),
[final] ).
cnf(i_0_15705,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_8697]),
[final] ).
cnf(i_0_15706,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_15707,plain,
( c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),esk316_2(X2,X1)),c_Wellfounded_Oacc(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9293]),
[final] ).
cnf(i_0_15708,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_9294]),
[final] ).
cnf(i_0_15709,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_9295]),
[final] ).
cnf(i_0_15710,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_9296]),
[final] ).
cnf(i_0_15711,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_8916]),
[final] ).
cnf(i_0_15712,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_9297]),
[final] ).
cnf(i_0_15713,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_9298]),
[final] ).
cnf(i_0_15714,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_9299]),
[final] ).
cnf(i_0_15715,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_9300,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_15716,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_9301,c_0_6014]),c_0_6015]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_15717,plain,
( X1 = hAPP(hAPP(c_Set_Oinsert(X2),esk148_3(X3,X1,X2)),esk149_3(X3,X1,X2))
| hAPP(c_Finite__Set_Ocard(X2),X1) != hAPP(c_Nat_OSuc,X3) ),
inference(split_conjunct,[status(thm)],[i_0_7860]),
[final] ).
cnf(i_0_15718,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_9302]),
[final] ).
cnf(i_0_15719,plain,
( hAPP(c_List_Ofilter(X3,X1),X2) = X2
| ~ hBOOL(hAPP(X1,esk483_3(X2,X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8711]),
[final] ).
cnf(i_0_15720,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_9303]),
[final] ).
cnf(i_0_15721,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_9304]),
[final] ).
cnf(i_0_15722,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_9084]),
[final] ).
cnf(i_0_15723,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_9305]),
[final] ).
cnf(i_0_15724,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_9306]),
[final] ).
cnf(i_0_15725,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_9307]),
[final] ).
cnf(i_0_15726,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_9308]),
[final] ).
cnf(i_0_15727,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_9309]),
[final] ).
cnf(i_0_15728,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_9310]),
[final] ).
cnf(i_0_15729,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_9311,c_0_7027]),
[final] ).
cnf(i_0_15730,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_9312]),
[final] ).
cnf(i_0_15731,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_9028]),
[final] ).
cnf(i_0_15732,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_9313]),
[final] ).
cnf(i_0_15733,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_9314]),
[final] ).
cnf(i_0_15734,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_9315]),
[final] ).
cnf(i_0_15735,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_9316]),
[final] ).
cnf(i_0_15736,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_9317]),
[final] ).
cnf(i_0_15737,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_9318]),
[final] ).
cnf(i_0_15738,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_9319]),
[final] ).
cnf(i_0_15739,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_9320]),
[final] ).
cnf(i_0_15740,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_9321]),
[final] ).
cnf(i_0_15741,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_9322]),
[final] ).
cnf(i_0_15742,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk37_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_9323]),
[final] ).
cnf(i_0_15743,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk74_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_8628]),
[final] ).
cnf(i_0_15744,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk73_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_8629]),
[final] ).
cnf(i_0_15745,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_9324,c_0_8159]),
[final] ).
cnf(i_0_15746,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_9185]),
[final] ).
cnf(i_0_15747,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_9325]),
[final] ).
cnf(i_0_15748,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_9326]),
[final] ).
cnf(i_0_15749,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_9327]),
[final] ).
cnf(i_0_15750,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_9328]),
[final] ).
cnf(i_0_15751,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_9329,c_0_6135]),
[final] ).
cnf(i_0_15752,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_9330]),
[final] ).
cnf(i_0_15753,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_9331]),
[final] ).
cnf(i_0_15754,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_9332]),
[final] ).
cnf(i_0_15755,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_9333]),
[final] ).
cnf(i_0_15756,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_9334]),
[final] ).
cnf(i_0_15757,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_9335]),
[final] ).
cnf(i_0_15758,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_9336]),
[final] ).
cnf(i_0_15759,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_9337]),
[final] ).
cnf(i_0_15760,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_9338]),
[final] ).
cnf(i_0_15761,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_9339]),
[final] ).
cnf(i_0_15762,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_9340]),
[final] ).
cnf(i_0_15763,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_9341]),
[final] ).
cnf(i_0_15764,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_9342]),
[final] ).
cnf(i_0_15765,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_9343]),
[final] ).
cnf(i_0_15766,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_9344]),
[final] ).
cnf(i_0_15767,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_9345]),
[final] ).
cnf(i_0_15768,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_9346]),
[final] ).
cnf(i_0_15769,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_9347]),
[final] ).
cnf(i_0_15770,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_9348]),
[final] ).
cnf(i_0_15771,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_9349]),
[final] ).
cnf(i_0_15772,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_9350]),
[final] ).
cnf(i_0_15773,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_9351]),
[final] ).
cnf(i_0_15774,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_9352]),
[final] ).
cnf(i_0_15775,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_9353]),
[final] ).
cnf(i_0_15776,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_9354]),
[final] ).
cnf(i_0_15777,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_9355]),
[final] ).
cnf(i_0_15778,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_9356]),
[final] ).
cnf(i_0_15779,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_9156]),
[final] ).
cnf(i_0_15780,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_15781,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_9357]),
[final] ).
cnf(i_0_15782,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_9358]),
[final] ).
cnf(i_0_15783,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_8989]),
[final] ).
cnf(i_0_15784,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_9359]),
[final] ).
cnf(i_0_15785,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_9360]),
[final] ).
cnf(i_0_15786,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_9361]),
[final] ).
cnf(i_0_15787,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_9362]),
[final] ).
cnf(i_0_15788,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_9363]),
[final] ).
cnf(i_0_15789,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_9364]),
[final] ).
cnf(i_0_15790,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_9365]),
[final] ).
cnf(i_0_15791,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_9366]),
[final] ).
cnf(i_0_15792,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_9367]),
[final] ).
cnf(i_0_15793,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_9368]),
[final] ).
cnf(i_0_15794,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_9369]),
[final] ).
cnf(i_0_15795,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_9370]),
[final] ).
cnf(i_0_15796,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_9371]),
[final] ).
cnf(i_0_15797,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_9372]),
[final] ).
cnf(i_0_15798,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_8055]),
[final] ).
cnf(i_0_15799,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_9373]),
[final] ).
cnf(i_0_15800,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_9167]),
[final] ).
cnf(i_0_15801,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_9374]),
[final] ).
cnf(i_0_15802,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_9375]),
[final] ).
cnf(i_0_15803,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_9376]),
[final] ).
cnf(i_0_15804,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk484_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_9141]),
[final] ).
cnf(i_0_15805,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_9326]),
[final] ).
cnf(i_0_15806,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_9328]),
[final] ).
cnf(i_0_15807,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_9377,c_0_6015]),
[final] ).
cnf(i_0_15808,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_9378,c_0_6015]),
[final] ).
cnf(i_0_15809,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_9379,c_0_6015]),
[final] ).
cnf(i_0_15810,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_9380,c_0_6015]),
[final] ).
cnf(i_0_15811,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_9381]),
[final] ).
cnf(i_0_15812,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_9382]),
[final] ).
cnf(i_0_15813,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_9381]),
[final] ).
cnf(i_0_15814,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_9382]),
[final] ).
cnf(i_0_15815,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_9383]),
[final] ).
cnf(i_0_15816,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_9384]),
[final] ).
cnf(i_0_15817,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_9385]),
[final] ).
cnf(i_0_15818,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_9386]),
[final] ).
cnf(i_0_15819,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_9387]),
[final] ).
cnf(i_0_15820,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_9388]),
[final] ).
cnf(i_0_15821,plain,
( hBOOL(hAPP(X2,X4))
| c_List_OtakeWhile(X1,X2,X3) != X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_8672]),
[final] ).
cnf(i_0_15822,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_8699]),
[final] ).
cnf(i_0_15823,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_9389]),
[final] ).
cnf(i_0_15824,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_9390]),
[final] ).
cnf(i_0_15825,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_9391,c_0_6053]),
[final] ).
cnf(i_0_15826,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_9392,c_0_6053]),
[final] ).
cnf(i_0_15827,plain,
hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X5),X4) = X5,
inference(split_conjunct,[status(thm)],[i_0_9393]),
[final] ).
cnf(i_0_15828,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_9394]),
[final] ).
cnf(i_0_15829,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_9395]),
[final] ).
cnf(i_0_15830,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_9396]),
[final] ).
cnf(i_0_15831,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_9397]),
[final] ).
cnf(i_0_15832,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_9398]),
[final] ).
cnf(i_0_15833,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_8804]),
[final] ).
cnf(i_0_15834,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_9399]),
[final] ).
cnf(i_0_15835,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_9400]),
[final] ).
cnf(i_0_15836,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_9401]),
[final] ).
cnf(i_0_15837,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_9222]),
[final] ).
cnf(i_0_15838,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_9223]),
[final] ).
cnf(i_0_15839,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_9402]),
[final] ).
cnf(i_0_15840,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_9403]),
[final] ).
cnf(i_0_15841,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_9404]),
[final] ).
cnf(i_0_15842,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_9405]),
[final] ).
cnf(i_0_15843,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_9406]),
[final] ).
cnf(i_0_15844,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_9407]),
[final] ).
cnf(i_0_15845,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_9408]),
[final] ).
cnf(i_0_15846,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_9409]),
[final] ).
cnf(i_0_15847,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_9410]),
[final] ).
cnf(i_0_15848,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_15849,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_9411]),
[final] ).
cnf(i_0_15850,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_9412]),
[final] ).
cnf(i_0_15851,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_9413]),
[final] ).
cnf(i_0_15852,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_9414]),
[final] ).
cnf(i_0_15853,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_9415]),
[final] ).
cnf(i_0_15854,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_9416,c_0_6062]),
[final] ).
cnf(i_0_15855,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_9417]),
[final] ).
cnf(i_0_15856,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_9298]),
[final] ).
cnf(i_0_15857,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_9418]),
[final] ).
cnf(i_0_15858,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_9419]),
[final] ).
cnf(i_0_15859,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_9420]),
[final] ).
cnf(i_0_15860,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_9264]),
[final] ).
cnf(i_0_15861,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_9200]),
[final] ).
cnf(i_0_15862,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_9421]),
[final] ).
cnf(i_0_15863,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_8890]),
[final] ).
cnf(i_0_15864,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_8889]),
[final] ).
cnf(i_0_15865,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_9422]),
[final] ).
cnf(i_0_15866,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_15867,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_9423]),
[final] ).
cnf(i_0_15868,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_9424,c_0_6053]),
[final] ).
cnf(i_0_15869,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_9425]),
[final] ).
cnf(i_0_15870,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_9426]),
[final] ).
cnf(i_0_15871,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_9427]),
[final] ).
cnf(i_0_15872,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_9428]),
[final] ).
cnf(i_0_15873,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_8625]),
[final] ).
cnf(i_0_15874,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_8624]),
[final] ).
cnf(i_0_15875,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_9155]),
[final] ).
cnf(i_0_15876,plain,
( X3 = X1
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_9429]),
[final] ).
cnf(i_0_15877,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_9430]),
[final] ).
cnf(i_0_15878,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_9431]),
[final] ).
cnf(i_0_15879,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_9432]),
[final] ).
cnf(i_0_15880,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_9433]),
[final] ).
cnf(i_0_15881,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_8886]),
[final] ).
cnf(i_0_15882,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_9434]),
[final] ).
cnf(i_0_15883,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_9435]),
[final] ).
cnf(i_0_15884,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_9436]),
[final] ).
cnf(i_0_15885,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_9437]),
[final] ).
cnf(i_0_15886,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_9438]),
[final] ).
cnf(i_0_15887,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_9439]),
[final] ).
cnf(i_0_15888,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_9440]),
[final] ).
cnf(i_0_15889,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_9441]),
[final] ).
cnf(i_0_15890,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_9442]),
[final] ).
cnf(i_0_15891,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_9443]),
[final] ).
cnf(i_0_15892,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk53_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_9444]),
[final] ).
cnf(i_0_15893,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_9445]),
[final] ).
cnf(i_0_15894,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_9446]),
[final] ).
cnf(i_0_15895,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_8856]),
[final] ).
cnf(i_0_15896,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_8856]),
[final] ).
cnf(i_0_15897,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_9200]),
[final] ).
cnf(i_0_15898,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_9447]),
[final] ).
cnf(i_0_15899,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_9448]),
[final] ).
cnf(i_0_15900,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_8711]),
[final] ).
cnf(i_0_15901,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_9449]),
[final] ).
cnf(i_0_15902,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_9250]),
[final] ).
cnf(i_0_15903,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_9251]),
[final] ).
cnf(i_0_15904,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_9252]),
[final] ).
cnf(i_0_15905,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_9450]),
[final] ).
cnf(i_0_15906,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_9303]),
[final] ).
cnf(i_0_15907,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_9304]),
[final] ).
cnf(i_0_15908,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_9451]),
[final] ).
cnf(i_0_15909,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_9202]),
[final] ).
cnf(i_0_15910,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_9201]),
[final] ).
cnf(i_0_15911,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_9203]),
[final] ).
cnf(i_0_15912,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_9205]),
[final] ).
cnf(i_0_15913,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_9204]),
[final] ).
cnf(i_0_15914,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_9206]),
[final] ).
cnf(i_0_15915,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_9452]),
[final] ).
cnf(i_0_15916,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_9453]),
[final] ).
cnf(i_0_15917,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_9454]),
[final] ).
cnf(i_0_15918,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_9455]),
[final] ).
cnf(i_0_15919,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_9306]),
[final] ).
cnf(i_0_15920,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_9456]),
[final] ).
cnf(i_0_15921,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_9457]),
[final] ).
cnf(i_0_15922,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_9458]),
[final] ).
cnf(i_0_15923,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_9459]),
[final] ).
cnf(i_0_15924,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_9460]),
[final] ).
cnf(i_0_15925,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_9461]),
[final] ).
cnf(i_0_15926,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_9462]),
[final] ).
cnf(i_0_15927,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_9463]),
[final] ).
cnf(i_0_15928,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_9464]),
[final] ).
cnf(i_0_15929,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_9465]),
[final] ).
cnf(i_0_15930,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_9466]),
[final] ).
cnf(i_0_15931,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_9467]),
[final] ).
cnf(i_0_15932,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,esk42_2(X2,X1))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9468]),
[final] ).
cnf(i_0_15933,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_9361]),
[final] ).
cnf(i_0_15934,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_9362]),
[final] ).
cnf(i_0_15935,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_9469,c_0_6135]),
[final] ).
cnf(i_0_15936,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_9470]),
[final] ).
cnf(i_0_15937,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_9471]),
[final] ).
cnf(i_0_15938,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_9472]),
[final] ).
cnf(i_0_15939,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_9473]),
[final] ).
cnf(i_0_15940,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_9474]),
[final] ).
cnf(i_0_15941,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_9475]),
[final] ).
cnf(i_0_15942,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_15943,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_9476]),
[final] ).
cnf(i_0_15944,plain,
( hBOOL(hAPP(c_Predicate_ODomainP(X4,X5,X1),X2))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9060]),
[final] ).
cnf(i_0_15945,plain,
( hBOOL(hAPP(c_Predicate_ODomainP(X4,X5,X1),X2))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9477]),
[final] ).
cnf(i_0_15946,plain,
( hBOOL(hAPP(c_Predicate_ORangeP(X4,X5,X1),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_8915]),
[final] ).
cnf(i_0_15947,plain,
( hBOOL(hAPP(c_Predicate_ORangeP(X4,X5,X1),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_9478]),
[final] ).
cnf(i_0_15948,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_8071]),
[final] ).
cnf(i_0_15949,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_9479]),
[final] ).
cnf(i_0_15950,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_9480]),
[final] ).
cnf(i_0_15951,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_9481]),
[final] ).
cnf(i_0_15952,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_9240]),
[final] ).
cnf(i_0_15953,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_9482,c_0_8159]),
[final] ).
cnf(i_0_15954,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_9483]),
[final] ).
cnf(i_0_15955,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_9021]),
[final] ).
cnf(i_0_15956,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_8976]),
[final] ).
cnf(i_0_15957,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_9484]),
[final] ).
cnf(i_0_15958,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_9485]),
[final] ).
cnf(i_0_15959,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_9486,c_0_6135]),
[final] ).
cnf(i_0_15960,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_9487]),
[final] ).
cnf(i_0_15961,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_9488]),
[final] ).
cnf(i_0_15962,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_9489]),
[final] ).
cnf(i_0_15963,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_9489]),
[final] ).
cnf(i_0_15964,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_9489]),
[final] ).
cnf(i_0_15965,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_7893]),
[final] ).
cnf(i_0_15966,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_8893]),
[final] ).
cnf(i_0_15967,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_8894]),
[final] ).
cnf(i_0_15968,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_9490]),
[final] ).
cnf(i_0_15969,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_9491]),
[final] ).
cnf(i_0_15970,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk453_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_8205]),
[final] ).
cnf(i_0_15971,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk452_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_8205]),
[final] ).
cnf(i_0_15972,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_9492]),
[final] ).
cnf(i_0_15973,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_9493]),
[final] ).
cnf(i_0_15974,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_9494,c_0_6053]),
[final] ).
cnf(i_0_15975,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_9495]),
[final] ).
cnf(i_0_15976,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_9496]),
[final] ).
cnf(i_0_15977,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_8463]),
[final] ).
cnf(i_0_15978,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_9497]),
[final] ).
cnf(i_0_15979,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_8934]),
[final] ).
cnf(i_0_15980,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_9498]),
[final] ).
cnf(i_0_15981,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_9499]),
[final] ).
cnf(i_0_15982,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_9500]),
[final] ).
cnf(i_0_15983,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_9200]),
[final] ).
cnf(i_0_15984,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_9501]),
[final] ).
cnf(i_0_15985,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_9502]),
[final] ).
cnf(i_0_15986,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_9503]),
[final] ).
cnf(i_0_15987,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_9504]),
[final] ).
cnf(i_0_15988,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_8083]),
[final] ).
cnf(i_0_15989,plain,
( hAPP(X1,esk246_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_15990,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_9505]),
[final] ).
cnf(i_0_15991,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_9506]),
[final] ).
cnf(i_0_15992,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),esk59_2(X2,X3)))
| ~ hBOOL(hAPP(X3,X1))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9067]),
[final] ).
cnf(i_0_15993,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_9507]),
[final] ).
cnf(i_0_15994,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_9508]),
[final] ).
cnf(i_0_15995,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_9509]),
[final] ).
cnf(i_0_15996,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_9510]),
[final] ).
cnf(i_0_15997,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_9511]),
[final] ).
cnf(i_0_15998,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_9512]),
[final] ).
cnf(i_0_15999,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_9513]),
[final] ).
cnf(i_0_16000,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_9514]),
[final] ).
cnf(i_0_16001,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_9515]),
[final] ).
cnf(i_0_16002,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_9516]),
[final] ).
cnf(i_0_16003,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_9517]),
[final] ).
cnf(i_0_16004,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_9518]),
[final] ).
cnf(i_0_16005,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_9519]),
[final] ).
cnf(i_0_16006,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_9520]),
[final] ).
cnf(i_0_16007,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_9521]),
[final] ).
cnf(i_0_16008,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_9522]),
[final] ).
cnf(i_0_16009,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_9282]),
[final] ).
cnf(i_0_16010,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_9283]),
[final] ).
cnf(i_0_16011,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_9523]),
[final] ).
cnf(i_0_16012,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_9524]),
[final] ).
cnf(i_0_16013,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_9525]),
[final] ).
cnf(i_0_16014,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_9526]),
[final] ).
cnf(i_0_16015,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_9527]),
[final] ).
cnf(i_0_16016,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_9406]),
[final] ).
cnf(i_0_16017,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_9404]),
[final] ).
cnf(i_0_16018,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_9407]),
[final] ).
cnf(i_0_16019,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_9405]),
[final] ).
cnf(i_0_16020,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_9403]),
[final] ).
cnf(i_0_16021,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_9402]),
[final] ).
cnf(i_0_16022,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_9210]),
[final] ).
cnf(i_0_16023,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_9528]),
[final] ).
cnf(i_0_16024,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_9224]),
[final] ).
cnf(i_0_16025,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_9529]),
[final] ).
cnf(i_0_16026,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_9530]),
[final] ).
cnf(i_0_16027,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_9496]),
[final] ).
cnf(i_0_16028,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_9531,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_16029,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_9532,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_16030,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_8826]),
[final] ).
cnf(i_0_16031,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_9533]),
[final] ).
cnf(i_0_16032,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_9534]),
[final] ).
cnf(i_0_16033,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_9535,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_16034,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_9536,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_16035,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_9537]),
[final] ).
cnf(i_0_16036,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_9538]),
[final] ).
cnf(i_0_16037,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_9539]),
[final] ).
cnf(i_0_16038,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_9540]),
[final] ).
cnf(i_0_16039,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,esk245_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_8624]),
[final] ).
cnf(i_0_16040,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,esk152_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_8625]),
[final] ).
cnf(i_0_16041,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_9541]),
[final] ).
cnf(i_0_16042,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_9542]),
[final] ).
cnf(i_0_16043,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_9543]),
[final] ).
cnf(i_0_16044,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_16045,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk127_2(X1,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9544]),
[final] ).
cnf(i_0_16046,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk129_2(X1,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9545]),
[final] ).
cnf(i_0_16047,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_9546]),
[final] ).
cnf(i_0_16048,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_8992]),
[final] ).
cnf(i_0_16049,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_9547]),
[final] ).
cnf(i_0_16050,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_9376]),
[final] ).
cnf(i_0_16051,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_9461]),
[final] ).
cnf(i_0_16052,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_9548]),
[final] ).
cnf(i_0_16053,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_9549]),
[final] ).
cnf(i_0_16054,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_9550]),
[final] ).
cnf(i_0_16055,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_9551]),
[final] ).
cnf(i_0_16056,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_9552]),
[final] ).
cnf(i_0_16057,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_9553]),
[final] ).
cnf(i_0_16058,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_9554]),
[final] ).
cnf(i_0_16059,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_9555]),
[final] ).
cnf(i_0_16060,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_9556]),
[final] ).
cnf(i_0_16061,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_9557]),
[final] ).
cnf(i_0_16062,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_9558]),
[final] ).
cnf(i_0_16063,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_9559]),
[final] ).
cnf(i_0_16064,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_9560]),
[final] ).
cnf(i_0_16065,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk489_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_7546]),
[final] ).
cnf(i_0_16066,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_7788]),
[final] ).
cnf(i_0_16067,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_9561]),
[final] ).
cnf(i_0_16068,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_9562]),
[final] ).
cnf(i_0_16069,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_9563]),
[final] ).
cnf(i_0_16070,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_9564]),
[final] ).
cnf(i_0_16071,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_9565]),
[final] ).
cnf(i_0_16072,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_9431]),
[final] ).
cnf(i_0_16073,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_9566]),
[final] ).
cnf(i_0_16074,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_9567]),
[final] ).
cnf(i_0_16075,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_9568]),
[final] ).
cnf(i_0_16076,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_9569]),
[final] ).
cnf(i_0_16077,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_9570]),
[final] ).
cnf(i_0_16078,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_9571]),
[final] ).
cnf(i_0_16079,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_9572]),
[final] ).
cnf(i_0_16080,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_9573]),
[final] ).
cnf(i_0_16081,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_9574]),
[final] ).
cnf(i_0_16082,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_9575]),
[final] ).
cnf(i_0_16083,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_9576]),
[final] ).
cnf(i_0_16084,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_9577]),
[final] ).
cnf(i_0_16085,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_9578]),
[final] ).
cnf(i_0_16086,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_8853]),
[final] ).
cnf(i_0_16087,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_8854]),
[final] ).
cnf(i_0_16088,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_9579]),
[final] ).
cnf(i_0_16089,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_9580]),
[final] ).
cnf(i_0_16090,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_9581]),
[final] ).
cnf(i_0_16091,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_9582]),
[final] ).
cnf(i_0_16092,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_9583]),
[final] ).
cnf(i_0_16093,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_9584]),
[final] ).
cnf(i_0_16094,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_9472]),
[final] ).
cnf(i_0_16095,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_9012]),
[final] ).
cnf(i_0_16096,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_9585]),
[final] ).
cnf(i_0_16097,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_9586]),
[final] ).
cnf(i_0_16098,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_9587]),
[final] ).
cnf(i_0_16099,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_9588]),
[final] ).
cnf(i_0_16100,plain,
( hBOOL(hAPP(X2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk50_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_9589]),
[final] ).
cnf(i_0_16101,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_9435]),
[final] ).
cnf(i_0_16102,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_9436]),
[final] ).
cnf(i_0_16103,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_9590]),
[final] ).
cnf(i_0_16104,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_9591]),
[final] ).
cnf(i_0_16105,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_9592]),
[final] ).
cnf(i_0_16106,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_9593]),
[final] ).
cnf(i_0_16107,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_9594]),
[final] ).
cnf(i_0_16108,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_9595]),
[final] ).
cnf(i_0_16109,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_9596,c_0_6135]),
[final] ).
cnf(i_0_16110,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_9597]),
[final] ).
cnf(i_0_16111,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_9598]),
[final] ).
cnf(i_0_16112,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_9599]),
[final] ).
cnf(i_0_16113,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_9600]),
[final] ).
cnf(i_0_16114,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_9601]),
[final] ).
cnf(i_0_16115,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_9602]),
[final] ).
cnf(i_0_16116,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_9603]),
[final] ).
cnf(i_0_16117,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_9604]),
[final] ).
cnf(i_0_16118,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_9605]),
[final] ).
cnf(i_0_16119,plain,
( hBOOL(hAPP(X2,esk55_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_9606]),
[final] ).
cnf(i_0_16120,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_9598]),
[final] ).
cnf(i_0_16121,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_9607]),
[final] ).
cnf(i_0_16122,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_9608,c_0_6015]),
[final] ).
cnf(i_0_16123,plain,
( hAPP(X1,esk248_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_16124,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_9609]),
[final] ).
cnf(i_0_16125,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_9610]),
[final] ).
cnf(i_0_16126,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_9611]),
[final] ).
cnf(i_0_16127,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_9612]),
[final] ).
cnf(i_0_16128,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_9613]),
[final] ).
cnf(i_0_16129,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_9614]),
[final] ).
cnf(i_0_16130,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_9615]),
[final] ).
cnf(i_0_16131,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_9616]),
[final] ).
cnf(i_0_16132,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_9617,c_0_6135]),
[final] ).
cnf(i_0_16133,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_8810]),
[final] ).
cnf(i_0_16134,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_9618]),
[final] ).
cnf(i_0_16135,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_9381]),
[final] ).
cnf(i_0_16136,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_9128]),
[final] ).
cnf(i_0_16137,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_9619]),
[final] ).
cnf(i_0_16138,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_9620]),
[final] ).
cnf(i_0_16139,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_9621]),
[final] ).
cnf(i_0_16140,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_9622]),
[final] ).
cnf(i_0_16141,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_9491]),
[final] ).
cnf(i_0_16142,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_9623]),
[final] ).
cnf(i_0_16143,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_9284]),
[final] ).
cnf(i_0_16144,plain,
( hBOOL(hAPP(c_List_Odistinct(X1),c_List_OtakeWhile(X1,X3,X2)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9624]),
[final] ).
cnf(i_0_16145,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_9625]),
[final] ).
cnf(i_0_16146,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_9626]),
[final] ).
cnf(i_0_16147,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_9627]),
[final] ).
cnf(i_0_16148,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_9628]),
[final] ).
cnf(i_0_16149,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_9629]),
[final] ).
cnf(i_0_16150,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_9630]),
[final] ).
cnf(i_0_16151,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_9631]),
[final] ).
cnf(i_0_16152,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_8879]),
[final] ).
cnf(i_0_16153,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_9549]),
[final] ).
cnf(i_0_16154,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_9632]),
[final] ).
cnf(i_0_16155,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_7552]),
[final] ).
cnf(i_0_16156,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_9633]),
[final] ).
cnf(i_0_16157,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_9634]),
[final] ).
cnf(i_0_16158,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_9635]),
[final] ).
cnf(i_0_16159,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_9636]),
[final] ).
cnf(i_0_16160,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_9637]),
[final] ).
cnf(i_0_16161,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_9638]),
[final] ).
cnf(i_0_16162,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_9639]),
[final] ).
cnf(i_0_16163,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_9640]),
[final] ).
cnf(i_0_16164,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_9641]),
[final] ).
cnf(i_0_16165,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_9642]),
[final] ).
cnf(i_0_16166,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_9643]),
[final] ).
cnf(i_0_16167,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_9644]),
[final] ).
cnf(i_0_16168,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_9645,c_0_6670]),
[final] ).
cnf(i_0_16169,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_9646]),
[final] ).
cnf(i_0_16170,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_9647]),
[final] ).
cnf(i_0_16171,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_9647]),
[final] ).
cnf(i_0_16172,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_9648]),
[final] ).
cnf(i_0_16173,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_9649]),
[final] ).
cnf(i_0_16174,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_9650]),
[final] ).
cnf(i_0_16175,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_9651]),
[final] ).
cnf(i_0_16176,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_9652,c_0_7027]),
[final] ).
cnf(i_0_16177,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_9653,c_0_8159]),
[final] ).
cnf(i_0_16178,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_9654,c_0_6135]),
[final] ).
cnf(i_0_16179,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_9655]),
[final] ).
cnf(i_0_16180,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_9656]),
[final] ).
cnf(i_0_16181,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_9657]),
[final] ).
cnf(i_0_16182,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_9658]),
[final] ).
cnf(i_0_16183,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_9659]),
[final] ).
cnf(i_0_16184,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_9660]),
[final] ).
cnf(i_0_16185,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_9661]),
[final] ).
cnf(i_0_16186,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_9662]),
[final] ).
cnf(i_0_16187,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_9663]),
[final] ).
cnf(i_0_16188,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_9664]),
[final] ).
cnf(i_0_16189,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_9665]),
[final] ).
cnf(i_0_16190,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_9666]),
[final] ).
cnf(i_0_16191,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_9667]),
[final] ).
cnf(i_0_16192,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_9668]),
[final] ).
cnf(i_0_16193,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_9669]),
[final] ).
cnf(i_0_16194,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_9670]),
[final] ).
cnf(i_0_16195,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_9671]),
[final] ).
cnf(i_0_16196,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_8841]),
[final] ).
cnf(i_0_16197,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_9152]),
[final] ).
cnf(i_0_16198,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_9672]),
[final] ).
cnf(i_0_16199,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_9673]),
[final] ).
cnf(i_0_16200,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_9674]),
[final] ).
cnf(i_0_16201,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_9267]),
[final] ).
cnf(i_0_16202,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_9675]),
[final] ).
cnf(i_0_16203,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_9676]),
[final] ).
cnf(i_0_16204,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_9677]),
[final] ).
cnf(i_0_16205,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_9678]),
[final] ).
cnf(i_0_16206,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_9679]),
[final] ).
cnf(i_0_16207,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_9680]),
[final] ).
cnf(i_0_16208,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,hAPP(c_Int_OAbs__Integ,esk334_2(X2,X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_8531]),
[final] ).
cnf(i_0_16209,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_9681]),
[final] ).
cnf(i_0_16210,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_9682]),
[final] ).
cnf(i_0_16211,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),esk126_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_9544]),
[final] ).
cnf(i_0_16212,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),esk128_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_9545]),
[final] ).
cnf(i_0_16213,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_16214,plain,
( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X2)))
| ~ hBOOL(hAPP(X1,esk56_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_9683]),
[final] ).
cnf(i_0_16215,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))),
inference(split_conjunct,[status(thm)],[i_0_9684]),
[final] ).
cnf(i_0_16216,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_9323]),
[final] ).
cnf(i_0_16217,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_16218,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_7562]),
[final] ).
cnf(i_0_16219,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_9528]),
[final] ).
cnf(i_0_16220,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_9685]),
[final] ).
cnf(i_0_16221,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_8916]),
[final] ).
cnf(i_0_16222,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_9686,c_0_6169]),
[final] ).
cnf(i_0_16223,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_9687,c_0_6016]),
[final] ).
cnf(i_0_16224,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_9688]),
[final] ).
cnf(i_0_16225,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_8727]),
[final] ).
cnf(i_0_16226,plain,
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,esk233_2(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8732]),
[final] ).
cnf(i_0_16227,plain,
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,esk201_2(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8566]),
[final] ).
cnf(i_0_16228,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_16229,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_9689]),
[final] ).
cnf(i_0_16230,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_9690]),
[final] ).
cnf(i_0_16231,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk40_2(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9691]),
[final] ).
cnf(i_0_16232,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_9564]),
[final] ).
cnf(i_0_16233,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_9692]),
[final] ).
cnf(i_0_16234,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,esk46_2(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9672]),
[final] ).
cnf(i_0_16235,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_9265]),
[final] ).
cnf(i_0_16236,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_9693]),
[final] ).
cnf(i_0_16237,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_9694]),
[final] ).
cnf(i_0_16238,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_9695,c_0_6169]),
[final] ).
cnf(i_0_16239,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_9696]),
[final] ).
cnf(i_0_16240,plain,
( hBOOL(hAPP(X1,X2))
| c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X2,X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7847]),
[final] ).
cnf(i_0_16241,plain,
( hBOOL(hAPP(X1,X2))
| c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X2,X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_9697]),
[final] ).
cnf(i_0_16242,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_9698]),
[final] ).
cnf(i_0_16243,plain,
( X2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk39_2(X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9699]),
[final] ).
cnf(i_0_16244,plain,
( X2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk38_2(X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9700]),
[final] ).
cnf(i_0_16245,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_9701]),
[final] ).
cnf(i_0_16246,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_9702]),
[final] ).
cnf(i_0_16247,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_9703]),
[final] ).
cnf(i_0_16248,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_9704]),
[final] ).
cnf(i_0_16249,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_16250,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_9264]),
[final] ).
cnf(i_0_16251,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_9200]),
[final] ).
cnf(i_0_16252,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_9705]),
[final] ).
cnf(i_0_16253,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_8530]),
[final] ).
cnf(i_0_16254,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_9706]),
[final] ).
cnf(i_0_16255,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_16256,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_7860]),
[final] ).
cnf(i_0_16257,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_8916]),
[final] ).
cnf(i_0_16258,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_9707]),
[final] ).
cnf(i_0_16259,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_9708]),
[final] ).
cnf(i_0_16260,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_9709]),
[final] ).
cnf(i_0_16261,plain,
c_Fun_Oinj__on(X1,tc_sum(X1,X2),c_Sum__Type_OInl(X1,X2),X3),
inference(split_conjunct,[status(thm)],[i_0_9710]),
[final] ).
cnf(i_0_16262,plain,
c_Fun_Oinj__on(X1,tc_sum(X2,X1),c_Sum__Type_OInr(X1,X2),X3),
inference(split_conjunct,[status(thm)],[i_0_9711]),
[final] ).
cnf(i_0_16263,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_9712]),
[final] ).
cnf(i_0_16264,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_16265,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_9714]),
[final] ).
cnf(i_0_16266,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_9715]),
[final] ).
cnf(i_0_16267,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_9716]),
[final] ).
cnf(i_0_16268,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_9717]),
[final] ).
cnf(i_0_16269,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_9718]),
[final] ).
cnf(i_0_16270,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_9719]),
[final] ).
cnf(i_0_16271,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_9720]),
[final] ).
cnf(i_0_16272,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_9721]),
[final] ).
cnf(i_0_16273,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_9722]),
[final] ).
cnf(i_0_16274,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_9723]),
[final] ).
cnf(i_0_16275,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_9724,c_0_6135]),
[final] ).
cnf(i_0_16276,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_9725]),
[final] ).
cnf(i_0_16277,plain,
X1 = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),esk5_2(X2,X1)),esk6_2(X2,X1)),esk7_2(X2,X1)),
inference(split_conjunct,[status(thm)],[i_0_9726]),
[final] ).
cnf(i_0_16278,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_8804]),
[final] ).
cnf(i_0_16279,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_9727]),
[final] ).
cnf(i_0_16280,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_9728]),
[final] ).
cnf(i_0_16281,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_9729]),
[final] ).
cnf(i_0_16282,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_9730]),
[final] ).
cnf(i_0_16283,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_9442]),
[final] ).
cnf(i_0_16284,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_9731]),
[final] ).
cnf(i_0_16285,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_9731]),
[final] ).
cnf(i_0_16286,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_9732]),
[final] ).
cnf(i_0_16287,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_9733]),
[final] ).
cnf(i_0_16288,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_9734]),
[final] ).
cnf(i_0_16289,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_9735]),
[final] ).
cnf(i_0_16290,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_9736]),
[final] ).
cnf(i_0_16291,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_9737]),
[final] ).
cnf(i_0_16292,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_9738]),
[final] ).
cnf(i_0_16293,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_9739]),
[final] ).
cnf(i_0_16294,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_9740]),
[final] ).
cnf(i_0_16295,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_9612]),
[final] ).
cnf(i_0_16296,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_9613]),
[final] ).
cnf(i_0_16297,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_9741,c_0_7027]),
[final] ).
cnf(i_0_16298,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_9742,c_0_7027]),
[final] ).
cnf(i_0_16299,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_9743]),
[final] ).
cnf(i_0_16300,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_16301,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_9744]),
[final] ).
cnf(i_0_16302,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_9744]),
[final] ).
cnf(i_0_16303,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_8219]),
[final] ).
cnf(i_0_16304,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_8219]),
[final] ).
cnf(i_0_16305,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_8514]),
[final] ).
cnf(i_0_16306,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_9745]),
[final] ).
cnf(i_0_16307,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_9746]),
[final] ).
cnf(i_0_16308,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_8927]),
[final] ).
cnf(i_0_16309,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_9481]),
[final] ).
cnf(i_0_16310,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_9747]),
[final] ).
cnf(i_0_16311,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_9748]),
[final] ).
cnf(i_0_16312,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_9749]),
[final] ).
cnf(i_0_16313,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_8055]),
[final] ).
cnf(i_0_16314,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_9468]),
[final] ).
cnf(i_0_16315,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_9750]),
[final] ).
cnf(i_0_16316,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_9751]),
[final] ).
cnf(i_0_16317,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_9752]),
[final] ).
cnf(i_0_16318,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_9751]),
[final] ).
cnf(i_0_16319,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_9752]),
[final] ).
cnf(i_0_16320,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_9753]),
[final] ).
cnf(i_0_16321,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_9754]),
[final] ).
cnf(i_0_16322,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_9755]),
[final] ).
cnf(i_0_16323,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_8957]),
[final] ).
cnf(i_0_16324,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_9756]),
[final] ).
cnf(i_0_16325,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_9757]),
[final] ).
cnf(i_0_16326,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_9758]),
[final] ).
cnf(i_0_16327,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_9759]),
[final] ).
cnf(i_0_16328,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_9760]),
[final] ).
cnf(i_0_16329,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_9615]),
[final] ).
cnf(i_0_16330,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_9670]),
[final] ).
cnf(i_0_16331,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_9761]),
[final] ).
cnf(i_0_16332,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_9648]),
[final] ).
cnf(i_0_16333,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_9762]),
[final] ).
cnf(i_0_16334,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_9580]),
[final] ).
cnf(i_0_16335,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_9022]),
[final] ).
cnf(i_0_16336,plain,
( hBOOL(hAPP(X1,esk482_3(X2,X1,X3)))
| hAPP(c_List_Ofilter(X3,X1),X2) = c_List_Olist_ONil(X3) ),
inference(split_conjunct,[status(thm)],[i_0_8699]),
[final] ).
cnf(i_0_16337,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_9763]),
[final] ).
cnf(i_0_16338,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_9764]),
[final] ).
cnf(i_0_16339,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_9496]),
[final] ).
cnf(i_0_16340,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_9765]),
[final] ).
cnf(i_0_16341,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_9766]),
[final] ).
cnf(i_0_16342,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_9767]),
[final] ).
cnf(i_0_16343,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_9768]),
[final] ).
cnf(i_0_16344,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_9254]),
[final] ).
cnf(i_0_16345,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk45_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_9769]),
[final] ).
cnf(i_0_16346,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_9770]),
[final] ).
cnf(i_0_16347,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_9770]),
[final] ).
cnf(i_0_16348,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_9771]),
[final] ).
cnf(i_0_16349,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_9772]),
[final] ).
cnf(i_0_16350,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_9773]),
[final] ).
cnf(i_0_16351,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_9774]),
[final] ).
cnf(i_0_16352,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_9775]),
[final] ).
cnf(i_0_16353,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_9776]),
[final] ).
cnf(i_0_16354,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_9777]),
[final] ).
cnf(i_0_16355,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_9778]),
[final] ).
cnf(i_0_16356,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_9779]),
[final] ).
cnf(i_0_16357,plain,
c_Nat_Onat_Onat__case(X1,X2,X3,hAPP(c_Nat_OSuc,X4)) = hAPP(X3,X4),
inference(split_conjunct,[status(thm)],[i_0_9780]),
[final] ).
cnf(i_0_16358,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_9781]),
[final] ).
cnf(i_0_16359,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_9782]),
[final] ).
cnf(i_0_16360,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_9383]),
[final] ).
cnf(i_0_16361,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_9550]),
[final] ).
cnf(i_0_16362,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_9783]),
[final] ).
cnf(i_0_16363,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_9784]),
[final] ).
cnf(i_0_16364,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_9785]),
[final] ).
cnf(i_0_16365,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_9786]),
[final] ).
cnf(i_0_16366,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_9787]),
[final] ).
cnf(i_0_16367,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_9788]),
[final] ).
cnf(i_0_16368,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_9789]),
[final] ).
cnf(i_0_16369,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_9790]),
[final] ).
cnf(i_0_16370,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_9791]),
[final] ).
cnf(i_0_16371,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_9792]),
[final] ).
cnf(i_0_16372,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_9793]),
[final] ).
cnf(i_0_16373,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_9794]),
[final] ).
cnf(i_0_16374,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_9795]),
[final] ).
cnf(i_0_16375,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_9796]),
[final] ).
cnf(i_0_16376,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_9797]),
[final] ).
cnf(i_0_16377,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_9798]),
[final] ).
cnf(i_0_16378,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_9799]),
[final] ).
cnf(i_0_16379,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_9800]),
[final] ).
cnf(i_0_16380,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_16381,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_16382,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_16383,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_16384,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_9801]),
[final] ).
cnf(i_0_16385,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_9802]),
[final] ).
cnf(i_0_16386,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_9803]),
[final] ).
cnf(i_0_16387,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk59_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_9067]),
[final] ).
cnf(i_0_16388,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X4),X1),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9401]),
[final] ).
cnf(i_0_16389,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_9804]),
[final] ).
cnf(i_0_16390,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_9496]),
[final] ).
cnf(i_0_16391,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_9805]),
[final] ).
cnf(i_0_16392,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_9431]),
[final] ).
cnf(i_0_16393,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_9788]),
[final] ).
cnf(i_0_16394,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_9789]),
[final] ).
cnf(i_0_16395,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_9806]),
[final] ).
cnf(i_0_16396,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_16397,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_9807]),
[final] ).
cnf(i_0_16398,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_9248]),
[final] ).
cnf(i_0_16399,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_9808]),
[final] ).
cnf(i_0_16400,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_9809]),
[final] ).
cnf(i_0_16401,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_9810,c_0_6016]),
[final] ).
cnf(i_0_16402,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_9418]),
[final] ).
cnf(i_0_16403,plain,
( esk130_3(X1,X2,X3) = esk131_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_8595]),
[final] ).
cnf(i_0_16404,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_9811]),
[final] ).
cnf(i_0_16405,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_9812]),
[final] ).
cnf(i_0_16406,plain,
( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk58_2(X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9813]),
[final] ).
cnf(i_0_16407,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_9814]),
[final] ).
cnf(i_0_16408,plain,
( hBOOL(hAPP(X1,esk234_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_8693]),
[final] ).
cnf(i_0_16409,plain,
( hBOOL(hAPP(X1,esk198_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_8528]),
[final] ).
cnf(i_0_16410,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_9815]),
[final] ).
cnf(i_0_16411,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_9815]),
[final] ).
cnf(i_0_16412,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,esk47_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_9816]),
[final] ).
cnf(i_0_16413,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_9817]),
[final] ).
cnf(i_0_16414,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_9818]),
[final] ).
cnf(i_0_16415,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_9819]),
[final] ).
cnf(i_0_16416,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_9820]),
[final] ).
cnf(i_0_16417,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_9598]),
[final] ).
cnf(i_0_16418,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_9821]),
[final] ).
cnf(i_0_16419,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_9822]),
[final] ).
cnf(i_0_16420,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_9476]),
[final] ).
cnf(i_0_16421,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_9823]),
[final] ).
cnf(i_0_16422,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_9824]),
[final] ).
cnf(i_0_16423,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk422_2(X2,X1)),esk421_2(X2,X1)))
| c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_6982]),
[final] ).
cnf(i_0_16424,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_9825]),
[final] ).
cnf(i_0_16425,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_8817]),
[final] ).
cnf(i_0_16426,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_9826]),
[final] ).
cnf(i_0_16427,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_9496]),
[final] ).
cnf(i_0_16428,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_9827]),
[final] ).
cnf(i_0_16429,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_9828]),
[final] ).
cnf(i_0_16430,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_9829]),
[final] ).
cnf(i_0_16431,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_9829]),
[final] ).
cnf(i_0_16432,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_9830]),
[final] ).
cnf(i_0_16433,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_9831]),
[final] ).
cnf(i_0_16434,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_9832]),
[final] ).
cnf(i_0_16435,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_9833]),
[final] ).
cnf(i_0_16436,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_9834]),
[final] ).
cnf(i_0_16437,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_9835]),
[final] ).
cnf(i_0_16438,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_9836]),
[final] ).
cnf(i_0_16439,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_9837]),
[final] ).
cnf(i_0_16440,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_9838]),
[final] ).
cnf(i_0_16441,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_9838]),
[final] ).
cnf(i_0_16442,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_9837]),
[final] ).
cnf(i_0_16443,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_8071]),
[final] ).
cnf(i_0_16444,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_7527]),
[final] ).
cnf(i_0_16445,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_9839]),
[final] ).
cnf(i_0_16446,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_9840]),
[final] ).
cnf(i_0_16447,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_9423]),
[final] ).
cnf(i_0_16448,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_16449,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_9841]),
[final] ).
cnf(i_0_16450,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_9842]),
[final] ).
cnf(i_0_16451,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_16452,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_16453,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_16454,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_9843]),
[final] ).
cnf(i_0_16455,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_9844]),
[final] ).
cnf(i_0_16456,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_9845]),
[final] ).
cnf(i_0_16457,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_9846]),
[final] ).
cnf(i_0_16458,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_9815]),
[final] ).
cnf(i_0_16459,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk490_2(X1,X2)),esk489_2(X1,X2)))
| c_List_Olinorder__class_Osorted(X2,X1)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[i_0_7546]),
[final] ).
cnf(i_0_16460,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_9847]),
[final] ).
cnf(i_0_16461,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_9848]),
[final] ).
cnf(i_0_16462,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_9849]),
[final] ).
cnf(i_0_16463,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_9850]),
[final] ).
cnf(i_0_16464,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_9851]),
[final] ).
cnf(i_0_16465,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_9852]),
[final] ).
cnf(i_0_16466,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_9853]),
[final] ).
cnf(i_0_16467,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_9853]),
[final] ).
cnf(i_0_16468,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_9854]),
[final] ).
cnf(i_0_16469,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_9496]),
[final] ).
cnf(i_0_16470,plain,
c_Com_Ovname_Ovname__rec(X1,X2,X3,c_Com_Ovname_OGlb(X4)) = hAPP(X2,X4),
inference(split_conjunct,[status(thm)],[i_0_9855]),
[final] ).
cnf(i_0_16471,plain,
c_Com_Ovname_Ovname__rec(X1,X2,X3,c_Com_Ovname_OLoc(X4)) = hAPP(X3,X4),
inference(split_conjunct,[status(thm)],[i_0_9856]),
[final] ).
cnf(i_0_16472,plain,
c_Com_Ovname_Ovname__case(X1,X2,X3,c_Com_Ovname_OGlb(X4)) = hAPP(X2,X4),
inference(split_conjunct,[status(thm)],[i_0_9857]),
[final] ).
cnf(i_0_16473,plain,
c_Com_Ovname_Ovname__case(X1,X2,X3,c_Com_Ovname_OLoc(X4)) = hAPP(X3,X4),
inference(split_conjunct,[status(thm)],[i_0_9858]),
[final] ).
cnf(i_0_16474,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,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9589]),
[final] ).
cnf(i_0_16475,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_9859]),
[final] ).
cnf(i_0_16476,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_9860]),
[final] ).
cnf(i_0_16477,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_9861]),
[final] ).
cnf(i_0_16478,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_9861]),
[final] ).
cnf(i_0_16479,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_9862]),
[final] ).
cnf(i_0_16480,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_7552]),
[final] ).
cnf(i_0_16481,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_7562]),
[final] ).
cnf(i_0_16482,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_9863]),
[final] ).
cnf(i_0_16483,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_9864]),
[final] ).
cnf(i_0_16484,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_9865]),
[final] ).
cnf(i_0_16485,plain,
( c_Equiv__Relations_Oequivp(X2,X1)
| ~ hBOOL(hAPP(hAPP(X1,esk273_1(X1)),esk274_1(X1)))
| hAPP(X1,esk273_1(X1)) != hAPP(X1,esk274_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9866]),
[final] ).
cnf(i_0_16486,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_9867]),
[final] ).
cnf(i_0_16487,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_9868]),
[final] ).
cnf(i_0_16488,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_9869]),
[final] ).
cnf(i_0_16489,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_9870]),
[final] ).
cnf(i_0_16490,plain,
( hBOOL(hAPP(X1,hAPP(c_Nat_OSuc,esk35_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_9871]),
[final] ).
cnf(i_0_16491,plain,
( X1 = hAPP(c_Nat_OSuc,esk37_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_9323]),
[final] ).
cnf(i_0_16492,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_9375]),
[final] ).
cnf(i_0_16493,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_8976]),
[final] ).
cnf(i_0_16494,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_9872]),
[final] ).
cnf(i_0_16495,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_9873]),
[final] ).
cnf(i_0_16496,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_9613]),
[final] ).
cnf(i_0_16497,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_9612]),
[final] ).
cnf(i_0_16498,plain,
( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X2)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,esk46_2(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9672]),
[final] ).
cnf(i_0_16499,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_9685]),
[final] ).
cnf(i_0_16500,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_9874]),
[final] ).
cnf(i_0_16501,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_9875]),
[final] ).
cnf(i_0_16502,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_9876]),
[final] ).
cnf(i_0_16503,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_9877]),
[final] ).
cnf(i_0_16504,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_8814]),
[final] ).
cnf(i_0_16505,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_8814]),
[final] ).
cnf(i_0_16506,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_9878]),
[final] ).
cnf(i_0_16507,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_9879]),
[final] ).
cnf(i_0_16508,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_9880]),
[final] ).
cnf(i_0_16509,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_9881]),
[final] ).
cnf(i_0_16510,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_7860]),
[final] ).
cnf(i_0_16511,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_9882]),
[final] ).
cnf(i_0_16512,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_9883]),
[final] ).
cnf(i_0_16513,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_9884]),
[final] ).
cnf(i_0_16514,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_9885]),
[final] ).
cnf(i_0_16515,plain,
c_Fun_Oinj__on(X1,tc_Option_Ooption(X1),c_Option_Ooption_OSome(X1),X2),
inference(split_conjunct,[status(thm)],[i_0_9886]),
[final] ).
cnf(i_0_16516,plain,
c_List_Olistrelp(X1,X2,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
inference(split_conjunct,[status(thm)],[i_0_9887]),
[final] ).
cnf(i_0_16517,plain,
c_List_Olistrelp(X1,X2,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
inference(split_conjunct,[status(thm)],[i_0_9888]),
[final] ).
cnf(i_0_16518,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_16519,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_16520,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_9731]),
[final] ).
cnf(i_0_16521,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_9889]),
[final] ).
cnf(i_0_16522,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_9764]),
[final] ).
cnf(i_0_16523,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_9890]),
[final] ).
cnf(i_0_16524,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_9891]),
[final] ).
cnf(i_0_16525,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_9891]),
[final] ).
cnf(i_0_16526,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_9892]),
[final] ).
cnf(i_0_16527,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_9893]),
[final] ).
cnf(i_0_16528,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_9837]),
[final] ).
cnf(i_0_16529,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_9838]),
[final] ).
cnf(i_0_16530,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_16531,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_9894]),
[final] ).
cnf(i_0_16532,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_9895]),
[final] ).
cnf(i_0_16533,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_9896]),
[final] ).
cnf(i_0_16534,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_9897]),
[final] ).
cnf(i_0_16535,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_9898]),
[final] ).
cnf(i_0_16536,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_9700]),
[final] ).
cnf(i_0_16537,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_9899,c_0_8159]),c_0_8159]),
[final] ).
cnf(i_0_16538,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_9900]),
[final] ).
cnf(i_0_16539,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_9901]),
[final] ).
cnf(i_0_16540,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_9902]),
[final] ).
cnf(i_0_16541,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_9903]),
[final] ).
cnf(i_0_16542,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_9904]),
[final] ).
cnf(i_0_16543,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_9905]),
[final] ).
cnf(i_0_16544,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_9906]),
[final] ).
cnf(i_0_16545,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_9907]),
[final] ).
cnf(i_0_16546,plain,
c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X2),
inference(split_conjunct,[status(thm)],[i_0_9908]),
[final] ).
cnf(i_0_16547,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(split_conjunct,[status(thm)],[i_0_9909]),
[final] ).
cnf(i_0_16548,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_7787]),
[final] ).
cnf(i_0_16549,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_9910]),
[final] ).
cnf(i_0_16550,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_9911]),
[final] ).
cnf(i_0_16551,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_9912]),
[final] ).
cnf(i_0_16552,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_9913,c_0_6062]),
[final] ).
cnf(i_0_16553,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_9914]),
[final] ).
cnf(i_0_16554,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_9915,c_0_8159]),
[final] ).
cnf(i_0_16555,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_9916]),
[final] ).
cnf(i_0_16556,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_9917]),
[final] ).
cnf(i_0_16557,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_9918]),
[final] ).
cnf(i_0_16558,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_16559,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_9919]),
[final] ).
cnf(i_0_16560,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_9920]),
[final] ).
cnf(i_0_16561,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_9921]),
[final] ).
cnf(i_0_16562,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_9922]),
[final] ).
cnf(i_0_16563,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_9923]),
[final] ).
cnf(i_0_16564,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_9924]),
[final] ).
cnf(i_0_16565,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_9925]),
[final] ).
cnf(i_0_16566,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_9926,c_0_6015]),c_0_6015]),
[final] ).
cnf(i_0_16567,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_9927]),
[final] ).
cnf(i_0_16568,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_9928]),
[final] ).
cnf(i_0_16569,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_9929]),
[final] ).
cnf(i_0_16570,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_9930]),
[final] ).
cnf(i_0_16571,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_9931]),
[final] ).
cnf(i_0_16572,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_16573,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_9932]),
[final] ).
cnf(i_0_16574,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_9932]),
[final] ).
cnf(i_0_16575,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_9933,c_0_6014]),c_0_6015]),c_0_6016]),c_0_6016]),
[final] ).
cnf(i_0_16576,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_9934]),
[final] ).
cnf(i_0_16577,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_9935]),
[final] ).
cnf(i_0_16578,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_9936]),
[final] ).
cnf(i_0_16579,plain,
c_Natural_Oevaln(c_Com_Ocom_OSKIP,X1,X2,X1),
inference(split_conjunct,[status(thm)],[i_0_9937]),
[final] ).
cnf(i_0_16580,plain,
c_Natural_Oevaln(c_Com_Ocom_OSKIP,X1,X2,X1),
inference(split_conjunct,[status(thm)],[i_0_9938]),
[final] ).
cnf(i_0_16581,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_9939]),
[final] ).
cnf(i_0_16582,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_9940]),
[final] ).
cnf(i_0_16583,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_9941]),
[final] ).
cnf(i_0_16584,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_9942]),
[final] ).
cnf(i_0_16585,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_9943]),
[final] ).
cnf(i_0_16586,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_9944]),
[final] ).
cnf(i_0_16587,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_9945]),
[final] ).
cnf(i_0_16588,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_9946]),
[final] ).
cnf(i_0_16589,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_9947]),
[final] ).
cnf(i_0_16590,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_9948]),
[final] ).
cnf(i_0_16591,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_9949]),
[final] ).
cnf(i_0_16592,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_9950]),
[final] ).
cnf(i_0_16593,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_9951]),
[final] ).
cnf(i_0_16594,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_9952]),
[final] ).
cnf(i_0_16595,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_9953]),
[final] ).
cnf(i_0_16596,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_9954]),
[final] ).
cnf(i_0_16597,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_9955]),
[final] ).
cnf(i_0_16598,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_9956]),
[final] ).
cnf(i_0_16599,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_9941]),
[final] ).
cnf(i_0_16600,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_9942]),
[final] ).
cnf(i_0_16601,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_9943]),
[final] ).
cnf(i_0_16602,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_9957]),
[final] ).
cnf(i_0_16603,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_9958]),
[final] ).
cnf(i_0_16604,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_9959]),
[final] ).
cnf(i_0_16605,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_9960]),
[final] ).
cnf(i_0_16606,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_9961]),
[final] ).
cnf(i_0_16607,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_16608,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_9962]),
[final] ).
cnf(i_0_16609,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_9963]),
[final] ).
cnf(i_0_16610,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_9964]),
[final] ).
cnf(i_0_16611,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_9965,c_0_6016]),
[final] ).
cnf(i_0_16612,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_8916]),
[final] ).
cnf(i_0_16613,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_9966]),
[final] ).
cnf(i_0_16614,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X2),esk106_2(X1,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9967]),
[final] ).
cnf(i_0_16615,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk107_2(X2,X1)),X2))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_9968]),
[final] ).
cnf(i_0_16616,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_9969]),
[final] ).
cnf(i_0_16617,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_9970,c_0_6135]),
[final] ).
cnf(i_0_16618,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_9649]),
[final] ).
cnf(i_0_16619,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_9401]),
[final] ).
cnf(i_0_16620,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_9971]),
[final] ).
cnf(i_0_16621,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_9972]),
[final] ).
cnf(i_0_16622,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_9973]),
[final] ).
cnf(i_0_16623,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_9974]),
[final] ).
cnf(i_0_16624,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_9479]),
[final] ).
cnf(i_0_16625,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_9975]),
[final] ).
cnf(i_0_16626,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_9976]),
[final] ).
cnf(i_0_16627,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_9977]),
[final] ).
cnf(i_0_16628,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_9978]),
[final] ).
cnf(i_0_16629,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_9979]),
[final] ).
cnf(i_0_16630,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_9980]),
[final] ).
cnf(i_0_16631,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_9981]),
[final] ).
cnf(i_0_16632,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_9982]),
[final] ).
cnf(i_0_16633,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_9983]),
[final] ).
cnf(i_0_16634,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_9984,c_0_6135]),
[final] ).
cnf(i_0_16635,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_9985,c_0_6135]),
[final] ).
cnf(i_0_16636,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_9986,c_0_6135]),
[final] ).
cnf(i_0_16637,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_9987]),
[final] ).
cnf(i_0_16638,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_9485]),
[final] ).
cnf(i_0_16639,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk129_2(X1,X2)),X1))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9545]),
[final] ).
cnf(i_0_16640,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk127_2(X1,X2)),X1))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_9544]),
[final] ).
cnf(i_0_16641,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_9504]),
[final] ).
cnf(i_0_16642,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_9503]),
[final] ).
cnf(i_0_16643,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_9988]),
[final] ).
cnf(i_0_16644,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_9989]),
[final] ).
cnf(i_0_16645,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_9990]),
[final] ).
cnf(i_0_16646,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_9991]),
[final] ).
cnf(i_0_16647,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_9992]),
[final] ).
cnf(i_0_16648,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_9993]),
[final] ).
cnf(i_0_16649,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_9994]),
[final] ).
cnf(i_0_16650,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_9995]),
[final] ).
cnf(i_0_16651,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_9546]),
[final] ).
cnf(i_0_16652,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_9996]),
[final] ).
cnf(i_0_16653,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_9997]),
[final] ).
cnf(i_0_16654,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_9998]),
[final] ).
cnf(i_0_16655,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_9999]),
[final] ).
cnf(i_0_16656,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_10000]),
[final] ).
cnf(i_0_16657,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_10001]),
[final] ).
cnf(i_0_16658,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_10002]),
[final] ).
cnf(i_0_16659,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_16660,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_10003]),
[final] ).
cnf(i_0_16661,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_10004]),
[final] ).
cnf(i_0_16662,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_10005]),
[final] ).
cnf(i_0_16663,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_10006]),
[final] ).
cnf(i_0_16664,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_10007]),
[final] ).
cnf(i_0_16665,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_9641]),
[final] ).
cnf(i_0_16666,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_10008]),
[final] ).
cnf(i_0_16667,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_16668,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_10009]),
[final] ).
cnf(i_0_16669,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_10010]),
[final] ).
cnf(i_0_16670,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_10011]),
[final] ).
cnf(i_0_16671,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_10012]),
[final] ).
cnf(i_0_16672,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_9932]),
[final] ).
cnf(i_0_16673,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_10013]),
[final] ).
cnf(i_0_16674,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_10014]),
[final] ).
cnf(i_0_16675,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_10015]),
[final] ).
cnf(i_0_16676,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_10016]),
[final] ).
cnf(i_0_16677,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_10017]),
[final] ).
cnf(i_0_16678,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_10018]),
[final] ).
cnf(i_0_16679,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_10019]),
[final] ).
cnf(i_0_16680,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_10020]),
[final] ).
cnf(i_0_16681,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_10021]),
[final] ).
cnf(i_0_16682,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_10022]),
[final] ).
cnf(i_0_16683,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_10023]),
[final] ).
cnf(i_0_16684,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_10024]),
[final] ).
cnf(i_0_16685,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_10025]),
[final] ).
cnf(i_0_16686,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_10026]),
[final] ).
cnf(i_0_16687,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_10027]),
[final] ).
cnf(i_0_16688,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_10028]),
[final] ).
cnf(i_0_16689,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_10029]),
[final] ).
cnf(i_0_16690,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_10030]),
[final] ).
cnf(i_0_16691,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_9748]),
[final] ).
cnf(i_0_16692,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_10031]),
[final] ).
cnf(i_0_16693,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_10032]),
[final] ).
cnf(i_0_16694,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_10033,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_16695,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_10034,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_16696,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_10035,c_0_6135]),
[final] ).
cnf(i_0_16697,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_10036]),
[final] ).
cnf(i_0_16698,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_10037]),
[final] ).
cnf(i_0_16699,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_10038]),
[final] ).
cnf(i_0_16700,plain,
( c_Relation_Osingle__valued(X3,X2,X1)
| esk380_3(X1,X2,X3) != esk381_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_6930]),
[final] ).
cnf(i_0_16701,plain,
( c_Relation_Ototal__on(X3,X2,X1)
| esk370_3(X1,X2,X3) != esk371_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_6756]),
[final] ).
cnf(i_0_16702,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_10039]),
[final] ).
cnf(i_0_16703,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_10040]),
[final] ).
cnf(i_0_16704,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_10041]),
[final] ).
cnf(i_0_16705,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_10042]),
[final] ).
cnf(i_0_16706,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_9121]),
[final] ).
cnf(i_0_16707,plain,
( c_Wellfounded_OwfP(X1,X2)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk325_2(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_10043]),
[final] ).
cnf(i_0_16708,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_10044]),
[final] ).
cnf(i_0_16709,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_10045,c_0_6135]),
[final] ).
cnf(i_0_16710,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_9473]),
[final] ).
cnf(i_0_16711,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_10046]),
[final] ).
cnf(i_0_16712,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_10047]),
[final] ).
cnf(i_0_16713,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_9783]),
[final] ).
cnf(i_0_16714,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_10048]),
[final] ).
cnf(i_0_16715,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_10049]),
[final] ).
cnf(i_0_16716,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_10050]),
[final] ).
cnf(i_0_16717,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_10051]),
[final] ).
cnf(i_0_16718,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_10052]),
[final] ).
cnf(i_0_16719,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_9573]),
[final] ).
cnf(i_0_16720,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_10053]),
[final] ).
cnf(i_0_16721,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_10054]),
[final] ).
cnf(i_0_16722,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_10055]),
[final] ).
cnf(i_0_16723,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_10056]),
[final] ).
cnf(i_0_16724,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_10057]),
[final] ).
cnf(i_0_16725,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_10058]),
[final] ).
cnf(i_0_16726,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_10059]),
[final] ).
cnf(i_0_16727,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_10060]),
[final] ).
cnf(i_0_16728,plain,
hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),hAPP(X3,X4)) = X3,
inference(split_conjunct,[status(thm)],[i_0_10061]),
[final] ).
cnf(i_0_16729,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_10062]),
[final] ).
cnf(i_0_16730,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_10063]),
[final] ).
cnf(i_0_16731,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_10064,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_16732,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk40_2(X2,X1)) = X2
| ~ 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_16733,plain,
( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk49_2(X2,X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10065]),
[final] ).
cnf(i_0_16734,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_10066]),
[final] ).
cnf(i_0_16735,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),esk46_2(X1,X2))
| hBOOL(hAPP(X2,hAPP(c_Int_Onat,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9672]),
[final] ).
cnf(i_0_16736,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_10067]),
[final] ).
cnf(i_0_16737,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_9815]),
[final] ).
cnf(i_0_16738,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_10068]),
[final] ).
cnf(i_0_16739,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_10069]),
[final] ).
cnf(i_0_16740,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_10070]),
[final] ).
cnf(i_0_16741,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_9572]),
[final] ).
cnf(i_0_16742,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_10071]),
[final] ).
cnf(i_0_16743,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_10072]),
[final] ).
cnf(i_0_16744,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_9570]),
[final] ).
cnf(i_0_16745,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_9623]),
[final] ).
cnf(i_0_16746,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_10073]),
[final] ).
cnf(i_0_16747,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_10074,c_0_6135]),
[final] ).
cnf(i_0_16748,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_10075,c_0_6135]),
[final] ).
cnf(i_0_16749,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_9578]),
[final] ).
cnf(i_0_16750,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_10076]),
[final] ).
cnf(i_0_16751,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_10077]),
[final] ).
cnf(i_0_16752,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_10078]),
[final] ).
cnf(i_0_16753,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_10079]),
[final] ).
cnf(i_0_16754,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_10080]),
[final] ).
cnf(i_0_16755,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_10081,c_0_6169]),c_0_6016]),
[final] ).
cnf(i_0_16756,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_9813]),
[final] ).
cnf(i_0_16757,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_9872]),
[final] ).
cnf(i_0_16758,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_9873]),
[final] ).
cnf(i_0_16759,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_10082]),
[final] ).
cnf(i_0_16760,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_10083]),
[final] ).
cnf(i_0_16761,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_10084]),
[final] ).
cnf(i_0_16762,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_10085]),
[final] ).
cnf(i_0_16763,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_10086]),
[final] ).
cnf(i_0_16764,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_10087]),
[final] ).
cnf(i_0_16765,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_10088]),
[final] ).
cnf(i_0_16766,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_10089]),
[final] ).
cnf(i_0_16767,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_10090]),
[final] ).
cnf(i_0_16768,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_10091]),
[final] ).
cnf(i_0_16769,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_10092]),
[final] ).
cnf(i_0_16770,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_10093]),
[final] ).
cnf(i_0_16771,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_10094]),
[final] ).
cnf(i_0_16772,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_10095]),
[final] ).
cnf(i_0_16773,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_10096]),
[final] ).
cnf(i_0_16774,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_10097,c_0_6016]),
[final] ).
cnf(i_0_16775,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_8122]),
[final] ).
cnf(i_0_16776,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_10098]),
[final] ).
cnf(i_0_16777,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_10099]),
[final] ).
cnf(i_0_16778,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_10100]),
[final] ).
cnf(i_0_16779,plain,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,esk35_2(X2,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9871]),
[final] ).
cnf(i_0_16780,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_10101]),
[final] ).
cnf(i_0_16781,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_10102]),
[final] ).
cnf(i_0_16782,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_10103]),
[final] ).
cnf(i_0_16783,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_10104]),
[final] ).
cnf(i_0_16784,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_10105]),
[final] ).
cnf(i_0_16785,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_10106]),
[final] ).
cnf(i_0_16786,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_10107]),
[final] ).
cnf(i_0_16787,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_10108]),
[final] ).
cnf(i_0_16788,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_10109]),
[final] ).
cnf(i_0_16789,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_10110]),
[final] ).
cnf(i_0_16790,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_10111]),
[final] ).
cnf(i_0_16791,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk52_1(X1)))
| hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9444]),
[final] ).
cnf(i_0_16792,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_9632]),
[final] ).
cnf(i_0_16793,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_10112]),
[final] ).
cnf(i_0_16794,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_10113]),
[final] ).
cnf(i_0_16795,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_10114]),
[final] ).
cnf(i_0_16796,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_10115]),
[final] ).
cnf(i_0_16797,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_9399]),
[final] ).
cnf(i_0_16798,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_9968]),
[final] ).
cnf(i_0_16799,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_10116]),
[final] ).
cnf(i_0_16800,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_9967]),
[final] ).
cnf(i_0_16801,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_10117]),
[final] ).
cnf(i_0_16802,plain,
( hBOOL(hAPP(X1,esk351_2(X2,X1)))
| ~ hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_10118]),
[final] ).
cnf(i_0_16803,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_10119]),
[final] ).
cnf(i_0_16804,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_10120]),
[final] ).
cnf(i_0_16805,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_10121]),
[final] ).
cnf(i_0_16806,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_10122]),
[final] ).
cnf(i_0_16807,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_10123]),
[final] ).
cnf(i_0_16808,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_7761]),
[final] ).
cnf(i_0_16809,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_10124]),
[final] ).
cnf(i_0_16810,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_10125]),
[final] ).
cnf(i_0_16811,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_16812,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_16813,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_10126]),
[final] ).
cnf(i_0_16814,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_10127]),
[final] ).
cnf(i_0_16815,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_10128]),
[final] ).
cnf(i_0_16816,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_10129]),
[final] ).
cnf(i_0_16817,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_10130]),
[final] ).
cnf(i_0_16818,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_10131]),
[final] ).
cnf(i_0_16819,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_10132]),
[final] ).
cnf(i_0_16820,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_10133]),
[final] ).
cnf(i_0_16821,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_10134]),
[final] ).
cnf(i_0_16822,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_10135]),
[final] ).
cnf(i_0_16823,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_10124]),
[final] ).
cnf(i_0_16824,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_10125]),
[final] ).
cnf(i_0_16825,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_10136]),
[final] ).
cnf(i_0_16826,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_10137]),
[final] ).
cnf(i_0_16827,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_10138]),
[final] ).
cnf(i_0_16828,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_10139]),
[final] ).
cnf(i_0_16829,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_10140]),
[final] ).
cnf(i_0_16830,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_10141]),
[final] ).
cnf(i_0_16831,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_10142]),
[final] ).
cnf(i_0_16832,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_10143,c_0_6135]),
[final] ).
cnf(i_0_16833,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_10144]),
[final] ).
cnf(i_0_16834,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_10145,c_0_6014]),c_0_6015]),c_0_6016]),
[final] ).
cnf(i_0_16835,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_9996]),
[final] ).
cnf(i_0_16836,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_10146]),
[final] ).
cnf(i_0_16837,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_10147]),
[final] ).
cnf(i_0_16838,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_10148]),
[final] ).
cnf(i_0_16839,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_9987]),
[final] ).
cnf(i_0_16840,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_10149]),
[final] ).
cnf(i_0_16841,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_7748]),
[final] ).
cnf(i_0_16842,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_7748]),
[final] ).
cnf(i_0_16843,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_8480]),
[final] ).
cnf(i_0_16844,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_8481]),
[final] ).
cnf(i_0_16845,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_10150,c_0_7027]),
[final] ).
cnf(i_0_16846,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_16847,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_10151]),
[final] ).
cnf(i_0_16848,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_10152]),
[final] ).
cnf(i_0_16849,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk448_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_9781]),
[final] ).
cnf(i_0_16850,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_10153]),
[final] ).
cnf(i_0_16851,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_10154]),
[final] ).
cnf(i_0_16852,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_9754]),
[final] ).
cnf(i_0_16853,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_10155]),
[final] ).
cnf(i_0_16854,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_10156]),
[final] ).
cnf(i_0_16855,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_9837]),
[final] ).
cnf(i_0_16856,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_9838]),
[final] ).
cnf(i_0_16857,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_10157]),
[final] ).
cnf(i_0_16858,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_10158]),
[final] ).
cnf(i_0_16859,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_10159]),
[final] ).
cnf(i_0_16860,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_10160]),
[final] ).
cnf(i_0_16861,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_10161]),
[final] ).
cnf(i_0_16862,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_10162]),
[final] ).
cnf(i_0_16863,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_10163]),
[final] ).
cnf(i_0_16864,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_10164]),
[final] ).
cnf(i_0_16865,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_10165]),
[final] ).
cnf(i_0_16866,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_10166]),
[final] ).
cnf(i_0_16867,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_10167]),
[final] ).
cnf(i_0_16868,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_10168]),
[final] ).
cnf(i_0_16869,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_10169]),
[final] ).
cnf(i_0_16870,plain,
( hAPP(hAPP(c_List_Onth(X1),X2),esk452_2(X2,X1)) = hAPP(hAPP(c_List_Onth(X1),X2),esk453_2(X2,X1))
| hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_8205]),
[final] ).
cnf(i_0_16871,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_10170]),
[final] ).
cnf(i_0_16872,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_10171]),
[final] ).
cnf(i_0_16873,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_10014]),
[final] ).
cnf(i_0_16874,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_10017]),
[final] ).
cnf(i_0_16875,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_10019]),
[final] ).
cnf(i_0_16876,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_10023]),
[final] ).
cnf(i_0_16877,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_10172]),
[final] ).
cnf(i_0_16878,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_10173,c_0_7027]),
[final] ).
cnf(i_0_16879,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_10174]),
[final] ).
cnf(i_0_16880,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_10175]),
[final] ).
cnf(i_0_16881,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_10176]),
[final] ).
cnf(i_0_16882,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_16883,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_16884,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_10177]),
[final] ).
cnf(i_0_16885,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_10178]),
[final] ).
cnf(i_0_16886,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_10179]),
[final] ).
cnf(i_0_16887,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_10180]),
[final] ).
cnf(i_0_16888,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_10181]),
[final] ).
cnf(i_0_16889,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_10182]),
[final] ).
cnf(i_0_16890,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_10183]),
[final] ).
cnf(i_0_16891,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_10184]),
[final] ).
cnf(i_0_16892,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_9701]),
[final] ).
cnf(i_0_16893,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_9702]),
[final] ).
cnf(i_0_16894,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_9703]),
[final] ).
cnf(i_0_16895,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_9704]),
[final] ).
cnf(i_0_16896,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_9281]),
[final] ).
cnf(i_0_16897,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_10185]),
[final] ).
cnf(i_0_16898,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_10186]),
[final] ).
cnf(i_0_16899,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_10187]),
[final] ).
cnf(i_0_16900,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_10188]),
[final] ).
cnf(i_0_16901,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_10189]),
[final] ).
cnf(i_0_16902,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_10190]),
[final] ).
cnf(i_0_16903,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_10191]),
[final] ).
cnf(i_0_16904,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_10192]),
[final] ).
cnf(i_0_16905,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_10193]),
[final] ).
cnf(i_0_16906,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_10194]),
[final] ).
cnf(i_0_16907,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_9884]),
[final] ).
cnf(i_0_16908,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_9885]),
[final] ).
cnf(i_0_16909,plain,
( X1 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk45_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_9769]),
[final] ).
cnf(i_0_16910,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_9850]),
[final] ).
cnf(i_0_16911,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)),esk124_1(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9877]),
[final] ).
cnf(i_0_16912,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_10195]),
[final] ).
cnf(i_0_16913,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_10196]),
[final] ).
cnf(i_0_16914,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_10197]),
[final] ).
cnf(i_0_16915,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_10198]),
[final] ).
cnf(i_0_16916,plain,
( hBOOL(hAPP(X1,esk51_1(X1)))
| ~ hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_9589]),
[final] ).
cnf(i_0_16917,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_5922]),
[final] ).
cnf(i_0_16918,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_16919,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_10199,c_0_7027]),
[final] ).
cnf(i_0_16920,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_10200]),
[final] ).
cnf(i_0_16921,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_10201]),
[final] ).
cnf(i_0_16922,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_9993]),
[final] ).
cnf(i_0_16923,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_10202]),
[final] ).
cnf(i_0_16924,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_10203]),
[final] ).
cnf(i_0_16925,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,esk57_1(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_9683]),
[final] ).
cnf(i_0_16926,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_10204]),
[final] ).
cnf(i_0_16927,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_10205]),
[final] ).
cnf(i_0_16928,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_10206]),
[final] ).
cnf(i_0_16929,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_10207]),
[final] ).
cnf(i_0_16930,plain,
( X1 = hAPP(c_Nat_OSuc,esk41_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_10208]),
[final] ).
cnf(i_0_16931,plain,
( X1 = hAPP(c_Nat_OSuc,esk36_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_10209]),
[final] ).
cnf(i_0_16932,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_10210]),
[final] ).
cnf(i_0_16933,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_10211]),
[final] ).
cnf(i_0_16934,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_10212]),
[final] ).
cnf(i_0_16935,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_10213]),
[final] ).
cnf(i_0_16936,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_10009]),
[final] ).
cnf(i_0_16937,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_10214]),
[final] ).
cnf(i_0_16938,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_10010]),
[final] ).
cnf(i_0_16939,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_10215]),
[final] ).
cnf(i_0_16940,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_10216]),
[final] ).
cnf(i_0_16941,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_10191]),
[final] ).
cnf(i_0_16942,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_10192]),
[final] ).
cnf(i_0_16943,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_10217]),
[final] ).
cnf(i_0_16944,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_10218]),
[final] ).
cnf(i_0_16945,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_9975]),
[final] ).
cnf(i_0_16946,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_10219]),
[final] ).
cnf(i_0_16947,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_10220]),
[final] ).
cnf(i_0_16948,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_10221]),
[final] ).
cnf(i_0_16949,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_10222]),
[final] ).
cnf(i_0_16950,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_10223]),
[final] ).
cnf(i_0_16951,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_10224,c_0_6135]),
[final] ).
cnf(i_0_16952,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_16953,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_9293]),
[final] ).
cnf(i_0_16954,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_10225]),
[final] ).
cnf(i_0_16955,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_9808]),
[final] ).
cnf(i_0_16956,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_9809]),
[final] ).
cnf(i_0_16957,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_9866]),
[final] ).
cnf(i_0_16958,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_10226]),
[final] ).
cnf(i_0_16959,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_10227]),
[final] ).
cnf(i_0_16960,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_10228]),
[final] ).
cnf(i_0_16961,plain,
( hAPP(c_Finite__Set_Ocard(X1),esk149_3(X2,X3,X1)) = X2
| hAPP(c_Finite__Set_Ocard(X1),X3) != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7860]),
[final] ).
cnf(i_0_16962,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_10229]),
[final] ).
cnf(i_0_16963,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_10230,c_0_6135]),
[final] ).
cnf(i_0_16964,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_9672]),
[final] ).
cnf(i_0_16965,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_9903]),
[final] ).
cnf(i_0_16966,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_9573]),
[final] ).
cnf(i_0_16967,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_9789]),
[final] ).
cnf(i_0_16968,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_10049]),
[final] ).
cnf(i_0_16969,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_10049]),
[final] ).
cnf(i_0_16970,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_10231]),
[final] ).
cnf(i_0_16971,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_10232]),
[final] ).
cnf(i_0_16972,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_10233]),
[final] ).
cnf(i_0_16973,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_9621]),
[final] ).
cnf(i_0_16974,plain,
( X2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk46_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_9672]),
[final] ).
cnf(i_0_16975,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_10234]),
[final] ).
cnf(i_0_16976,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_16977,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_10235,c_0_7214]),
[final] ).
cnf(i_0_16978,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_10236]),
[final] ).
cnf(i_0_16979,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_10237]),
[final] ).
cnf(i_0_16980,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_10237]),
[final] ).
cnf(i_0_16981,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_10238]),
[final] ).
cnf(i_0_16982,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_10239]),
[final] ).
cnf(i_0_16983,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_9753]),
[final] ).
cnf(i_0_16984,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_10240]),
[final] ).
cnf(i_0_16985,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_9421]),
[final] ).
cnf(i_0_16986,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_10241]),
[final] ).
cnf(i_0_16987,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_10207]),
[final] ).
cnf(i_0_16988,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10242]),
[final] ).
cnf(i_0_16989,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_9181]),
[final] ).
cnf(i_0_16990,plain,
( hBOOL(hAPP(hAPP(X1,esk273_1(X1)),esk274_1(X1)))
| hAPP(X1,esk273_1(X1)) = hAPP(X1,esk274_1(X1))
| c_Equiv__Relations_Oequivp(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_9866]),
[final] ).
cnf(i_0_16991,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_10243]),
[final] ).
cnf(i_0_16992,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_10244]),
[final] ).
cnf(i_0_16993,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_10245]),
[final] ).
cnf(i_0_16994,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_10246]),
[final] ).
cnf(i_0_16995,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_10247]),
[final] ).
cnf(i_0_16996,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_10248]),
[final] ).
cnf(i_0_16997,plain,
( X1 = X2
| c_Com_Ocom_OLocal(X1,X3,X4) != c_Com_Ocom_OLocal(X2,X5,X6) ),
inference(split_conjunct,[status(thm)],[i_0_10249]),
[final] ).
cnf(i_0_16998,plain,
( X1 = X2
| c_Com_Ocom_OLocal(X3,X1,X4) != c_Com_Ocom_OLocal(X5,X2,X6) ),
inference(split_conjunct,[status(thm)],[i_0_10249]),
[final] ).
cnf(i_0_16999,plain,
( X1 = X2
| c_Com_Ocom_OLocal(X3,X4,X1) != c_Com_Ocom_OLocal(X5,X6,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10249]),
[final] ).
cnf(i_0_17000,plain,
( X1 = X2
| c_Com_Ocom_OCond(X1,X3,X4) != c_Com_Ocom_OCond(X2,X5,X6) ),
inference(split_conjunct,[status(thm)],[i_0_10250]),
[final] ).
cnf(i_0_17001,plain,
( X1 = X2
| c_Com_Ocom_OCond(X3,X1,X4) != c_Com_Ocom_OCond(X5,X2,X6) ),
inference(split_conjunct,[status(thm)],[i_0_10250]),
[final] ).
cnf(i_0_17002,plain,
( X1 = X2
| c_Com_Ocom_OCond(X3,X4,X1) != c_Com_Ocom_OCond(X5,X6,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10250]),
[final] ).
cnf(i_0_17003,plain,
( X1 = X2
| c_Com_Ocom_OCall(X1,X3,X4) != c_Com_Ocom_OCall(X2,X5,X6) ),
inference(split_conjunct,[status(thm)],[i_0_10251]),
[final] ).
cnf(i_0_17004,plain,
( X1 = X2
| c_Com_Ocom_OCall(X3,X1,X4) != c_Com_Ocom_OCall(X5,X2,X6) ),
inference(split_conjunct,[status(thm)],[i_0_10251]),
[final] ).
cnf(i_0_17005,plain,
( X1 = X2
| c_Com_Ocom_OCall(X3,X4,X1) != c_Com_Ocom_OCall(X5,X6,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10251]),
[final] ).
cnf(i_0_17006,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_10252]),
[final] ).
cnf(i_0_17007,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_10253]),
[final] ).
cnf(i_0_17008,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_9891]),
[final] ).
cnf(i_0_17009,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_10254]),
[final] ).
cnf(i_0_17010,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_9860]),
[final] ).
cnf(i_0_17011,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_17012,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_10219]),
[final] ).
cnf(i_0_17013,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_10220]),
[final] ).
cnf(i_0_17014,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_10255]),
[final] ).
cnf(i_0_17015,plain,
c_Com_Ocom_OLocal(X1,X2,X3) != c_Com_Ocom_OCond(X4,X5,X6),
inference(split_conjunct,[status(thm)],[i_0_10256]),
[final] ).
cnf(i_0_17016,plain,
c_Com_Ocom_OLocal(X1,X2,X3) != c_Com_Ocom_OCall(X4,X5,X6),
inference(split_conjunct,[status(thm)],[i_0_10257]),
[final] ).
cnf(i_0_17017,plain,
c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OLocal(X4,X5,X6),
inference(split_conjunct,[status(thm)],[i_0_10258]),
[final] ).
cnf(i_0_17018,plain,
c_Com_Ocom_OCall(X1,X2,X3) != c_Com_Ocom_OLocal(X4,X5,X6),
inference(split_conjunct,[status(thm)],[i_0_10259]),
[final] ).
cnf(i_0_17019,plain,
c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OCall(X4,X5,X6),
inference(split_conjunct,[status(thm)],[i_0_10260]),
[final] ).
cnf(i_0_17020,plain,
c_Com_Ocom_OCall(X1,X2,X3) != c_Com_Ocom_OCond(X4,X5,X6),
inference(split_conjunct,[status(thm)],[i_0_10261]),
[final] ).
cnf(i_0_17021,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_10174]),
[final] ).
cnf(i_0_17022,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_10138]),
[final] ).
cnf(i_0_17023,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_9351]),
[final] ).
cnf(i_0_17024,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_10262]),
[final] ).
cnf(i_0_17025,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_10263]),
[final] ).
cnf(i_0_17026,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_10264]),
[final] ).
cnf(i_0_17027,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_10265]),
[final] ).
cnf(i_0_17028,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_17029,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_10266]),
[final] ).
cnf(i_0_17030,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_17031,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_10267]),
[final] ).
cnf(i_0_17032,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_10046]),
[final] ).
cnf(i_0_17033,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_10047]),
[final] ).
cnf(i_0_17034,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_10268]),
[final] ).
cnf(i_0_17035,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_10065]),
[final] ).
cnf(i_0_17036,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_10269]),
[final] ).
cnf(i_0_17037,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_10270]),
[final] ).
cnf(i_0_17038,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_10004]),
[final] ).
cnf(i_0_17039,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_10271]),
[final] ).
cnf(i_0_17040,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_10272]),
[final] ).
cnf(i_0_17041,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk54_1(X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9606]),
[final] ).
cnf(i_0_17042,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_10273]),
[final] ).
cnf(i_0_17043,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_10273]),
[final] ).
cnf(i_0_17044,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_10274]),
[final] ).
cnf(i_0_17045,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_10275]),
[final] ).
cnf(i_0_17046,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_10276]),
[final] ).
cnf(i_0_17047,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_10277]),
[final] ).
cnf(i_0_17048,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_10278]),
[final] ).
cnf(i_0_17049,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_10279]),
[final] ).
cnf(i_0_17050,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_9181]),
[final] ).
cnf(i_0_17051,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_17052,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_8605]),
[final] ).
cnf(i_0_17053,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_10280]),
[final] ).
cnf(i_0_17054,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_10281]),
[final] ).
cnf(i_0_17055,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_10282]),
[final] ).
cnf(i_0_17056,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_10283]),
[final] ).
cnf(i_0_17057,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_10284]),
[final] ).
cnf(i_0_17058,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_10285,c_0_6670]),
[final] ).
cnf(i_0_17059,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_10286]),
[final] ).
cnf(i_0_17060,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_10287]),
[final] ).
cnf(i_0_17061,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_10288]),
[final] ).
cnf(i_0_17062,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_10289]),
[final] ).
cnf(i_0_17063,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_10290]),
[final] ).
cnf(i_0_17064,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_10291]),
[final] ).
cnf(i_0_17065,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_9615]),
[final] ).
cnf(i_0_17066,plain,
( hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
| ~ hBOOL(hAPP(X1,esk52_1(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_9444]),
[final] ).
cnf(i_0_17067,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_10292]),
[final] ).
cnf(i_0_17068,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_9646]),
[final] ).
cnf(i_0_17069,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_9612]),
[final] ).
cnf(i_0_17070,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_9613]),
[final] ).
cnf(i_0_17071,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_10293]),
[final] ).
cnf(i_0_17072,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_10294]),
[final] ).
cnf(i_0_17073,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_10295]),
[final] ).
cnf(i_0_17074,plain,
( X1 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk60_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_10296]),
[final] ).
cnf(i_0_17075,plain,
( X1 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk66_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_10297]),
[final] ).
cnf(i_0_17076,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_10298]),
[final] ).
cnf(i_0_17077,plain,
( c_Wellfounded_Oacyclic(X1,X2)
| ~ c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10299]),
[final] ).
cnf(i_0_17078,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_9955]),
[final] ).
cnf(i_0_17079,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_10300]),
[final] ).
cnf(i_0_17080,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_10301]),
[final] ).
cnf(i_0_17081,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_10302]),
[final] ).
cnf(i_0_17082,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_10303]),
[final] ).
cnf(i_0_17083,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_10184]),
[final] ).
cnf(i_0_17084,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_10304]),
[final] ).
cnf(i_0_17085,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_10305]),
[final] ).
cnf(i_0_17086,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_10306]),
[final] ).
cnf(i_0_17087,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_10307]),
[final] ).
cnf(i_0_17088,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_10308]),
[final] ).
cnf(i_0_17089,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_10309]),
[final] ).
cnf(i_0_17090,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_10310]),
[final] ).
cnf(i_0_17091,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_10311]),
[final] ).
cnf(i_0_17092,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_10312]),
[final] ).
cnf(i_0_17093,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_fequal,X2)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_9961]),
[final] ).
cnf(i_0_17094,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_10313]),
[final] ).
cnf(i_0_17095,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_10314]),
[final] ).
cnf(i_0_17096,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_10315]),
[final] ).
cnf(i_0_17097,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_10316]),
[final] ).
cnf(i_0_17098,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_10317]),
[final] ).
cnf(i_0_17099,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X2),X1))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10170]),
[final] ).
cnf(i_0_17100,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_10318]),
[final] ).
cnf(i_0_17101,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_10319]),
[final] ).
cnf(i_0_17102,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_10320]),
[final] ).
cnf(i_0_17103,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_10321]),
[final] ).
cnf(i_0_17104,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_10322]),
[final] ).
cnf(i_0_17105,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_9837]),
[final] ).
cnf(i_0_17106,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_9838]),
[final] ).
cnf(i_0_17107,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_10323]),
[final] ).
cnf(i_0_17108,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_10324]),
[final] ).
cnf(i_0_17109,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_10325]),
[final] ).
cnf(i_0_17110,plain,
( X1 != X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9941]),
[final] ).
cnf(i_0_17111,plain,
( X1 != X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9942]),
[final] ).
cnf(i_0_17112,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_10326]),
[final] ).
cnf(i_0_17113,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_10327]),
[final] ).
cnf(i_0_17114,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_10197]),
[final] ).
cnf(i_0_17115,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_10197]),
[final] ).
cnf(i_0_17116,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_10277]),
[final] ).
cnf(i_0_17117,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_10328]),
[final] ).
cnf(i_0_17118,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_10277]),
[final] ).
cnf(i_0_17119,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_10328]),
[final] ).
cnf(i_0_17120,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_10329]),
[final] ).
cnf(i_0_17121,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_10330]),
[final] ).
cnf(i_0_17122,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_10331,c_0_7027]),
[final] ).
cnf(i_0_17123,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_10332]),
[final] ).
cnf(i_0_17124,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_10333,c_0_7027]),
[final] ).
cnf(i_0_17125,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_10334]),
[final] ).
cnf(i_0_17126,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_10335]),
[final] ).
cnf(i_0_17127,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_10336]),
[final] ).
cnf(i_0_17128,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_10337]),
[final] ).
cnf(i_0_17129,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_10338]),
[final] ).
cnf(i_0_17130,plain,
( hAPP(c_Com_Obody,X1) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),esk28_1(X1))
| ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_10339]),
[final] ).
cnf(i_0_17131,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_10340]),
[final] ).
cnf(i_0_17132,plain,
( X2 = X1
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10341]),
[final] ).
cnf(i_0_17133,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_10342]),
[final] ).
cnf(i_0_17134,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_10343]),
[final] ).
cnf(i_0_17135,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_10344]),
[final] ).
cnf(i_0_17136,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_10345]),
[final] ).
cnf(i_0_17137,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_10346]),
[final] ).
cnf(i_0_17138,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_10347]),
[final] ).
cnf(i_0_17139,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_10348]),
[final] ).
cnf(i_0_17140,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_10320]),
[final] ).
cnf(i_0_17141,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_10321]),
[final] ).
cnf(i_0_17142,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_10349]),
[final] ).
cnf(i_0_17143,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_10350]),
[final] ).
cnf(i_0_17144,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_10351]),
[final] ).
cnf(i_0_17145,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_10321]),
[final] ).
cnf(i_0_17146,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_10320]),
[final] ).
cnf(i_0_17147,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_10352]),
[final] ).
cnf(i_0_17148,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_10351]),
[final] ).
cnf(i_0_17149,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_10350]),
[final] ).
cnf(i_0_17150,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_10353]),
[final] ).
cnf(i_0_17151,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_10354]),
[final] ).
cnf(i_0_17152,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_10355]),
[final] ).
cnf(i_0_17153,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_10356]),
[final] ).
cnf(i_0_17154,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_10357]),
[final] ).
cnf(i_0_17155,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_10358]),
[final] ).
cnf(i_0_17156,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_9866]),
[final] ).
cnf(i_0_17157,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_10129]),
[final] ).
cnf(i_0_17158,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk57_1(X1)))
| hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9683]),
[final] ).
cnf(i_0_17159,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_10359]),
[final] ).
cnf(i_0_17160,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_10360]),
[final] ).
cnf(i_0_17161,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_10361]),
[final] ).
cnf(i_0_17162,plain,
( hBOOL(hAPP(X1,hAPP(c_Int_Onat,esk54_1(X1))))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9606]),
[final] ).
cnf(i_0_17163,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_10362]),
[final] ).
cnf(i_0_17164,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_10338]),
[final] ).
cnf(i_0_17165,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_9990]),
[final] ).
cnf(i_0_17166,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_10363,c_0_6015]),c_0_6015]),
[final] ).
cnf(i_0_17167,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_10364]),
[final] ).
cnf(i_0_17168,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_10365]),
[final] ).
cnf(i_0_17169,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_10366]),
[final] ).
cnf(i_0_17170,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_10367]),
[final] ).
cnf(i_0_17171,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_10368]),
[final] ).
cnf(i_0_17172,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_10369]),
[final] ).
cnf(i_0_17173,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_10370]),
[final] ).
cnf(i_0_17174,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_9323]),
[final] ).
cnf(i_0_17175,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_10371]),
[final] ).
cnf(i_0_17176,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_8518]),
[final] ).
cnf(i_0_17177,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_10372]),
[final] ).
cnf(i_0_17178,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_10373]),
[final] ).
cnf(i_0_17179,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_8520]),
[final] ).
cnf(i_0_17180,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_10374]),
[final] ).
cnf(i_0_17181,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_10375]),
[final] ).
cnf(i_0_17182,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_10186]),
[final] ).
cnf(i_0_17183,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_10376]),
[final] ).
cnf(i_0_17184,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_10377]),
[final] ).
cnf(i_0_17185,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_10378]),
[final] ).
cnf(i_0_17186,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_10379]),
[final] ).
cnf(i_0_17187,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_10380]),
[final] ).
cnf(i_0_17188,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_10381]),
[final] ).
cnf(i_0_17189,plain,
( c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X2))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10382]),
[final] ).
cnf(i_0_17190,plain,
( c_Wellfounded_Owf(X1,c_Wellfounded_Omlex__prod(X1,X3,X2))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10383]),
[final] ).
cnf(i_0_17191,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_9648]),
[final] ).
cnf(i_0_17192,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_10384]),
[final] ).
cnf(i_0_17193,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_10216]),
[final] ).
cnf(i_0_17194,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_10213]),
[final] ).
cnf(i_0_17195,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_10385]),
[final] ).
cnf(i_0_17196,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_10386]),
[final] ).
cnf(i_0_17197,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_10387]),
[final] ).
cnf(i_0_17198,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_10388]),
[final] ).
cnf(i_0_17199,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_10389]),
[final] ).
cnf(i_0_17200,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_10390]),
[final] ).
cnf(i_0_17201,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_10391]),
[final] ).
cnf(i_0_17202,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_10392]),
[final] ).
cnf(i_0_17203,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_10393]),
[final] ).
cnf(i_0_17204,plain,
( esk149_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_7860]),
[final] ).
cnf(i_0_17205,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_10162]),
[final] ).
cnf(i_0_17206,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_10394]),
[final] ).
cnf(i_0_17207,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_10395]),
[final] ).
cnf(i_0_17208,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_10396]),
[final] ).
cnf(i_0_17209,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_10397]),
[final] ).
cnf(i_0_17210,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_10398]),
[final] ).
cnf(i_0_17211,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_10399]),
[final] ).
cnf(i_0_17212,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_10400]),
[final] ).
cnf(i_0_17213,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_10401]),
[final] ).
cnf(i_0_17214,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_10402]),
[final] ).
cnf(i_0_17215,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_10394]),
[final] ).
cnf(i_0_17216,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_10403]),
[final] ).
cnf(i_0_17217,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_10404]),
[final] ).
cnf(i_0_17218,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_10405]),
[final] ).
cnf(i_0_17219,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_10406]),
[final] ).
cnf(i_0_17220,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_10407]),
[final] ).
cnf(i_0_17221,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_10135]),
[final] ).
cnf(i_0_17222,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_10408]),
[final] ).
cnf(i_0_17223,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_10409]),
[final] ).
cnf(i_0_17224,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_10410]),
[final] ).
cnf(i_0_17225,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_10411]),
[final] ).
cnf(i_0_17226,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_10412]),
[final] ).
cnf(i_0_17227,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_10413]),
[final] ).
cnf(i_0_17228,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_10120]),
[final] ).
cnf(i_0_17229,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_10414]),
[final] ).
cnf(i_0_17230,plain,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)),
inference(split_conjunct,[status(thm)],[i_0_10415]),
[final] ).
cnf(i_0_17231,plain,
hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_10416]),
[final] ).
cnf(i_0_17232,plain,
hAPP(c_Set_Ovimage(X1,X1,c_COMBI(X1)),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_10417]),
[final] ).
cnf(i_0_17233,plain,
hAPP(c_Set_Oimage(X1,X1,c_Fun_Oid(X1)),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_10418]),
[final] ).
cnf(i_0_17234,plain,
hAPP(c_Set_Oimage(X1,X1,c_COMBI(X1)),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_10419]),
[final] ).
cnf(i_0_17235,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_9612]),
[final] ).
cnf(i_0_17236,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_9613]),
[final] ).
cnf(i_0_17237,plain,
c_Sum__Type_OProjr(X1,X2,hAPP(c_Sum__Type_OInr(X2,X1),X3)) = X3,
inference(split_conjunct,[status(thm)],[i_0_10420]),
[final] ).
cnf(i_0_17238,plain,
c_Sum__Type_OProjl(X1,X2,hAPP(c_Sum__Type_OInl(X1,X2),X3)) = X3,
inference(split_conjunct,[status(thm)],[i_0_10421]),
[final] ).
cnf(i_0_17239,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_10422]),
[final] ).
cnf(i_0_17240,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_10124]),
[final] ).
cnf(i_0_17241,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_10125]),
[final] ).
cnf(i_0_17242,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_10423,c_0_8159]),
[final] ).
cnf(i_0_17243,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_10424,c_0_8159]),
[final] ).
cnf(i_0_17244,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_10234]),
[final] ).
cnf(i_0_17245,plain,
( hBOOL(X2)
| ~ hBOOL(hAPP(hAPP(c_fimplies,X1),X2))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10425]),
[final] ).
cnf(i_0_17246,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_10426]),
[final] ).
cnf(i_0_17247,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_10427]),
[final] ).
cnf(i_0_17248,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_10428]),
[final] ).
cnf(i_0_17249,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_10429]),
[final] ).
cnf(i_0_17250,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_10430]),
[final] ).
cnf(i_0_17251,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_10431]),
[final] ).
cnf(i_0_17252,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_10432]),
[final] ).
cnf(i_0_17253,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_10433]),
[final] ).
cnf(i_0_17254,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_10434]),
[final] ).
cnf(i_0_17255,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_10435]),
[final] ).
cnf(i_0_17256,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_10436]),
[final] ).
cnf(i_0_17257,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_10437]),
[final] ).
cnf(i_0_17258,plain,
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10438]),
[final] ).
cnf(i_0_17259,plain,
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10118]),
[final] ).
cnf(i_0_17260,plain,
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10439]),
[final] ).
cnf(i_0_17261,plain,
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10440]),
[final] ).
cnf(i_0_17262,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_10296]),
[final] ).
cnf(i_0_17263,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_10297]),
[final] ).
cnf(i_0_17264,plain,
( hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(hAPP(hAPP(c_fdisj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10441]),
[final] ).
cnf(i_0_17265,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_7552]),
[final] ).
cnf(i_0_17266,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_10163]),
[final] ).
cnf(i_0_17267,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_10442]),
[final] ).
cnf(i_0_17268,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_10443]),
[final] ).
cnf(i_0_17269,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_10209]),
[final] ).
cnf(i_0_17270,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_10444]),
[final] ).
cnf(i_0_17271,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_10445]),
[final] ).
cnf(i_0_17272,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_10446]),
[final] ).
cnf(i_0_17273,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_10447]),
[final] ).
cnf(i_0_17274,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10448]),
[final] ).
cnf(i_0_17275,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_10449]),
[final] ).
cnf(i_0_17276,plain,
( hAPP(hAPP(X2,X4),X3) = X4
| ~ c_Groups_Ocomm__monoid(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_10450]),
[final] ).
cnf(i_0_17277,plain,
( hAPP(hAPP(X2,X4),X4) = X4
| ~ c_Finite__Set_Ofolding__one__idem(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_10451]),
[final] ).
cnf(i_0_17278,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_10452]),
[final] ).
cnf(i_0_17279,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_10124]),
[final] ).
cnf(i_0_17280,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_10125]),
[final] ).
cnf(i_0_17281,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_10453]),
[final] ).
cnf(i_0_17282,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_10454]),
[final] ).
cnf(i_0_17283,plain,
hAPP(c_Sum__Type_OInl(X1,X2),X3) != hAPP(c_Sum__Type_OInr(X2,X1),X4),
inference(split_conjunct,[status(thm)],[i_0_10455]),
[final] ).
cnf(i_0_17284,plain,
hAPP(c_Sum__Type_OInl(X1,X2),X3) != hAPP(c_Sum__Type_OInr(X2,X1),X4),
inference(split_conjunct,[status(thm)],[i_0_10456]),
[final] ).
cnf(i_0_17285,plain,
hAPP(c_Sum__Type_OInr(X1,X2),X3) != hAPP(c_Sum__Type_OInl(X2,X1),X4),
inference(split_conjunct,[status(thm)],[i_0_10457]),
[final] ).
cnf(i_0_17286,plain,
hAPP(c_Sum__Type_OInr(X1,X2),X3) != hAPP(c_Sum__Type_OInl(X2,X1),X4),
inference(split_conjunct,[status(thm)],[i_0_10458]),
[final] ).
cnf(i_0_17287,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_10404]),
[final] ).
cnf(i_0_17288,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_10459]),
[final] ).
cnf(i_0_17289,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_10460]),
[final] ).
cnf(i_0_17290,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_10461]),
[final] ).
cnf(i_0_17291,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_10462]),
[final] ).
cnf(i_0_17292,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_10253]),
[final] ).
cnf(i_0_17293,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10463]),
[final] ).
cnf(i_0_17294,plain,
( hBOOL(X2)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10464]),
[final] ).
cnf(i_0_17295,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_10465]),
[final] ).
cnf(i_0_17296,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_10466]),
[final] ).
cnf(i_0_17297,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_10467]),
[final] ).
cnf(i_0_17298,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_10190]),
[final] ).
cnf(i_0_17299,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk124_1(X1)),X1))
| c_Nat__Transfer_Onat__set(X1) ),
inference(split_conjunct,[status(thm)],[i_0_9877]),
[final] ).
cnf(i_0_17300,plain,
hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = X3,
inference(split_conjunct,[status(thm)],[i_0_10468]),
[final] ).
cnf(i_0_17301,plain,
hAPP(c_List_Ohd(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = X2,
inference(split_conjunct,[status(thm)],[i_0_10469]),
[final] ).
cnf(i_0_17302,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_10470]),
[final] ).
cnf(i_0_17303,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_10470]),
[final] ).
cnf(i_0_17304,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_7562]),
[final] ).
cnf(i_0_17305,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_10471]),
[final] ).
cnf(i_0_17306,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_10282]),
[final] ).
cnf(i_0_17307,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_10284]),
[final] ).
cnf(i_0_17308,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_10329]),
[final] ).
cnf(i_0_17309,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_10472]),
[final] ).
cnf(i_0_17310,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_10473]),
[final] ).
cnf(i_0_17311,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_10474]),
[final] ).
cnf(i_0_17312,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_fequal,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10475]),
[final] ).
cnf(i_0_17313,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_10476]),
[final] ).
cnf(i_0_17314,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_10268]),
[final] ).
cnf(i_0_17315,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_10477]),
[final] ).
cnf(i_0_17316,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_10478]),
[final] ).
cnf(i_0_17317,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_10479]),
[final] ).
cnf(i_0_17318,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_10340]),
[final] ).
cnf(i_0_17319,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_10480]),
[final] ).
cnf(i_0_17320,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_10193]),
[final] ).
cnf(i_0_17321,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Oset(X1),X2))),
inference(split_conjunct,[status(thm)],[i_0_10481]),
[final] ).
cnf(i_0_17322,plain,
hAPP(c_Relation_Oconverse(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3)) = X3,
inference(split_conjunct,[status(thm)],[i_0_10482]),
[final] ).
cnf(i_0_17323,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_17324,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_10483]),
[final] ).
cnf(i_0_17325,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_10484]),
[final] ).
cnf(i_0_17326,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_10485]),
[final] ).
cnf(i_0_17327,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_10486]),
[final] ).
cnf(i_0_17328,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_10487]),
[final] ).
cnf(i_0_17329,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_10436]),
[final] ).
cnf(i_0_17330,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_10436]),
[final] ).
cnf(i_0_17331,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_10488]),
[final] ).
cnf(i_0_17332,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_10437]),
[final] ).
cnf(i_0_17333,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_10437]),
[final] ).
cnf(i_0_17334,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_10489]),
[final] ).
cnf(i_0_17335,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_9557]),
[final] ).
cnf(i_0_17336,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_9557]),
[final] ).
cnf(i_0_17337,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_9788]),
[final] ).
cnf(i_0_17338,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_10490]),
[final] ).
cnf(i_0_17339,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_10491]),
[final] ).
cnf(i_0_17340,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_10492]),
[final] ).
cnf(i_0_17341,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_10493]),
[final] ).
cnf(i_0_17342,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_10494]),
[final] ).
cnf(i_0_17343,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_10495]),
[final] ).
cnf(i_0_17344,plain,
( c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))
| ~ c_Wellfounded_Oacyclic(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10299]),
[final] ).
cnf(i_0_17345,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_10268]),
[final] ).
cnf(i_0_17346,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_10496]),
[final] ).
cnf(i_0_17347,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_10497]),
[final] ).
cnf(i_0_17348,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_10498]),
[final] ).
cnf(i_0_17349,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_10254]),
[final] ).
cnf(i_0_17350,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_10499]),
[final] ).
cnf(i_0_17351,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10500]),
[final] ).
cnf(i_0_17352,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_10497]),
[final] ).
cnf(i_0_17353,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_10497]),
[final] ).
cnf(i_0_17354,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_10501]),
[final] ).
cnf(i_0_17355,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_10502]),
[final] ).
cnf(i_0_17356,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_17357,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_17358,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_17359,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_10503]),
[final] ).
cnf(i_0_17360,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_10504]),
[final] ).
cnf(i_0_17361,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_10505]),
[final] ).
cnf(i_0_17362,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_10506]),
[final] ).
cnf(i_0_17363,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_10507]),
[final] ).
cnf(i_0_17364,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_10508]),
[final] ).
cnf(i_0_17365,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_10509]),
[final] ).
cnf(i_0_17366,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_10510]),
[final] ).
cnf(i_0_17367,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_10511]),
[final] ).
cnf(i_0_17368,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_10512]),
[final] ).
cnf(i_0_17369,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_10513]),
[final] ).
cnf(i_0_17370,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_10514]),
[final] ).
cnf(i_0_17371,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_10515]),
[final] ).
cnf(i_0_17372,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_10516]),
[final] ).
cnf(i_0_17373,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_10517]),
[final] ).
cnf(i_0_17374,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_9292]),
[final] ).
cnf(i_0_17375,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_10281]),
[final] ).
cnf(i_0_17376,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_10131]),
[final] ).
cnf(i_0_17377,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_10518]),
[final] ).
cnf(i_0_17378,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_10519]),
[final] ).
cnf(i_0_17379,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_10243]),
[final] ).
cnf(i_0_17380,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_17381,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_17382,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_10520]),
[final] ).
cnf(i_0_17383,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_10521]),
[final] ).
cnf(i_0_17384,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_10522]),
[final] ).
cnf(i_0_17385,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_17386,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_17387,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_10523]),
[final] ).
cnf(i_0_17388,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_10523]),
[final] ).
cnf(i_0_17389,plain,
c_Com_Ocom_OLocal(X1,X2,X3) != c_Com_Ocom_OWhile(X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10524]),
[final] ).
cnf(i_0_17390,plain,
c_Com_Ocom_OLocal(X1,X2,X3) != c_Com_Ocom_OSemi(X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10525]),
[final] ).
cnf(i_0_17391,plain,
c_Com_Ocom_OLocal(X1,X2,X3) != c_Com_Ocom_OAss(X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10526]),
[final] ).
cnf(i_0_17392,plain,
c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OWhile(X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10527]),
[final] ).
cnf(i_0_17393,plain,
c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OSemi(X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10528]),
[final] ).
cnf(i_0_17394,plain,
c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OAss(X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10529]),
[final] ).
cnf(i_0_17395,plain,
c_Com_Ocom_OCall(X1,X2,X3) != c_Com_Ocom_OWhile(X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10530]),
[final] ).
cnf(i_0_17396,plain,
c_Com_Ocom_OCall(X1,X2,X3) != c_Com_Ocom_OSemi(X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10531]),
[final] ).
cnf(i_0_17397,plain,
c_Com_Ocom_OCall(X1,X2,X3) != c_Com_Ocom_OAss(X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10532]),
[final] ).
cnf(i_0_17398,plain,
c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OLocal(X3,X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10533]),
[final] ).
cnf(i_0_17399,plain,
c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OCond(X3,X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10534]),
[final] ).
cnf(i_0_17400,plain,
c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OCall(X3,X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10535]),
[final] ).
cnf(i_0_17401,plain,
c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OLocal(X3,X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10536]),
[final] ).
cnf(i_0_17402,plain,
c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OCond(X3,X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10537]),
[final] ).
cnf(i_0_17403,plain,
c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OCall(X3,X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10538]),
[final] ).
cnf(i_0_17404,plain,
c_Com_Ocom_OAss(X1,X2) != c_Com_Ocom_OLocal(X3,X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10539]),
[final] ).
cnf(i_0_17405,plain,
c_Com_Ocom_OAss(X1,X2) != c_Com_Ocom_OCond(X3,X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10540]),
[final] ).
cnf(i_0_17406,plain,
c_Com_Ocom_OAss(X1,X2) != c_Com_Ocom_OCall(X3,X4,X5),
inference(split_conjunct,[status(thm)],[i_0_10541]),
[final] ).
cnf(i_0_17407,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_10542,c_0_8850]),
[final] ).
cnf(i_0_17408,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_10443]),
[final] ).
cnf(i_0_17409,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_10543]),
[final] ).
cnf(i_0_17410,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_10544]),
[final] ).
cnf(i_0_17411,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_10545]),
[final] ).
cnf(i_0_17412,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_10290]),
[final] ).
cnf(i_0_17413,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_10291]),
[final] ).
cnf(i_0_17414,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_10546]),
[final] ).
cnf(i_0_17415,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_10547]),
[final] ).
cnf(i_0_17416,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_10548]),
[final] ).
cnf(i_0_17417,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_10549]),
[final] ).
cnf(i_0_17418,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_10550]),
[final] ).
cnf(i_0_17419,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_10551]),
[final] ).
cnf(i_0_17420,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_10552]),
[final] ).
cnf(i_0_17421,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_10553]),
[final] ).
cnf(i_0_17422,plain,
c_Com_Ocom_OLocal(X1,X2,X3) != hAPP(c_Com_Ocom_OBODY,X4),
inference(split_conjunct,[status(thm)],[i_0_10554]),
[final] ).
cnf(i_0_17423,plain,
c_Com_Ocom_OCond(X1,X2,X3) != hAPP(c_Com_Ocom_OBODY,X4),
inference(split_conjunct,[status(thm)],[i_0_10555]),
[final] ).
cnf(i_0_17424,plain,
c_Com_Ocom_OCall(X1,X2,X3) != hAPP(c_Com_Ocom_OBODY,X4),
inference(split_conjunct,[status(thm)],[i_0_10556]),
[final] ).
cnf(i_0_17425,plain,
hAPP(c_Com_Ocom_OBODY,X1) != c_Com_Ocom_OLocal(X2,X3,X4),
inference(split_conjunct,[status(thm)],[i_0_10557]),
[final] ).
cnf(i_0_17426,plain,
hAPP(c_Com_Ocom_OBODY,X1) != c_Com_Ocom_OCond(X2,X3,X4),
inference(split_conjunct,[status(thm)],[i_0_10558]),
[final] ).
cnf(i_0_17427,plain,
hAPP(c_Com_Ocom_OBODY,X1) != c_Com_Ocom_OCall(X2,X3,X4),
inference(split_conjunct,[status(thm)],[i_0_10559]),
[final] ).
cnf(i_0_17428,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_10560]),
[final] ).
cnf(i_0_17429,plain,
hAPP(hAPP(c_List_Omap(X1,X1),c_COMBI(X1)),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_10561]),
[final] ).
cnf(i_0_17430,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
| ~ c_Wellfounded_OwfP(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10043]),
[final] ).
cnf(i_0_17431,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
| ~ c_Wellfounded_OwfP(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10562]),
[final] ).
cnf(i_0_17432,plain,
( hBOOL(hAPP(hAPP(X2,X3),X3))
| ~ c_Predicate_Oreflp(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10563]),
[final] ).
cnf(i_0_17433,plain,
( hBOOL(hAPP(hAPP(X2,X3),X3))
| ~ c_Equiv__Relations_Oequivp(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10564]),
[final] ).
cnf(i_0_17434,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_10320]),
[final] ).
cnf(i_0_17435,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_10321]),
[final] ).
cnf(i_0_17436,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_10436]),
[final] ).
cnf(i_0_17437,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_10437]),
[final] ).
cnf(i_0_17438,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_10308]),
[final] ).
cnf(i_0_17439,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_10310]),
[final] ).
cnf(i_0_17440,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_10309]),
[final] ).
cnf(i_0_17441,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_10311]),
[final] ).
cnf(i_0_17442,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_10565]),
[final] ).
cnf(i_0_17443,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_10566]),
[final] ).
cnf(i_0_17444,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_10567]),
[final] ).
cnf(i_0_17445,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_10568]),
[final] ).
cnf(i_0_17446,plain,
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,X2))
| X3 != c_Hilbert__Choice_OEps(X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_10569]),
[final] ).
cnf(i_0_17447,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_10570]),
[final] ).
cnf(i_0_17448,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_10571]),
[final] ).
cnf(i_0_17449,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_10572]),
[final] ).
cnf(i_0_17450,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_10573]),
[final] ).
cnf(i_0_17451,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_10574]),
[final] ).
cnf(i_0_17452,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_10575]),
[final] ).
cnf(i_0_17453,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_10576]),
[final] ).
cnf(i_0_17454,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_10577]),
[final] ).
cnf(i_0_17455,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_10578]),
[final] ).
cnf(i_0_17456,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_10578]),
[final] ).
cnf(i_0_17457,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_10579]),
[final] ).
cnf(i_0_17458,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_10579]),
[final] ).
cnf(i_0_17459,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_10580]),
[final] ).
cnf(i_0_17460,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_10581]),
[final] ).
cnf(i_0_17461,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_10582]),
[final] ).
cnf(i_0_17462,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_10583]),
[final] ).
cnf(i_0_17463,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_10584]),
[final] ).
cnf(i_0_17464,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_9473]),
[final] ).
cnf(i_0_17465,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_10585,c_0_8850]),
[final] ).
cnf(i_0_17466,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_9707]),
[final] ).
cnf(i_0_17467,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_10586]),
[final] ).
cnf(i_0_17468,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_10336]),
[final] ).
cnf(i_0_17469,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_10337]),
[final] ).
cnf(i_0_17470,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_10335]),
[final] ).
cnf(i_0_17471,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_10587]),
[final] ).
cnf(i_0_17472,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_10588]),
[final] ).
cnf(i_0_17473,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_9713]),
[final] ).
cnf(i_0_17474,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_9713]),
[final] ).
cnf(i_0_17475,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_9714]),
[final] ).
cnf(i_0_17476,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_10589]),
[final] ).
cnf(i_0_17477,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_10590]),
[final] ).
cnf(i_0_17478,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_9943]),
[final] ).
cnf(i_0_17479,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_9958]),
[final] ).
cnf(i_0_17480,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_10591]),
[final] ).
cnf(i_0_17481,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_10470]),
[final] ).
cnf(i_0_17482,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_10577]),
[final] ).
cnf(i_0_17483,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_10592]),
[final] ).
cnf(i_0_17484,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_10577]),
[final] ).
cnf(i_0_17485,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_10577]),
[final] ).
cnf(i_0_17486,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_10577]),
[final] ).
cnf(i_0_17487,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_10492]),
[final] ).
cnf(i_0_17488,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_10593]),
[final] ).
cnf(i_0_17489,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_10401]),
[final] ).
cnf(i_0_17490,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_10594]),
[final] ).
cnf(i_0_17491,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_10595]),
[final] ).
cnf(i_0_17492,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_10596]),
[final] ).
cnf(i_0_17493,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_10597]),
[final] ).
cnf(i_0_17494,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_17495,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_10598]),
[final] ).
cnf(i_0_17496,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_10599]),
[final] ).
cnf(i_0_17497,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_10600]),
[final] ).
cnf(i_0_17498,plain,
hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_10601]),
[final] ).
cnf(i_0_17499,plain,
hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_10602]),
[final] ).
cnf(i_0_17500,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_10436]),
[final] ).
cnf(i_0_17501,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_10436]),
[final] ).
cnf(i_0_17502,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_10437]),
[final] ).
cnf(i_0_17503,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_10437]),
[final] ).
cnf(i_0_17504,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_10603]),
[final] ).
cnf(i_0_17505,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_10603]),
[final] ).
cnf(i_0_17506,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_10604]),
[final] ).
cnf(i_0_17507,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_10604]),
[final] ).
cnf(i_0_17508,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_10605,c_0_6016]),
[final] ).
cnf(i_0_17509,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_10606,c_0_6169]),
[final] ).
cnf(i_0_17510,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_10607,c_0_6135]),
[final] ).
cnf(i_0_17511,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_10608]),
[final] ).
cnf(i_0_17512,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_10609]),
[final] ).
cnf(i_0_17513,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[i_0_10610]),
[final] ).
cnf(i_0_17514,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_10611,c_0_6135]),
[final] ).
cnf(i_0_17515,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_10612]),
[final] ).
cnf(i_0_17516,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_10613]),
[final] ).
cnf(i_0_17517,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_10614]),
[final] ).
cnf(i_0_17518,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_10615]),
[final] ).
cnf(i_0_17519,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_10616]),
[final] ).
cnf(i_0_17520,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_10617]),
[final] ).
cnf(i_0_17521,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_10618]),
[final] ).
cnf(i_0_17522,plain,
( hBOOL(hAPP(hAPP(c_fconj,X1),X2))
| ~ hBOOL(X1)
| ~ hBOOL(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10619]),
[final] ).
cnf(i_0_17523,plain,
( hBOOL(hAPP(X1,esk309_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_10473]),
[final] ).
cnf(i_0_17524,plain,
( hBOOL(hAPP(X1,esk310_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_10474]),
[final] ).
cnf(i_0_17525,plain,
( X2 = c_List_Olist_ONil(X1)
| hAPP(hAPP(c_List_Oappend(X1),X2),X3) != X3 ),
inference(split_conjunct,[status(thm)],[i_0_10620]),
[final] ).
cnf(i_0_17526,plain,
( X3 = c_List_Olist_ONil(X1)
| hAPP(hAPP(c_List_Oappend(X1),X2),X3) != X2 ),
inference(split_conjunct,[status(thm)],[i_0_10621]),
[final] ).
cnf(i_0_17527,plain,
( X3 = c_List_Olist_ONil(X2)
| X1 != hAPP(hAPP(c_List_Oappend(X2),X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_10622]),
[final] ).
cnf(i_0_17528,plain,
( X3 = c_List_Olist_ONil(X2)
| X1 != hAPP(hAPP(c_List_Oappend(X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[i_0_10623]),
[final] ).
cnf(i_0_17529,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_10624]),
[final] ).
cnf(i_0_17530,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_10625]),
[final] ).
cnf(i_0_17531,plain,
c_List_Olist_ONil(X1) != hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_10626]),
[final] ).
cnf(i_0_17532,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_10627]),
[final] ).
cnf(i_0_17533,plain,
hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_10628]),
[final] ).
cnf(i_0_17534,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_10488]),
[final] ).
cnf(i_0_17535,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_10629,c_0_6169]),
[final] ).
cnf(i_0_17536,plain,
( hBOOL(hAPP(c_List_Odistinct(X2),X1))
| esk452_2(X1,X2) != esk453_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_8205]),
[final] ).
cnf(i_0_17537,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_10624]),
[final] ).
cnf(i_0_17538,plain,
c_Com_Ocom_OLocal(X1,X2,X3) != c_Com_Ocom_OSKIP,
inference(split_conjunct,[status(thm)],[i_0_10630]),
[final] ).
cnf(i_0_17539,plain,
c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OSKIP,
inference(split_conjunct,[status(thm)],[i_0_10631]),
[final] ).
cnf(i_0_17540,plain,
c_Com_Ocom_OCall(X1,X2,X3) != c_Com_Ocom_OSKIP,
inference(split_conjunct,[status(thm)],[i_0_10632]),
[final] ).
cnf(i_0_17541,plain,
c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X1,X2,X3),
inference(split_conjunct,[status(thm)],[i_0_10633]),
[final] ).
cnf(i_0_17542,plain,
c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X1,X2,X3),
inference(split_conjunct,[status(thm)],[i_0_10634]),
[final] ).
cnf(i_0_17543,plain,
c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(X1,X2,X3),
inference(split_conjunct,[status(thm)],[i_0_10635]),
[final] ).
cnf(i_0_17544,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_10636]),
[final] ).
cnf(i_0_17545,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_10637]),
[final] ).
cnf(i_0_17546,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_10638]),
[final] ).
cnf(i_0_17547,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_10639]),
[final] ).
cnf(i_0_17548,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_10640]),
[final] ).
cnf(i_0_17549,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_10641]),
[final] ).
cnf(i_0_17550,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_10642]),
[final] ).
cnf(i_0_17551,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_17552,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_17553,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_17554,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_17555,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_17556,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_10643]),
[final] ).
cnf(i_0_17557,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_10644]),
[final] ).
cnf(i_0_17558,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_10645]),
[final] ).
cnf(i_0_17559,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_10646]),
[final] ).
cnf(i_0_17560,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_10647]),
[final] ).
cnf(i_0_17561,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != X3,
inference(split_conjunct,[status(thm)],[i_0_10648]),
[final] ).
cnf(i_0_17562,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
inference(split_conjunct,[status(thm)],[i_0_10649]),
[final] ).
cnf(i_0_17563,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_10650]),
[final] ).
cnf(i_0_17564,plain,
( hBOOL(hAPP(hAPP(c_fdisj,X1),X2))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10651]),
[final] ).
cnf(i_0_17565,plain,
( hBOOL(hAPP(hAPP(c_fdisj,X2),X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10652]),
[final] ).
cnf(i_0_17566,plain,
( hBOOL(hAPP(hAPP(c_fimplies,X2),X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10653]),
[final] ).
cnf(i_0_17567,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_10654]),
[final] ).
cnf(i_0_17568,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_10655]),
[final] ).
cnf(i_0_17569,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_10656]),
[final] ).
cnf(i_0_17570,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_10657]),
[final] ).
cnf(i_0_17571,plain,
~ c_Option_Ois__none(X1,hAPP(c_Option_Ooption_OSome(X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_10658]),
[final] ).
cnf(i_0_17572,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_10659]),
[final] ).
cnf(i_0_17573,plain,
c_List_Olist_ONil(tc_Nat_Onat) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),c_List_Olist_ONil(tc_Int_Oint)),
inference(rw,[status(thm)],[i_0_10660,c_0_10661]),
[final] ).
cnf(i_0_17574,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_10662]),
[final] ).
cnf(i_0_17575,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_10663]),
[final] ).
cnf(i_0_17576,plain,
( hBOOL(X1)
| hBOOL(hAPP(hAPP(c_fimplies,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10664]),
[final] ).
cnf(i_0_17577,plain,
c_Relation_Osingle__valued(X1,X1,c_Relation_OId__on(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_10665]),
[final] ).
cnf(i_0_17578,plain,
c_Relation_Orefl__on(X1,X2,c_Relation_OId__on(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_10666]),
[final] ).
cnf(i_0_17579,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_10667]),
[final] ).
cnf(i_0_17580,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_10667]),
[final] ).
cnf(i_0_17581,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_10668]),
[final] ).
cnf(i_0_17582,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_10668]),
[final] ).
cnf(i_0_17583,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_10669]),
[final] ).
cnf(i_0_17584,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_10669]),
[final] ).
cnf(i_0_17585,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_10578]),
[final] ).
cnf(i_0_17586,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_10579]),
[final] ).
cnf(i_0_17587,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_10670]),
[final] ).
cnf(i_0_17588,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_10671]),
[final] ).
cnf(i_0_17589,plain,
( hBOOL(hAPP(hAPP(c_fequal,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_10672]),
[final] ).
cnf(i_0_17590,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_10673]),
[final] ).
cnf(i_0_17591,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_10674]),
[final] ).
cnf(i_0_17592,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_10675]),
[final] ).
cnf(i_0_17593,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_10676]),
[final] ).
cnf(i_0_17594,plain,
hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_10677]),
[final] ).
cnf(i_0_17595,plain,
hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_10678]),
[final] ).
cnf(i_0_17596,plain,
( c_Wellfounded_Owf(X2,X1)
| esk350_2(X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_8097]),
[final] ).
cnf(i_0_17597,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_10679]),
[final] ).
cnf(i_0_17598,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_10680]),
[final] ).
cnf(i_0_17599,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_10523]),
[final] ).
cnf(i_0_17600,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_10681]),
[final] ).
cnf(i_0_17601,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_10682]),
[final] ).
cnf(i_0_17602,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_10683]),
[final] ).
cnf(i_0_17603,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_10684]),
[final] ).
cnf(i_0_17604,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_10320]),
[final] ).
cnf(i_0_17605,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_10321]),
[final] ).
cnf(i_0_17606,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_10685]),
[final] ).
cnf(i_0_17607,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_10686]),
[final] ).
cnf(i_0_17608,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_10687]),
[final] ).
cnf(i_0_17609,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_10688]),
[final] ).
cnf(i_0_17610,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_10689]),
[final] ).
cnf(i_0_17611,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_10690]),
[final] ).
cnf(i_0_17612,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_10691]),
[final] ).
cnf(i_0_17613,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_10692]),
[final] ).
cnf(i_0_17614,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_10693]),
[final] ).
cnf(i_0_17615,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_10694]),
[final] ).
cnf(i_0_17616,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_10695]),
[final] ).
cnf(i_0_17617,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_10696]),
[final] ).
cnf(i_0_17618,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_10697]),
[final] ).
cnf(i_0_17619,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_10698]),
[final] ).
cnf(i_0_17620,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_10699]),
[final] ).
cnf(i_0_17621,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_10700]),
[final] ).
cnf(i_0_17622,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_10701]),
[final] ).
cnf(i_0_17623,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_10702]),
[final] ).
cnf(i_0_17624,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_10703,c_0_6015]),
[final] ).
cnf(i_0_17625,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_10704,c_0_6015]),
[final] ).
cnf(i_0_17626,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_10705]),
[final] ).
cnf(i_0_17627,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_10603]),
[final] ).
cnf(i_0_17628,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_10604]),
[final] ).
cnf(i_0_17629,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_10706]),
[final] ).
cnf(i_0_17630,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_10707]),
[final] ).
cnf(i_0_17631,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1) != c_Int_OMin,
inference(rw,[status(thm)],[i_0_10708,c_0_6015]),
[final] ).
cnf(i_0_17632,plain,
c_Int_OMin != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1),
inference(rw,[status(thm)],[i_0_10709,c_0_6015]),
[final] ).
cnf(i_0_17633,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_10710]),
[final] ).
cnf(i_0_17634,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_10711]),
[final] ).
cnf(i_0_17635,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_10712]),
[final] ).
cnf(i_0_17636,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_10713]),
[final] ).
cnf(i_0_17637,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_10714]),
[final] ).
cnf(i_0_17638,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_10715]),
[final] ).
cnf(i_0_17639,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_10716]),
[final] ).
cnf(i_0_17640,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_10717]),
[final] ).
cnf(i_0_17641,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_10718]),
[final] ).
cnf(i_0_17642,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_10719]),
[final] ).
cnf(i_0_17643,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_10720]),
[final] ).
cnf(i_0_17644,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_10721]),
[final] ).
cnf(i_0_17645,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_10722]),
[final] ).
cnf(i_0_17646,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_10723]),
[final] ).
cnf(i_0_17647,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_10724]),
[final] ).
cnf(i_0_17648,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_10725]),
[final] ).
cnf(i_0_17649,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_10566]),
[final] ).
cnf(i_0_17650,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_10726]),
[final] ).
cnf(i_0_17651,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_10443]),
[final] ).
cnf(i_0_17652,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_10548]),
[final] ).
cnf(i_0_17653,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_10548]),
[final] ).
cnf(i_0_17654,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_10581]),
[final] ).
cnf(i_0_17655,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_10582]),
[final] ).
cnf(i_0_17656,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_10727]),
[final] ).
cnf(i_0_17657,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_10728]),
[final] ).
cnf(i_0_17658,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_10729]),
[final] ).
cnf(i_0_17659,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_10730]),
[final] ).
cnf(i_0_17660,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_10731]),
[final] ).
cnf(i_0_17661,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_10732]),
[final] ).
cnf(i_0_17662,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_10733]),
[final] ).
cnf(i_0_17663,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_10734]),
[final] ).
cnf(i_0_17664,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_10735]),
[final] ).
cnf(i_0_17665,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_10736]),
[final] ).
cnf(i_0_17666,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_10737]),
[final] ).
cnf(i_0_17667,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X3),c_List_Olist_ONil(X3)),X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_10738]),
[final] ).
cnf(i_0_17668,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_10593]),
[final] ).
cnf(i_0_17669,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_10726]),
[final] ).
cnf(i_0_17670,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_10739]),
[final] ).
cnf(i_0_17671,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_10740]),
[final] ).
cnf(i_0_17672,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_10741]),
[final] ).
cnf(i_0_17673,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_10742]),
[final] ).
cnf(i_0_17674,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_10743]),
[final] ).
cnf(i_0_17675,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_10744]),
[final] ).
cnf(i_0_17676,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_10745]),
[final] ).
cnf(i_0_17677,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_10746]),
[final] ).
cnf(i_0_17678,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_10747]),
[final] ).
cnf(i_0_17679,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_10748]),
[final] ).
cnf(i_0_17680,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_10488]),
[final] ).
cnf(i_0_17681,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_10587]),
[final] ).
cnf(i_0_17682,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_10588]),
[final] ).
cnf(i_0_17683,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_10430]),
[final] ).
cnf(i_0_17684,plain,
hAPP(c_Relation_ODomain(X1,X1),c_Relation_OId__on(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_10749]),
[final] ).
cnf(i_0_17685,plain,
hAPP(c_Relation_ORange(X1,X1),c_Relation_OId__on(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_10750]),
[final] ).
cnf(i_0_17686,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_10751]),
[final] ).
cnf(i_0_17687,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_10752]),
[final] ).
cnf(i_0_17688,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_10753]),
[final] ).
cnf(i_0_17689,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_10754]),
[final] ).
cnf(i_0_17690,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_10755]),
[final] ).
cnf(i_0_17691,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_10756]),
[final] ).
cnf(i_0_17692,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_10757]),
[final] ).
cnf(i_0_17693,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_10758]),
[final] ).
cnf(i_0_17694,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_10759]),
[final] ).
cnf(i_0_17695,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_10760]),
[final] ).
cnf(i_0_17696,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_10761]),
[final] ).
cnf(i_0_17697,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_10762]),
[final] ).
cnf(i_0_17698,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_10763]),
[final] ).
cnf(i_0_17699,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_10764]),
[final] ).
cnf(i_0_17700,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_10765]),
[final] ).
cnf(i_0_17701,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_10766]),
[final] ).
cnf(i_0_17702,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_10767]),
[final] ).
cnf(i_0_17703,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_10768]),
[final] ).
cnf(i_0_17704,plain,
( X2 = X3
| hAPP(c_List_Orev(X1),X2) != hAPP(c_List_Orev(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_10769]),
[final] ).
cnf(i_0_17705,plain,
( X2 = X3
| hAPP(c_Option_Ooption_OSome(X1),X2) != hAPP(c_Option_Ooption_OSome(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_10770]),
[final] ).
cnf(i_0_17706,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_8164]),
[final] ).
cnf(i_0_17707,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_10430]),
[final] ).
cnf(i_0_17708,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_10771]),
[final] ).
cnf(i_0_17709,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_10772]),
[final] ).
cnf(i_0_17710,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_17711,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_10773]),
[final] ).
cnf(i_0_17712,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_10591]),
[final] ).
cnf(i_0_17713,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_10774]),
[final] ).
cnf(i_0_17714,plain,
c_List_Osublist(X1,c_List_Olist_ONil(X1),X2) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_10775]),
[final] ).
cnf(i_0_17715,plain,
c_List_Oremove1(X1,X2,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_10776]),
[final] ).
cnf(i_0_17716,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_10777]),
[final] ).
cnf(i_0_17717,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_10778]),
[final] ).
cnf(i_0_17718,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_10779]),
[final] ).
cnf(i_0_17719,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_10780]),
[final] ).
cnf(i_0_17720,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_10781]),
[final] ).
cnf(i_0_17721,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_10782]),
[final] ).
cnf(i_0_17722,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_10783]),
[final] ).
cnf(i_0_17723,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_10784]),
[final] ).
cnf(i_0_17724,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_10785]),
[final] ).
cnf(i_0_17725,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_10591]),
[final] ).
cnf(i_0_17726,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_10786]),
[final] ).
cnf(i_0_17727,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_10786]),
[final] ).
cnf(i_0_17728,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_10787]),
[final] ).
cnf(i_0_17729,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_10787]),
[final] ).
cnf(i_0_17730,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_10788]),
[final] ).
cnf(i_0_17731,plain,
( hAPP(hAPP(c_List_Oappend(X2),X1),X3) = X3
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10620]),
[final] ).
cnf(i_0_17732,plain,
( hAPP(hAPP(c_List_Oappend(X2),X3),X1) = X3
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10621]),
[final] ).
cnf(i_0_17733,plain,
( X3 = hAPP(hAPP(c_List_Oappend(X2),X1),X3)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10623]),
[final] ).
cnf(i_0_17734,plain,
( X3 = hAPP(hAPP(c_List_Oappend(X2),X3),X1)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10622]),
[final] ).
cnf(i_0_17735,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_10789]),
[final] ).
cnf(i_0_17736,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_10790]),
[final] ).
cnf(i_0_17737,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_10791]),
[final] ).
cnf(i_0_17738,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_10792]),
[final] ).
cnf(i_0_17739,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_10793]),
[final] ).
cnf(i_0_17740,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_10794]),
[final] ).
cnf(i_0_17741,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_10577]),
[final] ).
cnf(i_0_17742,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_10667]),
[final] ).
cnf(i_0_17743,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_10668]),
[final] ).
cnf(i_0_17744,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_10669]),
[final] ).
cnf(i_0_17745,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_10795]),
[final] ).
cnf(i_0_17746,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_10796]),
[final] ).
cnf(i_0_17747,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X2) = X2
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10797]),
[final] ).
cnf(i_0_17748,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_10798]),
[final] ).
cnf(i_0_17749,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_10799]),
[final] ).
cnf(i_0_17750,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X2) = X2
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10800]),
[final] ).
cnf(i_0_17751,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X2) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10801]),
[final] ).
cnf(i_0_17752,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X2) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10802]),
[final] ).
cnf(i_0_17753,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X2) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10803]),
[final] ).
cnf(i_0_17754,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X2) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10804]),
[final] ).
cnf(i_0_17755,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_10805]),
[final] ).
cnf(i_0_17756,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_10806]),
[final] ).
cnf(i_0_17757,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_10807]),
[final] ).
cnf(i_0_17758,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_10808]),
[final] ).
cnf(i_0_17759,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_10809]),
[final] ).
cnf(i_0_17760,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_17761,plain,
hAPP(hAPP(c_List_Odrop(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_10810]),
[final] ).
cnf(i_0_17762,plain,
hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1)) = X2,
inference(split_conjunct,[status(thm)],[i_0_10811]),
[final] ).
cnf(i_0_17763,plain,
hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_10812]),
[final] ).
cnf(i_0_17764,plain,
hAPP(c_Option_Othe(X1),hAPP(c_Option_Ooption_OSome(X1),X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_10813]),
[final] ).
cnf(i_0_17765,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_10814]),
[final] ).
cnf(i_0_17766,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_10815]),
[final] ).
cnf(i_0_17767,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_17768,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_10816]),
[final] ).
cnf(i_0_17769,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_10817]),
[final] ).
cnf(i_0_17770,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_10818]),
[final] ).
cnf(i_0_17771,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_10819]),
[final] ).
cnf(i_0_17772,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_10820]),
[final] ).
cnf(i_0_17773,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_10821]),
[final] ).
cnf(i_0_17774,plain,
hAPP(c_Option_Omap(X1,X1),c_COMBI(X1)) = c_Fun_Oid(tc_Option_Ooption(X1)),
inference(split_conjunct,[status(thm)],[i_0_10822]),
[final] ).
cnf(i_0_17775,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_10823]),
[final] ).
cnf(i_0_17776,plain,
hAPP(c_List_Omap(X1,X1),c_COMBI(X1)) = c_Fun_Oid(tc_List_Olist(X1)),
inference(split_conjunct,[status(thm)],[i_0_10824]),
[final] ).
cnf(i_0_17777,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_10825]),
[final] ).
cnf(i_0_17778,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_10826]),
[final] ).
cnf(i_0_17779,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_10675]),
[final] ).
cnf(i_0_17780,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_10676]),
[final] ).
cnf(i_0_17781,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_10827]),
[final] ).
cnf(i_0_17782,plain,
( hAPP(c_List_Orev(X2),X1) = X3
| X1 != hAPP(c_List_Orev(X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_10828]),
[final] ).
cnf(i_0_17783,plain,
( X2 = hAPP(c_List_Orev(X1),X3)
| hAPP(c_List_Orev(X1),X2) != X3 ),
inference(split_conjunct,[status(thm)],[i_0_10828]),
[final] ).
cnf(i_0_17784,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_10829]),
[final] ).
cnf(i_0_17785,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_10830]),
[final] ).
cnf(i_0_17786,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_10831]),
[final] ).
cnf(i_0_17787,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_10832]),
[final] ).
cnf(i_0_17788,plain,
hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olist_ONil(X1))),
inference(split_conjunct,[status(thm)],[i_0_10833]),
[final] ).
cnf(i_0_17789,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_9458]),
[final] ).
cnf(i_0_17790,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_9496]),
[final] ).
cnf(i_0_17791,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_8911]),
[final] ).
cnf(i_0_17792,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_10647]),
[final] ).
cnf(i_0_17793,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_10647]),
[final] ).
cnf(i_0_17794,plain,
hAPP(c_New__DSequence_Opos__single(X1,X2),X3) = c_Lazy__Sequence_Osingle(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_10834]),
[final] ).
cnf(i_0_17795,plain,
hAPP(c_New__DSequence_Oneg__single(X1,X2),X3) = c_Lazy__Sequence_Ohb__single(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_10835]),
[final] ).
cnf(i_0_17796,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_10836]),
[final] ).
cnf(i_0_17797,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_10837]),
[final] ).
cnf(i_0_17798,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_10838]),
[final] ).
cnf(i_0_17799,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_10839]),
[final] ).
cnf(i_0_17800,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_10840]),
[final] ).
cnf(i_0_17801,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_10841]),
[final] ).
cnf(i_0_17802,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_10842]),
[final] ).
cnf(i_0_17803,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_8997]),
[final] ).
cnf(i_0_17804,plain,
( c_List_Otranspose(X2,X1) = c_List_Olist_ONil(tc_List_Olist(X2))
| esk484_2(X1,X2) != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9141]),
[final] ).
cnf(i_0_17805,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(split_conjunct,[status(thm)],[i_0_10843]),
[final] ).
cnf(i_0_17806,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(split_conjunct,[status(thm)],[i_0_10844]),
[final] ).
cnf(i_0_17807,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_10845]),
[final] ).
cnf(i_0_17808,plain,
( X1 = c_Option_Ooption_ONone(X2)
| X1 = hAPP(c_Option_Ooption_OSome(X2),esk33_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10846]),
[final] ).
cnf(i_0_17809,plain,
( X1 = hAPP(c_Option_Ooption_OSome(X2),esk30_2(X2,X1))
| X1 = c_Option_Ooption_ONone(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10847]),
[final] ).
cnf(i_0_17810,plain,
( X1 = c_Option_Ooption_ONone(X2)
| X1 = hAPP(c_Option_Ooption_OSome(X2),esk29_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10848]),
[final] ).
cnf(i_0_17811,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_10849]),
[final] ).
cnf(i_0_17812,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_10850]),
[final] ).
cnf(i_0_17813,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_10851]),
[final] ).
cnf(i_0_17814,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_10819]),
[final] ).
cnf(i_0_17815,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_10852]),
[final] ).
cnf(i_0_17816,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_10853]),
[final] ).
cnf(i_0_17817,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_10854]),
[final] ).
cnf(i_0_17818,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_10855]),
[final] ).
cnf(i_0_17819,plain,
( ~ hBOOL(hAPP(c_fNot,X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10856]),
[final] ).
cnf(i_0_17820,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_10857]),
[final] ).
cnf(i_0_17821,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_10858]),
[final] ).
cnf(i_0_17822,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_10859]),
[final] ).
cnf(i_0_17823,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_10860]),
[final] ).
cnf(i_0_17824,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_10861]),
[final] ).
cnf(i_0_17825,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_10862]),
[final] ).
cnf(i_0_17826,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_10863]),
[final] ).
cnf(i_0_17827,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_10864]),
[final] ).
cnf(i_0_17828,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_17829,plain,
hAPP(c_List_Ofilter(X1,X2),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_10865]),
[final] ).
cnf(i_0_17830,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_17831,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10866]),
[final] ).
cnf(i_0_17832,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10867]),
[final] ).
cnf(i_0_17833,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_10729]),
[final] ).
cnf(i_0_17834,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_10868]),
[final] ).
cnf(i_0_17835,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_10869]),
[final] ).
cnf(i_0_17836,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_17837,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_10870,c_0_6015]),
[final] ).
cnf(i_0_17838,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_10871,c_0_6015]),
[final] ).
cnf(i_0_17839,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_17840,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_10872]),
[final] ).
cnf(i_0_17841,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_10124]),
[final] ).
cnf(i_0_17842,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_10125]),
[final] ).
cnf(i_0_17843,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_10873]),
[final] ).
cnf(i_0_17844,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_10874]),
[final] ).
cnf(i_0_17845,plain,
( X1 = X2
| c_Com_Ocom_OWhile(X1,X3) != c_Com_Ocom_OWhile(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_10875]),
[final] ).
cnf(i_0_17846,plain,
( X1 = X2
| c_Com_Ocom_OWhile(X3,X1) != c_Com_Ocom_OWhile(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10875]),
[final] ).
cnf(i_0_17847,plain,
( X1 = X2
| c_Com_Ocom_OSemi(X1,X3) != c_Com_Ocom_OSemi(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_10876]),
[final] ).
cnf(i_0_17848,plain,
( X1 = X2
| c_Com_Ocom_OSemi(X3,X1) != c_Com_Ocom_OSemi(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10876]),
[final] ).
cnf(i_0_17849,plain,
( X1 = X2
| c_Com_Ocom_OAss(X1,X3) != c_Com_Ocom_OAss(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_10877]),
[final] ).
cnf(i_0_17850,plain,
( X1 = X2
| c_Com_Ocom_OAss(X3,X1) != c_Com_Ocom_OAss(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10877]),
[final] ).
cnf(i_0_17851,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_10878]),
[final] ).
cnf(i_0_17852,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_10879]),
[final] ).
cnf(i_0_17853,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_10880]),
[final] ).
cnf(i_0_17854,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OPls) = X1,
inference(split_conjunct,[status(thm)],[i_0_10881]),
[final] ).
cnf(i_0_17855,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OPls) = X1,
inference(split_conjunct,[status(thm)],[i_0_10882]),
[final] ).
cnf(i_0_17856,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_10883]),
[final] ).
cnf(i_0_17857,plain,
( class_Smallcheck_Osmall(tc_prod(X1,X2))
| ~ class_Smallcheck_Osmall(X1)
| ~ class_Smallcheck_Osmall(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10884]),
[final] ).
cnf(i_0_17858,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_10885]),
[final] ).
cnf(i_0_17859,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_10886]),
[final] ).
cnf(i_0_17860,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_10887]),
[final] ).
cnf(i_0_17861,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_10888]),
[final] ).
cnf(i_0_17862,plain,
c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OSemi(X3,X4),
inference(split_conjunct,[status(thm)],[i_0_10889]),
[final] ).
cnf(i_0_17863,plain,
c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OAss(X3,X4),
inference(split_conjunct,[status(thm)],[i_0_10890]),
[final] ).
cnf(i_0_17864,plain,
c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OWhile(X3,X4),
inference(split_conjunct,[status(thm)],[i_0_10891]),
[final] ).
cnf(i_0_17865,plain,
c_Com_Ocom_OAss(X1,X2) != c_Com_Ocom_OWhile(X3,X4),
inference(split_conjunct,[status(thm)],[i_0_10892]),
[final] ).
cnf(i_0_17866,plain,
c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OAss(X3,X4),
inference(split_conjunct,[status(thm)],[i_0_10893]),
[final] ).
cnf(i_0_17867,plain,
c_Com_Ocom_OAss(X1,X2) != c_Com_Ocom_OSemi(X3,X4),
inference(split_conjunct,[status(thm)],[i_0_10894]),
[final] ).
cnf(i_0_17868,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_17869,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_17870,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_10895]),
[final] ).
cnf(i_0_17871,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_10788]),
[final] ).
cnf(i_0_17872,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_10896]),
[final] ).
cnf(i_0_17873,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_10897]),
[final] ).
cnf(i_0_17874,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_10898]),
[final] ).
cnf(i_0_17875,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_10807]),
[final] ).
cnf(i_0_17876,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_10899]),
[final] ).
cnf(i_0_17877,plain,
c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X1)),
inference(split_conjunct,[status(thm)],[i_0_10900]),
[final] ).
cnf(i_0_17878,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_10901]),
[final] ).
cnf(i_0_17879,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_10902]),
[final] ).
cnf(i_0_17880,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_10135]),
[final] ).
cnf(i_0_17881,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_9860]),
[final] ).
cnf(i_0_17882,plain,
( X1 != c_Option_Ooption_ONone(X2)
| X1 != hAPP(c_Option_Ooption_OSome(X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_10847]),
[final] ).
cnf(i_0_17883,plain,
( X1 != hAPP(c_Option_Ooption_OSome(X2),X3)
| X1 != c_Option_Ooption_ONone(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10848]),
[final] ).
cnf(i_0_17884,plain,
hAPP(c_Com_Ocom_OBODY,X1) != c_Com_Ocom_OWhile(X2,X3),
inference(split_conjunct,[status(thm)],[i_0_10903]),
[final] ).
cnf(i_0_17885,plain,
hAPP(c_Com_Ocom_OBODY,X1) != c_Com_Ocom_OSemi(X2,X3),
inference(split_conjunct,[status(thm)],[i_0_10904]),
[final] ).
cnf(i_0_17886,plain,
hAPP(c_Com_Ocom_OBODY,X1) != c_Com_Ocom_OAss(X2,X3),
inference(split_conjunct,[status(thm)],[i_0_10905]),
[final] ).
cnf(i_0_17887,plain,
c_Com_Ocom_OWhile(X1,X2) != hAPP(c_Com_Ocom_OBODY,X3),
inference(split_conjunct,[status(thm)],[i_0_10906]),
[final] ).
cnf(i_0_17888,plain,
c_Com_Ocom_OSemi(X1,X2) != hAPP(c_Com_Ocom_OBODY,X3),
inference(split_conjunct,[status(thm)],[i_0_10907]),
[final] ).
cnf(i_0_17889,plain,
c_Com_Ocom_OAss(X1,X2) != hAPP(c_Com_Ocom_OBODY,X3),
inference(split_conjunct,[status(thm)],[i_0_10908]),
[final] ).
cnf(i_0_17890,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_10909,c_0_6016]),
[final] ).
cnf(i_0_17891,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_10910,c_0_6015]),
[final] ).
cnf(i_0_17892,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_10911,c_0_6169]),
[final] ).
cnf(i_0_17893,plain,
( X1 = X2
| hAPP(c_Int_ORep__Integ,X1) != hAPP(c_Int_ORep__Integ,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10912]),
[final] ).
cnf(i_0_17894,plain,
( X1 = X2
| hAPP(c_Code__Numeral_Onat__of,X1) != hAPP(c_Code__Numeral_Onat__of,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10913]),
[final] ).
cnf(i_0_17895,plain,
( X1 = X2
| hAPP(c_Code__Numeral_Onat__of,X1) != hAPP(c_Code__Numeral_Onat__of,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10914]),
[final] ).
cnf(i_0_17896,plain,
( X1 = X2
| hAPP(c_Code__Numeral_Oof__nat,X1) != hAPP(c_Code__Numeral_Oof__nat,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10915]),
[final] ).
cnf(i_0_17897,plain,
( X1 = X2
| hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10916]),
[final] ).
cnf(i_0_17898,plain,
( X1 = X2
| hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10917]),
[final] ).
cnf(i_0_17899,plain,
( X1 = X2
| hAPP(c_Com_Ocom_OBODY,X1) != hAPP(c_Com_Ocom_OBODY,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10918]),
[final] ).
cnf(i_0_17900,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_10919]),
[final] ).
cnf(i_0_17901,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_10920]),
[final] ).
cnf(i_0_17902,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_10921]),
[final] ).
cnf(i_0_17903,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_10854]),
[final] ).
cnf(i_0_17904,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_10855]),
[final] ).
cnf(i_0_17905,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_10853]),
[final] ).
cnf(i_0_17906,plain,
( ~ class_Rings_Osemiring__1(X1)
| ~ c_Int_Oiszero(X1,c_Groups_Oone__class_Oone(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10922]),
[final] ).
cnf(i_0_17907,plain,
c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_10923]),
[final] ).
cnf(i_0_17908,plain,
hAPP(c_Option_Ooption_OSome(X1),X2) != c_Option_Ooption_ONone(X1),
inference(split_conjunct,[status(thm)],[i_0_10924]),
[final] ).
cnf(i_0_17909,plain,
c_Option_Ooption_ONone(X1) != hAPP(c_Option_Ooption_OSome(X1),X2),
inference(split_conjunct,[status(thm)],[i_0_10925]),
[final] ).
cnf(i_0_17910,plain,
c_Hilbert__Choice_OEps(X1,hAPP(c_fequal,X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_10926]),
[final] ).
cnf(i_0_17911,plain,
c_HOL_OThe(X1,hAPP(c_fequal,X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_10927]),
[final] ).
cnf(i_0_17912,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_10928]),
[final] ).
cnf(i_0_17913,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_10929]),
[final] ).
cnf(i_0_17914,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_10930]),
[final] ).
cnf(i_0_17915,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_10931]),
[final] ).
cnf(i_0_17916,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_10932]),
[final] ).
cnf(i_0_17917,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_10933]),
[final] ).
cnf(i_0_17918,plain,
( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10934]),
[final] ).
cnf(i_0_17919,plain,
( class_Lattices_Obounded__lattice__top(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10935]),
[final] ).
cnf(i_0_17920,plain,
( class_Orderings_Otop(tc_fun(X2,X1))
| ~ class_Orderings_Otop(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10936]),
[final] ).
cnf(i_0_17921,plain,
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10937]),
[final] ).
cnf(i_0_17922,plain,
( class_Lattices_Odistrib__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10938]),
[final] ).
cnf(i_0_17923,plain,
( class_Lattices_Osemilattice__inf(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10939]),
[final] ).
cnf(i_0_17924,plain,
( class_Lattices_Osemilattice__sup(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10940]),
[final] ).
cnf(i_0_17925,plain,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10941]),
[final] ).
cnf(i_0_17926,plain,
( class_Lattices_Obounded__lattice__bot(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10942]),
[final] ).
cnf(i_0_17927,plain,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10943]),
[final] ).
cnf(i_0_17928,plain,
( class_Groups_Ominus(tc_fun(X2,X1))
| ~ class_Groups_Ominus(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10944]),
[final] ).
cnf(i_0_17929,plain,
( class_Groups_Ouminus(tc_fun(X2,X1))
| ~ class_Groups_Ouminus(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10945]),
[final] ).
cnf(i_0_17930,plain,
( class_Lattices_Oboolean__algebra(tc_fun(X2,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10946]),
[final] ).
cnf(i_0_17931,plain,
( class_Orderings_Oord(tc_fun(X2,X1))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10947]),
[final] ).
cnf(i_0_17932,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10948]),
[final] ).
cnf(i_0_17933,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10949]),
[final] ).
cnf(i_0_17934,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_10868]),
[final] ).
cnf(i_0_17935,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_17936,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_10869]),
[final] ).
cnf(i_0_17937,plain,
( c_Wellfounded_Oacyclic(X1,X2)
| ~ c_Nitpick_Owf_H(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_9860]),
[final] ).
cnf(i_0_17938,plain,
( c_Wellfounded_Oacyclic(X1,X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10950]),
[final] ).
cnf(i_0_17939,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_10878]),
[final] ).
cnf(i_0_17940,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_10879]),
[final] ).
cnf(i_0_17941,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_10951]),
[final] ).
cnf(i_0_17942,plain,
hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_10952]),
[final] ).
cnf(i_0_17943,plain,
hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_10953]),
[final] ).
cnf(i_0_17944,plain,
hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_10954]),
[final] ).
cnf(i_0_17945,plain,
hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_10955]),
[final] ).
cnf(i_0_17946,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_10956]),
[final] ).
cnf(i_0_17947,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_10957]),
[final] ).
cnf(i_0_17948,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_10958]),
[final] ).
cnf(i_0_17949,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_10959]),
[final] ).
cnf(i_0_17950,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_10960]),
[final] ).
cnf(i_0_17951,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_10961]),
[final] ).
cnf(i_0_17952,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_10962]),
[final] ).
cnf(i_0_17953,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_9975]),
[final] ).
cnf(i_0_17954,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_10919]),
[final] ).
cnf(i_0_17955,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_10896]),
[final] ).
cnf(i_0_17956,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_10897]),
[final] ).
cnf(i_0_17957,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_10898]),
[final] ).
cnf(i_0_17958,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_17959,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_17960,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_17961,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_10963]),
[final] ).
cnf(i_0_17962,plain,
( hBOOL(X1)
| hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10964]),
[final] ).
cnf(i_0_17963,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_10965]),
[final] ).
cnf(i_0_17964,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_10966]),
[final] ).
cnf(i_0_17965,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_10967]),
[final] ).
cnf(i_0_17966,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_17967,plain,
( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| esk448_1(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_9781]),
[final] ).
cnf(i_0_17968,plain,
hAPP(c_List_Orev(X1),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_10968]),
[final] ).
cnf(i_0_17969,plain,
hAPP(c_List_Otl(X1),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_10969]),
[final] ).
cnf(i_0_17970,plain,
hAPP(c_List_Orotate1(X1),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_9759]),
[final] ).
cnf(i_0_17971,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_10956]),
[final] ).
cnf(i_0_17972,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_10970]),
[final] ).
cnf(i_0_17973,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_10971]),
[final] ).
cnf(i_0_17974,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_10972]),
[final] ).
cnf(i_0_17975,plain,
( X2 = c_Option_Ooption_ONone(X1)
| ~ c_Option_Ois__none(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10973]),
[final] ).
cnf(i_0_17976,plain,
( c_List_Olinorder__class_Osorted(X1,c_List_Olist_ONil(X1))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10974]),
[final] ).
cnf(i_0_17977,plain,
( c_List_Olinorder__class_Osorted(X1,c_List_Olist_ONil(X1))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10975]),
[final] ).
cnf(i_0_17978,plain,
( c_Int_Oiszero(X1,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_10976]),
[final] ).
cnf(i_0_17979,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_10977]),
[final] ).
cnf(i_0_17980,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_10978]),
[final] ).
cnf(i_0_17981,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_10957]),
[final] ).
cnf(i_0_17982,plain,
hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
inference(split_conjunct,[status(thm)],[fact_WT_OSkip]),
[final] ).
cnf(i_0_17983,plain,
hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
inference(split_conjunct,[status(thm)],[fact_WT_Oequations_I1_J]),
[final] ).
cnf(i_0_17984,plain,
hAPP(c_New__DSequence_Opos__empty(X1),X2) = c_Lazy__Sequence_Oempty(X1),
inference(split_conjunct,[status(thm)],[i_0_10979]),
[final] ).
cnf(i_0_17985,plain,
c_List_Obutlast(X1,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_10980]),
[final] ).
cnf(i_0_17986,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10981]),
[final] ).
cnf(i_0_17987,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10982]),
[final] ).
cnf(i_0_17988,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_10983]),
[final] ).
cnf(i_0_17989,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_10984]),
[final] ).
cnf(i_0_17990,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_10985]),
[final] ).
cnf(i_0_17991,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_10986]),
[final] ).
cnf(i_0_17992,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = hAPP(c_Nat_OSuc,esk34_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_10987]),
[final] ).
cnf(i_0_17993,plain,
( c_Option_Ois__none(X2,X1)
| X1 != c_Option_Ooption_ONone(X2) ),
inference(split_conjunct,[status(thm)],[i_0_10973]),
[final] ).
cnf(i_0_17994,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_17995,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_17996,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_17997,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_17998,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_17999,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_18000,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_18001,plain,
c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OSKIP,
inference(split_conjunct,[status(thm)],[i_0_10988]),
[final] ).
cnf(i_0_18002,plain,
c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OSKIP,
inference(split_conjunct,[status(thm)],[i_0_10989]),
[final] ).
cnf(i_0_18003,plain,
c_Com_Ocom_OAss(X1,X2) != c_Com_Ocom_OSKIP,
inference(split_conjunct,[status(thm)],[i_0_10990]),
[final] ).
cnf(i_0_18004,plain,
c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_10991]),
[final] ).
cnf(i_0_18005,plain,
c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_10992]),
[final] ).
cnf(i_0_18006,plain,
c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_10993]),
[final] ).
cnf(i_0_18007,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_10994]),
[final] ).
cnf(i_0_18008,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_10995]),
[final] ).
cnf(i_0_18009,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(split_conjunct,[status(thm)],[i_0_10996]),
[final] ).
cnf(i_0_18010,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_10997]),
[final] ).
cnf(i_0_18011,plain,
hAPP(c_Fun_Oid(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_10998]),
[final] ).
cnf(i_0_18012,plain,
hAPP(c_Fun_Oid(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_10999]),
[final] ).
cnf(i_0_18013,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_11000]),
[final] ).
cnf(i_0_18014,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_11001]),
[final] ).
cnf(i_0_18015,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_10213]),
[final] ).
cnf(i_0_18016,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_18017,plain,
( c_Nitpick_Onat__gcd(X2,X1) = X2
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_10406]),
[final] ).
cnf(i_0_18018,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_18019,plain,
c_Option_Ois__none(X1,c_Option_Ooption_ONone(X1)),
inference(split_conjunct,[status(thm)],[i_0_11002]),
[final] ).
cnf(i_0_18020,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_11003]),
[final] ).
cnf(i_0_18021,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_11004]),
[final] ).
cnf(i_0_18022,plain,
hAPP(c_Com_Ocom_OBODY,X1) != c_Com_Ocom_OSKIP,
inference(split_conjunct,[status(thm)],[i_0_11005]),
[final] ).
cnf(i_0_18023,plain,
c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,X1),
inference(split_conjunct,[status(thm)],[i_0_11006]),
[final] ).
cnf(i_0_18024,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_10772]),
[final] ).
cnf(i_0_18025,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_11007]),
[final] ).
cnf(i_0_18026,plain,
X1 = hAPP(c_Int_OAbs__Integ,esk335_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_8757]),
[final] ).
cnf(i_0_18027,plain,
c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X1)),
inference(split_conjunct,[status(thm)],[i_0_11008]),
[final] ).
cnf(i_0_18028,plain,
c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X1)),
inference(split_conjunct,[status(thm)],[i_0_11009]),
[final] ).
cnf(i_0_18029,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_18030,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_18031,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_18032,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_18033,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_18034,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_18035,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_18036,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_18037,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_18038,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_18039,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_18040,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_18041,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_18042,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_11010]),
[final] ).
cnf(i_0_18043,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_11011]),
[final] ).
cnf(i_0_18044,plain,
( class_Finite__Set_Ofinite(tc_Option_Ooption(X1))
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_11012]),
[final] ).
cnf(i_0_18045,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_18046,plain,
( X1 = X2
| c_Com_Ovname_OGlb(X1) != c_Com_Ovname_OGlb(X2) ),
inference(split_conjunct,[status(thm)],[i_0_11013]),
[final] ).
cnf(i_0_18047,plain,
( X1 = X2
| c_Com_Ovname_OLoc(X1) != c_Com_Ovname_OLoc(X2) ),
inference(split_conjunct,[status(thm)],[i_0_11014]),
[final] ).
cnf(i_0_18048,plain,
c_Com_Ovname_OGlb(X1) != c_Com_Ovname_OLoc(X2),
inference(split_conjunct,[status(thm)],[i_0_11015]),
[final] ).
cnf(i_0_18049,plain,
c_Com_Ovname_OLoc(X1) != c_Com_Ovname_OGlb(X2),
inference(split_conjunct,[status(thm)],[i_0_11016]),
[final] ).
cnf(i_0_18050,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_11017]),
[final] ).
cnf(i_0_18051,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_11018]),
[final] ).
cnf(i_0_18052,plain,
c_Equiv__Relations_Oequivp(X1,c_fequal),
inference(split_conjunct,[status(thm)],[i_0_11019]),
[final] ).
cnf(i_0_18053,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(split_conjunct,[status(thm)],[fact_wf__pred__nat]),
[final] ).
cnf(i_0_18054,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
inference(split_conjunct,[status(thm)],[fact_wf__less__than]),
[final] ).
cnf(i_0_18055,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_18056,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_18057,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_18058,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_18059,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_18060,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_18061,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_18062,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_18063,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_18064,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_18065,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_18066,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_18067,plain,
~ hBOOL(c_fFalse),
inference(split_conjunct,[status(thm)],[i_0_11020]),
[final] ).
cnf(i_0_18068,plain,
class_Lattices_Obounded__lattice(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice]),
[final] ).
cnf(i_0_18069,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_18070,plain,
class_Groups_Osemigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Osemigroup__add]),
[final] ).
cnf(i_0_18071,plain,
class_Groups_Osemigroup__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Osemigroup__add]),
[final] ).
cnf(i_0_18072,plain,
class_Smallcheck_Osmall(tc_Product__Type_Ounit),
inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Smallcheck_Osmall]),
[final] ).
cnf(i_0_18073,plain,
class_Smallcheck_Osmall(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Smallcheck_Osmall]),
[final] ).
cnf(i_0_18074,plain,
class_Orderings_Owellorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Owellorder]),
[final] ).
cnf(i_0_18075,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_18076,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_18077,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_18078,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_18079,plain,
class_Orderings_Otop(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Otop]),
[final] ).
cnf(i_0_18080,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_18081,plain,
class_Lattices_Odistrib__lattice(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Odistrib__lattice]),
[final] ).
cnf(i_0_18082,plain,
class_Lattices_Odistrib__lattice(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Odistrib__lattice]),
[final] ).
cnf(i_0_18083,plain,
class_Lattices_Odistrib__lattice(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Odistrib__lattice]),
[final] ).
cnf(i_0_18084,plain,
class_Lattices_Osemilattice__inf(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Osemilattice__inf]),
[final] ).
cnf(i_0_18085,plain,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__inf]),
[final] ).
cnf(i_0_18086,plain,
class_Lattices_Osemilattice__inf(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__inf]),
[final] ).
cnf(i_0_18087,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_18088,plain,
class_Finite__Set_Ofinite(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Finite__Set_Ofinite]),
[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_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice__bot]),
[final] ).
cnf(i_0_18096,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring]),
[final] ).
cnf(i_0_18097,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_18098,plain,
class_Rings_Odvd(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Odvd]),
[final] ).
cnf(i_0_18099,plain,
class_Rings_Odvd(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Odvd]),
[final] ).
cnf(i_0_18100,plain,
class_Orderings_Obot(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Obot]),
[final] ).
cnf(i_0_18101,plain,
class_Orderings_Obot(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Obot]),
[final] ).
cnf(i_0_18102,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_18103,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]),
[final] ).
cnf(i_0_18104,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]),
[final] ).
cnf(i_0_18105,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_18106,plain,
class_Power_Opower(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Power_Opower]),
[final] ).
cnf(i_0_18107,plain,
class_Power_Opower(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Power_Opower]),
[final] ).
cnf(i_0_18108,plain,
class_Groups_Oabs__if(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oabs__if]),
[final] ).
cnf(i_0_18109,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_18110,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_18111,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_18112,plain,
class_Int_Onumber(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Onumber]),
[final] ).
cnf(i_0_18113,plain,
class_Int_Onumber(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Int_Onumber]),
[final] ).
cnf(i_0_18114,plain,
class_Int_Onumber__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Onumber__ring]),
[final] ).
cnf(i_0_18115,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_18116,plain,
class_Groups_Ominus(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ominus]),
[final] ).
cnf(i_0_18117,plain,
class_Groups_Ominus(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ominus]),
[final] ).
cnf(i_0_18118,plain,
class_Groups_Ominus(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ominus]),
[final] ).
cnf(i_0_18119,plain,
class_Groups_Ouminus(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ouminus]),
[final] ).
cnf(i_0_18120,plain,
class_Groups_Ouminus(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ouminus]),
[final] ).
cnf(i_0_18121,plain,
class_Divides_Oring__div(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Divides_Oring__div]),
[final] ).
cnf(i_0_18122,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_18123,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Divides_Osemiring__div]),
[final] ).
cnf(i_0_18124,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Divides_Osemiring__div]),
[final] ).
cnf(i_0_18125,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Oboolean__algebra]),
[final] ).
cnf(i_0_18126,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_18127,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_18128,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring]),
[final] ).
cnf(i_0_18129,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring]),
[final] ).
cnf(i_0_18130,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_18131,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_18132,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_18133,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_18134,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]),
[final] ).
cnf(i_0_18135,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]),
[final] ).
cnf(i_0_18136,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]),
[final] ).
cnf(i_0_18137,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_18138,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_18139,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_18140,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_18141,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_18142,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_18143,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_18144,plain,
class_Groups_Osgn__if(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Osgn__if]),
[final] ).
cnf(i_0_18145,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_18146,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_18147,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_18148,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_18149,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_18150,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_18151,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_18152,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]),
[final] ).
cnf(i_0_18153,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_18154,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_18155,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_18156,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_18157,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring]),
[final] ).
cnf(i_0_18158,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]),
[final] ).
cnf(i_0_18159,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_18160,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_18161,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_18162,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_18163,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_18164,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_18165,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_18166,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_18167,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]),
[final] ).
cnf(i_0_18168,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]),
[final] ).
cnf(i_0_18169,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_18170,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_18171,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_18172,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_18173,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_18174,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_18175,plain,
class_Groups_Oone(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oone]),
[final] ).
cnf(i_0_18176,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oone]),
[final] ).
cnf(i_0_18177,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_18178,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_18179,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_18180,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_18181,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_18182,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_18183,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]),
[final] ).
cnf(i_0_18184,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_18185,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_18186,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__1]),
[final] ).
cnf(i_0_18187,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oidom]),
[final] ).
cnf(i_0_18188,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_18189,plain,
class_Rings_Oring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring]),
[final] ).
cnf(i_0_18190,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_18191,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oord]),
[final] ).
cnf(i_0_18192,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]),
[final] ).
cnf(i_0_18193,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]),
[final] ).
cnf(i_0_18194,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_18195,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]),
[final] ).
cnf(i_0_18196,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]),
[final] ).
cnf(i_0_18197,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]),
[final] ).
cnf(i_0_18198,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_18199,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]),
[final] ).
cnf(i_0_18200,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]),
[final] ).
cnf(i_0_18201,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_18202,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oorder]),
[final] ).
cnf(i_0_18203,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]),
[final] ).
cnf(i_0_18204,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]),
[final] ).
cnf(i_0_18205,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_18206,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_18207,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_18208,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_18209,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_18210,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_18211,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]),
[final] ).
cnf(i_0_18212,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_18213,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_18214,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_18215,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_18216,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_18217,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_18218,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_18219,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_18220,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_18221,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_18222,plain,
class_Rings_Osemiring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__1]),
[final] ).
cnf(i_0_18223,plain,
class_Rings_Osemiring__1(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__1]),
[final] ).
cnf(i_0_18224,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_18225,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_18226,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_18227,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_18228,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_18229,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_18230,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_18231,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_18232,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_18233,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_18234,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]),
[final] ).
cnf(i_0_18235,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]),
[final] ).
cnf(i_0_18236,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_18237,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_18238,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_18239,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_18240,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_18241,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_18242,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_18243,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_18244,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_18245,plain,
hBOOL(c_fTrue),
inference(split_conjunct,[status(thm)],[help_c__fTrue__1]),
[final] ).
cnf(i_0_18246,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_18247,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ozero]),
[final] ).
cnf(i_0_18248,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ozero]),
[final] ).
cnf(i_0_18249,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_18250,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_18251,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]),
[final] ).
cnf(i_0_18252,plain,
c_Int_OPls != c_Int_OMin,
inference(split_conjunct,[status(thm)],[fact_rel__simps_I37_J]),
[final] ).
cnf(i_0_18253,plain,
c_Int_OMin != c_Int_OPls,
inference(split_conjunct,[status(thm)],[fact_rel__simps_I40_J]),
[final] ).
cnf(i_0_18254,axiom,
X1 = X1 ).
cnf(i_0_18255,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_18256,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_18257,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_18258,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_18259,axiom,
( X1 != X2
| c_Com_Ocom_OCond(X1,X3,X4) = c_Com_Ocom_OCond(X2,X3,X4) ) ).
cnf(i_0_18260,axiom,
( X1 != X2
| c_Com_Ocom_OCond(X3,X1,X4) = c_Com_Ocom_OCond(X3,X2,X4) ) ).
cnf(i_0_18261,axiom,
( X1 != X2
| c_Com_Ocom_OCond(X3,X4,X1) = c_Com_Ocom_OCond(X3,X4,X2) ) ).
cnf(i_0_18262,axiom,
( X1 != X2
| c_Map_Omap__upds(X1,X3,X4,X5,X6) = c_Map_Omap__upds(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18263,axiom,
( X1 != X2
| c_Map_Omap__upds(X3,X1,X4,X5,X6) = c_Map_Omap__upds(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18264,axiom,
( X1 != X2
| c_Map_Omap__upds(X3,X4,X1,X5,X6) = c_Map_Omap__upds(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18265,axiom,
( X1 != X2
| c_Map_Omap__upds(X3,X4,X5,X1,X6) = c_Map_Omap__upds(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18266,axiom,
( X1 != X2
| c_Map_Omap__upds(X3,X4,X5,X6,X1) = c_Map_Omap__upds(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18267,axiom,
( X1 != X2
| c_Com_Ocom_OSemi(X1,X3) = c_Com_Ocom_OSemi(X2,X3) ) ).
cnf(i_0_18268,axiom,
( X1 != X2
| c_Com_Ocom_OSemi(X3,X1) = c_Com_Ocom_OSemi(X3,X2) ) ).
cnf(i_0_18269,axiom,
( X1 != X2
| c_Big__Operators_Olinorder__class_OMin(X1,X3) = c_Big__Operators_Olinorder__class_OMin(X2,X3) ) ).
cnf(i_0_18270,axiom,
( X1 != X2
| c_Big__Operators_Olinorder__class_OMin(X3,X1) = c_Big__Operators_Olinorder__class_OMin(X3,X2) ) ).
cnf(i_0_18271,axiom,
( X1 != X2
| c_Big__Operators_Olinorder__class_OMax(X1,X3) = c_Big__Operators_Olinorder__class_OMax(X2,X3) ) ).
cnf(i_0_18272,axiom,
( X1 != X2
| c_Big__Operators_Olinorder__class_OMax(X3,X1) = c_Big__Operators_Olinorder__class_OMax(X3,X2) ) ).
cnf(i_0_18273,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__case(X1,X3,X4,X5) = c_Option_Ooption_Ooption__case(X2,X3,X4,X5) ) ).
cnf(i_0_18274,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__case(X3,X1,X4,X5) = c_Option_Ooption_Ooption__case(X3,X2,X4,X5) ) ).
cnf(i_0_18275,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__case(X3,X4,X1,X5) = c_Option_Ooption_Ooption__case(X3,X4,X2,X5) ) ).
cnf(i_0_18276,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__case(X3,X4,X5,X1) = c_Option_Ooption_Ooption__case(X3,X4,X5,X2) ) ).
cnf(i_0_18277,axiom,
( X1 != X2
| c_List_Olist_ONil(X1) = c_List_Olist_ONil(X2) ) ).
cnf(i_0_18278,axiom,
( X1 != X2
| c_List_Olistrel(X1,X3) = c_List_Olistrel(X2,X3) ) ).
cnf(i_0_18279,axiom,
( X1 != X2
| c_List_Olistrel(X3,X1) = c_List_Olistrel(X3,X2) ) ).
cnf(i_0_18280,axiom,
( X1 != X2
| c_Divides_Oadjust(X1) = c_Divides_Oadjust(X2) ) ).
cnf(i_0_18281,axiom,
( X1 != X2
| c_List_Opartition(X1,X3,X4) = c_List_Opartition(X2,X3,X4) ) ).
cnf(i_0_18282,axiom,
( X1 != X2
| c_List_Opartition(X3,X1,X4) = c_List_Opartition(X3,X2,X4) ) ).
cnf(i_0_18283,axiom,
( X1 != X2
| c_List_Opartition(X3,X4,X1) = c_List_Opartition(X3,X4,X2) ) ).
cnf(i_0_18284,axiom,
( X1 != X2
| c_Wellfounded_Olex__prod(X1,X3,X4,X5) = c_Wellfounded_Olex__prod(X2,X3,X4,X5) ) ).
cnf(i_0_18285,axiom,
( X1 != X2
| c_Wellfounded_Olex__prod(X3,X1,X4,X5) = c_Wellfounded_Olex__prod(X3,X2,X4,X5) ) ).
cnf(i_0_18286,axiom,
( X1 != X2
| c_Wellfounded_Olex__prod(X3,X4,X1,X5) = c_Wellfounded_Olex__prod(X3,X4,X2,X5) ) ).
cnf(i_0_18287,axiom,
( X1 != X2
| c_Wellfounded_Olex__prod(X3,X4,X5,X1) = c_Wellfounded_Olex__prod(X3,X4,X5,X2) ) ).
cnf(i_0_18288,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X1) = c_Power_Opower__class_Opower(X2) ) ).
cnf(i_0_18289,axiom,
( X1 != X2
| c_List_Osublist(X1,X3,X4) = c_List_Osublist(X2,X3,X4) ) ).
cnf(i_0_18290,axiom,
( X1 != X2
| c_List_Osublist(X3,X1,X4) = c_List_Osublist(X3,X2,X4) ) ).
cnf(i_0_18291,axiom,
( X1 != X2
| c_List_Osublist(X3,X4,X1) = c_List_Osublist(X3,X4,X2) ) ).
cnf(i_0_18292,axiom,
( X1 != X2
| c_List_Otranspose(X1,X3) = c_List_Otranspose(X2,X3) ) ).
cnf(i_0_18293,axiom,
( X1 != X2
| c_List_Otranspose(X3,X1) = c_List_Otranspose(X3,X2) ) ).
cnf(i_0_18294,axiom,
( X1 != X2
| c_Divides_Odivmod__int__rel(X1,X3) = c_Divides_Odivmod__int__rel(X2,X3) ) ).
cnf(i_0_18295,axiom,
( X1 != X2
| c_Divides_Odivmod__int__rel(X3,X1) = c_Divides_Odivmod__int__rel(X3,X2) ) ).
cnf(i_0_18296,axiom,
( X1 != X2
| c_Set_Othe__elem(X1,X3) = c_Set_Othe__elem(X2,X3) ) ).
cnf(i_0_18297,axiom,
( X1 != X2
| c_Set_Othe__elem(X3,X1) = c_Set_Othe__elem(X3,X2) ) ).
cnf(i_0_18298,axiom,
( X1 != X2
| c_Nitpick_Osetsum_H(X1,X3,X4,X5) = c_Nitpick_Osetsum_H(X2,X3,X4,X5) ) ).
cnf(i_0_18299,axiom,
( X1 != X2
| c_Nitpick_Osetsum_H(X3,X1,X4,X5) = c_Nitpick_Osetsum_H(X3,X2,X4,X5) ) ).
cnf(i_0_18300,axiom,
( X1 != X2
| c_Nitpick_Osetsum_H(X3,X4,X1,X5) = c_Nitpick_Osetsum_H(X3,X4,X2,X5) ) ).
cnf(i_0_18301,axiom,
( X1 != X2
| c_Nitpick_Osetsum_H(X3,X4,X5,X1) = c_Nitpick_Osetsum_H(X3,X4,X5,X2) ) ).
cnf(i_0_18302,axiom,
( X1 != X2
| c_List_Omonoid__add__class_Olistsum(X1) = c_List_Omonoid__add__class_Olistsum(X2) ) ).
cnf(i_0_18303,axiom,
( X1 != X2
| c_Hilbert__Choice_OEps(X1,X3) = c_Hilbert__Choice_OEps(X2,X3) ) ).
cnf(i_0_18304,axiom,
( X1 != X2
| c_Hilbert__Choice_OEps(X3,X1) = c_Hilbert__Choice_OEps(X3,X2) ) ).
cnf(i_0_18305,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_18306,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_18307,axiom,
( X1 != X2
| c_Random__Sequence_ORandom(X1,X3,X4,X5) = c_Random__Sequence_ORandom(X2,X3,X4,X5) ) ).
cnf(i_0_18308,axiom,
( X1 != X2
| c_Random__Sequence_ORandom(X3,X1,X4,X5) = c_Random__Sequence_ORandom(X3,X2,X4,X5) ) ).
cnf(i_0_18309,axiom,
( X1 != X2
| c_Random__Sequence_ORandom(X3,X4,X1,X5) = c_Random__Sequence_ORandom(X3,X4,X2,X5) ) ).
cnf(i_0_18310,axiom,
( X1 != X2
| c_Random__Sequence_ORandom(X3,X4,X5,X1) = c_Random__Sequence_ORandom(X3,X4,X5,X2) ) ).
cnf(i_0_18311,axiom,
( X1 != X2
| c_Lazy__Sequence_Ohb__not__seq(X1) = c_Lazy__Sequence_Ohb__not__seq(X2) ) ).
cnf(i_0_18312,axiom,
( X1 != X2
| c_Wellfounded_Omax__ext(X1,X3) = c_Wellfounded_Omax__ext(X2,X3) ) ).
cnf(i_0_18313,axiom,
( X1 != X2
| c_Wellfounded_Omax__ext(X3,X1) = c_Wellfounded_Omax__ext(X3,X2) ) ).
cnf(i_0_18314,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_18315,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).
cnf(i_0_18316,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).
cnf(i_0_18317,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).
cnf(i_0_18318,axiom,
( X1 != X2
| c_Wellfounded_Omin__ext(X1,X3) = c_Wellfounded_Omin__ext(X2,X3) ) ).
cnf(i_0_18319,axiom,
( X1 != X2
| c_Wellfounded_Omin__ext(X3,X1) = c_Wellfounded_Omin__ext(X3,X2) ) ).
cnf(i_0_18320,axiom,
( X1 != X2
| c_Wellfounded_Ofinite__psubset(X1) = c_Wellfounded_Ofinite__psubset(X2) ) ).
cnf(i_0_18321,axiom,
( X1 != X2
| c_Nitpick_Ocard_H(X1,X3) = c_Nitpick_Ocard_H(X2,X3) ) ).
cnf(i_0_18322,axiom,
( X1 != X2
| c_Nitpick_Ocard_H(X3,X1) = c_Nitpick_Ocard_H(X3,X2) ) ).
cnf(i_0_18323,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_18324,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_18325,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_18326,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_18327,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_18328,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_18329,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_18330,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_18331,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_18332,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_18333,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_18334,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X1) = c_Groups_Ominus__class_Ominus(X2) ) ).
cnf(i_0_18335,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_18336,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_18337,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_18338,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_18339,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_18340,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_18341,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_18342,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_18343,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_18344,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_18345,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_18346,axiom,
( X1 != X2
| c_Complete__Lattice_OSup__class_OSup(X1,X3) = c_Complete__Lattice_OSup__class_OSup(X2,X3) ) ).
cnf(i_0_18347,axiom,
( X1 != X2
| c_Complete__Lattice_OSup__class_OSup(X3,X1) = c_Complete__Lattice_OSup__class_OSup(X3,X2) ) ).
cnf(i_0_18348,axiom,
( X1 != X2
| c_Complete__Lattice_OInf__class_OInf(X1,X3) = c_Complete__Lattice_OInf__class_OInf(X2,X3) ) ).
cnf(i_0_18349,axiom,
( X1 != X2
| c_Complete__Lattice_OInf__class_OInf(X3,X1) = c_Complete__Lattice_OInf__class_OInf(X3,X2) ) ).
cnf(i_0_18350,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_18351,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_18352,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_18353,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_18354,axiom,
( X1 != X2
| c_New__DSequence_Oneg__bind(X1,X3,X4,X5) = c_New__DSequence_Oneg__bind(X2,X3,X4,X5) ) ).
cnf(i_0_18355,axiom,
( X1 != X2
| c_New__DSequence_Oneg__bind(X3,X1,X4,X5) = c_New__DSequence_Oneg__bind(X3,X2,X4,X5) ) ).
cnf(i_0_18356,axiom,
( X1 != X2
| c_New__DSequence_Oneg__bind(X3,X4,X1,X5) = c_New__DSequence_Oneg__bind(X3,X4,X2,X5) ) ).
cnf(i_0_18357,axiom,
( X1 != X2
| c_New__DSequence_Oneg__bind(X3,X4,X5,X1) = c_New__DSequence_Oneg__bind(X3,X4,X5,X2) ) ).
cnf(i_0_18358,axiom,
( X1 != X2
| esk383_5(X1,X3,X4,X5,X6) = esk383_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18359,axiom,
( X1 != X2
| esk383_5(X3,X1,X4,X5,X6) = esk383_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18360,axiom,
( X1 != X2
| esk383_5(X3,X4,X1,X5,X6) = esk383_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18361,axiom,
( X1 != X2
| esk383_5(X3,X4,X5,X1,X6) = esk383_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18362,axiom,
( X1 != X2
| esk383_5(X3,X4,X5,X6,X1) = esk383_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18363,axiom,
( X1 != X2
| esk382_5(X1,X3,X4,X5,X6) = esk382_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18364,axiom,
( X1 != X2
| esk382_5(X3,X1,X4,X5,X6) = esk382_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18365,axiom,
( X1 != X2
| esk382_5(X3,X4,X1,X5,X6) = esk382_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18366,axiom,
( X1 != X2
| esk382_5(X3,X4,X5,X1,X6) = esk382_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18367,axiom,
( X1 != X2
| esk382_5(X3,X4,X5,X6,X1) = esk382_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18368,axiom,
( X1 != X2
| esk377_5(X1,X3,X4,X5,X6) = esk377_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18369,axiom,
( X1 != X2
| esk377_5(X3,X1,X4,X5,X6) = esk377_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18370,axiom,
( X1 != X2
| esk377_5(X3,X4,X1,X5,X6) = esk377_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18371,axiom,
( X1 != X2
| esk377_5(X3,X4,X5,X1,X6) = esk377_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18372,axiom,
( X1 != X2
| esk377_5(X3,X4,X5,X6,X1) = esk377_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18373,axiom,
( X1 != X2
| esk378_5(X1,X3,X4,X5,X6) = esk378_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18374,axiom,
( X1 != X2
| esk378_5(X3,X1,X4,X5,X6) = esk378_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18375,axiom,
( X1 != X2
| esk378_5(X3,X4,X1,X5,X6) = esk378_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18376,axiom,
( X1 != X2
| esk378_5(X3,X4,X5,X1,X6) = esk378_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18377,axiom,
( X1 != X2
| esk378_5(X3,X4,X5,X6,X1) = esk378_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18378,axiom,
( X1 != X2
| c_Option_Ooption_ONone(X1) = c_Option_Ooption_ONone(X2) ) ).
cnf(i_0_18379,axiom,
( X1 != X2
| c_HOL_OThe(X1,X3) = c_HOL_OThe(X2,X3) ) ).
cnf(i_0_18380,axiom,
( X1 != X2
| c_HOL_OThe(X3,X1) = c_HOL_OThe(X3,X2) ) ).
cnf(i_0_18381,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_18382,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_18383,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_18384,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_18385,axiom,
( X1 != X2
| c_New__DSequence_Opos__bind(X1,X3,X4,X5) = c_New__DSequence_Opos__bind(X2,X3,X4,X5) ) ).
cnf(i_0_18386,axiom,
( X1 != X2
| c_New__DSequence_Opos__bind(X3,X1,X4,X5) = c_New__DSequence_Opos__bind(X3,X2,X4,X5) ) ).
cnf(i_0_18387,axiom,
( X1 != X2
| c_New__DSequence_Opos__bind(X3,X4,X1,X5) = c_New__DSequence_Opos__bind(X3,X4,X2,X5) ) ).
cnf(i_0_18388,axiom,
( X1 != X2
| c_New__DSequence_Opos__bind(X3,X4,X5,X1) = c_New__DSequence_Opos__bind(X3,X4,X5,X2) ) ).
cnf(i_0_18389,axiom,
( X1 != X2
| c_SetInterval_Oord_OatLeastLessThan(X1,X3,X4,X5,X6) = c_SetInterval_Oord_OatLeastLessThan(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18390,axiom,
( X1 != X2
| c_SetInterval_Oord_OatLeastLessThan(X3,X1,X4,X5,X6) = c_SetInterval_Oord_OatLeastLessThan(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18391,axiom,
( X1 != X2
| c_SetInterval_Oord_OatLeastLessThan(X3,X4,X1,X5,X6) = c_SetInterval_Oord_OatLeastLessThan(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18392,axiom,
( X1 != X2
| c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X1,X6) = c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18393,axiom,
( X1 != X2
| c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X6,X1) = c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18394,axiom,
( X1 != X2
| c_SetInterval_Oord_OgreaterThanAtMost(X1,X3,X4,X5,X6) = c_SetInterval_Oord_OgreaterThanAtMost(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18395,axiom,
( X1 != X2
| c_SetInterval_Oord_OgreaterThanAtMost(X3,X1,X4,X5,X6) = c_SetInterval_Oord_OgreaterThanAtMost(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18396,axiom,
( X1 != X2
| c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X1,X5,X6) = c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18397,axiom,
( X1 != X2
| c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X1,X6) = c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18398,axiom,
( X1 != X2
| c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X6,X1) = c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18399,axiom,
( X1 != X2
| c_Nitpick_Oprod(X1,X3,X4,X5) = c_Nitpick_Oprod(X2,X3,X4,X5) ) ).
cnf(i_0_18400,axiom,
( X1 != X2
| c_Nitpick_Oprod(X3,X1,X4,X5) = c_Nitpick_Oprod(X3,X2,X4,X5) ) ).
cnf(i_0_18401,axiom,
( X1 != X2
| c_Nitpick_Oprod(X3,X4,X1,X5) = c_Nitpick_Oprod(X3,X4,X2,X5) ) ).
cnf(i_0_18402,axiom,
( X1 != X2
| c_Nitpick_Oprod(X3,X4,X5,X1) = c_Nitpick_Oprod(X3,X4,X5,X2) ) ).
cnf(i_0_18403,axiom,
( X1 != X2
| esk264_6(X1,X3,X4,X5,X6,X7) = esk264_6(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_18404,axiom,
( X1 != X2
| esk264_6(X3,X1,X4,X5,X6,X7) = esk264_6(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_18405,axiom,
( X1 != X2
| esk264_6(X3,X4,X1,X5,X6,X7) = esk264_6(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_18406,axiom,
( X1 != X2
| esk264_6(X3,X4,X5,X1,X6,X7) = esk264_6(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_18407,axiom,
( X1 != X2
| esk264_6(X3,X4,X5,X6,X1,X7) = esk264_6(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_18408,axiom,
( X1 != X2
| esk264_6(X3,X4,X5,X6,X7,X1) = esk264_6(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_18409,axiom,
( X1 != X2
| esk263_6(X1,X3,X4,X5,X6,X7) = esk263_6(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_18410,axiom,
( X1 != X2
| esk263_6(X3,X1,X4,X5,X6,X7) = esk263_6(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_18411,axiom,
( X1 != X2
| esk263_6(X3,X4,X1,X5,X6,X7) = esk263_6(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_18412,axiom,
( X1 != X2
| esk263_6(X3,X4,X5,X1,X6,X7) = esk263_6(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_18413,axiom,
( X1 != X2
| esk263_6(X3,X4,X5,X6,X1,X7) = esk263_6(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_18414,axiom,
( X1 != X2
| esk263_6(X3,X4,X5,X6,X7,X1) = esk263_6(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_18415,axiom,
( X1 != X2
| c_Int_Onumber__class_Onumber__of(X1) = c_Int_Onumber__class_Onumber__of(X2) ) ).
cnf(i_0_18416,axiom,
( X1 != X2
| c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).
cnf(i_0_18417,axiom,
( X1 != X2
| c_Nitpick_Otimes__frac(X1,X3,X4) = c_Nitpick_Otimes__frac(X2,X3,X4) ) ).
cnf(i_0_18418,axiom,
( X1 != X2
| c_Nitpick_Otimes__frac(X3,X1,X4) = c_Nitpick_Otimes__frac(X3,X2,X4) ) ).
cnf(i_0_18419,axiom,
( X1 != X2
| c_Nitpick_Otimes__frac(X3,X4,X1) = c_Nitpick_Otimes__frac(X3,X4,X2) ) ).
cnf(i_0_18420,axiom,
( X1 != X2
| c_Divides_OnegDivAlg(X1,X3) = c_Divides_OnegDivAlg(X2,X3) ) ).
cnf(i_0_18421,axiom,
( X1 != X2
| c_Divides_OnegDivAlg(X3,X1) = c_Divides_OnegDivAlg(X3,X2) ) ).
cnf(i_0_18422,axiom,
( X1 != X2
| c_Divides_OposDivAlg(X1,X3) = c_Divides_OposDivAlg(X2,X3) ) ).
cnf(i_0_18423,axiom,
( X1 != X2
| c_Divides_OposDivAlg(X3,X1) = c_Divides_OposDivAlg(X3,X2) ) ).
cnf(i_0_18424,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat(X1) = c_Nat_Osemiring__1__class_Oof__nat(X2) ) ).
cnf(i_0_18425,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X1,X3,X4,X5) = c_Nat_Onat_Onat__case(X2,X3,X4,X5) ) ).
cnf(i_0_18426,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X3,X1,X4,X5) = c_Nat_Onat_Onat__case(X3,X2,X4,X5) ) ).
cnf(i_0_18427,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X3,X4,X1,X5) = c_Nat_Onat_Onat__case(X3,X4,X2,X5) ) ).
cnf(i_0_18428,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X3,X4,X5,X1) = c_Nat_Onat_Onat__case(X3,X4,X5,X2) ) ).
cnf(i_0_18429,axiom,
( X1 != X2
| c_List_Omap__filter(X1,X3,X4,X5) = c_List_Omap__filter(X2,X3,X4,X5) ) ).
cnf(i_0_18430,axiom,
( X1 != X2
| c_List_Omap__filter(X3,X1,X4,X5) = c_List_Omap__filter(X3,X2,X4,X5) ) ).
cnf(i_0_18431,axiom,
( X1 != X2
| c_List_Omap__filter(X3,X4,X1,X5) = c_List_Omap__filter(X3,X4,X2,X5) ) ).
cnf(i_0_18432,axiom,
( X1 != X2
| c_List_Omap__filter(X3,X4,X5,X1) = c_List_Omap__filter(X3,X4,X5,X2) ) ).
cnf(i_0_18433,axiom,
( X1 != X2
| c_Map_Odom(X1,X3,X4) = c_Map_Odom(X2,X3,X4) ) ).
cnf(i_0_18434,axiom,
( X1 != X2
| c_Map_Odom(X3,X1,X4) = c_Map_Odom(X3,X2,X4) ) ).
cnf(i_0_18435,axiom,
( X1 != X2
| c_Map_Odom(X3,X4,X1) = c_Map_Odom(X3,X4,X2) ) ).
cnf(i_0_18436,axiom,
( X1 != X2
| c_Fun_Oid(X1) = c_Fun_Oid(X2) ) ).
cnf(i_0_18437,axiom,
( X1 != X2
| c_SetInterval_Oord_OgreaterThanLessThan(X1,X3,X4,X5) = c_SetInterval_Oord_OgreaterThanLessThan(X2,X3,X4,X5) ) ).
cnf(i_0_18438,axiom,
( X1 != X2
| c_SetInterval_Oord_OgreaterThanLessThan(X3,X1,X4,X5) = c_SetInterval_Oord_OgreaterThanLessThan(X3,X2,X4,X5) ) ).
cnf(i_0_18439,axiom,
( X1 != X2
| c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X1,X5) = c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X2,X5) ) ).
cnf(i_0_18440,axiom,
( X1 != X2
| c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X5,X1) = c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X5,X2) ) ).
cnf(i_0_18441,axiom,
( X1 != X2
| c_Relation_OId__on(X1,X3) = c_Relation_OId__on(X2,X3) ) ).
cnf(i_0_18442,axiom,
( X1 != X2
| c_Relation_OId__on(X3,X1) = c_Relation_OId__on(X3,X2) ) ).
cnf(i_0_18443,axiom,
( X1 != X2
| c_Int_Oint__ge__less__than(X1) = c_Int_Oint__ge__less__than(X2) ) ).
cnf(i_0_18444,axiom,
( X1 != X2
| c_List_Olistrel1(X1,X3) = c_List_Olistrel1(X2,X3) ) ).
cnf(i_0_18445,axiom,
( X1 != X2
| c_List_Olistrel1(X3,X1) = c_List_Olistrel1(X3,X2) ) ).
cnf(i_0_18446,axiom,
( X1 != X2
| c_Finite__Set_Ofold(X1,X3,X4) = c_Finite__Set_Ofold(X2,X3,X4) ) ).
cnf(i_0_18447,axiom,
( X1 != X2
| c_Finite__Set_Ofold(X3,X1,X4) = c_Finite__Set_Ofold(X3,X2,X4) ) ).
cnf(i_0_18448,axiom,
( X1 != X2
| c_Finite__Set_Ofold(X3,X4,X1) = c_Finite__Set_Ofold(X3,X4,X2) ) ).
cnf(i_0_18449,axiom,
( X1 != X2
| c_Nitpick_Ouminus__frac(X1,X3) = c_Nitpick_Ouminus__frac(X2,X3) ) ).
cnf(i_0_18450,axiom,
( X1 != X2
| c_Nitpick_Ouminus__frac(X3,X1) = c_Nitpick_Ouminus__frac(X3,X2) ) ).
cnf(i_0_18451,axiom,
( X1 != X2
| c_Nitpick_OAbs__Frac(X1,X3) = c_Nitpick_OAbs__Frac(X2,X3) ) ).
cnf(i_0_18452,axiom,
( X1 != X2
| c_Nitpick_OAbs__Frac(X3,X1) = c_Nitpick_OAbs__Frac(X3,X2) ) ).
cnf(i_0_18453,axiom,
( X1 != X2
| esk476_4(X1,X3,X4,X5) = esk476_4(X2,X3,X4,X5) ) ).
cnf(i_0_18454,axiom,
( X1 != X2
| esk476_4(X3,X1,X4,X5) = esk476_4(X3,X2,X4,X5) ) ).
cnf(i_0_18455,axiom,
( X1 != X2
| esk476_4(X3,X4,X1,X5) = esk476_4(X3,X4,X2,X5) ) ).
cnf(i_0_18456,axiom,
( X1 != X2
| esk476_4(X3,X4,X5,X1) = esk476_4(X3,X4,X5,X2) ) ).
cnf(i_0_18457,axiom,
( X1 != X2
| esk475_4(X1,X3,X4,X5) = esk475_4(X2,X3,X4,X5) ) ).
cnf(i_0_18458,axiom,
( X1 != X2
| esk475_4(X3,X1,X4,X5) = esk475_4(X3,X2,X4,X5) ) ).
cnf(i_0_18459,axiom,
( X1 != X2
| esk475_4(X3,X4,X1,X5) = esk475_4(X3,X4,X2,X5) ) ).
cnf(i_0_18460,axiom,
( X1 != X2
| esk475_4(X3,X4,X5,X1) = esk475_4(X3,X4,X5,X2) ) ).
cnf(i_0_18461,axiom,
( X1 != X2
| c_Fun_Ooverride__on(X1,X3,X4,X5,X6) = c_Fun_Ooverride__on(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18462,axiom,
( X1 != X2
| c_Fun_Ooverride__on(X3,X1,X4,X5,X6) = c_Fun_Ooverride__on(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18463,axiom,
( X1 != X2
| c_Fun_Ooverride__on(X3,X4,X1,X5,X6) = c_Fun_Ooverride__on(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18464,axiom,
( X1 != X2
| c_Fun_Ooverride__on(X3,X4,X5,X1,X6) = c_Fun_Ooverride__on(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18465,axiom,
( X1 != X2
| c_Fun_Ooverride__on(X3,X4,X5,X6,X1) = c_Fun_Ooverride__on(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18466,axiom,
( X1 != X2
| c_Map_Oran(X1,X3,X4) = c_Map_Oran(X2,X3,X4) ) ).
cnf(i_0_18467,axiom,
( X1 != X2
| c_Map_Oran(X3,X1,X4) = c_Map_Oran(X3,X2,X4) ) ).
cnf(i_0_18468,axiom,
( X1 != X2
| c_Map_Oran(X3,X4,X1) = c_Map_Oran(X3,X4,X2) ) ).
cnf(i_0_18469,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X1,X3,X4,X5) = c_Sum__Type_OPlus(X2,X3,X4,X5) ) ).
cnf(i_0_18470,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X1,X4,X5) = c_Sum__Type_OPlus(X3,X2,X4,X5) ) ).
cnf(i_0_18471,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X1,X5) = c_Sum__Type_OPlus(X3,X4,X2,X5) ) ).
cnf(i_0_18472,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X5,X1) = c_Sum__Type_OPlus(X3,X4,X5,X2) ) ).
cnf(i_0_18473,axiom,
( X1 != X2
| c_Int_Oint__ge__less__than2(X1) = c_Int_Oint__ge__less__than2(X2) ) ).
cnf(i_0_18474,axiom,
( X1 != X2
| c_Nitpick_Oof__frac(X1,X3,X4) = c_Nitpick_Oof__frac(X2,X3,X4) ) ).
cnf(i_0_18475,axiom,
( X1 != X2
| c_Nitpick_Oof__frac(X3,X1,X4) = c_Nitpick_Oof__frac(X3,X2,X4) ) ).
cnf(i_0_18476,axiom,
( X1 != X2
| c_Nitpick_Oof__frac(X3,X4,X1) = c_Nitpick_Oof__frac(X3,X4,X2) ) ).
cnf(i_0_18477,axiom,
( X1 != X2
| c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).
cnf(i_0_18478,axiom,
( X1 != X2
| c_Random__Sequence_Omap(X1,X3,X4,X5) = c_Random__Sequence_Omap(X2,X3,X4,X5) ) ).
cnf(i_0_18479,axiom,
( X1 != X2
| c_Random__Sequence_Omap(X3,X1,X4,X5) = c_Random__Sequence_Omap(X3,X2,X4,X5) ) ).
cnf(i_0_18480,axiom,
( X1 != X2
| c_Random__Sequence_Omap(X3,X4,X1,X5) = c_Random__Sequence_Omap(X3,X4,X2,X5) ) ).
cnf(i_0_18481,axiom,
( X1 != X2
| c_Random__Sequence_Omap(X3,X4,X5,X1) = c_Random__Sequence_Omap(X3,X4,X5,X2) ) ).
cnf(i_0_18482,axiom,
( X1 != X2
| c_Random__Sequence_Obind(X1,X3,X4,X5) = c_Random__Sequence_Obind(X2,X3,X4,X5) ) ).
cnf(i_0_18483,axiom,
( X1 != X2
| c_Random__Sequence_Obind(X3,X1,X4,X5) = c_Random__Sequence_Obind(X3,X2,X4,X5) ) ).
cnf(i_0_18484,axiom,
( X1 != X2
| c_Random__Sequence_Obind(X3,X4,X1,X5) = c_Random__Sequence_Obind(X3,X4,X2,X5) ) ).
cnf(i_0_18485,axiom,
( X1 != X2
| c_Random__Sequence_Obind(X3,X4,X5,X1) = c_Random__Sequence_Obind(X3,X4,X5,X2) ) ).
cnf(i_0_18486,axiom,
( X1 != X2
| c_Orderings_Oord__class_Omax(X1) = c_Orderings_Oord__class_Omax(X2) ) ).
cnf(i_0_18487,axiom,
( X1 != X2
| c_Map_Orestrict__map(X1,X3,X4,X5) = c_Map_Orestrict__map(X2,X3,X4,X5) ) ).
cnf(i_0_18488,axiom,
( X1 != X2
| c_Map_Orestrict__map(X3,X1,X4,X5) = c_Map_Orestrict__map(X3,X2,X4,X5) ) ).
cnf(i_0_18489,axiom,
( X1 != X2
| c_Map_Orestrict__map(X3,X4,X1,X5) = c_Map_Orestrict__map(X3,X4,X2,X5) ) ).
cnf(i_0_18490,axiom,
( X1 != X2
| c_Map_Orestrict__map(X3,X4,X5,X1) = c_Map_Orestrict__map(X3,X4,X5,X2) ) ).
cnf(i_0_18491,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X4) ) ).
cnf(i_0_18492,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X4) ) ).
cnf(i_0_18493,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X2) ) ).
cnf(i_0_18494,axiom,
( X1 != X2
| c_Big__Operators_Olattice_OInf__fin(X1,X3,X4) = c_Big__Operators_Olattice_OInf__fin(X2,X3,X4) ) ).
cnf(i_0_18495,axiom,
( X1 != X2
| c_Big__Operators_Olattice_OInf__fin(X3,X1,X4) = c_Big__Operators_Olattice_OInf__fin(X3,X2,X4) ) ).
cnf(i_0_18496,axiom,
( X1 != X2
| c_Big__Operators_Olattice_OInf__fin(X3,X4,X1) = c_Big__Operators_Olattice_OInf__fin(X3,X4,X2) ) ).
cnf(i_0_18497,axiom,
( X1 != X2
| c_Orderings_Oord__class_Omin(X1) = c_Orderings_Oord__class_Omin(X2) ) ).
cnf(i_0_18498,axiom,
( X1 != X2
| c_List_Olist_Olist__size(X1,X3,X4) = c_List_Olist_Olist__size(X2,X3,X4) ) ).
cnf(i_0_18499,axiom,
( X1 != X2
| c_List_Olist_Olist__size(X3,X1,X4) = c_List_Olist_Olist__size(X3,X2,X4) ) ).
cnf(i_0_18500,axiom,
( X1 != X2
| c_List_Olist_Olist__size(X3,X4,X1) = c_List_Olist_Olist__size(X3,X4,X2) ) ).
cnf(i_0_18501,axiom,
( X1 != X2
| c_Big__Operators_Olattice_OSup__fin(X1,X3,X4) = c_Big__Operators_Olattice_OSup__fin(X2,X3,X4) ) ).
cnf(i_0_18502,axiom,
( X1 != X2
| c_Big__Operators_Olattice_OSup__fin(X3,X1,X4) = c_Big__Operators_Olattice_OSup__fin(X3,X2,X4) ) ).
cnf(i_0_18503,axiom,
( X1 != X2
| c_Big__Operators_Olattice_OSup__fin(X3,X4,X1) = c_Big__Operators_Olattice_OSup__fin(X3,X4,X2) ) ).
cnf(i_0_18504,axiom,
( X1 != X2
| c_Lattices_Osemilattice__inf__class_Oinf(X1) = c_Lattices_Osemilattice__inf__class_Oinf(X2) ) ).
cnf(i_0_18505,axiom,
( X1 != X2
| c_Random_Oselect__weight(X1,X3) = c_Random_Oselect__weight(X2,X3) ) ).
cnf(i_0_18506,axiom,
( X1 != X2
| c_Random_Oselect__weight(X3,X1) = c_Random_Oselect__weight(X3,X2) ) ).
cnf(i_0_18507,axiom,
( X1 != X2
| c_Random_Opick(X1,X3) = c_Random_Opick(X2,X3) ) ).
cnf(i_0_18508,axiom,
( X1 != X2
| c_Random_Opick(X3,X1) = c_Random_Opick(X3,X2) ) ).
cnf(i_0_18509,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_18510,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_18511,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_18512,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_18513,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_18514,axiom,
( X1 != X2
| c_List_Olists(X1,X3) = c_List_Olists(X2,X3) ) ).
cnf(i_0_18515,axiom,
( X1 != X2
| c_List_Olists(X3,X1) = c_List_Olists(X3,X2) ) ).
cnf(i_0_18516,axiom,
( X1 != X2
| c_Wellfounded_Omlex__prod(X1,X3,X4) = c_Wellfounded_Omlex__prod(X2,X3,X4) ) ).
cnf(i_0_18517,axiom,
( X1 != X2
| c_Wellfounded_Omlex__prod(X3,X1,X4) = c_Wellfounded_Omlex__prod(X3,X2,X4) ) ).
cnf(i_0_18518,axiom,
( X1 != X2
| c_Wellfounded_Omlex__prod(X3,X4,X1) = c_Wellfounded_Omlex__prod(X3,X4,X2) ) ).
cnf(i_0_18519,axiom,
( X1 != X2
| c_Big__Operators_Olattice__class_OSup__fin(X1,X3) = c_Big__Operators_Olattice__class_OSup__fin(X2,X3) ) ).
cnf(i_0_18520,axiom,
( X1 != X2
| c_Big__Operators_Olattice__class_OSup__fin(X3,X1) = c_Big__Operators_Olattice__class_OSup__fin(X3,X2) ) ).
cnf(i_0_18521,axiom,
( X1 != X2
| c_Nitpick_Onorm__frac(X1,X3) = c_Nitpick_Onorm__frac(X2,X3) ) ).
cnf(i_0_18522,axiom,
( X1 != X2
| c_Nitpick_Onorm__frac(X3,X1) = c_Nitpick_Onorm__frac(X3,X2) ) ).
cnf(i_0_18523,axiom,
( X1 != X2
| c_List_Oremove1(X1,X3,X4) = c_List_Oremove1(X2,X3,X4) ) ).
cnf(i_0_18524,axiom,
( X1 != X2
| c_List_Oremove1(X3,X1,X4) = c_List_Oremove1(X3,X2,X4) ) ).
cnf(i_0_18525,axiom,
( X1 != X2
| c_List_Oremove1(X3,X4,X1) = c_List_Oremove1(X3,X4,X2) ) ).
cnf(i_0_18526,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_18527,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_18528,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_18529,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_18530,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_18531,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_18532,axiom,
( X1 != X2
| c_Lattices_Osemilattice__sup__class_Osup(X1) = c_Lattices_Osemilattice__sup__class_Osup(X2) ) ).
cnf(i_0_18533,axiom,
( X1 != X2
| esk371_3(X1,X3,X4) = esk371_3(X2,X3,X4) ) ).
cnf(i_0_18534,axiom,
( X1 != X2
| esk371_3(X3,X1,X4) = esk371_3(X3,X2,X4) ) ).
cnf(i_0_18535,axiom,
( X1 != X2
| esk371_3(X3,X4,X1) = esk371_3(X3,X4,X2) ) ).
cnf(i_0_18536,axiom,
( X1 != X2
| esk370_3(X1,X3,X4) = esk370_3(X2,X3,X4) ) ).
cnf(i_0_18537,axiom,
( X1 != X2
| esk370_3(X3,X1,X4) = esk370_3(X3,X2,X4) ) ).
cnf(i_0_18538,axiom,
( X1 != X2
| esk370_3(X3,X4,X1) = esk370_3(X3,X4,X2) ) ).
cnf(i_0_18539,axiom,
( X1 != X2
| c_Smallcheck_Osmall_H(X1,X3,X4) = c_Smallcheck_Osmall_H(X2,X3,X4) ) ).
cnf(i_0_18540,axiom,
( X1 != X2
| c_Smallcheck_Osmall_H(X3,X1,X4) = c_Smallcheck_Osmall_H(X3,X2,X4) ) ).
cnf(i_0_18541,axiom,
( X1 != X2
| c_Smallcheck_Osmall_H(X3,X4,X1) = c_Smallcheck_Osmall_H(X3,X4,X2) ) ).
cnf(i_0_18542,axiom,
( X1 != X2
| c_Random_Oselect(X1,X3) = c_Random_Oselect(X2,X3) ) ).
cnf(i_0_18543,axiom,
( X1 != X2
| c_Random_Oselect(X3,X1) = c_Random_Oselect(X3,X2) ) ).
cnf(i_0_18544,axiom,
( X1 != X2
| c_SetInterval_Oord_OatLeastAtMost(X1,X3,X4,X5) = c_SetInterval_Oord_OatLeastAtMost(X2,X3,X4,X5) ) ).
cnf(i_0_18545,axiom,
( X1 != X2
| c_SetInterval_Oord_OatLeastAtMost(X3,X1,X4,X5) = c_SetInterval_Oord_OatLeastAtMost(X3,X2,X4,X5) ) ).
cnf(i_0_18546,axiom,
( X1 != X2
| c_SetInterval_Oord_OatLeastAtMost(X3,X4,X1,X5) = c_SetInterval_Oord_OatLeastAtMost(X3,X4,X2,X5) ) ).
cnf(i_0_18547,axiom,
( X1 != X2
| c_SetInterval_Oord_OatLeastAtMost(X3,X4,X5,X1) = c_SetInterval_Oord_OatLeastAtMost(X3,X4,X5,X2) ) ).
cnf(i_0_18548,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_18549,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_18550,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_18551,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_18552,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_18553,axiom,
( X1 != X2
| c_Big__Operators_Olattice__class_OInf__fin(X1,X3) = c_Big__Operators_Olattice__class_OInf__fin(X2,X3) ) ).
cnf(i_0_18554,axiom,
( X1 != X2
| c_Big__Operators_Olattice__class_OInf__fin(X3,X1) = c_Big__Operators_Olattice__class_OInf__fin(X3,X2) ) ).
cnf(i_0_18555,axiom,
( X1 != X2
| c_Com_Ocom_OLocal(X1,X3,X4) = c_Com_Ocom_OLocal(X2,X3,X4) ) ).
cnf(i_0_18556,axiom,
( X1 != X2
| c_Com_Ocom_OLocal(X3,X1,X4) = c_Com_Ocom_OLocal(X3,X2,X4) ) ).
cnf(i_0_18557,axiom,
( X1 != X2
| c_Com_Ocom_OLocal(X3,X4,X1) = c_Com_Ocom_OLocal(X3,X4,X2) ) ).
cnf(i_0_18558,axiom,
( X1 != X2
| c_Finite__Set_Ofold1(X1,X3) = c_Finite__Set_Ofold1(X2,X3) ) ).
cnf(i_0_18559,axiom,
( X1 != X2
| c_Finite__Set_Ofold1(X3,X1) = c_Finite__Set_Ofold1(X3,X2) ) ).
cnf(i_0_18560,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_18561,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_18562,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_18563,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_18564,axiom,
( X1 != X2
| c_Com_Ocom_OWhile(X1,X3) = c_Com_Ocom_OWhile(X2,X3) ) ).
cnf(i_0_18565,axiom,
( X1 != X2
| c_Com_Ocom_OWhile(X3,X1) = c_Com_Ocom_OWhile(X3,X2) ) ).
cnf(i_0_18566,axiom,
( X1 != X2
| c_List_Oset__Cons(X1,X3,X4) = c_List_Oset__Cons(X2,X3,X4) ) ).
cnf(i_0_18567,axiom,
( X1 != X2
| c_List_Oset__Cons(X3,X1,X4) = c_List_Oset__Cons(X3,X2,X4) ) ).
cnf(i_0_18568,axiom,
( X1 != X2
| c_List_Oset__Cons(X3,X4,X1) = c_List_Oset__Cons(X3,X4,X2) ) ).
cnf(i_0_18569,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_18570,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_18571,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_18572,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_18573,axiom,
( X1 != X2
| esk269_5(X1,X3,X4,X5,X6) = esk269_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18574,axiom,
( X1 != X2
| esk269_5(X3,X1,X4,X5,X6) = esk269_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18575,axiom,
( X1 != X2
| esk269_5(X3,X4,X1,X5,X6) = esk269_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18576,axiom,
( X1 != X2
| esk269_5(X3,X4,X5,X1,X6) = esk269_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18577,axiom,
( X1 != X2
| esk269_5(X3,X4,X5,X6,X1) = esk269_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18578,axiom,
( X1 != X2
| esk381_3(X1,X3,X4) = esk381_3(X2,X3,X4) ) ).
cnf(i_0_18579,axiom,
( X1 != X2
| esk381_3(X3,X1,X4) = esk381_3(X3,X2,X4) ) ).
cnf(i_0_18580,axiom,
( X1 != X2
| esk381_3(X3,X4,X1) = esk381_3(X3,X4,X2) ) ).
cnf(i_0_18581,axiom,
( X1 != X2
| esk380_3(X1,X3,X4) = esk380_3(X2,X3,X4) ) ).
cnf(i_0_18582,axiom,
( X1 != X2
| esk380_3(X3,X1,X4) = esk380_3(X3,X2,X4) ) ).
cnf(i_0_18583,axiom,
( X1 != X2
| esk380_3(X3,X4,X1) = esk380_3(X3,X4,X2) ) ).
cnf(i_0_18584,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_18585,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_18586,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_18587,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_18588,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_18589,axiom,
( X1 != X2
| c_Product__Type_Ocurry(X1,X3,X4,X5) = c_Product__Type_Ocurry(X2,X3,X4,X5) ) ).
cnf(i_0_18590,axiom,
( X1 != X2
| c_Product__Type_Ocurry(X3,X1,X4,X5) = c_Product__Type_Ocurry(X3,X2,X4,X5) ) ).
cnf(i_0_18591,axiom,
( X1 != X2
| c_Product__Type_Ocurry(X3,X4,X1,X5) = c_Product__Type_Ocurry(X3,X4,X2,X5) ) ).
cnf(i_0_18592,axiom,
( X1 != X2
| c_Product__Type_Ocurry(X3,X4,X5,X1) = c_Product__Type_Ocurry(X3,X4,X5,X2) ) ).
cnf(i_0_18593,axiom,
( X1 != X2
| c_Nitpick_Onat__gcd(X1,X3) = c_Nitpick_Onat__gcd(X2,X3) ) ).
cnf(i_0_18594,axiom,
( X1 != X2
| c_Nitpick_Onat__gcd(X3,X1) = c_Nitpick_Onat__gcd(X3,X2) ) ).
cnf(i_0_18595,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_18596,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_18597,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_18598,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_18599,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_18600,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_18601,axiom,
( X1 != X2
| c_Partial__Function_Oflat__lub(X1,X3,X4) = c_Partial__Function_Oflat__lub(X2,X3,X4) ) ).
cnf(i_0_18602,axiom,
( X1 != X2
| c_Partial__Function_Oflat__lub(X3,X1,X4) = c_Partial__Function_Oflat__lub(X3,X2,X4) ) ).
cnf(i_0_18603,axiom,
( X1 != X2
| c_Partial__Function_Oflat__lub(X3,X4,X1) = c_Partial__Function_Oflat__lub(X3,X4,X2) ) ).
cnf(i_0_18604,axiom,
( X1 != X2
| c_List_OtakeWhile(X1,X3,X4) = c_List_OtakeWhile(X2,X3,X4) ) ).
cnf(i_0_18605,axiom,
( X1 != X2
| c_List_OtakeWhile(X3,X1,X4) = c_List_OtakeWhile(X3,X2,X4) ) ).
cnf(i_0_18606,axiom,
( X1 != X2
| c_List_OtakeWhile(X3,X4,X1) = c_List_OtakeWhile(X3,X4,X2) ) ).
cnf(i_0_18607,axiom,
( X1 != X2
| c_Com_Ovname_OLoc(X1) = c_Com_Ovname_OLoc(X2) ) ).
cnf(i_0_18608,axiom,
( X1 != X2
| esk97_3(X1,X3,X4) = esk97_3(X2,X3,X4) ) ).
cnf(i_0_18609,axiom,
( X1 != X2
| esk97_3(X3,X1,X4) = esk97_3(X3,X2,X4) ) ).
cnf(i_0_18610,axiom,
( X1 != X2
| esk97_3(X3,X4,X1) = esk97_3(X3,X4,X2) ) ).
cnf(i_0_18611,axiom,
( X1 != X2
| esk247_4(X1,X3,X4,X5) = esk247_4(X2,X3,X4,X5) ) ).
cnf(i_0_18612,axiom,
( X1 != X2
| esk247_4(X3,X1,X4,X5) = esk247_4(X3,X2,X4,X5) ) ).
cnf(i_0_18613,axiom,
( X1 != X2
| esk247_4(X3,X4,X1,X5) = esk247_4(X3,X4,X2,X5) ) ).
cnf(i_0_18614,axiom,
( X1 != X2
| esk247_4(X3,X4,X5,X1) = esk247_4(X3,X4,X5,X2) ) ).
cnf(i_0_18615,axiom,
( X1 != X2
| esk249_4(X1,X3,X4,X5) = esk249_4(X2,X3,X4,X5) ) ).
cnf(i_0_18616,axiom,
( X1 != X2
| esk249_4(X3,X1,X4,X5) = esk249_4(X3,X2,X4,X5) ) ).
cnf(i_0_18617,axiom,
( X1 != X2
| esk249_4(X3,X4,X1,X5) = esk249_4(X3,X4,X2,X5) ) ).
cnf(i_0_18618,axiom,
( X1 != X2
| esk249_4(X3,X4,X5,X1) = esk249_4(X3,X4,X5,X2) ) ).
cnf(i_0_18619,axiom,
( X1 != X2
| c_Com_Ocom_OCall(X1,X3,X4) = c_Com_Ocom_OCall(X2,X3,X4) ) ).
cnf(i_0_18620,axiom,
( X1 != X2
| c_Com_Ocom_OCall(X3,X1,X4) = c_Com_Ocom_OCall(X3,X2,X4) ) ).
cnf(i_0_18621,axiom,
( X1 != X2
| c_Com_Ocom_OCall(X3,X4,X1) = c_Com_Ocom_OCall(X3,X4,X2) ) ).
cnf(i_0_18622,axiom,
( X1 != X2
| esk195_4(X1,X3,X4,X5) = esk195_4(X2,X3,X4,X5) ) ).
cnf(i_0_18623,axiom,
( X1 != X2
| esk195_4(X3,X1,X4,X5) = esk195_4(X3,X2,X4,X5) ) ).
cnf(i_0_18624,axiom,
( X1 != X2
| esk195_4(X3,X4,X1,X5) = esk195_4(X3,X4,X2,X5) ) ).
cnf(i_0_18625,axiom,
( X1 != X2
| esk195_4(X3,X4,X5,X1) = esk195_4(X3,X4,X5,X2) ) ).
cnf(i_0_18626,axiom,
( X1 != X2
| esk194_4(X1,X3,X4,X5) = esk194_4(X2,X3,X4,X5) ) ).
cnf(i_0_18627,axiom,
( X1 != X2
| esk194_4(X3,X1,X4,X5) = esk194_4(X3,X2,X4,X5) ) ).
cnf(i_0_18628,axiom,
( X1 != X2
| esk194_4(X3,X4,X1,X5) = esk194_4(X3,X4,X2,X5) ) ).
cnf(i_0_18629,axiom,
( X1 != X2
| esk194_4(X3,X4,X5,X1) = esk194_4(X3,X4,X5,X2) ) ).
cnf(i_0_18630,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_18631,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_18632,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_18633,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_18634,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_18635,axiom,
( X1 != X2
| c_Divides_Odivmod__int(X1,X3) = c_Divides_Odivmod__int(X2,X3) ) ).
cnf(i_0_18636,axiom,
( X1 != X2
| c_Divides_Odivmod__int(X3,X1) = c_Divides_Odivmod__int(X3,X2) ) ).
cnf(i_0_18637,axiom,
( X1 != X2
| c_Nitpick_Opair__box_OPairBox(X1,X3,X4,X5) = c_Nitpick_Opair__box_OPairBox(X2,X3,X4,X5) ) ).
cnf(i_0_18638,axiom,
( X1 != X2
| c_Nitpick_Opair__box_OPairBox(X3,X1,X4,X5) = c_Nitpick_Opair__box_OPairBox(X3,X2,X4,X5) ) ).
cnf(i_0_18639,axiom,
( X1 != X2
| c_Nitpick_Opair__box_OPairBox(X3,X4,X1,X5) = c_Nitpick_Opair__box_OPairBox(X3,X4,X2,X5) ) ).
cnf(i_0_18640,axiom,
( X1 != X2
| c_Nitpick_Opair__box_OPairBox(X3,X4,X5,X1) = c_Nitpick_Opair__box_OPairBox(X3,X4,X5,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
| esk407_3(X1,X3,X4) = esk407_3(X2,X3,X4) ) ).
cnf(i_0_18645,axiom,
( X1 != X2
| esk407_3(X3,X1,X4) = esk407_3(X3,X2,X4) ) ).
cnf(i_0_18646,axiom,
( X1 != X2
| esk407_3(X3,X4,X1) = esk407_3(X3,X4,X2) ) ).
cnf(i_0_18647,axiom,
( X1 != X2
| esk268_4(X1,X3,X4,X5) = esk268_4(X2,X3,X4,X5) ) ).
cnf(i_0_18648,axiom,
( X1 != X2
| esk268_4(X3,X1,X4,X5) = esk268_4(X3,X2,X4,X5) ) ).
cnf(i_0_18649,axiom,
( X1 != X2
| esk268_4(X3,X4,X1,X5) = esk268_4(X3,X4,X2,X5) ) ).
cnf(i_0_18650,axiom,
( X1 != X2
| esk268_4(X3,X4,X5,X1) = esk268_4(X3,X4,X5,X2) ) ).
cnf(i_0_18651,axiom,
( X1 != X2
| c_Groups_Osgn__class_Osgn(X1,X3) = c_Groups_Osgn__class_Osgn(X2,X3) ) ).
cnf(i_0_18652,axiom,
( X1 != X2
| c_Groups_Osgn__class_Osgn(X3,X1) = c_Groups_Osgn__class_Osgn(X3,X2) ) ).
cnf(i_0_18653,axiom,
( X1 != X2
| esk410_3(X1,X3,X4) = esk410_3(X2,X3,X4) ) ).
cnf(i_0_18654,axiom,
( X1 != X2
| esk410_3(X3,X1,X4) = esk410_3(X3,X2,X4) ) ).
cnf(i_0_18655,axiom,
( X1 != X2
| esk410_3(X3,X4,X1) = esk410_3(X3,X4,X2) ) ).
cnf(i_0_18656,axiom,
( X1 != X2
| esk409_3(X1,X3,X4) = esk409_3(X2,X3,X4) ) ).
cnf(i_0_18657,axiom,
( X1 != X2
| esk409_3(X3,X1,X4) = esk409_3(X3,X2,X4) ) ).
cnf(i_0_18658,axiom,
( X1 != X2
| esk409_3(X3,X4,X1) = esk409_3(X3,X4,X2) ) ).
cnf(i_0_18659,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_18660,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_18661,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_18662,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_18663,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_18664,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_18665,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_18666,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_18667,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_18668,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_18669,axiom,
( X1 != X2
| c_Divides_Opdivmod(X1,X3) = c_Divides_Opdivmod(X2,X3) ) ).
cnf(i_0_18670,axiom,
( X1 != X2
| c_Divides_Opdivmod(X3,X1) = c_Divides_Opdivmod(X3,X2) ) ).
cnf(i_0_18671,axiom,
( X1 != X2
| c_Lazy__Sequence_Ohb__bind(X1,X3,X4,X5) = c_Lazy__Sequence_Ohb__bind(X2,X3,X4,X5) ) ).
cnf(i_0_18672,axiom,
( X1 != X2
| c_Lazy__Sequence_Ohb__bind(X3,X1,X4,X5) = c_Lazy__Sequence_Ohb__bind(X3,X2,X4,X5) ) ).
cnf(i_0_18673,axiom,
( X1 != X2
| c_Lazy__Sequence_Ohb__bind(X3,X4,X1,X5) = c_Lazy__Sequence_Ohb__bind(X3,X4,X2,X5) ) ).
cnf(i_0_18674,axiom,
( X1 != X2
| c_Lazy__Sequence_Ohb__bind(X3,X4,X5,X1) = c_Lazy__Sequence_Ohb__bind(X3,X4,X5,X2) ) ).
cnf(i_0_18675,axiom,
( X1 != X2
| c_List_Obutlast(X1,X3) = c_List_Obutlast(X2,X3) ) ).
cnf(i_0_18676,axiom,
( X1 != X2
| c_List_Obutlast(X3,X1) = c_List_Obutlast(X3,X2) ) ).
cnf(i_0_18677,axiom,
( X1 != X2
| c_Lazy__Sequence_Obind(X1,X3,X4,X5) = c_Lazy__Sequence_Obind(X2,X3,X4,X5) ) ).
cnf(i_0_18678,axiom,
( X1 != X2
| c_Lazy__Sequence_Obind(X3,X1,X4,X5) = c_Lazy__Sequence_Obind(X3,X2,X4,X5) ) ).
cnf(i_0_18679,axiom,
( X1 != X2
| c_Lazy__Sequence_Obind(X3,X4,X1,X5) = c_Lazy__Sequence_Obind(X3,X4,X2,X5) ) ).
cnf(i_0_18680,axiom,
( X1 != X2
| c_Lazy__Sequence_Obind(X3,X4,X5,X1) = c_Lazy__Sequence_Obind(X3,X4,X5,X2) ) ).
cnf(i_0_18681,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_18682,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_18683,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_18684,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_18685,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_18686,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_18687,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_18688,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_18689,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_18690,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_18691,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_18692,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_18693,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_18694,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_18695,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_18696,axiom,
( X1 != X2
| esk149_3(X1,X3,X4) = esk149_3(X2,X3,X4) ) ).
cnf(i_0_18697,axiom,
( X1 != X2
| esk149_3(X3,X1,X4) = esk149_3(X3,X2,X4) ) ).
cnf(i_0_18698,axiom,
( X1 != X2
| esk149_3(X3,X4,X1) = esk149_3(X3,X4,X2) ) ).
cnf(i_0_18699,axiom,
( X1 != X2
| c_List_Oupto(X1,X3) = c_List_Oupto(X2,X3) ) ).
cnf(i_0_18700,axiom,
( X1 != X2
| c_List_Oupto(X3,X1) = c_List_Oupto(X3,X2) ) ).
cnf(i_0_18701,axiom,
( X1 != X2
| esk350_2(X1,X3) = esk350_2(X2,X3) ) ).
cnf(i_0_18702,axiom,
( X1 != X2
| esk350_2(X3,X1) = esk350_2(X3,X2) ) ).
cnf(i_0_18703,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_18704,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_18705,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_18706,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_18707,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_18708,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_18709,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_18710,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_18711,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_18712,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_18713,axiom,
( X1 != X2
| esk492_2(X1,X3) = esk492_2(X2,X3) ) ).
cnf(i_0_18714,axiom,
( X1 != X2
| esk492_2(X3,X1) = esk492_2(X3,X2) ) ).
cnf(i_0_18715,axiom,
( X1 != X2
| esk493_2(X1,X3) = esk493_2(X2,X3) ) ).
cnf(i_0_18716,axiom,
( X1 != X2
| esk493_2(X3,X1) = esk493_2(X3,X2) ) ).
cnf(i_0_18717,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_18718,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_18719,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_18720,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_18721,axiom,
( X1 != X2
| c_Com_Ocom_OAss(X1,X3) = c_Com_Ocom_OAss(X2,X3) ) ).
cnf(i_0_18722,axiom,
( X1 != X2
| c_Com_Ocom_OAss(X3,X1) = c_Com_Ocom_OAss(X3,X2) ) ).
cnf(i_0_18723,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X4) ) ).
cnf(i_0_18724,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X2,X4) ) ).
cnf(i_0_18725,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X2) ) ).
cnf(i_0_18726,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X3,X4) ) ).
cnf(i_0_18727,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X2,X4) ) ).
cnf(i_0_18728,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X2) ) ).
cnf(i_0_18729,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_18730,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_18731,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_18732,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_18733,axiom,
( X1 != X2
| c_Power_Opower_Opower(X1,X3,X4) = c_Power_Opower_Opower(X2,X3,X4) ) ).
cnf(i_0_18734,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X1,X4) = c_Power_Opower_Opower(X3,X2,X4) ) ).
cnf(i_0_18735,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X4,X1) = c_Power_Opower_Opower(X3,X4,X2) ) ).
cnf(i_0_18736,axiom,
( X1 != X2
| c_Sum__Type_OSumr(X1,X3,X4,X5) = c_Sum__Type_OSumr(X2,X3,X4,X5) ) ).
cnf(i_0_18737,axiom,
( X1 != X2
| c_Sum__Type_OSumr(X3,X1,X4,X5) = c_Sum__Type_OSumr(X3,X2,X4,X5) ) ).
cnf(i_0_18738,axiom,
( X1 != X2
| c_Sum__Type_OSumr(X3,X4,X1,X5) = c_Sum__Type_OSumr(X3,X4,X2,X5) ) ).
cnf(i_0_18739,axiom,
( X1 != X2
| c_Sum__Type_OSumr(X3,X4,X5,X1) = c_Sum__Type_OSumr(X3,X4,X5,X2) ) ).
cnf(i_0_18740,axiom,
( X1 != X2
| c_List_Olenlex(X1,X3) = c_List_Olenlex(X2,X3) ) ).
cnf(i_0_18741,axiom,
( X1 != X2
| c_List_Olenlex(X3,X1) = c_List_Olenlex(X3,X2) ) ).
cnf(i_0_18742,axiom,
( X1 != X2
| c_Sum__Type_OSuml(X1,X3,X4,X5) = c_Sum__Type_OSuml(X2,X3,X4,X5) ) ).
cnf(i_0_18743,axiom,
( X1 != X2
| c_Sum__Type_OSuml(X3,X1,X4,X5) = c_Sum__Type_OSuml(X3,X2,X4,X5) ) ).
cnf(i_0_18744,axiom,
( X1 != X2
| c_Sum__Type_OSuml(X3,X4,X1,X5) = c_Sum__Type_OSuml(X3,X4,X2,X5) ) ).
cnf(i_0_18745,axiom,
( X1 != X2
| c_Sum__Type_OSuml(X3,X4,X5,X1) = c_Sum__Type_OSuml(X3,X4,X5,X2) ) ).
cnf(i_0_18746,axiom,
( X1 != X2
| esk470_2(X1,X3) = esk470_2(X2,X3) ) ).
cnf(i_0_18747,axiom,
( X1 != X2
| esk470_2(X3,X1) = esk470_2(X3,X2) ) ).
cnf(i_0_18748,axiom,
( X1 != X2
| esk246_3(X1,X3,X4) = esk246_3(X2,X3,X4) ) ).
cnf(i_0_18749,axiom,
( X1 != X2
| esk246_3(X3,X1,X4) = esk246_3(X3,X2,X4) ) ).
cnf(i_0_18750,axiom,
( X1 != X2
| esk246_3(X3,X4,X1) = esk246_3(X3,X4,X2) ) ).
cnf(i_0_18751,axiom,
( X1 != X2
| esk248_3(X1,X3,X4) = esk248_3(X2,X3,X4) ) ).
cnf(i_0_18752,axiom,
( X1 != X2
| esk248_3(X3,X1,X4) = esk248_3(X3,X2,X4) ) ).
cnf(i_0_18753,axiom,
( X1 != X2
| esk248_3(X3,X4,X1) = esk248_3(X3,X4,X2) ) ).
cnf(i_0_18754,axiom,
( X1 != X2
| esk131_3(X1,X3,X4) = esk131_3(X2,X3,X4) ) ).
cnf(i_0_18755,axiom,
( X1 != X2
| esk131_3(X3,X1,X4) = esk131_3(X3,X2,X4) ) ).
cnf(i_0_18756,axiom,
( X1 != X2
| esk131_3(X3,X4,X1) = esk131_3(X3,X4,X2) ) ).
cnf(i_0_18757,axiom,
( X1 != X2
| esk130_3(X1,X3,X4) = esk130_3(X2,X3,X4) ) ).
cnf(i_0_18758,axiom,
( X1 != X2
| esk130_3(X3,X1,X4) = esk130_3(X3,X2,X4) ) ).
cnf(i_0_18759,axiom,
( X1 != X2
| esk130_3(X3,X4,X1) = esk130_3(X3,X4,X2) ) ).
cnf(i_0_18760,axiom,
( X1 != X2
| c_List_Olex(X1,X3) = c_List_Olex(X2,X3) ) ).
cnf(i_0_18761,axiom,
( X1 != X2
| c_List_Olex(X3,X1) = c_List_Olex(X3,X2) ) ).
cnf(i_0_18762,axiom,
( X1 != X2
| c_Nitpick_Oplus__frac(X1,X3,X4) = c_Nitpick_Oplus__frac(X2,X3,X4) ) ).
cnf(i_0_18763,axiom,
( X1 != X2
| c_Nitpick_Oplus__frac(X3,X1,X4) = c_Nitpick_Oplus__frac(X3,X2,X4) ) ).
cnf(i_0_18764,axiom,
( X1 != X2
| c_Nitpick_Oplus__frac(X3,X4,X1) = c_Nitpick_Oplus__frac(X3,X4,X2) ) ).
cnf(i_0_18765,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_18766,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_18767,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_18768,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_18769,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_18770,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_18771,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_18772,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_18773,axiom,
( X1 != X2
| c_Lazy__Sequence_Oempty(X1) = c_Lazy__Sequence_Oempty(X2) ) ).
cnf(i_0_18774,axiom,
( X1 != X2
| c_Lazy__Sequence_Ohit__bound(X1) = c_Lazy__Sequence_Ohit__bound(X2) ) ).
cnf(i_0_18775,axiom,
( X1 != X2
| c_Nat__Transfer_Otsub(X1,X3) = c_Nat__Transfer_Otsub(X2,X3) ) ).
cnf(i_0_18776,axiom,
( X1 != X2
| c_Nat__Transfer_Otsub(X3,X1) = c_Nat__Transfer_Otsub(X3,X2) ) ).
cnf(i_0_18777,axiom,
( X1 != X2
| c_List_Olast(X1,X3) = c_List_Olast(X2,X3) ) ).
cnf(i_0_18778,axiom,
( X1 != X2
| c_List_Olast(X3,X1) = c_List_Olast(X3,X2) ) ).
cnf(i_0_18779,axiom,
( X1 != X2
| c_Nitpick_Oint__lcm(X1,X3) = c_Nitpick_Oint__lcm(X2,X3) ) ).
cnf(i_0_18780,axiom,
( X1 != X2
| c_Nitpick_Oint__lcm(X3,X1) = c_Nitpick_Oint__lcm(X3,X2) ) ).
cnf(i_0_18781,axiom,
( X1 != X2
| c_Random_Olog(X1,X3) = c_Random_Olog(X2,X3) ) ).
cnf(i_0_18782,axiom,
( X1 != X2
| c_Random_Olog(X3,X1) = c_Random_Olog(X3,X2) ) ).
cnf(i_0_18783,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__size(X1) = c_Com_Ocom_Ocom__size(X2) ) ).
cnf(i_0_18784,axiom,
( X1 != X2
| c_Random_Ominus__shift(X1,X3,X4) = c_Random_Ominus__shift(X2,X3,X4) ) ).
cnf(i_0_18785,axiom,
( X1 != X2
| c_Random_Ominus__shift(X3,X1,X4) = c_Random_Ominus__shift(X3,X2,X4) ) ).
cnf(i_0_18786,axiom,
( X1 != X2
| c_Random_Ominus__shift(X3,X4,X1) = c_Random_Ominus__shift(X3,X4,X2) ) ).
cnf(i_0_18787,axiom,
( X1 != X2
| c_Random__Sequence_Oempty(X1,X3,X4) = c_Random__Sequence_Oempty(X2,X3,X4) ) ).
cnf(i_0_18788,axiom,
( X1 != X2
| c_Random__Sequence_Oempty(X3,X1,X4) = c_Random__Sequence_Oempty(X3,X2,X4) ) ).
cnf(i_0_18789,axiom,
( X1 != X2
| c_Random__Sequence_Oempty(X3,X4,X1) = c_Random__Sequence_Oempty(X3,X4,X2) ) ).
cnf(i_0_18790,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_18791,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_18792,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_18793,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_18794,axiom,
( X1 != X2
| esk484_2(X1,X3) = esk484_2(X2,X3) ) ).
cnf(i_0_18795,axiom,
( X1 != X2
| esk484_2(X3,X1) = esk484_2(X3,X2) ) ).
cnf(i_0_18796,axiom,
( X1 != X2
| c_List_Olistset(X1,X3) = c_List_Olistset(X2,X3) ) ).
cnf(i_0_18797,axiom,
( X1 != X2
| c_List_Olistset(X3,X1) = c_List_Olistset(X3,X2) ) ).
cnf(i_0_18798,axiom,
( X1 != X2
| c_Fun_Ocomp(X1,X3,X4,X5) = c_Fun_Ocomp(X2,X3,X4,X5) ) ).
cnf(i_0_18799,axiom,
( X1 != X2
| c_Fun_Ocomp(X3,X1,X4,X5) = c_Fun_Ocomp(X3,X2,X4,X5) ) ).
cnf(i_0_18800,axiom,
( X1 != X2
| c_Fun_Ocomp(X3,X4,X1,X5) = c_Fun_Ocomp(X3,X4,X2,X5) ) ).
cnf(i_0_18801,axiom,
( X1 != X2
| c_Fun_Ocomp(X3,X4,X5,X1) = c_Fun_Ocomp(X3,X4,X5,X2) ) ).
cnf(i_0_18802,axiom,
( X1 != X2
| c_Code__Numeral_Odiv__mod__code__numeral(X1,X3) = c_Code__Numeral_Odiv__mod__code__numeral(X2,X3) ) ).
cnf(i_0_18803,axiom,
( X1 != X2
| c_Code__Numeral_Odiv__mod__code__numeral(X3,X1) = c_Code__Numeral_Odiv__mod__code__numeral(X3,X2) ) ).
cnf(i_0_18804,axiom,
( X1 != X2
| esk453_2(X1,X3) = esk453_2(X2,X3) ) ).
cnf(i_0_18805,axiom,
( X1 != X2
| esk453_2(X3,X1) = esk453_2(X3,X2) ) ).
cnf(i_0_18806,axiom,
( X1 != X2
| esk452_2(X1,X3) = esk452_2(X2,X3) ) ).
cnf(i_0_18807,axiom,
( X1 != X2
| esk452_2(X3,X1) = esk452_2(X3,X2) ) ).
cnf(i_0_18808,axiom,
( X1 != X2
| c_SMT_Oz3div(X1,X3) = c_SMT_Oz3div(X2,X3) ) ).
cnf(i_0_18809,axiom,
( X1 != X2
| c_SMT_Oz3div(X3,X1) = c_SMT_Oz3div(X3,X2) ) ).
cnf(i_0_18810,axiom,
( X1 != X2
| c_Hoare__Mirabelle_Otriple_Otriple__size(X1,X3,X4) = c_Hoare__Mirabelle_Otriple_Otriple__size(X2,X3,X4) ) ).
cnf(i_0_18811,axiom,
( X1 != X2
| c_Hoare__Mirabelle_Otriple_Otriple__size(X3,X1,X4) = c_Hoare__Mirabelle_Otriple_Otriple__size(X3,X2,X4) ) ).
cnf(i_0_18812,axiom,
( X1 != X2
| c_Hoare__Mirabelle_Otriple_Otriple__size(X3,X4,X1) = c_Hoare__Mirabelle_Otriple_Otriple__size(X3,X4,X2) ) ).
cnf(i_0_18813,axiom,
( X1 != X2
| c_Orderings_Oord_Omax(X1,X3) = c_Orderings_Oord_Omax(X2,X3) ) ).
cnf(i_0_18814,axiom,
( X1 != X2
| c_Orderings_Oord_Omax(X3,X1) = c_Orderings_Oord_Omax(X3,X2) ) ).
cnf(i_0_18815,axiom,
( X1 != X2
| c_Orderings_Oord_Omin(X1,X3) = c_Orderings_Oord_Omin(X2,X3) ) ).
cnf(i_0_18816,axiom,
( X1 != X2
| c_Orderings_Oord_Omin(X3,X1) = c_Orderings_Oord_Omin(X3,X2) ) ).
cnf(i_0_18817,axiom,
( X1 != X2
| c_Option_Oset(X1,X3) = c_Option_Oset(X2,X3) ) ).
cnf(i_0_18818,axiom,
( X1 != X2
| c_Option_Oset(X3,X1) = c_Option_Oset(X3,X2) ) ).
cnf(i_0_18819,axiom,
( X1 != X2
| c_Com_Ovname_Ovname__rec(X1,X3,X4,X5) = c_Com_Ovname_Ovname__rec(X2,X3,X4,X5) ) ).
cnf(i_0_18820,axiom,
( X1 != X2
| c_Com_Ovname_Ovname__rec(X3,X1,X4,X5) = c_Com_Ovname_Ovname__rec(X3,X2,X4,X5) ) ).
cnf(i_0_18821,axiom,
( X1 != X2
| c_Com_Ovname_Ovname__rec(X3,X4,X1,X5) = c_Com_Ovname_Ovname__rec(X3,X4,X2,X5) ) ).
cnf(i_0_18822,axiom,
( X1 != X2
| c_Com_Ovname_Ovname__rec(X3,X4,X5,X1) = c_Com_Ovname_Ovname__rec(X3,X4,X5,X2) ) ).
cnf(i_0_18823,axiom,
( X1 != X2
| c_Com_Ovname_OGlb(X1) = c_Com_Ovname_OGlb(X2) ) ).
cnf(i_0_18824,axiom,
( X1 != X2
| c_Com_Ovname_Ovname__case(X1,X3,X4,X5) = c_Com_Ovname_Ovname__case(X2,X3,X4,X5) ) ).
cnf(i_0_18825,axiom,
( X1 != X2
| c_Com_Ovname_Ovname__case(X3,X1,X4,X5) = c_Com_Ovname_Ovname__case(X3,X2,X4,X5) ) ).
cnf(i_0_18826,axiom,
( X1 != X2
| c_Com_Ovname_Ovname__case(X3,X4,X1,X5) = c_Com_Ovname_Ovname__case(X3,X4,X2,X5) ) ).
cnf(i_0_18827,axiom,
( X1 != X2
| c_Com_Ovname_Ovname__case(X3,X4,X5,X1) = c_Com_Ovname_Ovname__case(X3,X4,X5,X2) ) ).
cnf(i_0_18828,axiom,
( X1 != X2
| c_New__DSequence_Opos__single(X1,X3) = c_New__DSequence_Opos__single(X2,X3) ) ).
cnf(i_0_18829,axiom,
( X1 != X2
| c_New__DSequence_Opos__single(X3,X1) = c_New__DSequence_Opos__single(X3,X2) ) ).
cnf(i_0_18830,axiom,
( X1 != X2
| c_New__DSequence_Oneg__single(X1,X3) = c_New__DSequence_Oneg__single(X2,X3) ) ).
cnf(i_0_18831,axiom,
( X1 != X2
| c_New__DSequence_Oneg__single(X3,X1) = c_New__DSequence_Oneg__single(X3,X2) ) ).
cnf(i_0_18832,axiom,
( X1 != X2
| c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X1) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X2) ) ).
cnf(i_0_18833,axiom,
( X1 != X2
| c_SMT_Oz3mod(X1,X3) = c_SMT_Oz3mod(X2,X3) ) ).
cnf(i_0_18834,axiom,
( X1 != X2
| c_SMT_Oz3mod(X3,X1) = c_SMT_Oz3mod(X3,X2) ) ).
cnf(i_0_18835,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__size(X1,X3,X4) = c_Option_Ooption_Ooption__size(X2,X3,X4) ) ).
cnf(i_0_18836,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__size(X3,X1,X4) = c_Option_Ooption_Ooption__size(X3,X2,X4) ) ).
cnf(i_0_18837,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__size(X3,X4,X1) = c_Option_Ooption_Ooption__size(X3,X4,X2) ) ).
cnf(i_0_18838,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_18839,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_18840,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_18841,axiom,
( X1 != X2
| c_Smallcheck_Ofull__small_H(X1,X3,X4) = c_Smallcheck_Ofull__small_H(X2,X3,X4) ) ).
cnf(i_0_18842,axiom,
( X1 != X2
| c_Smallcheck_Ofull__small_H(X3,X1,X4) = c_Smallcheck_Ofull__small_H(X3,X2,X4) ) ).
cnf(i_0_18843,axiom,
( X1 != X2
| c_Smallcheck_Ofull__small_H(X3,X4,X1) = c_Smallcheck_Ofull__small_H(X3,X4,X2) ) ).
cnf(i_0_18844,axiom,
( X1 != X2
| esk448_1(X1) = esk448_1(X2) ) ).
cnf(i_0_18845,axiom,
( X1 != X2
| c_Quickcheck_Obeyond(X1,X3) = c_Quickcheck_Obeyond(X2,X3) ) ).
cnf(i_0_18846,axiom,
( X1 != X2
| c_Quickcheck_Obeyond(X3,X1) = c_Quickcheck_Obeyond(X3,X2) ) ).
cnf(i_0_18847,axiom,
( X1 != X2
| c_Sum__Type_OProjr(X1,X3,X4) = c_Sum__Type_OProjr(X2,X3,X4) ) ).
cnf(i_0_18848,axiom,
( X1 != X2
| c_Sum__Type_OProjr(X3,X1,X4) = c_Sum__Type_OProjr(X3,X2,X4) ) ).
cnf(i_0_18849,axiom,
( X1 != X2
| c_Sum__Type_OProjr(X3,X4,X1) = c_Sum__Type_OProjr(X3,X4,X2) ) ).
cnf(i_0_18850,axiom,
( X1 != X2
| c_Sum__Type_OProjl(X1,X3,X4) = c_Sum__Type_OProjl(X2,X3,X4) ) ).
cnf(i_0_18851,axiom,
( X1 != X2
| c_Sum__Type_OProjl(X3,X1,X4) = c_Sum__Type_OProjl(X3,X2,X4) ) ).
cnf(i_0_18852,axiom,
( X1 != X2
| c_Sum__Type_OProjl(X3,X4,X1) = c_Sum__Type_OProjl(X3,X4,X2) ) ).
cnf(i_0_18853,axiom,
( X1 != X2
| c_Nat_Onat_Onat__size(X1) = c_Nat_Onat_Onat__size(X2) ) ).
cnf(i_0_18854,axiom,
( X1 != X2
| c_Random_Oinc__shift(X1,X3) = c_Random_Oinc__shift(X2,X3) ) ).
cnf(i_0_18855,axiom,
( X1 != X2
| c_Random_Oinc__shift(X3,X1) = c_Random_Oinc__shift(X3,X2) ) ).
cnf(i_0_18856,axiom,
( X1 != X2
| c_Lazy__Sequence_Osingle(X1,X3) = c_Lazy__Sequence_Osingle(X2,X3) ) ).
cnf(i_0_18857,axiom,
( X1 != X2
| c_Lazy__Sequence_Osingle(X3,X1) = c_Lazy__Sequence_Osingle(X3,X2) ) ).
cnf(i_0_18858,axiom,
( X1 != X2
| c_Lazy__Sequence_Ohb__single(X1,X3) = c_Lazy__Sequence_Ohb__single(X2,X3) ) ).
cnf(i_0_18859,axiom,
( X1 != X2
| c_Lazy__Sequence_Ohb__single(X3,X1) = c_Lazy__Sequence_Ohb__single(X3,X2) ) ).
cnf(i_0_18860,axiom,
( X1 != X2
| c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).
cnf(i_0_18861,axiom,
( X1 != X2
| c_Com_Ovname_Ovname__size(X1) = c_Com_Ovname_Ovname__size(X2) ) ).
cnf(i_0_18862,axiom,
( X1 != X2
| c_HOL_Obool_Obool__size(X1) = c_HOL_Obool_Obool__size(X2) ) ).
cnf(i_0_18863,axiom,
( X1 != X2
| c_Transitive__Closure_Ortrancl(X1,X3) = c_Transitive__Closure_Ortrancl(X2,X3) ) ).
cnf(i_0_18864,axiom,
( X1 != X2
| c_Transitive__Closure_Ortrancl(X3,X1) = c_Transitive__Closure_Ortrancl(X3,X2) ) ).
cnf(i_0_18865,axiom,
( X1 != X2
| c_Int_Oring__1__class_Oof__int(X1) = c_Int_Oring__1__class_Oof__int(X2) ) ).
cnf(i_0_18866,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_18867,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_18868,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_18869,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_18870,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_18871,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_18872,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_18873,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_18874,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_18875,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_18876,axiom,
( X1 != X2
| c_FunDef_Orp__inv__image(X1,X3) = c_FunDef_Orp__inv__image(X2,X3) ) ).
cnf(i_0_18877,axiom,
( X1 != X2
| c_FunDef_Orp__inv__image(X3,X1) = c_FunDef_Orp__inv__image(X3,X2) ) ).
cnf(i_0_18878,axiom,
( X1 != X2
| c_Map_Omap__add(X1,X3,X4,X5) = c_Map_Omap__add(X2,X3,X4,X5) ) ).
cnf(i_0_18879,axiom,
( X1 != X2
| c_Map_Omap__add(X3,X1,X4,X5) = c_Map_Omap__add(X3,X2,X4,X5) ) ).
cnf(i_0_18880,axiom,
( X1 != X2
| c_Map_Omap__add(X3,X4,X1,X5) = c_Map_Omap__add(X3,X4,X2,X5) ) ).
cnf(i_0_18881,axiom,
( X1 != X2
| c_Map_Omap__add(X3,X4,X5,X1) = c_Map_Omap__add(X3,X4,X5,X2) ) ).
cnf(i_0_18882,axiom,
( X1 != X2
| c_Map_Omap__of(X1,X3,X4) = c_Map_Omap__of(X2,X3,X4) ) ).
cnf(i_0_18883,axiom,
( X1 != X2
| c_Map_Omap__of(X3,X1,X4) = c_Map_Omap__of(X3,X2,X4) ) ).
cnf(i_0_18884,axiom,
( X1 != X2
| c_Map_Omap__of(X3,X4,X1) = c_Map_Omap__of(X3,X4,X2) ) ).
cnf(i_0_18885,axiom,
( X1 != X2
| c_List_Ofoldl(X1,X3,X4,X5) = c_List_Ofoldl(X2,X3,X4,X5) ) ).
cnf(i_0_18886,axiom,
( X1 != X2
| c_List_Ofoldl(X3,X1,X4,X5) = c_List_Ofoldl(X3,X2,X4,X5) ) ).
cnf(i_0_18887,axiom,
( X1 != X2
| c_List_Ofoldl(X3,X4,X1,X5) = c_List_Ofoldl(X3,X4,X2,X5) ) ).
cnf(i_0_18888,axiom,
( X1 != X2
| c_List_Ofoldl(X3,X4,X5,X1) = c_List_Ofoldl(X3,X4,X5,X2) ) ).
cnf(i_0_18889,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_18890,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_18891,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_18892,axiom,
( X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).
cnf(i_0_18893,axiom,
( X1 != X2
| ~ c_Predicate_Oreflp(X1,X3)
| c_Predicate_Oreflp(X2,X3) ) ).
cnf(i_0_18894,axiom,
( X1 != X2
| ~ c_Predicate_Oreflp(X3,X1)
| c_Predicate_Oreflp(X3,X2) ) ).
cnf(i_0_18895,axiom,
( X1 != X2
| ~ class_Rings_Oordered__comm__semiring(X1)
| class_Rings_Oordered__comm__semiring(X2) ) ).
cnf(i_0_18896,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__comm__semiring__strict(X1)
| class_Rings_Olinordered__comm__semiring__strict(X2) ) ).
cnf(i_0_18897,axiom,
( X1 != X2
| ~ class_Divides_Oring__div(X1)
| class_Divides_Oring__div(X2) ) ).
cnf(i_0_18898,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_18899,axiom,
( X1 != X2
| ~ class_Rings_Oordered__cancel__semiring(X1)
| class_Rings_Oordered__cancel__semiring(X2) ) ).
cnf(i_0_18900,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring__abs(X1)
| class_Rings_Oordered__ring__abs(X2) ) ).
cnf(i_0_18901,axiom,
( X1 != X2
| ~ class_Orderings_Owellorder(X1)
| class_Orderings_Owellorder(X2) ) ).
cnf(i_0_18902,axiom,
( X1 != X2
| ~ class_Rings_Oring__1(X1)
| class_Rings_Oring__1(X2) ) ).
cnf(i_0_18903,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring__1(X1)
| class_Rings_Ocomm__ring__1(X2) ) ).
cnf(i_0_18904,axiom,
( X1 != X2
| ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(X2) ) ).
cnf(i_0_18905,axiom,
( X1 != X2
| ~ class_Rings_Odivision__ring(X1)
| class_Rings_Odivision__ring(X2) ) ).
cnf(i_0_18906,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring(X1)
| class_Rings_Ocomm__semiring(X2) ) ).
cnf(i_0_18907,axiom,
( X1 != X2
| ~ class_Groups_Ominus(X1)
| class_Groups_Ominus(X2) ) ).
cnf(i_0_18908,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_18909,axiom,
( X1 != X2
| ~ c_Groups_Osemigroup(X1,X3)
| c_Groups_Osemigroup(X2,X3) ) ).
cnf(i_0_18910,axiom,
( X1 != X2
| ~ c_Groups_Osemigroup(X3,X1)
| c_Groups_Osemigroup(X3,X2) ) ).
cnf(i_0_18911,axiom,
( X1 != X2
| ~ class_Groups_Ogroup__add(X1)
| class_Groups_Ogroup__add(X2) ) ).
cnf(i_0_18912,axiom,
( X1 != X2
| ~ c_Nat__Transfer_Otransfer__morphism(X1,X3,X4,X5)
| c_Nat__Transfer_Otransfer__morphism(X2,X3,X4,X5) ) ).
cnf(i_0_18913,axiom,
( X1 != X2
| ~ c_Nat__Transfer_Otransfer__morphism(X3,X1,X4,X5)
| c_Nat__Transfer_Otransfer__morphism(X3,X2,X4,X5) ) ).
cnf(i_0_18914,axiom,
( X1 != X2
| ~ c_Nat__Transfer_Otransfer__morphism(X3,X4,X1,X5)
| c_Nat__Transfer_Otransfer__morphism(X3,X4,X2,X5) ) ).
cnf(i_0_18915,axiom,
( X1 != X2
| ~ c_Nat__Transfer_Otransfer__morphism(X3,X4,X5,X1)
| c_Nat__Transfer_Otransfer__morphism(X3,X4,X5,X2) ) ).
cnf(i_0_18916,axiom,
( X1 != X2
| ~ class_Nat_Osemiring__char__0(X1)
| class_Nat_Osemiring__char__0(X2) ) ).
cnf(i_0_18917,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__mult(X1)
| class_Groups_Ocomm__monoid__mult(X2) ) ).
cnf(i_0_18918,axiom,
( X1 != X2
| ~ c_Nitpick_Owf_H(X1,X3)
| c_Nitpick_Owf_H(X2,X3) ) ).
cnf(i_0_18919,axiom,
( X1 != X2
| ~ c_Nitpick_Owf_H(X3,X1)
| c_Nitpick_Owf_H(X3,X2) ) ).
cnf(i_0_18920,axiom,
( X1 != X2
| ~ class_Groups_Osgn__if(X1)
| class_Groups_Osgn__if(X2) ) ).
cnf(i_0_18921,axiom,
( X1 != X2
| ~ class_Power_Opower(X1)
| class_Power_Opower(X2) ) ).
cnf(i_0_18922,axiom,
( X1 != X2
| ~ class_Groups_Oabs__if(X1)
| class_Groups_Oabs__if(X2) ) ).
cnf(i_0_18923,axiom,
( X1 != X2
| ~ class_Groups_Ouminus(X1)
| class_Groups_Ouminus(X2) ) ).
cnf(i_0_18924,axiom,
( X1 != X2
| ~ c_Big__Operators_Osemilattice__big(X1,X3,X4)
| c_Big__Operators_Osemilattice__big(X2,X3,X4) ) ).
cnf(i_0_18925,axiom,
( X1 != X2
| ~ c_Big__Operators_Osemilattice__big(X3,X1,X4)
| c_Big__Operators_Osemilattice__big(X3,X2,X4) ) ).
cnf(i_0_18926,axiom,
( X1 != X2
| ~ c_Big__Operators_Osemilattice__big(X3,X4,X1)
| c_Big__Operators_Osemilattice__big(X3,X4,X2) ) ).
cnf(i_0_18927,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_18928,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_18929,axiom,
( X1 != X2
| ~ c_Nitpick_Ounknown(X1)
| c_Nitpick_Ounknown(X2) ) ).
cnf(i_0_18930,axiom,
( X1 != X2
| ~ class_Finite__Set_Ofinite(X1)
| class_Finite__Set_Ofinite(X2) ) ).
cnf(i_0_18931,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_18932,axiom,
( X1 != X2
| ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(X2) ) ).
cnf(i_0_18933,axiom,
( X1 != X2
| ~ c_Groups_Ocomm__monoid(X1,X3,X4)
| c_Groups_Ocomm__monoid(X2,X3,X4) ) ).
cnf(i_0_18934,axiom,
( X1 != X2
| ~ c_Groups_Ocomm__monoid(X3,X1,X4)
| c_Groups_Ocomm__monoid(X3,X2,X4) ) ).
cnf(i_0_18935,axiom,
( X1 != X2
| ~ c_Groups_Ocomm__monoid(X3,X4,X1)
| c_Groups_Ocomm__monoid(X3,X4,X2) ) ).
cnf(i_0_18936,axiom,
( X1 != X2
| ~ class_Orderings_Otop(X1)
| class_Orderings_Otop(X2) ) ).
cnf(i_0_18937,axiom,
( X1 != X2
| ~ class_Rings_Omult__zero(X1)
| class_Rings_Omult__zero(X2) ) ).
cnf(i_0_18938,axiom,
( X1 != X2
| ~ class_Rings_Ozero__neq__one(X1)
| class_Rings_Ozero__neq__one(X2) ) ).
cnf(i_0_18939,axiom,
( X1 != X2
| ~ class_Rings_Oring__no__zero__divisors(X1)
| class_Rings_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_18940,axiom,
( X1 != X2
| ~ class_Lattices_Obounded__lattice__top(X1)
| class_Lattices_Obounded__lattice__top(X2) ) ).
cnf(i_0_18941,axiom,
( X1 != X2
| ~ class_Lattices_Obounded__lattice__bot(X1)
| class_Lattices_Obounded__lattice__bot(X2) ) ).
cnf(i_0_18942,axiom,
( X1 != X2
| ~ c_Option_Ois__none(X1,X3)
| c_Option_Ois__none(X2,X3) ) ).
cnf(i_0_18943,axiom,
( X1 != X2
| ~ c_Option_Ois__none(X3,X1)
| c_Option_Ois__none(X3,X2) ) ).
cnf(i_0_18944,axiom,
( X1 != X2
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| class_Rings_Odivision__ring__inverse__zero(X2) ) ).
cnf(i_0_18945,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__semigroup__add(X1)
| class_Groups_Olinordered__ab__semigroup__add(X2) ) ).
cnf(i_0_18946,axiom,
( X1 != X2
| ~ c_List_Onat__list(X1)
| c_List_Onat__list(X2) ) ).
cnf(i_0_18947,axiom,
( X1 != X2
| ~ class_Lattices_Obounded__lattice(X1)
| class_Lattices_Obounded__lattice(X2) ) ).
cnf(i_0_18948,axiom,
( X1 != X2
| ~ class_Groups_Oone(X1)
| class_Groups_Oone(X2) ) ).
cnf(i_0_18949,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_18950,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_18951,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_18952,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_18953,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_18954,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_18955,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_18956,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_18957,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_18958,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_18959,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_18960,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_18961,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_18962,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_18963,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_18964,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_18965,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_18966,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_18967,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_18968,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_18969,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_18970,axiom,
( X1 != X2
| ~ c_Natural_Oevaln(X1,X3,X4,X5)
| c_Natural_Oevaln(X2,X3,X4,X5) ) ).
cnf(i_0_18971,axiom,
( X1 != X2
| ~ c_Natural_Oevaln(X3,X1,X4,X5)
| c_Natural_Oevaln(X3,X2,X4,X5) ) ).
cnf(i_0_18972,axiom,
( X1 != X2
| ~ c_Natural_Oevaln(X3,X4,X1,X5)
| c_Natural_Oevaln(X3,X4,X2,X5) ) ).
cnf(i_0_18973,axiom,
( X1 != X2
| ~ c_Natural_Oevaln(X3,X4,X5,X1)
| c_Natural_Oevaln(X3,X4,X5,X2) ) ).
cnf(i_0_18974,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_18975,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_18976,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_18977,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_18978,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_18979,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_18980,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_18981,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_18982,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X1,X3,X4)
| c_Relation_Orefl__on(X2,X3,X4) ) ).
cnf(i_0_18983,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X3,X1,X4)
| c_Relation_Orefl__on(X3,X2,X4) ) ).
cnf(i_0_18984,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X3,X4,X1)
| c_Relation_Orefl__on(X3,X4,X2) ) ).
cnf(i_0_18985,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X1,X3,X4,X5)
| c_Wellfounded_Omax__extp(X2,X3,X4,X5) ) ).
cnf(i_0_18986,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X3,X1,X4,X5)
| c_Wellfounded_Omax__extp(X3,X2,X4,X5) ) ).
cnf(i_0_18987,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X3,X4,X1,X5)
| c_Wellfounded_Omax__extp(X3,X4,X2,X5) ) ).
cnf(i_0_18988,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X3,X4,X5,X1)
| c_Wellfounded_Omax__extp(X3,X4,X5,X2) ) ).
cnf(i_0_18989,axiom,
( X1 != X2
| ~ c_List_Olistrelp(X1,X3,X4,X5)
| c_List_Olistrelp(X2,X3,X4,X5) ) ).
cnf(i_0_18990,axiom,
( X1 != X2
| ~ c_List_Olistrelp(X3,X1,X4,X5)
| c_List_Olistrelp(X3,X2,X4,X5) ) ).
cnf(i_0_18991,axiom,
( X1 != X2
| ~ c_List_Olistrelp(X3,X4,X1,X5)
| c_List_Olistrelp(X3,X4,X2,X5) ) ).
cnf(i_0_18992,axiom,
( X1 != X2
| ~ c_List_Olistrelp(X3,X4,X5,X1)
| c_List_Olistrelp(X3,X4,X5,X2) ) ).
cnf(i_0_18993,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequivp(X1,X3)
| c_Equiv__Relations_Oequivp(X2,X3) ) ).
cnf(i_0_18994,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequivp(X3,X1)
| c_Equiv__Relations_Oequivp(X3,X2) ) ).
cnf(i_0_18995,axiom,
( X1 != X2
| ~ c_Wellfounded_Owf(X1,X3)
| c_Wellfounded_Owf(X2,X3) ) ).
cnf(i_0_18996,axiom,
( X1 != X2
| ~ c_Wellfounded_Owf(X3,X1)
| c_Wellfounded_Owf(X3,X2) ) ).
cnf(i_0_18997,axiom,
( X1 != X2
| ~ c_Wellfounded_OwfP(X1,X3)
| c_Wellfounded_OwfP(X2,X3) ) ).
cnf(i_0_18998,axiom,
( X1 != X2
| ~ c_Wellfounded_OwfP(X3,X1)
| c_Wellfounded_OwfP(X3,X2) ) ).
cnf(i_0_18999,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofun__left__comm(X1,X3,X4)
| c_Finite__Set_Ofun__left__comm(X2,X3,X4) ) ).
cnf(i_0_19000,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofun__left__comm(X3,X1,X4)
| c_Finite__Set_Ofun__left__comm(X3,X2,X4) ) ).
cnf(i_0_19001,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofun__left__comm(X3,X4,X1)
| c_Finite__Set_Ofun__left__comm(X3,X4,X2) ) ).
cnf(i_0_19002,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_19003,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequiv(X1,X3,X4)
| c_Equiv__Relations_Oequiv(X2,X3,X4) ) ).
cnf(i_0_19004,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequiv(X3,X1,X4)
| c_Equiv__Relations_Oequiv(X3,X2,X4) ) ).
cnf(i_0_19005,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequiv(X3,X4,X1)
| c_Equiv__Relations_Oequiv(X3,X4,X2) ) ).
cnf(i_0_19006,axiom,
( X1 != X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| class_Complete__Lattice_Ocomplete__lattice(X2) ) ).
cnf(i_0_19007,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add(X1)
| class_Groups_Oordered__ab__group__add(X2) ) ).
cnf(i_0_19008,axiom,
( X1 != X2
| ~ class_Smallcheck_Osmall(X1)
| class_Smallcheck_Osmall(X2) ) ).
cnf(i_0_19009,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_19010,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Ostrict__mono(X1,X3,X4,X5)
| c_Orderings_Oorder_Ostrict__mono(X2,X3,X4,X5) ) ).
cnf(i_0_19011,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Ostrict__mono(X3,X1,X4,X5)
| c_Orderings_Oorder_Ostrict__mono(X3,X2,X4,X5) ) ).
cnf(i_0_19012,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Ostrict__mono(X3,X4,X1,X5)
| c_Orderings_Oorder_Ostrict__mono(X3,X4,X2,X5) ) ).
cnf(i_0_19013,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Ostrict__mono(X3,X4,X5,X1)
| c_Orderings_Oorder_Ostrict__mono(X3,X4,X5,X2) ) ).
cnf(i_0_19014,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Omono(X1,X3,X4,X5)
| c_Orderings_Oorder_Omono(X2,X3,X4,X5) ) ).
cnf(i_0_19015,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Omono(X3,X1,X4,X5)
| c_Orderings_Oorder_Omono(X3,X2,X4,X5) ) ).
cnf(i_0_19016,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Omono(X3,X4,X1,X5)
| c_Orderings_Oorder_Omono(X3,X4,X2,X5) ) ).
cnf(i_0_19017,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Omono(X3,X4,X5,X1)
| c_Orderings_Oorder_Omono(X3,X4,X5,X2) ) ).
cnf(i_0_19018,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__mult(X1)
| class_Groups_Omonoid__mult(X2) ) ).
cnf(i_0_19019,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__mult(X1)
| class_Groups_Oab__semigroup__mult(X2) ) ).
cnf(i_0_19020,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_19021,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_19022,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__0(X1)
| class_Rings_Osemiring__0(X2) ) ).
cnf(i_0_19023,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_19024,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one__idem(X1,X3,X4)
| c_Finite__Set_Ofolding__one__idem(X2,X3,X4) ) ).
cnf(i_0_19025,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one__idem(X3,X1,X4)
| c_Finite__Set_Ofolding__one__idem(X3,X2,X4) ) ).
cnf(i_0_19026,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one__idem(X3,X4,X1)
| c_Finite__Set_Ofolding__one__idem(X3,X4,X2) ) ).
cnf(i_0_19027,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__1(X1)
| class_Rings_Osemiring__1(X2) ) ).
cnf(i_0_19028,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one(X1,X3,X4)
| c_Finite__Set_Ofolding__one(X2,X3,X4) ) ).
cnf(i_0_19029,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one(X3,X1,X4)
| c_Finite__Set_Ofolding__one(X3,X2,X4) ) ).
cnf(i_0_19030,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one(X3,X4,X1)
| c_Finite__Set_Ofolding__one(X3,X4,X2) ) ).
cnf(i_0_19031,axiom,
( X1 != X2
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| class_Fields_Olinordered__field__inverse__zero(X2) ) ).
cnf(i_0_19032,axiom,
( X1 != X2
| ~ c_FunDef_Oreduction__pair(X1,X3)
| c_FunDef_Oreduction__pair(X2,X3) ) ).
cnf(i_0_19033,axiom,
( X1 != X2
| ~ c_FunDef_Oreduction__pair(X3,X1)
| c_FunDef_Oreduction__pair(X3,X2) ) ).
cnf(i_0_19034,axiom,
( X1 != X2
| ~ c_List_Olinorder__class_Osorted(X1,X3)
| c_List_Olinorder__class_Osorted(X2,X3) ) ).
cnf(i_0_19035,axiom,
( X1 != X2
| ~ c_List_Olinorder__class_Osorted(X3,X1)
| c_List_Olinorder__class_Osorted(X3,X2) ) ).
cnf(i_0_19036,axiom,
( X1 != X2
| ~ c_Nat__Transfer_Ois__nat(X1)
| c_Nat__Transfer_Ois__nat(X2) ) ).
cnf(i_0_19037,axiom,
( X1 != X2
| ~ c_Nitpick_Oless__eq__frac(X1,X3,X4)
| c_Nitpick_Oless__eq__frac(X2,X3,X4) ) ).
cnf(i_0_19038,axiom,
( X1 != X2
| ~ c_Nitpick_Oless__eq__frac(X3,X1,X4)
| c_Nitpick_Oless__eq__frac(X3,X2,X4) ) ).
cnf(i_0_19039,axiom,
( X1 != X2
| ~ c_Nitpick_Oless__eq__frac(X3,X4,X1)
| c_Nitpick_Oless__eq__frac(X3,X4,X2) ) ).
cnf(i_0_19040,axiom,
( X1 != X2
| ~ c_Nitpick_Oless__frac(X1,X3,X4)
| c_Nitpick_Oless__frac(X2,X3,X4) ) ).
cnf(i_0_19041,axiom,
( X1 != X2
| ~ c_Nitpick_Oless__frac(X3,X1,X4)
| c_Nitpick_Oless__frac(X3,X2,X4) ) ).
cnf(i_0_19042,axiom,
( X1 != X2
| ~ c_Nitpick_Oless__frac(X3,X4,X1)
| c_Nitpick_Oless__frac(X3,X4,X2) ) ).
cnf(i_0_19043,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X1,X3,X4,X5)
| c_Fun_Oinj__on(X2,X3,X4,X5) ) ).
cnf(i_0_19044,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X1,X4,X5)
| c_Fun_Oinj__on(X3,X2,X4,X5) ) ).
cnf(i_0_19045,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X1,X5)
| c_Fun_Oinj__on(X3,X4,X2,X5) ) ).
cnf(i_0_19046,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X1)
| c_Fun_Oinj__on(X3,X4,X5,X2) ) ).
cnf(i_0_19047,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_19048,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring(X1)
| class_Rings_Oordered__ring(X2) ) ).
cnf(i_0_19049,axiom,
( X1 != X2
| ~ class_Groups_Oab__group__add(X1)
| class_Groups_Oab__group__add(X2) ) ).
cnf(i_0_19050,axiom,
( X1 != X2
| ~ class_Rings_Oinverse(X1)
| class_Rings_Oinverse(X2) ) ).
cnf(i_0_19051,axiom,
( X1 != X2
| ~ class_Fields_Ofield(X1)
| class_Fields_Ofield(X2) ) ).
cnf(i_0_19052,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_19053,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_19054,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_19055,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_19056,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_19057,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_19058,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| class_Groups_Oordered__ab__group__add__abs(X2) ) ).
cnf(i_0_19059,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_19060,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_19061,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_19062,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_19063,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_19064,axiom,
( X1 != X2
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| class_Rings_Oring__1__no__zero__divisors(X2) ) ).
cnf(i_0_19065,axiom,
( X1 != X2
| ~ c_Nat__Transfer_Onat__set(X1)
| c_Nat__Transfer_Onat__set(X2) ) ).
cnf(i_0_19066,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_19067,axiom,
( X1 != X2
| ~ class_Fields_Ofield__inverse__zero(X1)
| class_Fields_Ofield__inverse__zero(X2) ) ).
cnf(i_0_19068,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_19069,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_19070,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_19071,axiom,
( X1 != X2
| ~ class_Lattices_Osemilattice__sup(X1)
| class_Lattices_Osemilattice__sup(X2) ) ).
cnf(i_0_19072,axiom,
( X1 != X2
| ~ c_Int_Oiszero(X1,X3)
| c_Int_Oiszero(X2,X3) ) ).
cnf(i_0_19073,axiom,
( X1 != X2
| ~ c_Int_Oiszero(X3,X1)
| c_Int_Oiszero(X3,X2) ) ).
cnf(i_0_19074,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X1,X3,X4)
| c_Relation_Ototal__on(X2,X3,X4) ) ).
cnf(i_0_19075,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X3,X1,X4)
| c_Relation_Ototal__on(X3,X2,X4) ) ).
cnf(i_0_19076,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X3,X4,X1)
| c_Relation_Ototal__on(X3,X4,X2) ) ).
cnf(i_0_19077,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X1,X3,X4)
| c_Relation_Osingle__valued(X2,X3,X4) ) ).
cnf(i_0_19078,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X3,X1,X4)
| c_Relation_Osingle__valued(X3,X2,X4) ) ).
cnf(i_0_19079,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X3,X4,X1)
| c_Relation_Osingle__valued(X3,X4,X2) ) ).
cnf(i_0_19080,axiom,
( X1 != X2
| ~ class_Int_Onumber(X1)
| class_Int_Onumber(X2) ) ).
cnf(i_0_19081,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Otriple__valid(X1,X3,X4)
| c_Hoare__Mirabelle_Otriple__valid(X2,X3,X4) ) ).
cnf(i_0_19082,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Otriple__valid(X3,X1,X4)
| c_Hoare__Mirabelle_Otriple__valid(X3,X2,X4) ) ).
cnf(i_0_19083,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Otriple__valid(X3,X4,X1)
| c_Hoare__Mirabelle_Otriple__valid(X3,X4,X2) ) ).
cnf(i_0_19084,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring(X1)
| class_Rings_Ocomm__ring(X2) ) ).
cnf(i_0_19085,axiom,
( X1 != X2
| ~ class_Rings_Odvd(X1)
| class_Rings_Odvd(X2) ) ).
cnf(i_0_19086,axiom,
( X1 != X2
| ~ class_Lattices_Odistrib__lattice(X1)
| class_Lattices_Odistrib__lattice(X2) ) ).
cnf(i_0_19087,axiom,
( X1 != X2
| ~ class_Divides_Osemiring__div(X1)
| class_Divides_Osemiring__div(X2) ) ).
cnf(i_0_19088,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring__strict(X1)
| class_Rings_Olinordered__ring__strict(X2) ) ).
cnf(i_0_19089,axiom,
( X1 != X2
| ~ class_Lattices_Olattice(X1)
| class_Lattices_Olattice(X2) ) ).
cnf(i_0_19090,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring(X1)
| class_Rings_Olinordered__ring(X2) ) ).
cnf(i_0_19091,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding(X1,X3,X4,X5)
| c_Finite__Set_Ofolding(X2,X3,X4,X5) ) ).
cnf(i_0_19092,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding(X3,X1,X4,X5)
| c_Finite__Set_Ofolding(X3,X2,X4,X5) ) ).
cnf(i_0_19093,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding(X3,X4,X1,X5)
| c_Finite__Set_Ofolding(X3,X4,X2,X5) ) ).
cnf(i_0_19094,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding(X3,X4,X5,X1)
| c_Finite__Set_Ofolding(X3,X4,X5,X2) ) ).
cnf(i_0_19095,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1(X1)
| class_Rings_Olinordered__semiring__1(X2) ) ).
cnf(i_0_19096,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1__strict(X1)
| class_Rings_Olinordered__semiring__1__strict(X2) ) ).
cnf(i_0_19097,axiom,
( X1 != X2
| ~ class_Lattices_Osemilattice__inf(X1)
| class_Lattices_Osemilattice__inf(X2) ) ).
cnf(i_0_19098,axiom,
( X1 != X2
| ~ class_Fields_Olinordered__field(X1)
| class_Fields_Olinordered__field(X2) ) ).
cnf(i_0_19099,axiom,
( X1 != X2
| ~ c_Wellfounded_Oacyclic(X1,X3)
| c_Wellfounded_Oacyclic(X2,X3) ) ).
cnf(i_0_19100,axiom,
( X1 != X2
| ~ c_Wellfounded_Oacyclic(X3,X1)
| c_Wellfounded_Oacyclic(X3,X2) ) ).
cnf(i_0_19101,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X4)
| c_Hoare__Mirabelle_Ohoare__derivs(X2,X3,X4) ) ).
cnf(i_0_19102,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X1,X4)
| c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X4) ) ).
cnf(i_0_19103,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X1)
| c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X2) ) ).
cnf(i_0_19104,axiom,
( X1 != X2
| ~ class_Lattices_Oab__semigroup__idem__mult(X1)
| class_Lattices_Oab__semigroup__idem__mult(X2) ) ).
cnf(i_0_19105,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X1,X3)
| c_Nitpick_Orefl_H(X2,X3) ) ).
cnf(i_0_19106,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X3,X1)
| c_Nitpick_Orefl_H(X3,X2) ) ).
cnf(i_0_19107,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__idem(X1,X3,X4,X5)
| c_Finite__Set_Ofolding__idem(X2,X3,X4,X5) ) ).
cnf(i_0_19108,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__idem(X3,X1,X4,X5)
| c_Finite__Set_Ofolding__idem(X3,X2,X4,X5) ) ).
cnf(i_0_19109,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__idem(X3,X4,X1,X5)
| c_Finite__Set_Ofolding__idem(X3,X4,X2,X5) ) ).
cnf(i_0_19110,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__idem(X3,X4,X5,X1)
| c_Finite__Set_Ofolding__idem(X3,X4,X5,X2) ) ).
cnf(i_0_19111,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_19112,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_19113,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_19114,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_19115,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_19116,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Ohoare__valids(X1,X3,X4)
| c_Hoare__Mirabelle_Ohoare__valids(X2,X3,X4) ) ).
cnf(i_0_19117,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Ohoare__valids(X3,X1,X4)
| c_Hoare__Mirabelle_Ohoare__valids(X3,X2,X4) ) ).
cnf(i_0_19118,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Ohoare__valids(X3,X4,X1)
| c_Hoare__Mirabelle_Ohoare__valids(X3,X4,X2) ) ).
cnf(i_0_19119,axiom,
( X1 != X2
| ~ class_Rings_Ono__zero__divisors(X1)
| class_Rings_Ono__zero__divisors(X2) ) ).
cnf(i_0_19120,axiom,
( X1 != X2
| ~ c_Typedef_Otype__definition(X1,X3,X4,X5,X6)
| c_Typedef_Otype__definition(X2,X3,X4,X5,X6) ) ).
cnf(i_0_19121,axiom,
( X1 != X2
| ~ c_Typedef_Otype__definition(X3,X1,X4,X5,X6)
| c_Typedef_Otype__definition(X3,X2,X4,X5,X6) ) ).
cnf(i_0_19122,axiom,
( X1 != X2
| ~ c_Typedef_Otype__definition(X3,X4,X1,X5,X6)
| c_Typedef_Otype__definition(X3,X4,X2,X5,X6) ) ).
cnf(i_0_19123,axiom,
( X1 != X2
| ~ c_Typedef_Otype__definition(X3,X4,X5,X1,X6)
| c_Typedef_Otype__definition(X3,X4,X5,X2,X6) ) ).
cnf(i_0_19124,axiom,
( X1 != X2
| ~ c_Typedef_Otype__definition(X3,X4,X5,X6,X1)
| c_Typedef_Otype__definition(X3,X4,X5,X6,X2) ) ).
cnf(i_0_19125,axiom,
( X1 != X2
| ~ class_Rings_Oring(X1)
| class_Rings_Oring(X2) ) ).
cnf(i_0_19126,axiom,
( X1 != X2
| ~ class_Rings_Osemiring(X1)
| class_Rings_Osemiring(X2) ) ).
cnf(i_0_19127,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X1,X3,X4,X5)
| c_Equiv__Relations_Ocongruent(X2,X3,X4,X5) ) ).
cnf(i_0_19128,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X3,X1,X4,X5)
| c_Equiv__Relations_Ocongruent(X3,X2,X4,X5) ) ).
cnf(i_0_19129,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X3,X4,X1,X5)
| c_Equiv__Relations_Ocongruent(X3,X4,X2,X5) ) ).
cnf(i_0_19130,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X3,X4,X5,X1)
| c_Equiv__Relations_Ocongruent(X3,X4,X5,X2) ) ).
cnf(i_0_19131,axiom,
( X1 != X2
| ~ class_Groups_Osemigroup__add(X1)
| class_Groups_Osemigroup__add(X2) ) ).
cnf(i_0_19132,axiom,
( X1 != X2
| ~ c_Relation_Oirrefl(X1,X3)
| c_Relation_Oirrefl(X2,X3) ) ).
cnf(i_0_19133,axiom,
( X1 != X2
| ~ c_Relation_Oirrefl(X3,X1)
| c_Relation_Oirrefl(X3,X2) ) ).
cnf(i_0_19134,axiom,
( X1 != X2
| ~ epred2_3(X1,X3,X4)
| epred2_3(X2,X3,X4) ) ).
cnf(i_0_19135,axiom,
( X1 != X2
| ~ epred2_3(X3,X1,X4)
| epred2_3(X3,X2,X4) ) ).
cnf(i_0_19136,axiom,
( X1 != X2
| ~ epred2_3(X3,X4,X1)
| epred2_3(X3,X4,X2) ) ).
cnf(i_0_19137,axiom,
( X1 != X2
| ~ epred1_3(X1,X3,X4)
| epred1_3(X2,X3,X4) ) ).
cnf(i_0_19138,axiom,
( X1 != X2
| ~ epred1_3(X3,X1,X4)
| epred1_3(X3,X2,X4) ) ).
cnf(i_0_19139,axiom,
( X1 != X2
| ~ epred1_3(X3,X4,X1)
| epred1_3(X3,X4,X2) ) ).
cnf(i_0_19140,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_19141,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_19142,axiom,
( X1 != X2
| ~ class_Rings_Oordered__semiring(X1)
| class_Rings_Oordered__semiring(X2) ) ).
cnf(i_0_19143,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__strict(X1)
| class_Rings_Olinordered__semiring__strict(X2) ) ).
cnf(i_0_19144,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring(X1)
| class_Rings_Olinordered__semiring(X2) ) ).
cnf(i_0_19145,axiom,
( X1 != X2
| ~ class_Rings_Oidom(X1)
| class_Rings_Oidom(X2) ) ).
cnf(i_0_18254_001,axiom,
X1 = X1 ).
cnf(i_0_18255_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_18256_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_18257_004,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_18258_005,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_18259_006,axiom,
( X1 != X2
| c_Com_Ocom_OCond(X1,X3,X4) = c_Com_Ocom_OCond(X2,X3,X4) ) ).
cnf(i_0_18260_007,axiom,
( X1 != X2
| c_Com_Ocom_OCond(X3,X1,X4) = c_Com_Ocom_OCond(X3,X2,X4) ) ).
cnf(i_0_18261_008,axiom,
( X1 != X2
| c_Com_Ocom_OCond(X3,X4,X1) = c_Com_Ocom_OCond(X3,X4,X2) ) ).
cnf(i_0_18262_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_18263_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_18264_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_18265_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_18266_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_18267_014,axiom,
( X1 != X2
| c_Com_Ocom_OSemi(X1,X3) = c_Com_Ocom_OSemi(X2,X3) ) ).
cnf(i_0_18268_015,axiom,
( X1 != X2
| c_Com_Ocom_OSemi(X3,X1) = c_Com_Ocom_OSemi(X3,X2) ) ).
cnf(i_0_18269_016,axiom,
( X1 != X2
| c_Big__Operators_Olinorder__class_OMin(X1,X3) = c_Big__Operators_Olinorder__class_OMin(X2,X3) ) ).
cnf(i_0_18270_017,axiom,
( X1 != X2
| c_Big__Operators_Olinorder__class_OMin(X3,X1) = c_Big__Operators_Olinorder__class_OMin(X3,X2) ) ).
cnf(i_0_18271_018,axiom,
( X1 != X2
| c_Big__Operators_Olinorder__class_OMax(X1,X3) = c_Big__Operators_Olinorder__class_OMax(X2,X3) ) ).
cnf(i_0_18272_019,axiom,
( X1 != X2
| c_Big__Operators_Olinorder__class_OMax(X3,X1) = c_Big__Operators_Olinorder__class_OMax(X3,X2) ) ).
cnf(i_0_18273_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_18274_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_18275_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_18276_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_18277_024,axiom,
( X1 != X2
| c_List_Olist_ONil(X1) = c_List_Olist_ONil(X2) ) ).
cnf(i_0_18278_025,axiom,
( X1 != X2
| c_List_Olistrel(X1,X3) = c_List_Olistrel(X2,X3) ) ).
cnf(i_0_18279_026,axiom,
( X1 != X2
| c_List_Olistrel(X3,X1) = c_List_Olistrel(X3,X2) ) ).
cnf(i_0_18280_027,axiom,
( X1 != X2
| c_Divides_Oadjust(X1) = c_Divides_Oadjust(X2) ) ).
cnf(i_0_18281_028,axiom,
( X1 != X2
| c_List_Opartition(X1,X3,X4) = c_List_Opartition(X2,X3,X4) ) ).
cnf(i_0_18282_029,axiom,
( X1 != X2
| c_List_Opartition(X3,X1,X4) = c_List_Opartition(X3,X2,X4) ) ).
cnf(i_0_18283_030,axiom,
( X1 != X2
| c_List_Opartition(X3,X4,X1) = c_List_Opartition(X3,X4,X2) ) ).
cnf(i_0_18284_031,axiom,
( X1 != X2
| c_Wellfounded_Olex__prod(X1,X3,X4,X5) = c_Wellfounded_Olex__prod(X2,X3,X4,X5) ) ).
cnf(i_0_18285_032,axiom,
( X1 != X2
| c_Wellfounded_Olex__prod(X3,X1,X4,X5) = c_Wellfounded_Olex__prod(X3,X2,X4,X5) ) ).
cnf(i_0_18286_033,axiom,
( X1 != X2
| c_Wellfounded_Olex__prod(X3,X4,X1,X5) = c_Wellfounded_Olex__prod(X3,X4,X2,X5) ) ).
cnf(i_0_18287_034,axiom,
( X1 != X2
| c_Wellfounded_Olex__prod(X3,X4,X5,X1) = c_Wellfounded_Olex__prod(X3,X4,X5,X2) ) ).
cnf(i_0_18288_035,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X1) = c_Power_Opower__class_Opower(X2) ) ).
cnf(i_0_18289_036,axiom,
( X1 != X2
| c_List_Osublist(X1,X3,X4) = c_List_Osublist(X2,X3,X4) ) ).
cnf(i_0_18290_037,axiom,
( X1 != X2
| c_List_Osublist(X3,X1,X4) = c_List_Osublist(X3,X2,X4) ) ).
cnf(i_0_18291_038,axiom,
( X1 != X2
| c_List_Osublist(X3,X4,X1) = c_List_Osublist(X3,X4,X2) ) ).
cnf(i_0_18292_039,axiom,
( X1 != X2
| c_List_Otranspose(X1,X3) = c_List_Otranspose(X2,X3) ) ).
cnf(i_0_18293_040,axiom,
( X1 != X2
| c_List_Otranspose(X3,X1) = c_List_Otranspose(X3,X2) ) ).
cnf(i_0_18294_041,axiom,
( X1 != X2
| c_Divides_Odivmod__int__rel(X1,X3) = c_Divides_Odivmod__int__rel(X2,X3) ) ).
cnf(i_0_18295_042,axiom,
( X1 != X2
| c_Divides_Odivmod__int__rel(X3,X1) = c_Divides_Odivmod__int__rel(X3,X2) ) ).
cnf(i_0_18296_043,axiom,
( X1 != X2
| c_Set_Othe__elem(X1,X3) = c_Set_Othe__elem(X2,X3) ) ).
cnf(i_0_18297_044,axiom,
( X1 != X2
| c_Set_Othe__elem(X3,X1) = c_Set_Othe__elem(X3,X2) ) ).
cnf(i_0_18298_045,axiom,
( X1 != X2
| c_Nitpick_Osetsum_H(X1,X3,X4,X5) = c_Nitpick_Osetsum_H(X2,X3,X4,X5) ) ).
cnf(i_0_18299_046,axiom,
( X1 != X2
| c_Nitpick_Osetsum_H(X3,X1,X4,X5) = c_Nitpick_Osetsum_H(X3,X2,X4,X5) ) ).
cnf(i_0_18300_047,axiom,
( X1 != X2
| c_Nitpick_Osetsum_H(X3,X4,X1,X5) = c_Nitpick_Osetsum_H(X3,X4,X2,X5) ) ).
cnf(i_0_18301_048,axiom,
( X1 != X2
| c_Nitpick_Osetsum_H(X3,X4,X5,X1) = c_Nitpick_Osetsum_H(X3,X4,X5,X2) ) ).
cnf(i_0_18302_049,axiom,
( X1 != X2
| c_List_Omonoid__add__class_Olistsum(X1) = c_List_Omonoid__add__class_Olistsum(X2) ) ).
cnf(i_0_18303_050,axiom,
( X1 != X2
| c_Hilbert__Choice_OEps(X1,X3) = c_Hilbert__Choice_OEps(X2,X3) ) ).
cnf(i_0_18304_051,axiom,
( X1 != X2
| c_Hilbert__Choice_OEps(X3,X1) = c_Hilbert__Choice_OEps(X3,X2) ) ).
cnf(i_0_18305_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_18306_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_18307_054,axiom,
( X1 != X2
| c_Random__Sequence_ORandom(X1,X3,X4,X5) = c_Random__Sequence_ORandom(X2,X3,X4,X5) ) ).
cnf(i_0_18308_055,axiom,
( X1 != X2
| c_Random__Sequence_ORandom(X3,X1,X4,X5) = c_Random__Sequence_ORandom(X3,X2,X4,X5) ) ).
cnf(i_0_18309_056,axiom,
( X1 != X2
| c_Random__Sequence_ORandom(X3,X4,X1,X5) = c_Random__Sequence_ORandom(X3,X4,X2,X5) ) ).
cnf(i_0_18310_057,axiom,
( X1 != X2
| c_Random__Sequence_ORandom(X3,X4,X5,X1) = c_Random__Sequence_ORandom(X3,X4,X5,X2) ) ).
cnf(i_0_18311_058,axiom,
( X1 != X2
| c_Lazy__Sequence_Ohb__not__seq(X1) = c_Lazy__Sequence_Ohb__not__seq(X2) ) ).
cnf(i_0_18312_059,axiom,
( X1 != X2
| c_Wellfounded_Omax__ext(X1,X3) = c_Wellfounded_Omax__ext(X2,X3) ) ).
cnf(i_0_18313_060,axiom,
( X1 != X2
| c_Wellfounded_Omax__ext(X3,X1) = c_Wellfounded_Omax__ext(X3,X2) ) ).
cnf(i_0_18314_061,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_18315_062,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).
cnf(i_0_18316_063,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).
cnf(i_0_18317_064,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).
cnf(i_0_18318_065,axiom,
( X1 != X2
| c_Wellfounded_Omin__ext(X1,X3) = c_Wellfounded_Omin__ext(X2,X3) ) ).
cnf(i_0_18319_066,axiom,
( X1 != X2
| c_Wellfounded_Omin__ext(X3,X1) = c_Wellfounded_Omin__ext(X3,X2) ) ).
cnf(i_0_18320_067,axiom,
( X1 != X2
| c_Wellfounded_Ofinite__psubset(X1) = c_Wellfounded_Ofinite__psubset(X2) ) ).
cnf(i_0_18321_068,axiom,
( X1 != X2
| c_Nitpick_Ocard_H(X1,X3) = c_Nitpick_Ocard_H(X2,X3) ) ).
cnf(i_0_18322_069,axiom,
( X1 != X2
| c_Nitpick_Ocard_H(X3,X1) = c_Nitpick_Ocard_H(X3,X2) ) ).
cnf(i_0_18323_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_18324_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_18325_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_18326_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_18327_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_18328_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_18329_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_18330_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_18331_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_18332_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_18333_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_18334_081,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X1) = c_Groups_Ominus__class_Ominus(X2) ) ).
cnf(i_0_18335_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_18336_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_18337_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_18338_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_18339_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_18340_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_18341_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_18342_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_18343_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_18344_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_18345_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_18346_093,axiom,
( X1 != X2
| c_Complete__Lattice_OSup__class_OSup(X1,X3) = c_Complete__Lattice_OSup__class_OSup(X2,X3) ) ).
cnf(i_0_18347_094,axiom,
( X1 != X2
| c_Complete__Lattice_OSup__class_OSup(X3,X1) = c_Complete__Lattice_OSup__class_OSup(X3,X2) ) ).
cnf(i_0_18348_095,axiom,
( X1 != X2
| c_Complete__Lattice_OInf__class_OInf(X1,X3) = c_Complete__Lattice_OInf__class_OInf(X2,X3) ) ).
cnf(i_0_18349_096,axiom,
( X1 != X2
| c_Complete__Lattice_OInf__class_OInf(X3,X1) = c_Complete__Lattice_OInf__class_OInf(X3,X2) ) ).
cnf(i_0_18350_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_18351_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_18352_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_18353_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_18354_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_18355_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_18356_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_18357_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_18358_105,axiom,
( X1 != X2
| esk383_5(X1,X3,X4,X5,X6) = esk383_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18359_106,axiom,
( X1 != X2
| esk383_5(X3,X1,X4,X5,X6) = esk383_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18360_107,axiom,
( X1 != X2
| esk383_5(X3,X4,X1,X5,X6) = esk383_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18361_108,axiom,
( X1 != X2
| esk383_5(X3,X4,X5,X1,X6) = esk383_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18362_109,axiom,
( X1 != X2
| esk383_5(X3,X4,X5,X6,X1) = esk383_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18363_110,axiom,
( X1 != X2
| esk382_5(X1,X3,X4,X5,X6) = esk382_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18364_111,axiom,
( X1 != X2
| esk382_5(X3,X1,X4,X5,X6) = esk382_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18365_112,axiom,
( X1 != X2
| esk382_5(X3,X4,X1,X5,X6) = esk382_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18366_113,axiom,
( X1 != X2
| esk382_5(X3,X4,X5,X1,X6) = esk382_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18367_114,axiom,
( X1 != X2
| esk382_5(X3,X4,X5,X6,X1) = esk382_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18368_115,axiom,
( X1 != X2
| esk377_5(X1,X3,X4,X5,X6) = esk377_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18369_116,axiom,
( X1 != X2
| esk377_5(X3,X1,X4,X5,X6) = esk377_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18370_117,axiom,
( X1 != X2
| esk377_5(X3,X4,X1,X5,X6) = esk377_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18371_118,axiom,
( X1 != X2
| esk377_5(X3,X4,X5,X1,X6) = esk377_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18372_119,axiom,
( X1 != X2
| esk377_5(X3,X4,X5,X6,X1) = esk377_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18373_120,axiom,
( X1 != X2
| esk378_5(X1,X3,X4,X5,X6) = esk378_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18374_121,axiom,
( X1 != X2
| esk378_5(X3,X1,X4,X5,X6) = esk378_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18375_122,axiom,
( X1 != X2
| esk378_5(X3,X4,X1,X5,X6) = esk378_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18376_123,axiom,
( X1 != X2
| esk378_5(X3,X4,X5,X1,X6) = esk378_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18377_124,axiom,
( X1 != X2
| esk378_5(X3,X4,X5,X6,X1) = esk378_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18378_125,axiom,
( X1 != X2
| c_Option_Ooption_ONone(X1) = c_Option_Ooption_ONone(X2) ) ).
cnf(i_0_18379_126,axiom,
( X1 != X2
| c_HOL_OThe(X1,X3) = c_HOL_OThe(X2,X3) ) ).
cnf(i_0_18380_127,axiom,
( X1 != X2
| c_HOL_OThe(X3,X1) = c_HOL_OThe(X3,X2) ) ).
cnf(i_0_18381_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_18382_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_18383_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_18384_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_18385_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_18386_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_18387_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_18388_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_18389_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_18390_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_18391_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_18392_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_18393_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_18394_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_18395_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_18396_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_18397_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_18398_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_18399_146,axiom,
( X1 != X2
| c_Nitpick_Oprod(X1,X3,X4,X5) = c_Nitpick_Oprod(X2,X3,X4,X5) ) ).
cnf(i_0_18400_147,axiom,
( X1 != X2
| c_Nitpick_Oprod(X3,X1,X4,X5) = c_Nitpick_Oprod(X3,X2,X4,X5) ) ).
cnf(i_0_18401_148,axiom,
( X1 != X2
| c_Nitpick_Oprod(X3,X4,X1,X5) = c_Nitpick_Oprod(X3,X4,X2,X5) ) ).
cnf(i_0_18402_149,axiom,
( X1 != X2
| c_Nitpick_Oprod(X3,X4,X5,X1) = c_Nitpick_Oprod(X3,X4,X5,X2) ) ).
cnf(i_0_18403_150,axiom,
( X1 != X2
| esk264_6(X1,X3,X4,X5,X6,X7) = esk264_6(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_18404_151,axiom,
( X1 != X2
| esk264_6(X3,X1,X4,X5,X6,X7) = esk264_6(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_18405_152,axiom,
( X1 != X2
| esk264_6(X3,X4,X1,X5,X6,X7) = esk264_6(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_18406_153,axiom,
( X1 != X2
| esk264_6(X3,X4,X5,X1,X6,X7) = esk264_6(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_18407_154,axiom,
( X1 != X2
| esk264_6(X3,X4,X5,X6,X1,X7) = esk264_6(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_18408_155,axiom,
( X1 != X2
| esk264_6(X3,X4,X5,X6,X7,X1) = esk264_6(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_18409_156,axiom,
( X1 != X2
| esk263_6(X1,X3,X4,X5,X6,X7) = esk263_6(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_18410_157,axiom,
( X1 != X2
| esk263_6(X3,X1,X4,X5,X6,X7) = esk263_6(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_18411_158,axiom,
( X1 != X2
| esk263_6(X3,X4,X1,X5,X6,X7) = esk263_6(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_18412_159,axiom,
( X1 != X2
| esk263_6(X3,X4,X5,X1,X6,X7) = esk263_6(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_18413_160,axiom,
( X1 != X2
| esk263_6(X3,X4,X5,X6,X1,X7) = esk263_6(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_18414_161,axiom,
( X1 != X2
| esk263_6(X3,X4,X5,X6,X7,X1) = esk263_6(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_18415_162,axiom,
( X1 != X2
| c_Int_Onumber__class_Onumber__of(X1) = c_Int_Onumber__class_Onumber__of(X2) ) ).
cnf(i_0_18416_163,axiom,
( X1 != X2
| c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).
cnf(i_0_18417_164,axiom,
( X1 != X2
| c_Nitpick_Otimes__frac(X1,X3,X4) = c_Nitpick_Otimes__frac(X2,X3,X4) ) ).
cnf(i_0_18418_165,axiom,
( X1 != X2
| c_Nitpick_Otimes__frac(X3,X1,X4) = c_Nitpick_Otimes__frac(X3,X2,X4) ) ).
cnf(i_0_18419_166,axiom,
( X1 != X2
| c_Nitpick_Otimes__frac(X3,X4,X1) = c_Nitpick_Otimes__frac(X3,X4,X2) ) ).
cnf(i_0_18420_167,axiom,
( X1 != X2
| c_Divides_OnegDivAlg(X1,X3) = c_Divides_OnegDivAlg(X2,X3) ) ).
cnf(i_0_18421_168,axiom,
( X1 != X2
| c_Divides_OnegDivAlg(X3,X1) = c_Divides_OnegDivAlg(X3,X2) ) ).
cnf(i_0_18422_169,axiom,
( X1 != X2
| c_Divides_OposDivAlg(X1,X3) = c_Divides_OposDivAlg(X2,X3) ) ).
cnf(i_0_18423_170,axiom,
( X1 != X2
| c_Divides_OposDivAlg(X3,X1) = c_Divides_OposDivAlg(X3,X2) ) ).
cnf(i_0_18424_171,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat(X1) = c_Nat_Osemiring__1__class_Oof__nat(X2) ) ).
cnf(i_0_18425_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_18426_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_18427_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_18428_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_18429_176,axiom,
( X1 != X2
| c_List_Omap__filter(X1,X3,X4,X5) = c_List_Omap__filter(X2,X3,X4,X5) ) ).
cnf(i_0_18430_177,axiom,
( X1 != X2
| c_List_Omap__filter(X3,X1,X4,X5) = c_List_Omap__filter(X3,X2,X4,X5) ) ).
cnf(i_0_18431_178,axiom,
( X1 != X2
| c_List_Omap__filter(X3,X4,X1,X5) = c_List_Omap__filter(X3,X4,X2,X5) ) ).
cnf(i_0_18432_179,axiom,
( X1 != X2
| c_List_Omap__filter(X3,X4,X5,X1) = c_List_Omap__filter(X3,X4,X5,X2) ) ).
cnf(i_0_18433_180,axiom,
( X1 != X2
| c_Map_Odom(X1,X3,X4) = c_Map_Odom(X2,X3,X4) ) ).
cnf(i_0_18434_181,axiom,
( X1 != X2
| c_Map_Odom(X3,X1,X4) = c_Map_Odom(X3,X2,X4) ) ).
cnf(i_0_18435_182,axiom,
( X1 != X2
| c_Map_Odom(X3,X4,X1) = c_Map_Odom(X3,X4,X2) ) ).
cnf(i_0_18436_183,axiom,
( X1 != X2
| c_Fun_Oid(X1) = c_Fun_Oid(X2) ) ).
cnf(i_0_18437_184,axiom,
( X1 != X2
| c_SetInterval_Oord_OgreaterThanLessThan(X1,X3,X4,X5) = c_SetInterval_Oord_OgreaterThanLessThan(X2,X3,X4,X5) ) ).
cnf(i_0_18438_185,axiom,
( X1 != X2
| c_SetInterval_Oord_OgreaterThanLessThan(X3,X1,X4,X5) = c_SetInterval_Oord_OgreaterThanLessThan(X3,X2,X4,X5) ) ).
cnf(i_0_18439_186,axiom,
( X1 != X2
| c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X1,X5) = c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X2,X5) ) ).
cnf(i_0_18440_187,axiom,
( X1 != X2
| c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X5,X1) = c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X5,X2) ) ).
cnf(i_0_18441_188,axiom,
( X1 != X2
| c_Relation_OId__on(X1,X3) = c_Relation_OId__on(X2,X3) ) ).
cnf(i_0_18442_189,axiom,
( X1 != X2
| c_Relation_OId__on(X3,X1) = c_Relation_OId__on(X3,X2) ) ).
cnf(i_0_18443_190,axiom,
( X1 != X2
| c_Int_Oint__ge__less__than(X1) = c_Int_Oint__ge__less__than(X2) ) ).
cnf(i_0_18444_191,axiom,
( X1 != X2
| c_List_Olistrel1(X1,X3) = c_List_Olistrel1(X2,X3) ) ).
cnf(i_0_18445_192,axiom,
( X1 != X2
| c_List_Olistrel1(X3,X1) = c_List_Olistrel1(X3,X2) ) ).
cnf(i_0_18446_193,axiom,
( X1 != X2
| c_Finite__Set_Ofold(X1,X3,X4) = c_Finite__Set_Ofold(X2,X3,X4) ) ).
cnf(i_0_18447_194,axiom,
( X1 != X2
| c_Finite__Set_Ofold(X3,X1,X4) = c_Finite__Set_Ofold(X3,X2,X4) ) ).
cnf(i_0_18448_195,axiom,
( X1 != X2
| c_Finite__Set_Ofold(X3,X4,X1) = c_Finite__Set_Ofold(X3,X4,X2) ) ).
cnf(i_0_18449_196,axiom,
( X1 != X2
| c_Nitpick_Ouminus__frac(X1,X3) = c_Nitpick_Ouminus__frac(X2,X3) ) ).
cnf(i_0_18450_197,axiom,
( X1 != X2
| c_Nitpick_Ouminus__frac(X3,X1) = c_Nitpick_Ouminus__frac(X3,X2) ) ).
cnf(i_0_18451_198,axiom,
( X1 != X2
| c_Nitpick_OAbs__Frac(X1,X3) = c_Nitpick_OAbs__Frac(X2,X3) ) ).
cnf(i_0_18452_199,axiom,
( X1 != X2
| c_Nitpick_OAbs__Frac(X3,X1) = c_Nitpick_OAbs__Frac(X3,X2) ) ).
cnf(i_0_18453_200,axiom,
( X1 != X2
| esk476_4(X1,X3,X4,X5) = esk476_4(X2,X3,X4,X5) ) ).
cnf(i_0_18454_201,axiom,
( X1 != X2
| esk476_4(X3,X1,X4,X5) = esk476_4(X3,X2,X4,X5) ) ).
cnf(i_0_18455_202,axiom,
( X1 != X2
| esk476_4(X3,X4,X1,X5) = esk476_4(X3,X4,X2,X5) ) ).
cnf(i_0_18456_203,axiom,
( X1 != X2
| esk476_4(X3,X4,X5,X1) = esk476_4(X3,X4,X5,X2) ) ).
cnf(i_0_18457_204,axiom,
( X1 != X2
| esk475_4(X1,X3,X4,X5) = esk475_4(X2,X3,X4,X5) ) ).
cnf(i_0_18458_205,axiom,
( X1 != X2
| esk475_4(X3,X1,X4,X5) = esk475_4(X3,X2,X4,X5) ) ).
cnf(i_0_18459_206,axiom,
( X1 != X2
| esk475_4(X3,X4,X1,X5) = esk475_4(X3,X4,X2,X5) ) ).
cnf(i_0_18460_207,axiom,
( X1 != X2
| esk475_4(X3,X4,X5,X1) = esk475_4(X3,X4,X5,X2) ) ).
cnf(i_0_18461_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_18462_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_18463_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_18464_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_18465_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_18466_213,axiom,
( X1 != X2
| c_Map_Oran(X1,X3,X4) = c_Map_Oran(X2,X3,X4) ) ).
cnf(i_0_18467_214,axiom,
( X1 != X2
| c_Map_Oran(X3,X1,X4) = c_Map_Oran(X3,X2,X4) ) ).
cnf(i_0_18468_215,axiom,
( X1 != X2
| c_Map_Oran(X3,X4,X1) = c_Map_Oran(X3,X4,X2) ) ).
cnf(i_0_18469_216,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X1,X3,X4,X5) = c_Sum__Type_OPlus(X2,X3,X4,X5) ) ).
cnf(i_0_18470_217,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X1,X4,X5) = c_Sum__Type_OPlus(X3,X2,X4,X5) ) ).
cnf(i_0_18471_218,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X1,X5) = c_Sum__Type_OPlus(X3,X4,X2,X5) ) ).
cnf(i_0_18472_219,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X5,X1) = c_Sum__Type_OPlus(X3,X4,X5,X2) ) ).
cnf(i_0_18473_220,axiom,
( X1 != X2
| c_Int_Oint__ge__less__than2(X1) = c_Int_Oint__ge__less__than2(X2) ) ).
cnf(i_0_18474_221,axiom,
( X1 != X2
| c_Nitpick_Oof__frac(X1,X3,X4) = c_Nitpick_Oof__frac(X2,X3,X4) ) ).
cnf(i_0_18475_222,axiom,
( X1 != X2
| c_Nitpick_Oof__frac(X3,X1,X4) = c_Nitpick_Oof__frac(X3,X2,X4) ) ).
cnf(i_0_18476_223,axiom,
( X1 != X2
| c_Nitpick_Oof__frac(X3,X4,X1) = c_Nitpick_Oof__frac(X3,X4,X2) ) ).
cnf(i_0_18477_224,axiom,
( X1 != X2
| c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).
cnf(i_0_18478_225,axiom,
( X1 != X2
| c_Random__Sequence_Omap(X1,X3,X4,X5) = c_Random__Sequence_Omap(X2,X3,X4,X5) ) ).
cnf(i_0_18479_226,axiom,
( X1 != X2
| c_Random__Sequence_Omap(X3,X1,X4,X5) = c_Random__Sequence_Omap(X3,X2,X4,X5) ) ).
cnf(i_0_18480_227,axiom,
( X1 != X2
| c_Random__Sequence_Omap(X3,X4,X1,X5) = c_Random__Sequence_Omap(X3,X4,X2,X5) ) ).
cnf(i_0_18481_228,axiom,
( X1 != X2
| c_Random__Sequence_Omap(X3,X4,X5,X1) = c_Random__Sequence_Omap(X3,X4,X5,X2) ) ).
cnf(i_0_18482_229,axiom,
( X1 != X2
| c_Random__Sequence_Obind(X1,X3,X4,X5) = c_Random__Sequence_Obind(X2,X3,X4,X5) ) ).
cnf(i_0_18483_230,axiom,
( X1 != X2
| c_Random__Sequence_Obind(X3,X1,X4,X5) = c_Random__Sequence_Obind(X3,X2,X4,X5) ) ).
cnf(i_0_18484_231,axiom,
( X1 != X2
| c_Random__Sequence_Obind(X3,X4,X1,X5) = c_Random__Sequence_Obind(X3,X4,X2,X5) ) ).
cnf(i_0_18485_232,axiom,
( X1 != X2
| c_Random__Sequence_Obind(X3,X4,X5,X1) = c_Random__Sequence_Obind(X3,X4,X5,X2) ) ).
cnf(i_0_18486_233,axiom,
( X1 != X2
| c_Orderings_Oord__class_Omax(X1) = c_Orderings_Oord__class_Omax(X2) ) ).
cnf(i_0_18487_234,axiom,
( X1 != X2
| c_Map_Orestrict__map(X1,X3,X4,X5) = c_Map_Orestrict__map(X2,X3,X4,X5) ) ).
cnf(i_0_18488_235,axiom,
( X1 != X2
| c_Map_Orestrict__map(X3,X1,X4,X5) = c_Map_Orestrict__map(X3,X2,X4,X5) ) ).
cnf(i_0_18489_236,axiom,
( X1 != X2
| c_Map_Orestrict__map(X3,X4,X1,X5) = c_Map_Orestrict__map(X3,X4,X2,X5) ) ).
cnf(i_0_18490_237,axiom,
( X1 != X2
| c_Map_Orestrict__map(X3,X4,X5,X1) = c_Map_Orestrict__map(X3,X4,X5,X2) ) ).
cnf(i_0_18491_238,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X4) ) ).
cnf(i_0_18492_239,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X4) ) ).
cnf(i_0_18493_240,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X2) ) ).
cnf(i_0_18494_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_18495_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_18496_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_18497_244,axiom,
( X1 != X2
| c_Orderings_Oord__class_Omin(X1) = c_Orderings_Oord__class_Omin(X2) ) ).
cnf(i_0_18498_245,axiom,
( X1 != X2
| c_List_Olist_Olist__size(X1,X3,X4) = c_List_Olist_Olist__size(X2,X3,X4) ) ).
cnf(i_0_18499_246,axiom,
( X1 != X2
| c_List_Olist_Olist__size(X3,X1,X4) = c_List_Olist_Olist__size(X3,X2,X4) ) ).
cnf(i_0_18500_247,axiom,
( X1 != X2
| c_List_Olist_Olist__size(X3,X4,X1) = c_List_Olist_Olist__size(X3,X4,X2) ) ).
cnf(i_0_18501_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_18502_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_18503_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_18504_251,axiom,
( X1 != X2
| c_Lattices_Osemilattice__inf__class_Oinf(X1) = c_Lattices_Osemilattice__inf__class_Oinf(X2) ) ).
cnf(i_0_18505_252,axiom,
( X1 != X2
| c_Random_Oselect__weight(X1,X3) = c_Random_Oselect__weight(X2,X3) ) ).
cnf(i_0_18506_253,axiom,
( X1 != X2
| c_Random_Oselect__weight(X3,X1) = c_Random_Oselect__weight(X3,X2) ) ).
cnf(i_0_18507_254,axiom,
( X1 != X2
| c_Random_Opick(X1,X3) = c_Random_Opick(X2,X3) ) ).
cnf(i_0_18508_255,axiom,
( X1 != X2
| c_Random_Opick(X3,X1) = c_Random_Opick(X3,X2) ) ).
cnf(i_0_18509_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_18510_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_18511_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_18512_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_18513_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_18514_261,axiom,
( X1 != X2
| c_List_Olists(X1,X3) = c_List_Olists(X2,X3) ) ).
cnf(i_0_18515_262,axiom,
( X1 != X2
| c_List_Olists(X3,X1) = c_List_Olists(X3,X2) ) ).
cnf(i_0_18516_263,axiom,
( X1 != X2
| c_Wellfounded_Omlex__prod(X1,X3,X4) = c_Wellfounded_Omlex__prod(X2,X3,X4) ) ).
cnf(i_0_18517_264,axiom,
( X1 != X2
| c_Wellfounded_Omlex__prod(X3,X1,X4) = c_Wellfounded_Omlex__prod(X3,X2,X4) ) ).
cnf(i_0_18518_265,axiom,
( X1 != X2
| c_Wellfounded_Omlex__prod(X3,X4,X1) = c_Wellfounded_Omlex__prod(X3,X4,X2) ) ).
cnf(i_0_18519_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_18520_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_18521_268,axiom,
( X1 != X2
| c_Nitpick_Onorm__frac(X1,X3) = c_Nitpick_Onorm__frac(X2,X3) ) ).
cnf(i_0_18522_269,axiom,
( X1 != X2
| c_Nitpick_Onorm__frac(X3,X1) = c_Nitpick_Onorm__frac(X3,X2) ) ).
cnf(i_0_18523_270,axiom,
( X1 != X2
| c_List_Oremove1(X1,X3,X4) = c_List_Oremove1(X2,X3,X4) ) ).
cnf(i_0_18524_271,axiom,
( X1 != X2
| c_List_Oremove1(X3,X1,X4) = c_List_Oremove1(X3,X2,X4) ) ).
cnf(i_0_18525_272,axiom,
( X1 != X2
| c_List_Oremove1(X3,X4,X1) = c_List_Oremove1(X3,X4,X2) ) ).
cnf(i_0_18526_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_18527_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_18528_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_18529_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_18530_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_18531_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_18532_279,axiom,
( X1 != X2
| c_Lattices_Osemilattice__sup__class_Osup(X1) = c_Lattices_Osemilattice__sup__class_Osup(X2) ) ).
cnf(i_0_18533_280,axiom,
( X1 != X2
| esk371_3(X1,X3,X4) = esk371_3(X2,X3,X4) ) ).
cnf(i_0_18534_281,axiom,
( X1 != X2
| esk371_3(X3,X1,X4) = esk371_3(X3,X2,X4) ) ).
cnf(i_0_18535_282,axiom,
( X1 != X2
| esk371_3(X3,X4,X1) = esk371_3(X3,X4,X2) ) ).
cnf(i_0_18536_283,axiom,
( X1 != X2
| esk370_3(X1,X3,X4) = esk370_3(X2,X3,X4) ) ).
cnf(i_0_18537_284,axiom,
( X1 != X2
| esk370_3(X3,X1,X4) = esk370_3(X3,X2,X4) ) ).
cnf(i_0_18538_285,axiom,
( X1 != X2
| esk370_3(X3,X4,X1) = esk370_3(X3,X4,X2) ) ).
cnf(i_0_18539_286,axiom,
( X1 != X2
| c_Smallcheck_Osmall_H(X1,X3,X4) = c_Smallcheck_Osmall_H(X2,X3,X4) ) ).
cnf(i_0_18540_287,axiom,
( X1 != X2
| c_Smallcheck_Osmall_H(X3,X1,X4) = c_Smallcheck_Osmall_H(X3,X2,X4) ) ).
cnf(i_0_18541_288,axiom,
( X1 != X2
| c_Smallcheck_Osmall_H(X3,X4,X1) = c_Smallcheck_Osmall_H(X3,X4,X2) ) ).
cnf(i_0_18542_289,axiom,
( X1 != X2
| c_Random_Oselect(X1,X3) = c_Random_Oselect(X2,X3) ) ).
cnf(i_0_18543_290,axiom,
( X1 != X2
| c_Random_Oselect(X3,X1) = c_Random_Oselect(X3,X2) ) ).
cnf(i_0_18544_291,axiom,
( X1 != X2
| c_SetInterval_Oord_OatLeastAtMost(X1,X3,X4,X5) = c_SetInterval_Oord_OatLeastAtMost(X2,X3,X4,X5) ) ).
cnf(i_0_18545_292,axiom,
( X1 != X2
| c_SetInterval_Oord_OatLeastAtMost(X3,X1,X4,X5) = c_SetInterval_Oord_OatLeastAtMost(X3,X2,X4,X5) ) ).
cnf(i_0_18546_293,axiom,
( X1 != X2
| c_SetInterval_Oord_OatLeastAtMost(X3,X4,X1,X5) = c_SetInterval_Oord_OatLeastAtMost(X3,X4,X2,X5) ) ).
cnf(i_0_18547_294,axiom,
( X1 != X2
| c_SetInterval_Oord_OatLeastAtMost(X3,X4,X5,X1) = c_SetInterval_Oord_OatLeastAtMost(X3,X4,X5,X2) ) ).
cnf(i_0_18548_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_18549_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_18550_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_18551_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_18552_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_18553_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_18554_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_18555_302,axiom,
( X1 != X2
| c_Com_Ocom_OLocal(X1,X3,X4) = c_Com_Ocom_OLocal(X2,X3,X4) ) ).
cnf(i_0_18556_303,axiom,
( X1 != X2
| c_Com_Ocom_OLocal(X3,X1,X4) = c_Com_Ocom_OLocal(X3,X2,X4) ) ).
cnf(i_0_18557_304,axiom,
( X1 != X2
| c_Com_Ocom_OLocal(X3,X4,X1) = c_Com_Ocom_OLocal(X3,X4,X2) ) ).
cnf(i_0_18558_305,axiom,
( X1 != X2
| c_Finite__Set_Ofold1(X1,X3) = c_Finite__Set_Ofold1(X2,X3) ) ).
cnf(i_0_18559_306,axiom,
( X1 != X2
| c_Finite__Set_Ofold1(X3,X1) = c_Finite__Set_Ofold1(X3,X2) ) ).
cnf(i_0_18560_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_18561_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_18562_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_18563_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_18564_311,axiom,
( X1 != X2
| c_Com_Ocom_OWhile(X1,X3) = c_Com_Ocom_OWhile(X2,X3) ) ).
cnf(i_0_18565_312,axiom,
( X1 != X2
| c_Com_Ocom_OWhile(X3,X1) = c_Com_Ocom_OWhile(X3,X2) ) ).
cnf(i_0_18566_313,axiom,
( X1 != X2
| c_List_Oset__Cons(X1,X3,X4) = c_List_Oset__Cons(X2,X3,X4) ) ).
cnf(i_0_18567_314,axiom,
( X1 != X2
| c_List_Oset__Cons(X3,X1,X4) = c_List_Oset__Cons(X3,X2,X4) ) ).
cnf(i_0_18568_315,axiom,
( X1 != X2
| c_List_Oset__Cons(X3,X4,X1) = c_List_Oset__Cons(X3,X4,X2) ) ).
cnf(i_0_18569_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_18570_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_18571_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_18572_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_18573_320,axiom,
( X1 != X2
| esk269_5(X1,X3,X4,X5,X6) = esk269_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_18574_321,axiom,
( X1 != X2
| esk269_5(X3,X1,X4,X5,X6) = esk269_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_18575_322,axiom,
( X1 != X2
| esk269_5(X3,X4,X1,X5,X6) = esk269_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_18576_323,axiom,
( X1 != X2
| esk269_5(X3,X4,X5,X1,X6) = esk269_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_18577_324,axiom,
( X1 != X2
| esk269_5(X3,X4,X5,X6,X1) = esk269_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_18578_325,axiom,
( X1 != X2
| esk381_3(X1,X3,X4) = esk381_3(X2,X3,X4) ) ).
cnf(i_0_18579_326,axiom,
( X1 != X2
| esk381_3(X3,X1,X4) = esk381_3(X3,X2,X4) ) ).
cnf(i_0_18580_327,axiom,
( X1 != X2
| esk381_3(X3,X4,X1) = esk381_3(X3,X4,X2) ) ).
cnf(i_0_18581_328,axiom,
( X1 != X2
| esk380_3(X1,X3,X4) = esk380_3(X2,X3,X4) ) ).
cnf(i_0_18582_329,axiom,
( X1 != X2
| esk380_3(X3,X1,X4) = esk380_3(X3,X2,X4) ) ).
cnf(i_0_18583_330,axiom,
( X1 != X2
| esk380_3(X3,X4,X1) = esk380_3(X3,X4,X2) ) ).
cnf(i_0_18584_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_18585_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_18586_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_18587_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_18588_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_18589_336,axiom,
( X1 != X2
| c_Product__Type_Ocurry(X1,X3,X4,X5) = c_Product__Type_Ocurry(X2,X3,X4,X5) ) ).
cnf(i_0_18590_337,axiom,
( X1 != X2
| c_Product__Type_Ocurry(X3,X1,X4,X5) = c_Product__Type_Ocurry(X3,X2,X4,X5) ) ).
cnf(i_0_18591_338,axiom,
( X1 != X2
| c_Product__Type_Ocurry(X3,X4,X1,X5) = c_Product__Type_Ocurry(X3,X4,X2,X5) ) ).
cnf(i_0_18592_339,axiom,
( X1 != X2
| c_Product__Type_Ocurry(X3,X4,X5,X1) = c_Product__Type_Ocurry(X3,X4,X5,X2) ) ).
cnf(i_0_18593_340,axiom,
( X1 != X2
| c_Nitpick_Onat__gcd(X1,X3) = c_Nitpick_Onat__gcd(X2,X3) ) ).
cnf(i_0_18594_341,axiom,
( X1 != X2
| c_Nitpick_Onat__gcd(X3,X1) = c_Nitpick_Onat__gcd(X3,X2) ) ).
cnf(i_0_18595_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_18596_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_18597_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_18598_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_18599_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_18600_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_18601_348,axiom,
( X1 != X2
| c_Partial__Function_Oflat__lub(X1,X3,X4) = c_Partial__Function_Oflat__lub(X2,X3,X4) ) ).
cnf(i_0_18602_349,axiom,
( X1 != X2
| c_Partial__Function_Oflat__lub(X3,X1,X4) = c_Partial__Function_Oflat__lub(X3,X2,X4) ) ).
cnf(i_0_18603_350,axiom,
( X1 != X2
| c_Partial__Function_Oflat__lub(X3,X4,X1) = c_Partial__Function_Oflat__lub(X3,X4,X2) ) ).
cnf(i_0_18604_351,axiom,
( X1 != X2
| c_List_OtakeWhile(X1,X3,X4) = c_List_OtakeWhile(X2,X3,X4) ) ).
cnf(i_0_18605_352,axiom,
( X1 != X2
| c_List_OtakeWhile(X3,X1,X4) = c_List_OtakeWhile(X3,X2,X4) ) ).
cnf(i_0_18606_353,axiom,
( X1 != X2
| c_List_OtakeWhile(X3,X4,X1) = c_List_OtakeWhile(X3,X4,X2) ) ).
cnf(i_0_18607_354,axiom,
( X1 != X2
| c_Com_Ovname_OLoc(X1) = c_Com_Ovname_OLoc(X2) ) ).
cnf(i_0_18608_355,axiom,
( X1 != X2
| esk97_3(X1,X3,X4) = esk97_3(X2,X3,X4) ) ).
cnf(i_0_18609_356,axiom,
( X1 != X2
| esk97_3(X3,X1,X4) = esk97_3(X3,X2,X4) ) ).
cnf(i_0_18610_357,axiom,
( X1 != X2
| esk97_3(X3,X4,X1) = esk97_3(X3,X4,X2) ) ).
cnf(i_0_18611_358,axiom,
( X1 != X2
| esk247_4(X1,X3,X4,X5) = esk247_4(X2,X3,X4,X5) ) ).
cnf(i_0_18612_359,axiom,
( X1 != X2
| esk247_4(X3,X1,X4,X5) = esk247_4(X3,X2,X4,X5) ) ).
cnf(i_0_18613_360,axiom,
( X1 != X2
| esk247_4(X3,X4,X1,X5) = esk247_4(X3,X4,X2,X5) ) ).
cnf(i_0_18614_361,axiom,
( X1 != X2
| esk247_4(X3,X4,X5,X1) = esk247_4(X3,X4,X5,X2) ) ).
cnf(i_0_18615_362,axiom,
( X1 != X2
| esk249_4(X1,X3,X4,X5) = esk249_4(X2,X3,X4,X5) ) ).
cnf(i_0_18616_363,axiom,
( X1 != X2
| esk249_4(X3,X1,X4,X5) = esk249_4(X3,X2,X4,X5) ) ).
cnf(i_0_18617_364,axiom,
( X1 != X2
| esk249_4(X3,X4,X1,X5) = esk249_4(X3,X4,X2,X5) ) ).
cnf(i_0_18618_365,axiom,
( X1 != X2
| esk249_4(X3,X4,X5,X1) = esk249_4(X3,X4,X5,X2) ) ).
cnf(i_0_18619_366,axiom,
( X1 != X2
| c_Com_Ocom_OCall(X1,X3,X4) = c_Com_Ocom_OCall(X2,X3,X4) ) ).
cnf(i_0_18620_367,axiom,
( X1 != X2
| c_Com_Ocom_OCall(X3,X1,X4) = c_Com_Ocom_OCall(X3,X2,X4) ) ).
cnf(i_0_18621_368,axiom,
( X1 != X2
| c_Com_Ocom_OCall(X3,X4,X1) = c_Com_Ocom_OCall(X3,X4,X2) ) ).
cnf(i_0_18622_369,axiom,
( X1 != X2
| esk195_4(X1,X3,X4,X5) = esk195_4(X2,X3,X4,X5) ) ).
cnf(i_0_18623_370,axiom,
( X1 != X2
| esk195_4(X3,X1,X4,X5) = esk195_4(X3,X2,X4,X5) ) ).
cnf(i_0_18624_371,axiom,
( X1 != X2
| esk195_4(X3,X4,X1,X5) = esk195_4(X3,X4,X2,X5) ) ).
cnf(i_0_18625_372,axiom,
( X1 != X2
| esk195_4(X3,X4,X5,X1) = esk195_4(X3,X4,X5,X2) ) ).
cnf(i_0_18626_373,axiom,
( X1 != X2
| esk194_4(X1,X3,X4,X5) = esk194_4(X2,X3,X4,X5) ) ).
cnf(i_0_18627_374,axiom,
( X1 != X2
| esk194_4(X3,X1,X4,X5) = esk194_4(X3,X2,X4,X5) ) ).
cnf(i_0_18628_375,axiom,
( X1 != X2
| esk194_4(X3,X4,X1,X5) = esk194_4(X3,X4,X2,X5) ) ).
cnf(i_0_18629_376,axiom,
( X1 != X2
| esk194_4(X3,X4,X5,X1) = esk194_4(X3,X4,X5,X2) ) ).
cnf(i_0_18630_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_18631_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_18632_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_18633_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_18634_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_18635_382,axiom,
( X1 != X2
| c_Divides_Odivmod__int(X1,X3) = c_Divides_Odivmod__int(X2,X3) ) ).
cnf(i_0_18636_383,axiom,
( X1 != X2
| c_Divides_Odivmod__int(X3,X1) = c_Divides_Odivmod__int(X3,X2) ) ).
cnf(i_0_18637_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_18638_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_18639_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_18640_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_18641_388,axiom,
( X1 != X2
| esk406_3(X1,X3,X4) = esk406_3(X2,X3,X4) ) ).
cnf(i_0_18642_389,axiom,
( X1 != X2
| esk406_3(X3,X1,X4) = esk406_3(X3,X2,X4) ) ).
cnf(i_0_18643_390,axiom,
( X1 != X2
| esk406_3(X3,X4,X1) = esk406_3(X3,X4,X2) ) ).
cnf(i_0_18644_391,axiom,
( X1 != X2
| esk407_3(X1,X3,X4) = esk407_3(X2,X3,X4) ) ).
cnf(i_0_18645_392,axiom,
( X1 != X2
| esk407_3(X3,X1,X4) = esk407_3(X3,X2,X4) ) ).
cnf(i_0_18646_393,axiom,
( X1 != X2
| esk407_3(X3,X4,X1) = esk407_3(X3,X4,X2) ) ).
cnf(i_0_18647_394,axiom,
( X1 != X2
| esk268_4(X1,X3,X4,X5) = esk268_4(X2,X3,X4,X5) ) ).
cnf(i_0_18648_395,axiom,
( X1 != X2
| esk268_4(X3,X1,X4,X5) = esk268_4(X3,X2,X4,X5) ) ).
cnf(i_0_18649_396,axiom,
( X1 != X2
| esk268_4(X3,X4,X1,X5) = esk268_4(X3,X4,X2,X5) ) ).
cnf(i_0_18650_397,axiom,
( X1 != X2
| esk268_4(X3,X4,X5,X1) = esk268_4(X3,X4,X5,X2) ) ).
cnf(i_0_18651_398,axiom,
( X1 != X2
| c_Groups_Osgn__class_Osgn(X1,X3) = c_Groups_Osgn__class_Osgn(X2,X3) ) ).
cnf(i_0_18652_399,axiom,
( X1 != X2
| c_Groups_Osgn__class_Osgn(X3,X1) = c_Groups_Osgn__class_Osgn(X3,X2) ) ).
cnf(i_0_18653_400,axiom,
( X1 != X2
| esk410_3(X1,X3,X4) = esk410_3(X2,X3,X4) ) ).
cnf(i_0_18654_401,axiom,
( X1 != X2
| esk410_3(X3,X1,X4) = esk410_3(X3,X2,X4) ) ).
cnf(i_0_18655_402,axiom,
( X1 != X2
| esk410_3(X3,X4,X1) = esk410_3(X3,X4,X2) ) ).
cnf(i_0_18656_403,axiom,
( X1 != X2
| esk409_3(X1,X3,X4) = esk409_3(X2,X3,X4) ) ).
cnf(i_0_18657_404,axiom,
( X1 != X2
| esk409_3(X3,X1,X4) = esk409_3(X3,X2,X4) ) ).
cnf(i_0_18658_405,axiom,
( X1 != X2
| esk409_3(X3,X4,X1) = esk409_3(X3,X4,X2) ) ).
cnf(i_0_18659_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_18660_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_18661_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_18662_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_18663_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_18664_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_18665_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_18666_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_18667_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_18668_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_18669_416,axiom,
( X1 != X2
| c_Divides_Opdivmod(X1,X3) = c_Divides_Opdivmod(X2,X3) ) ).
cnf(i_0_18670_417,axiom,
( X1 != X2
| c_Divides_Opdivmod(X3,X1) = c_Divides_Opdivmod(X3,X2) ) ).
cnf(i_0_18671_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_18672_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_18673_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_18674_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_18675_422,axiom,
( X1 != X2
| c_List_Obutlast(X1,X3) = c_List_Obutlast(X2,X3) ) ).
cnf(i_0_18676_423,axiom,
( X1 != X2
| c_List_Obutlast(X3,X1) = c_List_Obutlast(X3,X2) ) ).
cnf(i_0_18677_424,axiom,
( X1 != X2
| c_Lazy__Sequence_Obind(X1,X3,X4,X5) = c_Lazy__Sequence_Obind(X2,X3,X4,X5) ) ).
cnf(i_0_18678_425,axiom,
( X1 != X2
| c_Lazy__Sequence_Obind(X3,X1,X4,X5) = c_Lazy__Sequence_Obind(X3,X2,X4,X5) ) ).
cnf(i_0_18679_426,axiom,
( X1 != X2
| c_Lazy__Sequence_Obind(X3,X4,X1,X5) = c_Lazy__Sequence_Obind(X3,X4,X2,X5) ) ).
cnf(i_0_18680_427,axiom,
( X1 != X2
| c_Lazy__Sequence_Obind(X3,X4,X5,X1) = c_Lazy__Sequence_Obind(X3,X4,X5,X2) ) ).
cnf(i_0_18681_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_18682_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_18683_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_18684_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_18685_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_18686_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_18687_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_18688_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_18689_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_18690_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_18691_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_18692_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_18693_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_18694_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_18695_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_18696_443,axiom,
( X1 != X2
| esk149_3(X1,X3,X4) = esk149_3(X2,X3,X4) ) ).
cnf(i_0_18697_444,axiom,
( X1 != X2
| esk149_3(X3,X1,X4) = esk149_3(X3,X2,X4) ) ).
cnf(i_0_18698_445,axiom,
( X1 != X2
| esk149_3(X3,X4,X1) = esk149_3(X3,X4,X2) ) ).
cnf(i_0_18699_446,axiom,
( X1 != X2
| c_List_Oupto(X1,X3) = c_List_Oupto(X2,X3) ) ).
cnf(i_0_18700_447,axiom,
( X1 != X2
| c_List_Oupto(X3,X1) = c_List_Oupto(X3,X2) ) ).
cnf(i_0_18701_448,axiom,
( X1 != X2
| esk350_2(X1,X3) = esk350_2(X2,X3) ) ).
cnf(i_0_18702_449,axiom,
( X1 != X2
| esk350_2(X3,X1) = esk350_2(X3,X2) ) ).
cnf(i_0_18703_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_18704_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_18705_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_18706_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_18707_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_18708_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_18709_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_18710_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_18711_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_18712_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_18713_460,axiom,
( X1 != X2
| esk492_2(X1,X3) = esk492_2(X2,X3) ) ).
cnf(i_0_18714_461,axiom,
( X1 != X2
| esk492_2(X3,X1) = esk492_2(X3,X2) ) ).
cnf(i_0_18715_462,axiom,
( X1 != X2
| esk493_2(X1,X3) = esk493_2(X2,X3) ) ).
cnf(i_0_18716_463,axiom,
( X1 != X2
| esk493_2(X3,X1) = esk493_2(X3,X2) ) ).
cnf(i_0_18717_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_18718_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_18719_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_18720_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_18721_468,axiom,
( X1 != X2
| c_Com_Ocom_OAss(X1,X3) = c_Com_Ocom_OAss(X2,X3) ) ).
cnf(i_0_18722_469,axiom,
( X1 != X2
| c_Com_Ocom_OAss(X3,X1) = c_Com_Ocom_OAss(X3,X2) ) ).
cnf(i_0_18723_470,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X4) ) ).
cnf(i_0_18724_471,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X2,X4) ) ).
cnf(i_0_18725_472,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X2) ) ).
cnf(i_0_18726_473,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X3,X4) ) ).
cnf(i_0_18727_474,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X2,X4) ) ).
cnf(i_0_18728_475,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X2) ) ).
cnf(i_0_18729_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_18730_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_18731_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_18732_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_18733_480,axiom,
( X1 != X2
| c_Power_Opower_Opower(X1,X3,X4) = c_Power_Opower_Opower(X2,X3,X4) ) ).
cnf(i_0_18734_481,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X1,X4) = c_Power_Opower_Opower(X3,X2,X4) ) ).
cnf(i_0_18735_482,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X4,X1) = c_Power_Opower_Opower(X3,X4,X2) ) ).
cnf(i_0_18736_483,axiom,
( X1 != X2
| c_Sum__Type_OSumr(X1,X3,X4,X5) = c_Sum__Type_OSumr(X2,X3,X4,X5) ) ).
cnf(i_0_18737_484,axiom,
( X1 != X2
| c_Sum__Type_OSumr(X3,X1,X4,X5) = c_Sum__Type_OSumr(X3,X2,X4,X5) ) ).
cnf(i_0_18738_485,axiom,
( X1 != X2
| c_Sum__Type_OSumr(X3,X4,X1,X5) = c_Sum__Type_OSumr(X3,X4,X2,X5) ) ).
cnf(i_0_18739_486,axiom,
( X1 != X2
| c_Sum__Type_OSumr(X3,X4,X5,X1) = c_Sum__Type_OSumr(X3,X4,X5,X2) ) ).
cnf(i_0_18740_487,axiom,
( X1 != X2
| c_List_Olenlex(X1,X3) = c_List_Olenlex(X2,X3) ) ).
cnf(i_0_18741_488,axiom,
( X1 != X2
| c_List_Olenlex(X3,X1) = c_List_Olenlex(X3,X2) ) ).
cnf(i_0_18742_489,axiom,
( X1 != X2
| c_Sum__Type_OSuml(X1,X3,X4,X5) = c_Sum__Type_OSuml(X2,X3,X4,X5) ) ).
cnf(i_0_18743_490,axiom,
( X1 != X2
| c_Sum__Type_OSuml(X3,X1,X4,X5) = c_Sum__Type_OSuml(X3,X2,X4,X5) ) ).
cnf(i_0_18744_491,axiom,
( X1 != X2
| c_Sum__Type_OSuml(X3,X4,X1,X5) = c_Sum__Type_OSuml(X3,X4,X2,X5) ) ).
cnf(i_0_18745_492,axiom,
( X1 != X2
| c_Sum__Type_OSuml(X3,X4,X5,X1) = c_Sum__Type_OSuml(X3,X4,X5,X2) ) ).
cnf(i_0_18746_493,axiom,
( X1 != X2
| esk470_2(X1,X3) = esk470_2(X2,X3) ) ).
cnf(i_0_18747_494,axiom,
( X1 != X2
| esk470_2(X3,X1) = esk470_2(X3,X2) ) ).
cnf(i_0_18748_495,axiom,
( X1 != X2
| esk246_3(X1,X3,X4) = esk246_3(X2,X3,X4) ) ).
cnf(i_0_18749_496,axiom,
( X1 != X2
| esk246_3(X3,X1,X4) = esk246_3(X3,X2,X4) ) ).
cnf(i_0_18750_497,axiom,
( X1 != X2
| esk246_3(X3,X4,X1) = esk246_3(X3,X4,X2) ) ).
cnf(i_0_18751_498,axiom,
( X1 != X2
| esk248_3(X1,X3,X4) = esk248_3(X2,X3,X4) ) ).
cnf(i_0_18752_499,axiom,
( X1 != X2
| esk248_3(X3,X1,X4) = esk248_3(X3,X2,X4) ) ).
cnf(i_0_18753_500,axiom,
( X1 != X2
| esk248_3(X3,X4,X1) = esk248_3(X3,X4,X2) ) ).
cnf(i_0_18754_501,axiom,
( X1 != X2
| esk131_3(X1,X3,X4) = esk131_3(X2,X3,X4) ) ).
cnf(i_0_18755_502,axiom,
( X1 != X2
| esk131_3(X3,X1,X4) = esk131_3(X3,X2,X4) ) ).
cnf(i_0_18756_503,axiom,
( X1 != X2
| esk131_3(X3,X4,X1) = esk131_3(X3,X4,X2) ) ).
cnf(i_0_18757_504,axiom,
( X1 != X2
| esk130_3(X1,X3,X4) = esk130_3(X2,X3,X4) ) ).
cnf(i_0_18758_505,axiom,
( X1 != X2
| esk130_3(X3,X1,X4) = esk130_3(X3,X2,X4) ) ).
cnf(i_0_18759_506,axiom,
( X1 != X2
| esk130_3(X3,X4,X1) = esk130_3(X3,X4,X2) ) ).
cnf(i_0_18760_507,axiom,
( X1 != X2
| c_List_Olex(X1,X3) = c_List_Olex(X2,X3) ) ).
cnf(i_0_18761_508,axiom,
( X1 != X2
| c_List_Olex(X3,X1) = c_List_Olex(X3,X2) ) ).
cnf(i_0_18762_509,axiom,
( X1 != X2
| c_Nitpick_Oplus__frac(X1,X3,X4) = c_Nitpick_Oplus__frac(X2,X3,X4) ) ).
cnf(i_0_18763_510,axiom,
( X1 != X2
| c_Nitpick_Oplus__frac(X3,X1,X4) = c_Nitpick_Oplus__frac(X3,X2,X4) ) ).
cnf(i_0_18764_511,axiom,
( X1 != X2
| c_Nitpick_Oplus__frac(X3,X4,X1) = c_Nitpick_Oplus__frac(X3,X4,X2) ) ).
cnf(i_0_18765_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_18766_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_18767_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_18768_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_18769_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_18770_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_18771_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_18772_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_18773_520,axiom,
( X1 != X2
| c_Lazy__Sequence_Oempty(X1) = c_Lazy__Sequence_Oempty(X2) ) ).
cnf(i_0_18774_521,axiom,
( X1 != X2
| c_Lazy__Sequence_Ohit__bound(X1) = c_Lazy__Sequence_Ohit__bound(X2) ) ).
cnf(i_0_18775_522,axiom,
( X1 != X2
| c_Nat__Transfer_Otsub(X1,X3) = c_Nat__Transfer_Otsub(X2,X3) ) ).
cnf(i_0_18776_523,axiom,
( X1 != X2
| c_Nat__Transfer_Otsub(X3,X1) = c_Nat__Transfer_Otsub(X3,X2) ) ).
cnf(i_0_18777_524,axiom,
( X1 != X2
| c_List_Olast(X1,X3) = c_List_Olast(X2,X3) ) ).
cnf(i_0_18778_525,axiom,
( X1 != X2
| c_List_Olast(X3,X1) = c_List_Olast(X3,X2) ) ).
cnf(i_0_18779_526,axiom,
( X1 != X2
| c_Nitpick_Oint__lcm(X1,X3) = c_Nitpick_Oint__lcm(X2,X3) ) ).
cnf(i_0_18780_527,axiom,
( X1 != X2
| c_Nitpick_Oint__lcm(X3,X1) = c_Nitpick_Oint__lcm(X3,X2) ) ).
cnf(i_0_18781_528,axiom,
( X1 != X2
| c_Random_Olog(X1,X3) = c_Random_Olog(X2,X3) ) ).
cnf(i_0_18782_529,axiom,
( X1 != X2
| c_Random_Olog(X3,X1) = c_Random_Olog(X3,X2) ) ).
cnf(i_0_18783_530,axiom,
( X1 != X2
| c_Com_Ocom_Ocom__size(X1) = c_Com_Ocom_Ocom__size(X2) ) ).
cnf(i_0_18784_531,axiom,
( X1 != X2
| c_Random_Ominus__shift(X1,X3,X4) = c_Random_Ominus__shift(X2,X3,X4) ) ).
cnf(i_0_18785_532,axiom,
( X1 != X2
| c_Random_Ominus__shift(X3,X1,X4) = c_Random_Ominus__shift(X3,X2,X4) ) ).
cnf(i_0_18786_533,axiom,
( X1 != X2
| c_Random_Ominus__shift(X3,X4,X1) = c_Random_Ominus__shift(X3,X4,X2) ) ).
cnf(i_0_18787_534,axiom,
( X1 != X2
| c_Random__Sequence_Oempty(X1,X3,X4) = c_Random__Sequence_Oempty(X2,X3,X4) ) ).
cnf(i_0_18788_535,axiom,
( X1 != X2
| c_Random__Sequence_Oempty(X3,X1,X4) = c_Random__Sequence_Oempty(X3,X2,X4) ) ).
cnf(i_0_18789_536,axiom,
( X1 != X2
| c_Random__Sequence_Oempty(X3,X4,X1) = c_Random__Sequence_Oempty(X3,X4,X2) ) ).
cnf(i_0_18790_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_18791_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_18792_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_18793_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_18794_541,axiom,
( X1 != X2
| esk484_2(X1,X3) = esk484_2(X2,X3) ) ).
cnf(i_0_18795_542,axiom,
( X1 != X2
| esk484_2(X3,X1) = esk484_2(X3,X2) ) ).
cnf(i_0_18796_543,axiom,
( X1 != X2
| c_List_Olistset(X1,X3) = c_List_Olistset(X2,X3) ) ).
cnf(i_0_18797_544,axiom,
( X1 != X2
| c_List_Olistset(X3,X1) = c_List_Olistset(X3,X2) ) ).
cnf(i_0_18798_545,axiom,
( X1 != X2
| c_Fun_Ocomp(X1,X3,X4,X5) = c_Fun_Ocomp(X2,X3,X4,X5) ) ).
cnf(i_0_18799_546,axiom,
( X1 != X2
| c_Fun_Ocomp(X3,X1,X4,X5) = c_Fun_Ocomp(X3,X2,X4,X5) ) ).
cnf(i_0_18800_547,axiom,
( X1 != X2
| c_Fun_Ocomp(X3,X4,X1,X5) = c_Fun_Ocomp(X3,X4,X2,X5) ) ).
cnf(i_0_18801_548,axiom,
( X1 != X2
| c_Fun_Ocomp(X3,X4,X5,X1) = c_Fun_Ocomp(X3,X4,X5,X2) ) ).
cnf(i_0_18802_549,axiom,
( X1 != X2
| c_Code__Numeral_Odiv__mod__code__numeral(X1,X3) = c_Code__Numeral_Odiv__mod__code__numeral(X2,X3) ) ).
cnf(i_0_18803_550,axiom,
( X1 != X2
| c_Code__Numeral_Odiv__mod__code__numeral(X3,X1) = c_Code__Numeral_Odiv__mod__code__numeral(X3,X2) ) ).
cnf(i_0_18804_551,axiom,
( X1 != X2
| esk453_2(X1,X3) = esk453_2(X2,X3) ) ).
cnf(i_0_18805_552,axiom,
( X1 != X2
| esk453_2(X3,X1) = esk453_2(X3,X2) ) ).
cnf(i_0_18806_553,axiom,
( X1 != X2
| esk452_2(X1,X3) = esk452_2(X2,X3) ) ).
cnf(i_0_18807_554,axiom,
( X1 != X2
| esk452_2(X3,X1) = esk452_2(X3,X2) ) ).
cnf(i_0_18808_555,axiom,
( X1 != X2
| c_SMT_Oz3div(X1,X3) = c_SMT_Oz3div(X2,X3) ) ).
cnf(i_0_18809_556,axiom,
( X1 != X2
| c_SMT_Oz3div(X3,X1) = c_SMT_Oz3div(X3,X2) ) ).
cnf(i_0_18810_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_18811_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_18812_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_18813_560,axiom,
( X1 != X2
| c_Orderings_Oord_Omax(X1,X3) = c_Orderings_Oord_Omax(X2,X3) ) ).
cnf(i_0_18814_561,axiom,
( X1 != X2
| c_Orderings_Oord_Omax(X3,X1) = c_Orderings_Oord_Omax(X3,X2) ) ).
cnf(i_0_18815_562,axiom,
( X1 != X2
| c_Orderings_Oord_Omin(X1,X3) = c_Orderings_Oord_Omin(X2,X3) ) ).
cnf(i_0_18816_563,axiom,
( X1 != X2
| c_Orderings_Oord_Omin(X3,X1) = c_Orderings_Oord_Omin(X3,X2) ) ).
cnf(i_0_18817_564,axiom,
( X1 != X2
| c_Option_Oset(X1,X3) = c_Option_Oset(X2,X3) ) ).
cnf(i_0_18818_565,axiom,
( X1 != X2
| c_Option_Oset(X3,X1) = c_Option_Oset(X3,X2) ) ).
cnf(i_0_18819_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_18820_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_18821_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_18822_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_18823_570,axiom,
( X1 != X2
| c_Com_Ovname_OGlb(X1) = c_Com_Ovname_OGlb(X2) ) ).
cnf(i_0_18824_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_18825_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_18826_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_18827_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_18828_575,axiom,
( X1 != X2
| c_New__DSequence_Opos__single(X1,X3) = c_New__DSequence_Opos__single(X2,X3) ) ).
cnf(i_0_18829_576,axiom,
( X1 != X2
| c_New__DSequence_Opos__single(X3,X1) = c_New__DSequence_Opos__single(X3,X2) ) ).
cnf(i_0_18830_577,axiom,
( X1 != X2
| c_New__DSequence_Oneg__single(X1,X3) = c_New__DSequence_Oneg__single(X2,X3) ) ).
cnf(i_0_18831_578,axiom,
( X1 != X2
| c_New__DSequence_Oneg__single(X3,X1) = c_New__DSequence_Oneg__single(X3,X2) ) ).
cnf(i_0_18832_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_18833_580,axiom,
( X1 != X2
| c_SMT_Oz3mod(X1,X3) = c_SMT_Oz3mod(X2,X3) ) ).
cnf(i_0_18834_581,axiom,
( X1 != X2
| c_SMT_Oz3mod(X3,X1) = c_SMT_Oz3mod(X3,X2) ) ).
cnf(i_0_18835_582,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__size(X1,X3,X4) = c_Option_Ooption_Ooption__size(X2,X3,X4) ) ).
cnf(i_0_18836_583,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__size(X3,X1,X4) = c_Option_Ooption_Ooption__size(X3,X2,X4) ) ).
cnf(i_0_18837_584,axiom,
( X1 != X2
| c_Option_Ooption_Ooption__size(X3,X4,X1) = c_Option_Ooption_Ooption__size(X3,X4,X2) ) ).
cnf(i_0_18838_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_18839_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_18840_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_18841_588,axiom,
( X1 != X2
| c_Smallcheck_Ofull__small_H(X1,X3,X4) = c_Smallcheck_Ofull__small_H(X2,X3,X4) ) ).
cnf(i_0_18842_589,axiom,
( X1 != X2
| c_Smallcheck_Ofull__small_H(X3,X1,X4) = c_Smallcheck_Ofull__small_H(X3,X2,X4) ) ).
cnf(i_0_18843_590,axiom,
( X1 != X2
| c_Smallcheck_Ofull__small_H(X3,X4,X1) = c_Smallcheck_Ofull__small_H(X3,X4,X2) ) ).
cnf(i_0_18844_591,axiom,
( X1 != X2
| esk448_1(X1) = esk448_1(X2) ) ).
cnf(i_0_18845_592,axiom,
( X1 != X2
| c_Quickcheck_Obeyond(X1,X3) = c_Quickcheck_Obeyond(X2,X3) ) ).
cnf(i_0_18846_593,axiom,
( X1 != X2
| c_Quickcheck_Obeyond(X3,X1) = c_Quickcheck_Obeyond(X3,X2) ) ).
cnf(i_0_18847_594,axiom,
( X1 != X2
| c_Sum__Type_OProjr(X1,X3,X4) = c_Sum__Type_OProjr(X2,X3,X4) ) ).
cnf(i_0_18848_595,axiom,
( X1 != X2
| c_Sum__Type_OProjr(X3,X1,X4) = c_Sum__Type_OProjr(X3,X2,X4) ) ).
cnf(i_0_18849_596,axiom,
( X1 != X2
| c_Sum__Type_OProjr(X3,X4,X1) = c_Sum__Type_OProjr(X3,X4,X2) ) ).
cnf(i_0_18850_597,axiom,
( X1 != X2
| c_Sum__Type_OProjl(X1,X3,X4) = c_Sum__Type_OProjl(X2,X3,X4) ) ).
cnf(i_0_18851_598,axiom,
( X1 != X2
| c_Sum__Type_OProjl(X3,X1,X4) = c_Sum__Type_OProjl(X3,X2,X4) ) ).
cnf(i_0_18852_599,axiom,
( X1 != X2
| c_Sum__Type_OProjl(X3,X4,X1) = c_Sum__Type_OProjl(X3,X4,X2) ) ).
cnf(i_0_18853_600,axiom,
( X1 != X2
| c_Nat_Onat_Onat__size(X1) = c_Nat_Onat_Onat__size(X2) ) ).
cnf(i_0_18854_601,axiom,
( X1 != X2
| c_Random_Oinc__shift(X1,X3) = c_Random_Oinc__shift(X2,X3) ) ).
cnf(i_0_18855_602,axiom,
( X1 != X2
| c_Random_Oinc__shift(X3,X1) = c_Random_Oinc__shift(X3,X2) ) ).
cnf(i_0_18856_603,axiom,
( X1 != X2
| c_Lazy__Sequence_Osingle(X1,X3) = c_Lazy__Sequence_Osingle(X2,X3) ) ).
cnf(i_0_18857_604,axiom,
( X1 != X2
| c_Lazy__Sequence_Osingle(X3,X1) = c_Lazy__Sequence_Osingle(X3,X2) ) ).
cnf(i_0_18858_605,axiom,
( X1 != X2
| c_Lazy__Sequence_Ohb__single(X1,X3) = c_Lazy__Sequence_Ohb__single(X2,X3) ) ).
cnf(i_0_18859_606,axiom,
( X1 != X2
| c_Lazy__Sequence_Ohb__single(X3,X1) = c_Lazy__Sequence_Ohb__single(X3,X2) ) ).
cnf(i_0_18860_607,axiom,
( X1 != X2
| c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).
cnf(i_0_18861_608,axiom,
( X1 != X2
| c_Com_Ovname_Ovname__size(X1) = c_Com_Ovname_Ovname__size(X2) ) ).
cnf(i_0_18862_609,axiom,
( X1 != X2
| c_HOL_Obool_Obool__size(X1) = c_HOL_Obool_Obool__size(X2) ) ).
cnf(i_0_18863_610,axiom,
( X1 != X2
| c_Transitive__Closure_Ortrancl(X1,X3) = c_Transitive__Closure_Ortrancl(X2,X3) ) ).
cnf(i_0_18864_611,axiom,
( X1 != X2
| c_Transitive__Closure_Ortrancl(X3,X1) = c_Transitive__Closure_Ortrancl(X3,X2) ) ).
cnf(i_0_18865_612,axiom,
( X1 != X2
| c_Int_Oring__1__class_Oof__int(X1) = c_Int_Oring__1__class_Oof__int(X2) ) ).
cnf(i_0_18866_613,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_18867_614,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_18868_615,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_18869_616,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_18870_617,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_18871_618,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_18872_619,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_18873_620,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_18874_621,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_18875_622,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_18876_623,axiom,
( X1 != X2
| c_FunDef_Orp__inv__image(X1,X3) = c_FunDef_Orp__inv__image(X2,X3) ) ).
cnf(i_0_18877_624,axiom,
( X1 != X2
| c_FunDef_Orp__inv__image(X3,X1) = c_FunDef_Orp__inv__image(X3,X2) ) ).
cnf(i_0_18878_625,axiom,
( X1 != X2
| c_Map_Omap__add(X1,X3,X4,X5) = c_Map_Omap__add(X2,X3,X4,X5) ) ).
cnf(i_0_18879_626,axiom,
( X1 != X2
| c_Map_Omap__add(X3,X1,X4,X5) = c_Map_Omap__add(X3,X2,X4,X5) ) ).
cnf(i_0_18880_627,axiom,
( X1 != X2
| c_Map_Omap__add(X3,X4,X1,X5) = c_Map_Omap__add(X3,X4,X2,X5) ) ).
cnf(i_0_18881_628,axiom,
( X1 != X2
| c_Map_Omap__add(X3,X4,X5,X1) = c_Map_Omap__add(X3,X4,X5,X2) ) ).
cnf(i_0_18882_629,axiom,
( X1 != X2
| c_Map_Omap__of(X1,X3,X4) = c_Map_Omap__of(X2,X3,X4) ) ).
cnf(i_0_18883_630,axiom,
( X1 != X2
| c_Map_Omap__of(X3,X1,X4) = c_Map_Omap__of(X3,X2,X4) ) ).
cnf(i_0_18884_631,axiom,
( X1 != X2
| c_Map_Omap__of(X3,X4,X1) = c_Map_Omap__of(X3,X4,X2) ) ).
cnf(i_0_18885_632,axiom,
( X1 != X2
| c_List_Ofoldl(X1,X3,X4,X5) = c_List_Ofoldl(X2,X3,X4,X5) ) ).
cnf(i_0_18886_633,axiom,
( X1 != X2
| c_List_Ofoldl(X3,X1,X4,X5) = c_List_Ofoldl(X3,X2,X4,X5) ) ).
cnf(i_0_18887_634,axiom,
( X1 != X2
| c_List_Ofoldl(X3,X4,X1,X5) = c_List_Ofoldl(X3,X4,X2,X5) ) ).
cnf(i_0_18888_635,axiom,
( X1 != X2
| c_List_Ofoldl(X3,X4,X5,X1) = c_List_Ofoldl(X3,X4,X5,X2) ) ).
cnf(i_0_18889_636,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_18890_637,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_18891_638,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_18892_639,axiom,
( X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).
cnf(i_0_18893_640,axiom,
( X1 != X2
| ~ c_Predicate_Oreflp(X1,X3)
| c_Predicate_Oreflp(X2,X3) ) ).
cnf(i_0_18894_641,axiom,
( X1 != X2
| ~ c_Predicate_Oreflp(X3,X1)
| c_Predicate_Oreflp(X3,X2) ) ).
cnf(i_0_18895_642,axiom,
( X1 != X2
| ~ class_Rings_Oordered__comm__semiring(X1)
| class_Rings_Oordered__comm__semiring(X2) ) ).
cnf(i_0_18896_643,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__comm__semiring__strict(X1)
| class_Rings_Olinordered__comm__semiring__strict(X2) ) ).
cnf(i_0_18897_644,axiom,
( X1 != X2
| ~ class_Divides_Oring__div(X1)
| class_Divides_Oring__div(X2) ) ).
cnf(i_0_18898_645,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_18899_646,axiom,
( X1 != X2
| ~ class_Rings_Oordered__cancel__semiring(X1)
| class_Rings_Oordered__cancel__semiring(X2) ) ).
cnf(i_0_18900_647,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring__abs(X1)
| class_Rings_Oordered__ring__abs(X2) ) ).
cnf(i_0_18901_648,axiom,
( X1 != X2
| ~ class_Orderings_Owellorder(X1)
| class_Orderings_Owellorder(X2) ) ).
cnf(i_0_18902_649,axiom,
( X1 != X2
| ~ class_Rings_Oring__1(X1)
| class_Rings_Oring__1(X2) ) ).
cnf(i_0_18903_650,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring__1(X1)
| class_Rings_Ocomm__ring__1(X2) ) ).
cnf(i_0_18904_651,axiom,
( X1 != X2
| ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(X2) ) ).
cnf(i_0_18905_652,axiom,
( X1 != X2
| ~ class_Rings_Odivision__ring(X1)
| class_Rings_Odivision__ring(X2) ) ).
cnf(i_0_18906_653,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring(X1)
| class_Rings_Ocomm__semiring(X2) ) ).
cnf(i_0_18907_654,axiom,
( X1 != X2
| ~ class_Groups_Ominus(X1)
| class_Groups_Ominus(X2) ) ).
cnf(i_0_18908_655,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_18909_656,axiom,
( X1 != X2
| ~ c_Groups_Osemigroup(X1,X3)
| c_Groups_Osemigroup(X2,X3) ) ).
cnf(i_0_18910_657,axiom,
( X1 != X2
| ~ c_Groups_Osemigroup(X3,X1)
| c_Groups_Osemigroup(X3,X2) ) ).
cnf(i_0_18911_658,axiom,
( X1 != X2
| ~ class_Groups_Ogroup__add(X1)
| class_Groups_Ogroup__add(X2) ) ).
cnf(i_0_18912_659,axiom,
( X1 != X2
| ~ c_Nat__Transfer_Otransfer__morphism(X1,X3,X4,X5)
| c_Nat__Transfer_Otransfer__morphism(X2,X3,X4,X5) ) ).
cnf(i_0_18913_660,axiom,
( X1 != X2
| ~ c_Nat__Transfer_Otransfer__morphism(X3,X1,X4,X5)
| c_Nat__Transfer_Otransfer__morphism(X3,X2,X4,X5) ) ).
cnf(i_0_18914_661,axiom,
( X1 != X2
| ~ c_Nat__Transfer_Otransfer__morphism(X3,X4,X1,X5)
| c_Nat__Transfer_Otransfer__morphism(X3,X4,X2,X5) ) ).
cnf(i_0_18915_662,axiom,
( X1 != X2
| ~ c_Nat__Transfer_Otransfer__morphism(X3,X4,X5,X1)
| c_Nat__Transfer_Otransfer__morphism(X3,X4,X5,X2) ) ).
cnf(i_0_18916_663,axiom,
( X1 != X2
| ~ class_Nat_Osemiring__char__0(X1)
| class_Nat_Osemiring__char__0(X2) ) ).
cnf(i_0_18917_664,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__mult(X1)
| class_Groups_Ocomm__monoid__mult(X2) ) ).
cnf(i_0_18918_665,axiom,
( X1 != X2
| ~ c_Nitpick_Owf_H(X1,X3)
| c_Nitpick_Owf_H(X2,X3) ) ).
cnf(i_0_18919_666,axiom,
( X1 != X2
| ~ c_Nitpick_Owf_H(X3,X1)
| c_Nitpick_Owf_H(X3,X2) ) ).
cnf(i_0_18920_667,axiom,
( X1 != X2
| ~ class_Groups_Osgn__if(X1)
| class_Groups_Osgn__if(X2) ) ).
cnf(i_0_18921_668,axiom,
( X1 != X2
| ~ class_Power_Opower(X1)
| class_Power_Opower(X2) ) ).
cnf(i_0_18922_669,axiom,
( X1 != X2
| ~ class_Groups_Oabs__if(X1)
| class_Groups_Oabs__if(X2) ) ).
cnf(i_0_18923_670,axiom,
( X1 != X2
| ~ class_Groups_Ouminus(X1)
| class_Groups_Ouminus(X2) ) ).
cnf(i_0_18924_671,axiom,
( X1 != X2
| ~ c_Big__Operators_Osemilattice__big(X1,X3,X4)
| c_Big__Operators_Osemilattice__big(X2,X3,X4) ) ).
cnf(i_0_18925_672,axiom,
( X1 != X2
| ~ c_Big__Operators_Osemilattice__big(X3,X1,X4)
| c_Big__Operators_Osemilattice__big(X3,X2,X4) ) ).
cnf(i_0_18926_673,axiom,
( X1 != X2
| ~ c_Big__Operators_Osemilattice__big(X3,X4,X1)
| c_Big__Operators_Osemilattice__big(X3,X4,X2) ) ).
cnf(i_0_18927_674,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_18928_675,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_18929_676,axiom,
( X1 != X2
| ~ c_Nitpick_Ounknown(X1)
| c_Nitpick_Ounknown(X2) ) ).
cnf(i_0_18930_677,axiom,
( X1 != X2
| ~ class_Finite__Set_Ofinite(X1)
| class_Finite__Set_Ofinite(X2) ) ).
cnf(i_0_18931_678,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_18932_679,axiom,
( X1 != X2
| ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(X2) ) ).
cnf(i_0_18933_680,axiom,
( X1 != X2
| ~ c_Groups_Ocomm__monoid(X1,X3,X4)
| c_Groups_Ocomm__monoid(X2,X3,X4) ) ).
cnf(i_0_18934_681,axiom,
( X1 != X2
| ~ c_Groups_Ocomm__monoid(X3,X1,X4)
| c_Groups_Ocomm__monoid(X3,X2,X4) ) ).
cnf(i_0_18935_682,axiom,
( X1 != X2
| ~ c_Groups_Ocomm__monoid(X3,X4,X1)
| c_Groups_Ocomm__monoid(X3,X4,X2) ) ).
cnf(i_0_18936_683,axiom,
( X1 != X2
| ~ class_Orderings_Otop(X1)
| class_Orderings_Otop(X2) ) ).
cnf(i_0_18937_684,axiom,
( X1 != X2
| ~ class_Rings_Omult__zero(X1)
| class_Rings_Omult__zero(X2) ) ).
cnf(i_0_18938_685,axiom,
( X1 != X2
| ~ class_Rings_Ozero__neq__one(X1)
| class_Rings_Ozero__neq__one(X2) ) ).
cnf(i_0_18939_686,axiom,
( X1 != X2
| ~ class_Rings_Oring__no__zero__divisors(X1)
| class_Rings_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_18940_687,axiom,
( X1 != X2
| ~ class_Lattices_Obounded__lattice__top(X1)
| class_Lattices_Obounded__lattice__top(X2) ) ).
cnf(i_0_18941_688,axiom,
( X1 != X2
| ~ class_Lattices_Obounded__lattice__bot(X1)
| class_Lattices_Obounded__lattice__bot(X2) ) ).
cnf(i_0_18942_689,axiom,
( X1 != X2
| ~ c_Option_Ois__none(X1,X3)
| c_Option_Ois__none(X2,X3) ) ).
cnf(i_0_18943_690,axiom,
( X1 != X2
| ~ c_Option_Ois__none(X3,X1)
| c_Option_Ois__none(X3,X2) ) ).
cnf(i_0_18944_691,axiom,
( X1 != X2
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| class_Rings_Odivision__ring__inverse__zero(X2) ) ).
cnf(i_0_18945_692,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__semigroup__add(X1)
| class_Groups_Olinordered__ab__semigroup__add(X2) ) ).
cnf(i_0_18946_693,axiom,
( X1 != X2
| ~ c_List_Onat__list(X1)
| c_List_Onat__list(X2) ) ).
cnf(i_0_18947_694,axiom,
( X1 != X2
| ~ class_Lattices_Obounded__lattice(X1)
| class_Lattices_Obounded__lattice(X2) ) ).
cnf(i_0_18948_695,axiom,
( X1 != X2
| ~ class_Groups_Oone(X1)
| class_Groups_Oone(X2) ) ).
cnf(i_0_18949_696,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_18950_697,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_18951_698,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_18952_699,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_18953_700,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_18954_701,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_18955_702,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_18956_703,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_18957_704,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_18958_705,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_18959_706,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_18960_707,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_18961_708,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_18962_709,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_18963_710,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_18964_711,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_18965_712,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_18966_713,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_18967_714,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_18968_715,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_18969_716,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_18970_717,axiom,
( X1 != X2
| ~ c_Natural_Oevaln(X1,X3,X4,X5)
| c_Natural_Oevaln(X2,X3,X4,X5) ) ).
cnf(i_0_18971_718,axiom,
( X1 != X2
| ~ c_Natural_Oevaln(X3,X1,X4,X5)
| c_Natural_Oevaln(X3,X2,X4,X5) ) ).
cnf(i_0_18972_719,axiom,
( X1 != X2
| ~ c_Natural_Oevaln(X3,X4,X1,X5)
| c_Natural_Oevaln(X3,X4,X2,X5) ) ).
cnf(i_0_18973_720,axiom,
( X1 != X2
| ~ c_Natural_Oevaln(X3,X4,X5,X1)
| c_Natural_Oevaln(X3,X4,X5,X2) ) ).
cnf(i_0_18974_721,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_18975_722,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_18976_723,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_18977_724,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_18978_725,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_18979_726,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_18980_727,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_18981_728,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_18982_729,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X1,X3,X4)
| c_Relation_Orefl__on(X2,X3,X4) ) ).
cnf(i_0_18983_730,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X3,X1,X4)
| c_Relation_Orefl__on(X3,X2,X4) ) ).
cnf(i_0_18984_731,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X3,X4,X1)
| c_Relation_Orefl__on(X3,X4,X2) ) ).
cnf(i_0_18985_732,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X1,X3,X4,X5)
| c_Wellfounded_Omax__extp(X2,X3,X4,X5) ) ).
cnf(i_0_18986_733,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X3,X1,X4,X5)
| c_Wellfounded_Omax__extp(X3,X2,X4,X5) ) ).
cnf(i_0_18987_734,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X3,X4,X1,X5)
| c_Wellfounded_Omax__extp(X3,X4,X2,X5) ) ).
cnf(i_0_18988_735,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X3,X4,X5,X1)
| c_Wellfounded_Omax__extp(X3,X4,X5,X2) ) ).
cnf(i_0_18989_736,axiom,
( X1 != X2
| ~ c_List_Olistrelp(X1,X3,X4,X5)
| c_List_Olistrelp(X2,X3,X4,X5) ) ).
cnf(i_0_18990_737,axiom,
( X1 != X2
| ~ c_List_Olistrelp(X3,X1,X4,X5)
| c_List_Olistrelp(X3,X2,X4,X5) ) ).
cnf(i_0_18991_738,axiom,
( X1 != X2
| ~ c_List_Olistrelp(X3,X4,X1,X5)
| c_List_Olistrelp(X3,X4,X2,X5) ) ).
cnf(i_0_18992_739,axiom,
( X1 != X2
| ~ c_List_Olistrelp(X3,X4,X5,X1)
| c_List_Olistrelp(X3,X4,X5,X2) ) ).
cnf(i_0_18993_740,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequivp(X1,X3)
| c_Equiv__Relations_Oequivp(X2,X3) ) ).
cnf(i_0_18994_741,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequivp(X3,X1)
| c_Equiv__Relations_Oequivp(X3,X2) ) ).
cnf(i_0_18995_742,axiom,
( X1 != X2
| ~ c_Wellfounded_Owf(X1,X3)
| c_Wellfounded_Owf(X2,X3) ) ).
cnf(i_0_18996_743,axiom,
( X1 != X2
| ~ c_Wellfounded_Owf(X3,X1)
| c_Wellfounded_Owf(X3,X2) ) ).
cnf(i_0_18997_744,axiom,
( X1 != X2
| ~ c_Wellfounded_OwfP(X1,X3)
| c_Wellfounded_OwfP(X2,X3) ) ).
cnf(i_0_18998_745,axiom,
( X1 != X2
| ~ c_Wellfounded_OwfP(X3,X1)
| c_Wellfounded_OwfP(X3,X2) ) ).
cnf(i_0_18999_746,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofun__left__comm(X1,X3,X4)
| c_Finite__Set_Ofun__left__comm(X2,X3,X4) ) ).
cnf(i_0_19000_747,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofun__left__comm(X3,X1,X4)
| c_Finite__Set_Ofun__left__comm(X3,X2,X4) ) ).
cnf(i_0_19001_748,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofun__left__comm(X3,X4,X1)
| c_Finite__Set_Ofun__left__comm(X3,X4,X2) ) ).
cnf(i_0_19002_749,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_19003_750,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequiv(X1,X3,X4)
| c_Equiv__Relations_Oequiv(X2,X3,X4) ) ).
cnf(i_0_19004_751,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequiv(X3,X1,X4)
| c_Equiv__Relations_Oequiv(X3,X2,X4) ) ).
cnf(i_0_19005_752,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequiv(X3,X4,X1)
| c_Equiv__Relations_Oequiv(X3,X4,X2) ) ).
cnf(i_0_19006_753,axiom,
( X1 != X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| class_Complete__Lattice_Ocomplete__lattice(X2) ) ).
cnf(i_0_19007_754,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add(X1)
| class_Groups_Oordered__ab__group__add(X2) ) ).
cnf(i_0_19008_755,axiom,
( X1 != X2
| ~ class_Smallcheck_Osmall(X1)
| class_Smallcheck_Osmall(X2) ) ).
cnf(i_0_19009_756,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_19010_757,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Ostrict__mono(X1,X3,X4,X5)
| c_Orderings_Oorder_Ostrict__mono(X2,X3,X4,X5) ) ).
cnf(i_0_19011_758,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Ostrict__mono(X3,X1,X4,X5)
| c_Orderings_Oorder_Ostrict__mono(X3,X2,X4,X5) ) ).
cnf(i_0_19012_759,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Ostrict__mono(X3,X4,X1,X5)
| c_Orderings_Oorder_Ostrict__mono(X3,X4,X2,X5) ) ).
cnf(i_0_19013_760,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Ostrict__mono(X3,X4,X5,X1)
| c_Orderings_Oorder_Ostrict__mono(X3,X4,X5,X2) ) ).
cnf(i_0_19014_761,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Omono(X1,X3,X4,X5)
| c_Orderings_Oorder_Omono(X2,X3,X4,X5) ) ).
cnf(i_0_19015_762,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Omono(X3,X1,X4,X5)
| c_Orderings_Oorder_Omono(X3,X2,X4,X5) ) ).
cnf(i_0_19016_763,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Omono(X3,X4,X1,X5)
| c_Orderings_Oorder_Omono(X3,X4,X2,X5) ) ).
cnf(i_0_19017_764,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Omono(X3,X4,X5,X1)
| c_Orderings_Oorder_Omono(X3,X4,X5,X2) ) ).
cnf(i_0_19018_765,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__mult(X1)
| class_Groups_Omonoid__mult(X2) ) ).
cnf(i_0_19019_766,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__mult(X1)
| class_Groups_Oab__semigroup__mult(X2) ) ).
cnf(i_0_19020_767,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_19021_768,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_19022_769,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__0(X1)
| class_Rings_Osemiring__0(X2) ) ).
cnf(i_0_19023_770,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_19024_771,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one__idem(X1,X3,X4)
| c_Finite__Set_Ofolding__one__idem(X2,X3,X4) ) ).
cnf(i_0_19025_772,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one__idem(X3,X1,X4)
| c_Finite__Set_Ofolding__one__idem(X3,X2,X4) ) ).
cnf(i_0_19026_773,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one__idem(X3,X4,X1)
| c_Finite__Set_Ofolding__one__idem(X3,X4,X2) ) ).
cnf(i_0_19027_774,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__1(X1)
| class_Rings_Osemiring__1(X2) ) ).
cnf(i_0_19028_775,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one(X1,X3,X4)
| c_Finite__Set_Ofolding__one(X2,X3,X4) ) ).
cnf(i_0_19029_776,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one(X3,X1,X4)
| c_Finite__Set_Ofolding__one(X3,X2,X4) ) ).
cnf(i_0_19030_777,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one(X3,X4,X1)
| c_Finite__Set_Ofolding__one(X3,X4,X2) ) ).
cnf(i_0_19031_778,axiom,
( X1 != X2
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| class_Fields_Olinordered__field__inverse__zero(X2) ) ).
cnf(i_0_19032_779,axiom,
( X1 != X2
| ~ c_FunDef_Oreduction__pair(X1,X3)
| c_FunDef_Oreduction__pair(X2,X3) ) ).
cnf(i_0_19033_780,axiom,
( X1 != X2
| ~ c_FunDef_Oreduction__pair(X3,X1)
| c_FunDef_Oreduction__pair(X3,X2) ) ).
cnf(i_0_19034_781,axiom,
( X1 != X2
| ~ c_List_Olinorder__class_Osorted(X1,X3)
| c_List_Olinorder__class_Osorted(X2,X3) ) ).
cnf(i_0_19035_782,axiom,
( X1 != X2
| ~ c_List_Olinorder__class_Osorted(X3,X1)
| c_List_Olinorder__class_Osorted(X3,X2) ) ).
cnf(i_0_19036_783,axiom,
( X1 != X2
| ~ c_Nat__Transfer_Ois__nat(X1)
| c_Nat__Transfer_Ois__nat(X2) ) ).
cnf(i_0_19037_784,axiom,
( X1 != X2
| ~ c_Nitpick_Oless__eq__frac(X1,X3,X4)
| c_Nitpick_Oless__eq__frac(X2,X3,X4) ) ).
cnf(i_0_19038_785,axiom,
( X1 != X2
| ~ c_Nitpick_Oless__eq__frac(X3,X1,X4)
| c_Nitpick_Oless__eq__frac(X3,X2,X4) ) ).
cnf(i_0_19039_786,axiom,
( X1 != X2
| ~ c_Nitpick_Oless__eq__frac(X3,X4,X1)
| c_Nitpick_Oless__eq__frac(X3,X4,X2) ) ).
cnf(i_0_19040_787,axiom,
( X1 != X2
| ~ c_Nitpick_Oless__frac(X1,X3,X4)
| c_Nitpick_Oless__frac(X2,X3,X4) ) ).
cnf(i_0_19041_788,axiom,
( X1 != X2
| ~ c_Nitpick_Oless__frac(X3,X1,X4)
| c_Nitpick_Oless__frac(X3,X2,X4) ) ).
cnf(i_0_19042_789,axiom,
( X1 != X2
| ~ c_Nitpick_Oless__frac(X3,X4,X1)
| c_Nitpick_Oless__frac(X3,X4,X2) ) ).
cnf(i_0_19043_790,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X1,X3,X4,X5)
| c_Fun_Oinj__on(X2,X3,X4,X5) ) ).
cnf(i_0_19044_791,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X1,X4,X5)
| c_Fun_Oinj__on(X3,X2,X4,X5) ) ).
cnf(i_0_19045_792,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X1,X5)
| c_Fun_Oinj__on(X3,X4,X2,X5) ) ).
cnf(i_0_19046_793,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X1)
| c_Fun_Oinj__on(X3,X4,X5,X2) ) ).
cnf(i_0_19047_794,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_19048_795,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring(X1)
| class_Rings_Oordered__ring(X2) ) ).
cnf(i_0_19049_796,axiom,
( X1 != X2
| ~ class_Groups_Oab__group__add(X1)
| class_Groups_Oab__group__add(X2) ) ).
cnf(i_0_19050_797,axiom,
( X1 != X2
| ~ class_Rings_Oinverse(X1)
| class_Rings_Oinverse(X2) ) ).
cnf(i_0_19051_798,axiom,
( X1 != X2
| ~ class_Fields_Ofield(X1)
| class_Fields_Ofield(X2) ) ).
cnf(i_0_19052_799,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_19053_800,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_19054_801,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_19055_802,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_19056_803,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_19057_804,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_19058_805,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| class_Groups_Oordered__ab__group__add__abs(X2) ) ).
cnf(i_0_19059_806,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_19060_807,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_19061_808,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_19062_809,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_19063_810,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_19064_811,axiom,
( X1 != X2
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| class_Rings_Oring__1__no__zero__divisors(X2) ) ).
cnf(i_0_19065_812,axiom,
( X1 != X2
| ~ c_Nat__Transfer_Onat__set(X1)
| c_Nat__Transfer_Onat__set(X2) ) ).
cnf(i_0_19066_813,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_19067_814,axiom,
( X1 != X2
| ~ class_Fields_Ofield__inverse__zero(X1)
| class_Fields_Ofield__inverse__zero(X2) ) ).
cnf(i_0_19068_815,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_19069_816,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_19070_817,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_19071_818,axiom,
( X1 != X2
| ~ class_Lattices_Osemilattice__sup(X1)
| class_Lattices_Osemilattice__sup(X2) ) ).
cnf(i_0_19072_819,axiom,
( X1 != X2
| ~ c_Int_Oiszero(X1,X3)
| c_Int_Oiszero(X2,X3) ) ).
cnf(i_0_19073_820,axiom,
( X1 != X2
| ~ c_Int_Oiszero(X3,X1)
| c_Int_Oiszero(X3,X2) ) ).
cnf(i_0_19074_821,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X1,X3,X4)
| c_Relation_Ototal__on(X2,X3,X4) ) ).
cnf(i_0_19075_822,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X3,X1,X4)
| c_Relation_Ototal__on(X3,X2,X4) ) ).
cnf(i_0_19076_823,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X3,X4,X1)
| c_Relation_Ototal__on(X3,X4,X2) ) ).
cnf(i_0_19077_824,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X1,X3,X4)
| c_Relation_Osingle__valued(X2,X3,X4) ) ).
cnf(i_0_19078_825,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X3,X1,X4)
| c_Relation_Osingle__valued(X3,X2,X4) ) ).
cnf(i_0_19079_826,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X3,X4,X1)
| c_Relation_Osingle__valued(X3,X4,X2) ) ).
cnf(i_0_19080_827,axiom,
( X1 != X2
| ~ class_Int_Onumber(X1)
| class_Int_Onumber(X2) ) ).
cnf(i_0_19081_828,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Otriple__valid(X1,X3,X4)
| c_Hoare__Mirabelle_Otriple__valid(X2,X3,X4) ) ).
cnf(i_0_19082_829,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Otriple__valid(X3,X1,X4)
| c_Hoare__Mirabelle_Otriple__valid(X3,X2,X4) ) ).
cnf(i_0_19083_830,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Otriple__valid(X3,X4,X1)
| c_Hoare__Mirabelle_Otriple__valid(X3,X4,X2) ) ).
cnf(i_0_19084_831,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring(X1)
| class_Rings_Ocomm__ring(X2) ) ).
cnf(i_0_19085_832,axiom,
( X1 != X2
| ~ class_Rings_Odvd(X1)
| class_Rings_Odvd(X2) ) ).
cnf(i_0_19086_833,axiom,
( X1 != X2
| ~ class_Lattices_Odistrib__lattice(X1)
| class_Lattices_Odistrib__lattice(X2) ) ).
cnf(i_0_19087_834,axiom,
( X1 != X2
| ~ class_Divides_Osemiring__div(X1)
| class_Divides_Osemiring__div(X2) ) ).
cnf(i_0_19088_835,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring__strict(X1)
| class_Rings_Olinordered__ring__strict(X2) ) ).
cnf(i_0_19089_836,axiom,
( X1 != X2
| ~ class_Lattices_Olattice(X1)
| class_Lattices_Olattice(X2) ) ).
cnf(i_0_19090_837,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring(X1)
| class_Rings_Olinordered__ring(X2) ) ).
cnf(i_0_19091_838,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding(X1,X3,X4,X5)
| c_Finite__Set_Ofolding(X2,X3,X4,X5) ) ).
cnf(i_0_19092_839,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding(X3,X1,X4,X5)
| c_Finite__Set_Ofolding(X3,X2,X4,X5) ) ).
cnf(i_0_19093_840,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding(X3,X4,X1,X5)
| c_Finite__Set_Ofolding(X3,X4,X2,X5) ) ).
cnf(i_0_19094_841,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding(X3,X4,X5,X1)
| c_Finite__Set_Ofolding(X3,X4,X5,X2) ) ).
cnf(i_0_19095_842,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1(X1)
| class_Rings_Olinordered__semiring__1(X2) ) ).
cnf(i_0_19096_843,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1__strict(X1)
| class_Rings_Olinordered__semiring__1__strict(X2) ) ).
cnf(i_0_19097_844,axiom,
( X1 != X2
| ~ class_Lattices_Osemilattice__inf(X1)
| class_Lattices_Osemilattice__inf(X2) ) ).
cnf(i_0_19098_845,axiom,
( X1 != X2
| ~ class_Fields_Olinordered__field(X1)
| class_Fields_Olinordered__field(X2) ) ).
cnf(i_0_19099_846,axiom,
( X1 != X2
| ~ c_Wellfounded_Oacyclic(X1,X3)
| c_Wellfounded_Oacyclic(X2,X3) ) ).
cnf(i_0_19100_847,axiom,
( X1 != X2
| ~ c_Wellfounded_Oacyclic(X3,X1)
| c_Wellfounded_Oacyclic(X3,X2) ) ).
cnf(i_0_19101_848,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X4)
| c_Hoare__Mirabelle_Ohoare__derivs(X2,X3,X4) ) ).
cnf(i_0_19102_849,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X1,X4)
| c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X4) ) ).
cnf(i_0_19103_850,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X1)
| c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X2) ) ).
cnf(i_0_19104_851,axiom,
( X1 != X2
| ~ class_Lattices_Oab__semigroup__idem__mult(X1)
| class_Lattices_Oab__semigroup__idem__mult(X2) ) ).
cnf(i_0_19105_852,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X1,X3)
| c_Nitpick_Orefl_H(X2,X3) ) ).
cnf(i_0_19106_853,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X3,X1)
| c_Nitpick_Orefl_H(X3,X2) ) ).
cnf(i_0_19107_854,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__idem(X1,X3,X4,X5)
| c_Finite__Set_Ofolding__idem(X2,X3,X4,X5) ) ).
cnf(i_0_19108_855,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__idem(X3,X1,X4,X5)
| c_Finite__Set_Ofolding__idem(X3,X2,X4,X5) ) ).
cnf(i_0_19109_856,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__idem(X3,X4,X1,X5)
| c_Finite__Set_Ofolding__idem(X3,X4,X2,X5) ) ).
cnf(i_0_19110_857,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__idem(X3,X4,X5,X1)
| c_Finite__Set_Ofolding__idem(X3,X4,X5,X2) ) ).
cnf(i_0_19111_858,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_19112_859,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_19113_860,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_19114_861,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_19115_862,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_19116_863,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Ohoare__valids(X1,X3,X4)
| c_Hoare__Mirabelle_Ohoare__valids(X2,X3,X4) ) ).
cnf(i_0_19117_864,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Ohoare__valids(X3,X1,X4)
| c_Hoare__Mirabelle_Ohoare__valids(X3,X2,X4) ) ).
cnf(i_0_19118_865,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Ohoare__valids(X3,X4,X1)
| c_Hoare__Mirabelle_Ohoare__valids(X3,X4,X2) ) ).
cnf(i_0_19119_866,axiom,
( X1 != X2
| ~ class_Rings_Ono__zero__divisors(X1)
| class_Rings_Ono__zero__divisors(X2) ) ).
cnf(i_0_19120_867,axiom,
( X1 != X2
| ~ c_Typedef_Otype__definition(X1,X3,X4,X5,X6)
| c_Typedef_Otype__definition(X2,X3,X4,X5,X6) ) ).
cnf(i_0_19121_868,axiom,
( X1 != X2
| ~ c_Typedef_Otype__definition(X3,X1,X4,X5,X6)
| c_Typedef_Otype__definition(X3,X2,X4,X5,X6) ) ).
cnf(i_0_19122_869,axiom,
( X1 != X2
| ~ c_Typedef_Otype__definition(X3,X4,X1,X5,X6)
| c_Typedef_Otype__definition(X3,X4,X2,X5,X6) ) ).
cnf(i_0_19123_870,axiom,
( X1 != X2
| ~ c_Typedef_Otype__definition(X3,X4,X5,X1,X6)
| c_Typedef_Otype__definition(X3,X4,X5,X2,X6) ) ).
cnf(i_0_19124_871,axiom,
( X1 != X2
| ~ c_Typedef_Otype__definition(X3,X4,X5,X6,X1)
| c_Typedef_Otype__definition(X3,X4,X5,X6,X2) ) ).
cnf(i_0_19125_872,axiom,
( X1 != X2
| ~ class_Rings_Oring(X1)
| class_Rings_Oring(X2) ) ).
cnf(i_0_19126_873,axiom,
( X1 != X2
| ~ class_Rings_Osemiring(X1)
| class_Rings_Osemiring(X2) ) ).
cnf(i_0_19127_874,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X1,X3,X4,X5)
| c_Equiv__Relations_Ocongruent(X2,X3,X4,X5) ) ).
cnf(i_0_19128_875,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X3,X1,X4,X5)
| c_Equiv__Relations_Ocongruent(X3,X2,X4,X5) ) ).
cnf(i_0_19129_876,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X3,X4,X1,X5)
| c_Equiv__Relations_Ocongruent(X3,X4,X2,X5) ) ).
cnf(i_0_19130_877,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X3,X4,X5,X1)
| c_Equiv__Relations_Ocongruent(X3,X4,X5,X2) ) ).
cnf(i_0_19131_878,axiom,
( X1 != X2
| ~ class_Groups_Osemigroup__add(X1)
| class_Groups_Osemigroup__add(X2) ) ).
cnf(i_0_19132_879,axiom,
( X1 != X2
| ~ c_Relation_Oirrefl(X1,X3)
| c_Relation_Oirrefl(X2,X3) ) ).
cnf(i_0_19133_880,axiom,
( X1 != X2
| ~ c_Relation_Oirrefl(X3,X1)
| c_Relation_Oirrefl(X3,X2) ) ).
cnf(i_0_19134_881,axiom,
( X1 != X2
| ~ epred2_3(X1,X3,X4)
| epred2_3(X2,X3,X4) ) ).
cnf(i_0_19135_882,axiom,
( X1 != X2
| ~ epred2_3(X3,X1,X4)
| epred2_3(X3,X2,X4) ) ).
cnf(i_0_19136_883,axiom,
( X1 != X2
| ~ epred2_3(X3,X4,X1)
| epred2_3(X3,X4,X2) ) ).
cnf(i_0_19137_884,axiom,
( X1 != X2
| ~ epred1_3(X1,X3,X4)
| epred1_3(X2,X3,X4) ) ).
cnf(i_0_19138_885,axiom,
( X1 != X2
| ~ epred1_3(X3,X1,X4)
| epred1_3(X3,X2,X4) ) ).
cnf(i_0_19139_886,axiom,
( X1 != X2
| ~ epred1_3(X3,X4,X1)
| epred1_3(X3,X4,X2) ) ).
cnf(i_0_19140_887,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_19141_888,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_19142_889,axiom,
( X1 != X2
| ~ class_Rings_Oordered__semiring(X1)
| class_Rings_Oordered__semiring(X2) ) ).
cnf(i_0_19143_890,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__strict(X1)
| class_Rings_Olinordered__semiring__strict(X2) ) ).
cnf(i_0_19144_891,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring(X1)
| class_Rings_Olinordered__semiring(X2) ) ).
cnf(i_0_19145_892,axiom,
( X1 != X2
| ~ class_Rings_Oidom(X1)
| class_Rings_Oidom(X2) ) ).
cnf(i_0_19146,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),esk169_7(X4,X4,X6,X5,X3,X2,X1)),esk170_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,[],[11062]) ).
cnf(i_0_19147,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,[],[11075]) ).
cnf(i_0_19148,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),esk265_8(X6,X7,hAPP(c_Set_Oimage(X1,X2,X3),X4),X4,X3,X2,X1,X5)),X4)) ),
inference(equality_inference,[],[11076]) ).
cnf(i_0_19149,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)),esk443_4(X3,X2,X2,X1))) ),
inference(equality_inference,[],[11098]) ).
cnf(i_0_19150,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),esk170_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,[],[11147]) ).
cnf(i_0_19151,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),esk169_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,[],[11148]) ).
cnf(i_0_19152,plain,
X1 = X1,
inference(equality_inference,[],[11187]) ).
cnf(i_0_19153,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,esk169_7(X1,X1,X6,X5,X4,X3,X2)) = hAPP(X6,esk170_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,[],[11200]) ).
cnf(i_0_19154,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,esk253_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,[],[11251]) ).
cnf(i_0_19155,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),esk253_6(X5,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X3),X4,X3,X2,X1)),X3)) ),
inference(equality_inference,[],[11321]) ).
cnf(i_0_19156,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),esk491_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,[],[11331]) ).
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_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),esk455_4(X3,X2,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X2),esk455_4(X3,X2,X2,X1)))),X3)) ),
inference(equality_inference,[],[11342]) ).
cnf(i_0_19158,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,[],[11384]) ).
cnf(i_0_19159,plain,
hAPP(X1,hAPP(c_Product__Type_Osnd(X2,X3),X4)) = hAPP(X1,hAPP(c_Product__Type_Osnd(X2,X3),X4)),
inference(equality_inference,[],[11391]) ).
cnf(i_0_19160,plain,
hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),X4)) = hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),X4)),
inference(equality_inference,[],[11392]) ).
cnf(i_0_19161,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,[],[11421]) ).
cnf(i_0_19162,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,[],[11474]) ).
cnf(i_0_19163,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,[],[11475]) ).
cnf(i_0_19164,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,[],[11549]) ).
cnf(i_0_19165,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,[],[11552]) ).
cnf(i_0_19166,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,[],[11645]) ).
cnf(i_0_19167,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,[],[11671]) ).
cnf(i_0_19168,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,[],[11695]) ).
cnf(i_0_19169,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,[],[11710]) ).
cnf(i_0_19170,plain,
( hAPP(hAPP(c_List_Oappend(X1),esk461_5(X2,X3,X2,X3,X1)),X2) = X2
| X2 = hAPP(hAPP(c_List_Oappend(X1),esk462_5(X2,X3,X2,X3,X1)),X2) ),
inference(equality_inference,[],[11745]) ).
cnf(i_0_19171,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,esk197_4(X4,X1,X2,hAPP(c_Set_Oimage(X1,X2,X3),X4))),hAPP(c_Set_Oimage(X1,X2,X3),X4))),X4)) ),
inference(equality_inference,[],[11762]) ).
cnf(i_0_19172,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,[],[11792]) ).
cnf(i_0_19173,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,[],[11807]) ).
cnf(i_0_19174,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,[],[11809]) ).
cnf(i_0_19175,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,[],[11810]) ).
cnf(i_0_19176,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,[],[11811]) ).
cnf(i_0_19177,plain,
hAPP(hAPP(c_List_Omap(X1,X2),X3),X4) = hAPP(hAPP(c_List_Omap(X1,X2),X3),X4),
inference(equality_inference,[],[11845]) ).
cnf(i_0_19178,plain,
( hAPP(hAPP(c_List_Oappend(X1),X2),esk462_5(X3,X2,X3,X2,X1)) = X2
| hAPP(hAPP(c_List_Oappend(X1),esk461_5(X3,X2,X3,X2,X1)),X3) = X3 ),
inference(equality_inference,[],[11868]) ).
cnf(i_0_19179,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),X1),esk461_5(X3,X1,X3,X1,X2))
| X3 = hAPP(hAPP(c_List_Oappend(X2),esk462_5(X3,X1,X3,X1,X2)),X3) ),
inference(equality_inference,[],[11869]) ).
cnf(i_0_19180,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,[],[11900]) ).
cnf(i_0_19181,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,[],[11904]) ).
cnf(i_0_19182,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,[],[11905]) ).
cnf(i_0_19183,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,[],[11906]) ).
cnf(i_0_19184,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,[],[11907]) ).
cnf(i_0_19185,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,[],[11908]) ).
cnf(i_0_19186,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,[],[11928]) ).
cnf(i_0_19187,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,[],[11971]) ).
cnf(i_0_19188,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,[],[11972]) ).
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_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,[],[11978]) ).
cnf(i_0_19190,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,[],[12036]) ).
cnf(i_0_19191,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,[],[12045]) ).
cnf(i_0_19192,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,[],[12047]) ).
cnf(i_0_19193,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,[],[12052]) ).
cnf(i_0_19194,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,[],[12053]) ).
cnf(i_0_19195,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,[],[12054]) ).
cnf(i_0_19196,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)),esk267_5(X4,X3,X1,X1,X2))) ),
inference(equality_inference,[],[12065]) ).
cnf(i_0_19197,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)),esk261_5(X4,X3,X1,X1,X2))) ),
inference(equality_inference,[],[12066]) ).
cnf(i_0_19198,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),X1),esk461_5(X3,X1,X3,X1,X2))
| hAPP(hAPP(c_List_Oappend(X2),X1),esk462_5(X3,X1,X3,X1,X2)) = X1 ),
inference(equality_inference,[],[12070]) ).
cnf(i_0_19199,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)),esk443_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,[],[12073]) ).
cnf(i_0_19200,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,[],[12156]) ).
cnf(i_0_19201,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,[],[12159]) ).
cnf(i_0_19202,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),esk455_4(X3,X2,X2,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))) ),
inference(equality_inference,[],[12195]) ).
cnf(i_0_19203,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,[],[12200]) ).
cnf(i_0_19204,plain,
X1 = X1,
inference(equality_inference,[],[12218]) ).
cnf(i_0_19205,plain,
X1 = X1,
inference(equality_inference,[],[12219]) ).
cnf(i_0_19206,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,[],[12258]) ).
cnf(i_0_19207,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,[],[12261]) ).
cnf(i_0_19208,plain,
( hAPP(c_Map_Omap__of(X1,X1,hAPP(hAPP(c_List_Ozip(X1,X1),X2),X2)),X3) = hAPP(c_Option_Ooption_OSome(X1),esk442_5(X3,X2,X1,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2))) ),
inference(equality_inference,[],[12327]) ).
cnf(i_0_19209,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,[],[12344]) ).
cnf(i_0_19210,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,[],[12353]) ).
cnf(i_0_19211,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,[],[12398]) ).
cnf(i_0_19212,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,[],[12399]) ).
cnf(i_0_19213,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,[],[12425]) ).
cnf(i_0_19214,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),esk210_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,[],[12548]) ).
cnf(i_0_19215,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),esk208_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,[],[12549]) ).
cnf(i_0_19216,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,[],[12578]) ).
cnf(i_0_19217,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,[],[12579]) ).
cnf(i_0_19218,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,[],[12586]) ).
cnf(i_0_19219,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,[],[12588]) ).
cnf(i_0_19220,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,[],[12621]) ).
cnf(i_0_19221,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,[],[12632]) ).
cnf(i_0_19222,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),esk247_4(c_Nat_OSuc,X2,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)) ),
inference(equality_inference,[],[12634]) ).
cnf(i_0_19223,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),esk211_4(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),X2,X1)),X3)) ),
inference(equality_inference,[],[12636]) ).
cnf(i_0_19224,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),esk209_4(X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2),X2,X1)),X3)) ),
inference(equality_inference,[],[12637]) ).
cnf(i_0_19225,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,[],[12677]) ).
cnf(i_0_19226,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,[],[12689]) ).
cnf(i_0_19227,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,[],[12713]) ).
cnf(i_0_19228,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,[],[12739]) ).
cnf(i_0_19229,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,[],[12748]) ).
cnf(i_0_19230,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,[],[12749]) ).
cnf(i_0_19231,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,[],[12759]) ).
cnf(i_0_19232,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,[],[12802]) ).
cnf(i_0_19233,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,[],[12803]) ).
cnf(i_0_19234,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,[],[12865]) ).
cnf(i_0_19235,plain,
( X1 = esk268_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,[],[12871]) ).
cnf(i_0_19236,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,[],[12902]) ).
cnf(i_0_19237,plain,
( X1 = X1
| ~ c_Typedef_Otype__definition(X2,X3,X4,X5,X6) ),
inference(equality_inference,[],[12909]) ).
cnf(i_0_19238,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,[],[12913]) ).
cnf(i_0_19239,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),esk209_4(X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2),X2,X1)),esk208_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,[],[12918]) ).
cnf(i_0_19240,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),esk211_4(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),X2,X1)),esk210_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,[],[12919]) ).
cnf(i_0_19241,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,[],[12934]) ).
cnf(i_0_19242,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,[],[12935]) ).
cnf(i_0_19243,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,[],[12943]) ).
cnf(i_0_19244,plain,
( X1 = X1
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),esk441_3(X2,X1,X1)),hAPP(c_List_Oset(tc_prod(X2,X2)),hAPP(hAPP(c_List_Ozip(X2,X2),X1),X1)))) ),
inference(equality_inference,[],[12945]) ).
cnf(i_0_19245,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,[],[12986]) ).
cnf(i_0_19246,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,[],[12987]) ).
cnf(i_0_19247,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,[],[13004]) ).
cnf(i_0_19248,plain,
hAPP(X1,hAPP(X2,X3)) = hAPP(X1,hAPP(X2,X3)),
inference(equality_inference,[],[13086]) ).
cnf(i_0_19249,plain,
hAPP(c_Fun_Oid(X1),hAPP(X2,X3)) = hAPP(X2,X3),
inference(equality_inference,[],[13091]) ).
cnf(i_0_19250,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,[],[13099]) ).
cnf(i_0_19251,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,[],[13120]) ).
cnf(i_0_19252,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,[],[13121]) ).
cnf(i_0_19253,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,[],[13122]) ).
cnf(i_0_19254,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,[],[13254]) ).
cnf(i_0_19255,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,[],[13310]) ).
cnf(i_0_19256,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,[],[13333]) ).
cnf(i_0_19257,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,[],[13352]) ).
cnf(i_0_19258,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,[],[13372]) ).
cnf(i_0_19259,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,[],[13446]) ).
cnf(i_0_19260,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,[],[13475]) ).
cnf(i_0_19261,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,[],[13501]) ).
cnf(i_0_19262,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,[],[13556]) ).
cnf(i_0_19263,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,[],[13577]) ).
cnf(i_0_19264,plain,
( X1 = X1
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2,X2,tc_HOL_Obool),c_fequal),esk441_3(X2,X1,X1))) ),
inference(equality_inference,[],[13592]) ).
cnf(i_0_19265,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,[],[13652]) ).
cnf(i_0_19266,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,[],[13655]) ).
cnf(i_0_19267,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,[],[13675]) ).
cnf(i_0_19268,plain,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X2 = X3
| X4 = X4 ),
inference(equality_inference,[],[13699]) ).
cnf(i_0_19269,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,[],[13739]) ).
cnf(i_0_19270,plain,
X1 = X1,
inference(equality_inference,[],[13750]) ).
cnf(i_0_19271,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,[],[13772]) ).
cnf(i_0_19272,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,[],[13792]) ).
cnf(i_0_19273,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,[],[13794]) ).
cnf(i_0_19274,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,[],[13820]) ).
cnf(i_0_19275,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,[],[13837]) ).
cnf(i_0_19276,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,[],[13898]) ).
cnf(i_0_19277,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,[],[13906]) ).
cnf(i_0_19278,plain,
( X1 = X1
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X4)) ),
inference(equality_inference,[],[13950]) ).
cnf(i_0_19279,plain,
( c_Fun_Oinj__on(X1,X2,esk197_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,[],[14004]) ).
cnf(i_0_19280,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,[],[14007]) ).
cnf(i_0_19281,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,[],[14008]) ).
cnf(i_0_19282,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,[],[14054]) ).
cnf(i_0_19283,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,[],[14055]) ).
cnf(i_0_19284,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,[],[14119]) ).
cnf(i_0_19285,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,[],[14129]) ).
cnf(i_0_19286,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,[],[14130]) ).
cnf(i_0_19287,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,[],[14144]) ).
cnf(i_0_19288,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,[],[14167]) ).
cnf(i_0_19289,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,[],[14172]) ).
cnf(i_0_19290,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,[],[14200]) ).
cnf(i_0_19291,plain,
X1 = X1,
inference(equality_inference,[],[14203]) ).
cnf(i_0_19292,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,[],[14240]) ).
cnf(i_0_19293,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,[],[14256]) ).
cnf(i_0_19294,plain,
( X1 = X1
| ~ c_Fun_Oinj__on(X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
inference(equality_inference,[],[14288]) ).
cnf(i_0_19295,plain,
hAPP(X1,hAPP(X2,X3)) = hAPP(hAPP(c_Fun_Ocomp(X4,X5,X6,X1),X2),X3),
inference(equality_inference,[],[14292]) ).
cnf(i_0_19296,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,[],[14336]) ).
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__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,[],[14342]) ).
cnf(i_0_19298,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,[],[14360]) ).
cnf(i_0_19299,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,[],[14361]) ).
cnf(i_0_19300,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,[],[14374]) ).
cnf(i_0_19301,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,[],[14376]) ).
cnf(i_0_19302,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,[],[14377]) ).
cnf(i_0_19303,plain,
( X1 = X2
| X1 = X1 ),
inference(equality_inference,[],[14378]) ).
cnf(i_0_19304,plain,
( X1 = X2
| X1 = X1 ),
inference(equality_inference,[],[14379]) ).
cnf(i_0_19305,plain,
( X1 = X2
| X2 = X2 ),
inference(equality_inference,[],[14380]) ).
cnf(i_0_19306,plain,
( X1 = X2
| X2 = X2 ),
inference(equality_inference,[],[14381]) ).
cnf(i_0_19307,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,[],[14385]) ).
cnf(i_0_19308,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,[],[14448]) ).
cnf(i_0_19309,plain,
X1 = X1,
inference(equality_inference,[],[14495]) ).
cnf(i_0_19310,plain,
X1 = X1,
inference(equality_inference,[],[14496]) ).
cnf(i_0_19311,plain,
X1 = X1,
inference(equality_inference,[],[14497]) ).
cnf(i_0_19312,plain,
X1 = X1,
inference(equality_inference,[],[14498]) ).
cnf(i_0_19313,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),esk470_2(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_List_Oset(tc_Nat_Onat),X1))) ),
inference(equality_inference,[],[14501]) ).
cnf(i_0_19314,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,[],[14502]) ).
cnf(i_0_19315,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,[],[14505]) ).
cnf(i_0_19316,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,[],[14514]) ).
cnf(i_0_19317,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,[],[14518]) ).
cnf(i_0_19318,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,[],[14523]) ).
cnf(i_0_19319,plain,
( X1 = X1
| ~ c_Fun_Oinj__on(X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
inference(equality_inference,[],[14533]) ).
cnf(i_0_19320,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,[],[14569]) ).
cnf(i_0_19321,plain,
( X1 = X1
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk451_3(X2,X1,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1))) ),
inference(equality_inference,[],[14577]) ).
cnf(i_0_19322,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,[],[14629]) ).
cnf(i_0_19323,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,[],[14630]) ).
cnf(i_0_19324,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,[],[14650]) ).
cnf(i_0_19325,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,[],[14688]) ).
cnf(i_0_19326,plain,
X1 = X1,
inference(equality_inference,[],[14704]) ).
cnf(i_0_19327,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,[],[14725]) ).
cnf(i_0_19328,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,[],[14795]) ).
cnf(i_0_19329,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk76_3(X1,X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1)) ),
inference(equality_inference,[],[14823]) ).
cnf(i_0_19330,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,[],[14851]) ).
cnf(i_0_19331,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,[],[14868]) ).
cnf(i_0_19332,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,[],[14901]) ).
cnf(i_0_19333,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,[],[14903]) ).
cnf(i_0_19334,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,[],[14932]) ).
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_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,[],[14933]) ).
cnf(i_0_19336,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,[],[14950]) ).
cnf(i_0_19337,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,[],[14977]) ).
cnf(i_0_19338,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,[],[14978]) ).
cnf(i_0_19339,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,[],[15006]) ).
cnf(i_0_19340,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,[],[15016]) ).
cnf(i_0_19341,plain,
( hAPP(X1,X2) = hAPP(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X4))) ),
inference(equality_inference,[],[15021]) ).
cnf(i_0_19342,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,[],[15073]) ).
cnf(i_0_19343,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,[],[15121]) ).
cnf(i_0_19344,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,[],[15163]) ).
cnf(i_0_19345,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,[],[15168]) ).
cnf(i_0_19346,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,[],[15182]) ).
cnf(i_0_19347,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,[],[15183]) ).
cnf(i_0_19348,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,[],[15184]) ).
cnf(i_0_19349,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,[],[15189]) ).
cnf(i_0_19350,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,[],[15202]) ).
cnf(i_0_19351,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,[],[15296]) ).
cnf(i_0_19352,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,[],[15297]) ).
cnf(i_0_19353,plain,
X1 = X1,
inference(equality_inference,[],[15314]) ).
cnf(i_0_19354,plain,
X1 = X1,
inference(equality_inference,[],[15315]) ).
cnf(i_0_19355,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,[],[15332]) ).
cnf(i_0_19356,plain,
( X1 = X1
| ~ c_Fun_Oinj__on(X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
inference(equality_inference,[],[15357]) ).
cnf(i_0_19357,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,[],[15359]) ).
cnf(i_0_19358,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,[],[15360]) ).
cnf(i_0_19359,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,[],[15471]) ).
cnf(i_0_19360,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,[],[15495]) ).
cnf(i_0_19361,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,[],[15519]) ).
cnf(i_0_19362,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,[],[15520]) ).
cnf(i_0_19363,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
inference(equality_inference,[],[15562]) ).
cnf(i_0_19364,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,[],[15575]) ).
cnf(i_0_19365,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,[],[15616]) ).
cnf(i_0_19366,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,[],[15626]) ).
cnf(i_0_19367,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,[],[15627]) ).
cnf(i_0_19368,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,[],[15644]) ).
cnf(i_0_19369,plain,
~ c_Wellfounded_Omax__extp(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(equality_inference,[],[15662]) ).
cnf(i_0_19370,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,[],[15672]) ).
cnf(i_0_19371,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X3)),
inference(equality_inference,[],[15699]) ).
cnf(i_0_19372,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,[],[15711]) ).
cnf(i_0_19373,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,[],[15720]) ).
cnf(i_0_19374,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,[],[15721]) ).
cnf(i_0_19375,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,[],[15798]) ).
cnf(i_0_19376,plain,
hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X5),X4) = X5,
inference(equality_inference,[],[15806]) ).
cnf(i_0_19377,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,[],[15832]) ).
cnf(i_0_19378,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,[],[15895]) ).
cnf(i_0_19379,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,[],[15896]) ).
cnf(i_0_19380,plain,
X1 = X1,
inference(equality_inference,[],[15905]) ).
cnf(i_0_19381,plain,
( X1 = X1
| hBOOL(hAPP(hAPP(c_member(X2),X3),X1))
| hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ),
inference(equality_inference,[],[15916]) ).
cnf(i_0_19382,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,[],[15917]) ).
cnf(i_0_19383,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,[],[15919]) ).
cnf(i_0_19384,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,[],[15931]) ).
cnf(i_0_19385,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Oran(X3,X1,c_Option_Ooption_OSome(X1)))),
inference(equality_inference,[],[15940]) ).
cnf(i_0_19386,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Odom(X1,X3,c_Option_Ooption_OSome(X3)))),
inference(equality_inference,[],[15941]) ).
cnf(i_0_19387,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,[],[15948]) ).
cnf(i_0_19388,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,[],[15949]) ).
cnf(i_0_19389,plain,
( ~ c_Nat__Transfer_Onat__set(X1)
| ~ c_Nat__Transfer_Onat__set(X1)
| X1 = X1 ),
inference(equality_inference,[],[15961]) ).
cnf(i_0_19390,plain,
X1 = X1,
inference(equality_inference,[],[15962]) ).
cnf(i_0_19391,plain,
X1 = X1,
inference(equality_inference,[],[15963]) ).
cnf(i_0_19392,plain,
X1 = X1,
inference(equality_inference,[],[15964]) ).
cnf(i_0_19393,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,[],[15982]) ).
cnf(i_0_19394,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,[],[16032]) ).
cnf(i_0_19395,plain,
X1 = hAPP(c_Product__Type_Ofst(X2,X3),hAPP(hAPP(c_Product__Type_OPair(X2,X3),X1),X4)),
inference(equality_inference,[],[16036]) ).
cnf(i_0_19396,plain,
X1 = hAPP(c_Product__Type_Osnd(X2,X3),hAPP(hAPP(c_Product__Type_OPair(X2,X3),X4),X1)),
inference(equality_inference,[],[16037]) ).
cnf(i_0_19397,plain,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3)),X2),X2)) ),
inference(equality_inference,[],[16044]) ).
cnf(i_0_19398,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,[],[16069]) ).
cnf(i_0_19399,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,[],[16085]) ).
cnf(i_0_19400,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,[],[16111]) ).
cnf(i_0_19401,plain,
X1 = X1,
inference(equality_inference,[],[16125]) ).
cnf(i_0_19402,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,[],[16136]) ).
cnf(i_0_19403,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,[],[16141]) ).
cnf(i_0_19404,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,[],[16168]) ).
cnf(i_0_19405,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,[],[16170]) ).
cnf(i_0_19406,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,[],[16171]) ).
cnf(i_0_19407,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,[],[16193]) ).
cnf(i_0_19408,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))),
inference(equality_inference,[],[16197]) ).
cnf(i_0_19409,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,[],[16216]) ).
cnf(i_0_19410,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,[],[16221]) ).
cnf(i_0_19411,plain,
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),X3,X4,X3)
| hBOOL(hAPP(X1,X3)) ),
inference(equality_inference,[],[16228]) ).
cnf(i_0_19412,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,[],[16278]) ).
cnf(i_0_19413,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
inference(equality_inference,[],[16306]) ).
cnf(i_0_19414,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
inference(equality_inference,[],[16307]) ).
cnf(i_0_19415,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,[],[16308]) ).
cnf(i_0_19416,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,[],[16313]) ).
cnf(i_0_19417,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,[],[16314]) ).
cnf(i_0_19418,plain,
X1 = X1,
inference(equality_inference,[],[16315]) ).
cnf(i_0_19419,plain,
X1 = X1,
inference(equality_inference,[],[16317]) ).
cnf(i_0_19420,plain,
X1 = X1,
inference(equality_inference,[],[16319]) ).
cnf(i_0_19421,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,[],[16323]) ).
cnf(i_0_19422,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,[],[16344]) ).
cnf(i_0_19423,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,[],[16346]) ).
cnf(i_0_19424,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,[],[16347]) ).
cnf(i_0_19425,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,[],[16410]) ).
cnf(i_0_19426,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,[],[16411]) ).
cnf(i_0_19427,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,[],[16444]) ).
cnf(i_0_19428,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,[],[16466]) ).
cnf(i_0_19429,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,[],[16467]) ).
cnf(i_0_19430,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,[],[16475]) ).
cnf(i_0_19431,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,[],[16492]) ).
cnf(i_0_19432,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,[],[16504]) ).
cnf(i_0_19433,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,[],[16505]) ).
cnf(i_0_19434,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,[],[16522]) ).
cnf(i_0_19435,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,[],[16536]) ).
cnf(i_0_19436,plain,
X1 = X1,
inference(equality_inference,[],[16537]) ).
cnf(i_0_19437,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,[],[16550]) ).
cnf(i_0_19438,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,[],[16587]) ).
cnf(i_0_19439,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,[],[16612]) ).
cnf(i_0_19440,plain,
hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X2)),
inference(equality_inference,[],[16619]) ).
cnf(i_0_19441,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,[],[16641]) ).
cnf(i_0_19442,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,[],[16642]) ).
cnf(i_0_19443,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,[],[16694]) ).
cnf(i_0_19444,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,[],[16695]) ).
cnf(i_0_19445,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,[],[16713]) ).
cnf(i_0_19446,plain,
hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),hAPP(X3,X4)) = X3,
inference(equality_inference,[],[16746]) ).
cnf(i_0_19447,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,[],[16756]) ).
cnf(i_0_19448,plain,
hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olists(X1,X2))),
inference(equality_inference,[],[16775]) ).
cnf(i_0_19449,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,[],[16797]) ).
cnf(i_0_19450,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(equality_inference,[],[16800]) ).
cnf(i_0_19451,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,[],[16809]) ).
cnf(i_0_19452,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,[],[16810]) ).
cnf(i_0_19453,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,[],[16811]) ).
cnf(i_0_19454,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,[],[16812]) ).
cnf(i_0_19455,plain,
X1 = X1,
inference(equality_inference,[],[16813]) ).
cnf(i_0_19456,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,[],[16822]) ).
cnf(i_0_19457,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,[],[16823]) ).
cnf(i_0_19458,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,[],[16824]) ).
cnf(i_0_19459,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,[],[16877]) ).
cnf(i_0_19460,plain,
( ~ class_Rings_Oidom(X1)
| X2 = X2
| X2 = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) ),
inference(equality_inference,[],[16898]) ).
cnf(i_0_19461,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,[],[16902]) ).
cnf(i_0_19462,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,[],[16903]) ).
cnf(i_0_19463,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,[],[16904]) ).
cnf(i_0_19464,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,[],[16907]) ).
cnf(i_0_19465,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,[],[16908]) ).
cnf(i_0_19466,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Option_Oset(X1,hAPP(c_Option_Ooption_OSome(X1),X2)))),
inference(equality_inference,[],[16910]) ).
cnf(i_0_19467,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,[],[16964]) ).
cnf(i_0_19468,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(equality_inference,[],[16968]) ).
cnf(i_0_19469,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(equality_inference,[],[16969]) ).
cnf(i_0_19470,plain,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(equality_inference,[],[16970]) ).
cnf(i_0_19471,plain,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(equality_inference,[],[16972]) ).
cnf(i_0_19472,plain,
( ~ class_Rings_Olinordered__idom(X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X2)) ),
inference(equality_inference,[],[16978]) ).
cnf(i_0_19473,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,[],[16987]) ).
cnf(i_0_19474,plain,
( ~ class_Groups_Ocancel__semigroup__add(X1)
| X2 = X2 ),
inference(equality_inference,[],[16993]) ).
cnf(i_0_19475,plain,
( X1 = X1
| ~ class_Groups_Ocancel__ab__semigroup__add(X2) ),
inference(equality_inference,[],[16994]) ).
cnf(i_0_19476,plain,
( ~ class_Groups_Ocancel__semigroup__add(X1)
| X2 = X2 ),
inference(equality_inference,[],[16996]) ).
cnf(i_0_19477,plain,
X1 = X1,
inference(equality_inference,[],[16997]) ).
cnf(i_0_19478,plain,
X1 = X1,
inference(equality_inference,[],[16998]) ).
cnf(i_0_19479,plain,
X1 = X1,
inference(equality_inference,[],[16999]) ).
cnf(i_0_19480,plain,
X1 = X1,
inference(equality_inference,[],[17000]) ).
cnf(i_0_19481,plain,
X1 = X1,
inference(equality_inference,[],[17001]) ).
cnf(i_0_19482,plain,
X1 = X1,
inference(equality_inference,[],[17002]) ).
cnf(i_0_19483,plain,
X1 = X1,
inference(equality_inference,[],[17003]) ).
cnf(i_0_19484,plain,
X1 = X1,
inference(equality_inference,[],[17004]) ).
cnf(i_0_19485,plain,
X1 = X1,
inference(equality_inference,[],[17005]) ).
cnf(i_0_19486,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,[],[17011]) ).
cnf(i_0_19487,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,[],[17012]) ).
cnf(i_0_19488,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,[],[17013]) ).
cnf(i_0_19489,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,[],[17031]) ).
cnf(i_0_19490,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,[],[17032]) ).
cnf(i_0_19491,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,[],[17033]) ).
cnf(i_0_19492,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,[],[17035]) ).
cnf(i_0_19493,plain,
X1 = X1,
inference(equality_inference,[],[17042]) ).
cnf(i_0_19494,plain,
X1 = X1,
inference(equality_inference,[],[17043]) ).
cnf(i_0_19495,plain,
X1 = X1,
inference(equality_inference,[],[17044]) ).
cnf(i_0_19496,plain,
X1 = X1,
inference(equality_inference,[],[17045]) ).
cnf(i_0_19497,plain,
c_List_Oremove1(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = X3,
inference(equality_inference,[],[17068]) ).
cnf(i_0_19498,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(equality_inference,[],[17093]) ).
cnf(i_0_19499,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_inference,[],[17100]) ).
cnf(i_0_19500,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X1)),
inference(equality_inference,[],[17110]) ).
cnf(i_0_19501,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(equality_inference,[],[17114]) ).
cnf(i_0_19502,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(equality_inference,[],[17115]) ).
cnf(i_0_19503,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,[],[17124]) ).
cnf(i_0_19504,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(equality_inference,[],[17126]) ).
cnf(i_0_19505,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(equality_inference,[],[17128]) ).
cnf(i_0_19506,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,[],[17129]) ).
cnf(i_0_19507,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,[],[17140]) ).
cnf(i_0_19508,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,[],[17141]) ).
cnf(i_0_19509,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,[],[17143]) ).
cnf(i_0_19510,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,[],[17144]) ).
cnf(i_0_19511,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,[],[17145]) ).
cnf(i_0_19512,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,[],[17146]) ).
cnf(i_0_19513,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,[],[17148]) ).
cnf(i_0_19514,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,[],[17149]) ).
cnf(i_0_19515,plain,
( ~ c_Equiv__Relations_Oequivp(X1,X2)
| hBOOL(hAPP(hAPP(X2,X3),X3)) ),
inference(equality_inference,[],[17156]) ).
cnf(i_0_19516,plain,
X1 = X1,
inference(equality_inference,[],[17166]) ).
cnf(i_0_19517,plain,
X1 = X1,
inference(equality_inference,[],[17167]) ).
cnf(i_0_19518,plain,
X1 = X1,
inference(equality_inference,[],[17168]) ).
cnf(i_0_19519,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,[],[17174]) ).
cnf(i_0_19520,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,[],[17182]) ).
cnf(i_0_19521,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(equality_inference,[],[17191]) ).
cnf(i_0_19522,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,[],[17205]) ).
cnf(i_0_19523,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,[],[17207]) ).
cnf(i_0_19524,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,[],[17213]) ).
cnf(i_0_19525,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,[],[17221]) ).
cnf(i_0_19526,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,[],[17240]) ).
cnf(i_0_19527,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,[],[17241]) ).
cnf(i_0_19528,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,[],[17262]) ).
cnf(i_0_19529,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,[],[17263]) ).
cnf(i_0_19530,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,[],[17265]) ).
cnf(i_0_19531,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,[],[17266]) ).
cnf(i_0_19532,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,[],[17269]) ).
cnf(i_0_19533,plain,
X1 = X1,
inference(equality_inference,[],[17271]) ).
cnf(i_0_19534,plain,
X1 = X1,
inference(equality_inference,[],[17273]) ).
cnf(i_0_19535,plain,
X1 = X1,
inference(equality_inference,[],[17274]) ).
cnf(i_0_19536,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,[],[17279]) ).
cnf(i_0_19537,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,[],[17280]) ).
cnf(i_0_19538,plain,
c_List_Olast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))) = X2,
inference(equality_inference,[],[17288]) ).
cnf(i_0_19539,plain,
( ~ epred1_3(X1,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(X1,X2)) ),
inference(equality_inference,[],[17304]) ).
cnf(i_0_19540,plain,
( ~ class_Orderings_Opreorder(X1)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2)) ),
inference(equality_inference,[],[17334]) ).
cnf(i_0_19541,plain,
( ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2)) ),
inference(equality_inference,[],[17336]) ).
cnf(i_0_19542,plain,
( ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2)) ),
inference(equality_inference,[],[17337]) ).
cnf(i_0_19543,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,[],[17381]) ).
cnf(i_0_19544,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,[],[17386]) ).
cnf(i_0_19545,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,[],[17408]) ).
cnf(i_0_19546,plain,
hAPP(hAPP(c_List_Olist__update(X1,c_List_Olist_ONil(X1)),X2),X3) = c_List_Olist_ONil(X1),
inference(equality_inference,[],[17438]) ).
cnf(i_0_19547,plain,
hAPP(hAPP(c_Option_Omap(X1,X2),X3),c_Option_Ooption_ONone(X1)) = c_Option_Ooption_ONone(X2),
inference(equality_inference,[],[17439]) ).
cnf(i_0_19548,plain,
hAPP(hAPP(c_List_Omap(X1,X2),X3),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X2),
inference(equality_inference,[],[17440]) ).
cnf(i_0_19549,plain,
c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Omap(X2,X1),X3),c_List_Olist_ONil(X2)),
inference(equality_inference,[],[17441]) ).
cnf(i_0_19550,plain,
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X2,X1)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(equality_inference,[],[17446]) ).
cnf(i_0_19551,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,[],[17465]) ).
cnf(i_0_19552,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,[],[17469]) ).
cnf(i_0_19553,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,[],[17470]) ).
cnf(i_0_19554,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X1)),
inference(equality_inference,[],[17474]) ).
cnf(i_0_19555,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X1)),
inference(equality_inference,[],[17476]) ).
cnf(i_0_19556,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1)),
inference(equality_inference,[],[17479]) ).
cnf(i_0_19557,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,[],[17481]) ).
cnf(i_0_19558,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,[],[17487]) ).
cnf(i_0_19559,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,[],[17514]) ).
cnf(i_0_19560,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,[],[17529]) ).
cnf(i_0_19561,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,[],[17534]) ).
cnf(i_0_19562,plain,
( ~ class_Int_Onumber__ring(X1)
| ~ class_Int_Oring__char__0(X1)
| X2 = X2 ),
inference(equality_inference,[],[17587]) ).
cnf(i_0_19563,plain,
hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
inference(equality_inference,[],[17589]) ).
cnf(i_0_19564,plain,
( ~ class_Orderings_Olinorder(X1)
| X2 = X2 ),
inference(equality_inference,[],[17633]) ).
cnf(i_0_19565,plain,
( ~ class_Orderings_Olinorder(X1)
| X2 = X2 ),
inference(equality_inference,[],[17634]) ).
cnf(i_0_19566,plain,
( ~ class_Orderings_Olinorder(X1)
| X2 = X2 ),
inference(equality_inference,[],[17635]) ).
cnf(i_0_19567,plain,
( ~ class_Orderings_Olinorder(X1)
| X2 = X2 ),
inference(equality_inference,[],[17636]) ).
cnf(i_0_19568,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| X2 = X2 ),
inference(equality_inference,[],[17637]) ).
cnf(i_0_19569,plain,
( ~ class_Groups_Ogroup__add(X1)
| X2 = X2 ),
inference(equality_inference,[],[17638]) ).
cnf(i_0_19570,plain,
( ~ class_Int_Oring__char__0(X1)
| X2 = X2 ),
inference(equality_inference,[],[17639]) ).
cnf(i_0_19571,plain,
( ~ class_Nat_Osemiring__char__0(X1)
| X2 = X2 ),
inference(equality_inference,[],[17640]) ).
cnf(i_0_19572,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,[],[17649]) ).
cnf(i_0_19573,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,[],[17650]) ).
cnf(i_0_19574,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,[],[17651]) ).
cnf(i_0_19575,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,[],[17652]) ).
cnf(i_0_19576,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,[],[17653]) ).
cnf(i_0_19577,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,[],[17654]) ).
cnf(i_0_19578,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,[],[17655]) ).
cnf(i_0_19579,plain,
X1 = hAPP(hAPP(c_List_Oappend(X2),c_List_Olist_ONil(X2)),X1),
inference(equality_inference,[],[17667]) ).
cnf(i_0_19580,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,[],[17668]) ).
cnf(i_0_19581,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,[],[17680]) ).
cnf(i_0_19582,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,[],[17681]) ).
cnf(i_0_19583,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,[],[17682]) ).
cnf(i_0_19584,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,[],[17683]) ).
cnf(i_0_19585,plain,
X1 = X1,
inference(equality_inference,[],[17704]) ).
cnf(i_0_19586,plain,
X1 = X1,
inference(equality_inference,[],[17705]) ).
cnf(i_0_19587,plain,
hAPP(hAPP(c_List_Otake(X1),X2),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(equality_inference,[],[17712]) ).
cnf(i_0_19588,plain,
hAPP(hAPP(c_List_Otake(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) = c_List_Olist_ONil(X1),
inference(equality_inference,[],[17725]) ).
cnf(i_0_19589,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,[],[17727]) ).
cnf(i_0_19590,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,[],[17729]) ).
cnf(i_0_19591,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2) = X2,
inference(equality_inference,[],[17731]) ).
cnf(i_0_19592,plain,
hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1)) = X2,
inference(equality_inference,[],[17732]) ).
cnf(i_0_19593,plain,
X1 = hAPP(hAPP(c_List_Oappend(X2),c_List_Olist_ONil(X2)),X1),
inference(equality_inference,[],[17733]) ).
cnf(i_0_19594,plain,
X1 = hAPP(hAPP(c_List_Oappend(X2),X1),c_List_Olist_ONil(X2)),
inference(equality_inference,[],[17734]) ).
cnf(i_0_19595,plain,
X1 = X1,
inference(equality_inference,[],[17778]) ).
cnf(i_0_19596,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,[],[17779]) ).
cnf(i_0_19597,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,[],[17780]) ).
cnf(i_0_19598,plain,
hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
inference(equality_inference,[],[17782]) ).
cnf(i_0_19599,plain,
X1 = hAPP(c_List_Orev(X2),hAPP(c_List_Orev(X2),X1)),
inference(equality_inference,[],[17783]) ).
cnf(i_0_19600,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,[],[17789]) ).
cnf(i_0_19601,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,[],[17790]) ).
cnf(i_0_19602,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,[],[17792]) ).
cnf(i_0_19603,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,[],[17793]) ).
cnf(i_0_19604,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = X1,
inference(equality_inference,[],[17803]) ).
cnf(i_0_19605,plain,
c_Option_Oset(X1,c_Option_Ooption_ONone(X1)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(equality_inference,[],[17833]) ).
cnf(i_0_19606,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls) = c_Int_OPls,
inference(equality_inference,[],[17837]) ).
cnf(i_0_19607,plain,
c_Int_OPls = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls),
inference(equality_inference,[],[17838]) ).
cnf(i_0_19608,plain,
X1 = X1,
inference(equality_inference,[],[17845]) ).
cnf(i_0_19609,plain,
X1 = X1,
inference(equality_inference,[],[17846]) ).
cnf(i_0_19610,plain,
X1 = X1,
inference(equality_inference,[],[17847]) ).
cnf(i_0_19611,plain,
X1 = X1,
inference(equality_inference,[],[17848]) ).
cnf(i_0_19612,plain,
X1 = X1,
inference(equality_inference,[],[17849]) ).
cnf(i_0_19613,plain,
X1 = X1,
inference(equality_inference,[],[17850]) ).
cnf(i_0_19614,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,[],[17875]) ).
cnf(i_0_19615,plain,
X1 = hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),
inference(equality_inference,[],[17880]) ).
cnf(i_0_19616,plain,
X1 = X1,
inference(equality_inference,[],[17893]) ).
cnf(i_0_19617,plain,
X1 = X1,
inference(equality_inference,[],[17895]) ).
cnf(i_0_19618,plain,
X1 = X1,
inference(equality_inference,[],[17896]) ).
cnf(i_0_19619,plain,
X1 = X1,
inference(equality_inference,[],[17898]) ).
cnf(i_0_19620,plain,
X1 = X1,
inference(equality_inference,[],[17899]) ).
cnf(i_0_19621,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,[],[17903]) ).
cnf(i_0_19622,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,[],[17904]) ).
cnf(i_0_19623,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,[],[17905]) ).
cnf(i_0_19624,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,[],[17934]) ).
cnf(i_0_19625,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,[],[17935]) ).
cnf(i_0_19626,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,[],[17936]) ).
cnf(i_0_19627,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,[],[17939]) ).
cnf(i_0_19628,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,[],[17940]) ).
cnf(i_0_19629,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,[],[17953]) ).
cnf(i_0_19630,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,[],[17954]) ).
cnf(i_0_19631,plain,
hAPP(c_List_Orev(X1),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(equality_inference,[],[17955]) ).
cnf(i_0_19632,plain,
hAPP(c_List_Orotate1(X1),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(equality_inference,[],[17956]) ).
cnf(i_0_19633,plain,
c_List_Olist_ONil(X1) = hAPP(c_List_Orev(X1),c_List_Olist_ONil(X1)),
inference(equality_inference,[],[17957]) ).
cnf(i_0_19634,plain,
( ~ class_Rings_Osemiring__1(X1)
| c_Int_Oiszero(X1,c_Groups_Ozero__class_Ozero(X1)) ),
inference(equality_inference,[],[17971]) ).
cnf(i_0_19635,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,[],[17981]) ).
cnf(i_0_19636,plain,
c_Option_Ois__none(X1,c_Option_Ooption_ONone(X1)),
inference(equality_inference,[],[17993]) ).
cnf(i_0_19637,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,[],[18015]) ).
cnf(i_0_19638,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,[],[18016]) ).
cnf(i_0_19639,plain,
c_Nitpick_Onat__gcd(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(equality_inference,[],[18017]) ).
cnf(i_0_19640,plain,
c_Random_Oinc__shift(X1,X1) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),
inference(equality_inference,[],[18024]) ).
cnf(i_0_19641,plain,
X1 = X1,
inference(equality_inference,[],[18046]) ).
cnf(i_0_19642,plain,
X1 = X1,
inference(equality_inference,[],[18047]) ).
cnf(i_0_19643,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)),
inference(scs_inference,[],[i_0_19500,i_0_19454]) ).
cnf(i_0_19644,plain,
c_Hoare__Mirabelle_Otriple__valid(X1,X2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_fun(X4,tc_HOL_Obool)))),X5),X6)),
inference(scs_inference,[],[i_0_13839,i_0_12321]) ).
cnf(i_0_19645,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4)),
inference(rename_variables,[],[i_0_13839]) ).
cnf(i_0_19646,plain,
( hBOOL(hAPP(hAPP(X1,esk2_4(X2,X3,X1,X4)),esk3_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(rename_variables,[],[i_0_12321]) ).
cnf(i_0_19647,plain,
c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),esk3_4(v_Q,hAPP(c_Com_Ocom_OBODY,v_pn),v_P,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),esk4_4(v_Q,hAPP(c_Com_Ocom_OBODY,v_pn),v_P,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_15374,i_0_13839,i_0_12321,i_0_13229]) ).
cnf(i_0_19648,plain,
( c_Hoare__Mirabelle_Otriple__valid(X1,X2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),X4),X5))
| c_Natural_Oevaln(X4,esk3_4(X5,X4,X3,X2),X2,esk4_4(X5,X4,X3,X2)) ),
inference(rename_variables,[],[i_0_13229]) ).
cnf(i_0_19649,plain,
hAPP(c_Option_Ooption_OSome(X1),esk435_7(X2,X2,c_Option_Ooption_OSome(X3),c_Option_Ooption_OSome(X1),X4,X1,X3)) = hAPP(c_Option_Ooption_OSome(X1),X2),
inference(scs_inference,[],[i_0_15374,i_0_15176,i_0_13839,i_0_12321,i_0_13229,i_0_11286]) ).
cnf(i_0_19650,plain,
hAPP(c_Option_Ooption_Ooption__case(X1,X2,X3,X4),hAPP(c_Option_Ooption_OSome(X2),X5)) = hAPP(X4,X5),
inference(rename_variables,[],[i_0_15176]) ).
cnf(i_0_19651,plain,
( hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X1),X2,c_Option_Ooption_ONone(X1),X3),hAPP(X4,X5)) != hAPP(c_Option_Ooption_OSome(X1),X6)
| hAPP(X3,esk435_7(X6,X5,X4,X3,X7,X1,X2)) = hAPP(c_Option_Ooption_OSome(X1),X6) ),
inference(rename_variables,[],[i_0_11286]) ).
cnf(i_0_19652,plain,
hAPP(c_Option_Ooption_OSome(X1),X2) = hAPP(c_Option_Ooption_OSome(X1),esk435_7(X2,X2,c_Option_Ooption_OSome(X1),c_Option_Ooption_OSome(X3),X4,X3,X1)),
inference(scs_inference,[],[i_0_15374,i_0_15176,i_0_19650,i_0_13839,i_0_12321,i_0_13229,i_0_11286,i_0_11287]) ).
cnf(i_0_19653,plain,
hAPP(c_Option_Ooption_Ooption__case(X1,X2,X3,X4),hAPP(c_Option_Ooption_OSome(X2),X5)) = hAPP(X4,X5),
inference(rename_variables,[],[i_0_15176]) ).
cnf(i_0_19654,plain,
( hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X1),X2,c_Option_Ooption_ONone(X1),X3),hAPP(X4,X5)) != hAPP(c_Option_Ooption_OSome(X1),X6)
| hAPP(X4,X5) = hAPP(c_Option_Ooption_OSome(X2),esk435_7(X6,X5,X4,X3,X7,X1,X2)) ),
inference(rename_variables,[],[i_0_11287]) ).
cnf(i_0_19655,plain,
~ c_Predicate_Opred__comp(X1,X2,X3,X4,c_member(X5),X6,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_15374,i_0_15176,i_0_19650,i_0_16117,i_0_13839,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317]) ).
cnf(i_0_19656,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_16117]) ).
cnf(i_0_19657,plain,
( hBOOL(hAPP(hAPP(X1,esk317_4(X2,X3,X1,X4)),X2))
| ~ c_Predicate_Opred__comp(X5,X6,X7,X4,X1,X3,X2) ),
inference(rename_variables,[],[i_0_11317]) ).
cnf(i_0_19658,plain,
~ c_Predicate_Opred__comp(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_fun(X5,tc_HOL_Obool))),X6,X7,X8),
inference(scs_inference,[],[i_0_15374,i_0_15176,i_0_19650,i_0_16117,i_0_13839,i_0_19645,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323]) ).
cnf(i_0_19659,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4)),
inference(rename_variables,[],[i_0_13839]) ).
cnf(i_0_19660,plain,
( hBOOL(hAPP(hAPP(X1,X2),esk317_4(X3,X2,X4,X1)))
| ~ c_Predicate_Opred__comp(X5,X6,X7,X1,X4,X2,X3) ),
inference(rename_variables,[],[i_0_11323]) ).
cnf(i_0_19661,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_OImage(X3,X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X1),tc_HOL_Obool))),X4))),
inference(scs_inference,[],[i_0_15374,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_13839,i_0_19645,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376]) ).
cnf(i_0_19662,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_16117]) ).
cnf(i_0_19663,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk123_5(X3,X4,X1,X5,X2)),X5)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Relation_OImage(X1,X2,X4),X3))) ),
inference(rename_variables,[],[i_0_11376]) ).
cnf(i_0_19664,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_Relation_OImage(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omax__ext(X1,X2)),X3))),
inference(scs_inference,[],[i_0_15374,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_13839,i_0_19645,i_0_19192,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377]) ).
cnf(i_0_19665,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(rename_variables,[],[i_0_19192]) ).
cnf(i_0_19666,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk119_5(X3,X4,X1,X5,X2)),X5)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Relation_OImage(X1,X2,X4),X3))) ),
inference(rename_variables,[],[i_0_11377]) ).
cnf(i_0_19667,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)))),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_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
inference(scs_inference,[],[i_0_15374,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_13839,i_0_19645,i_0_19192,i_0_19333,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403]) ).
cnf(i_0_19668,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)))),X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
inference(rename_variables,[],[i_0_11403]) ).
cnf(i_0_19669,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)))),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_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
inference(scs_inference,[],[i_0_15374,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_13839,i_0_19645,i_0_19192,i_0_19333,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405]) ).
cnf(i_0_19670,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)))),X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
inference(rename_variables,[],[i_0_11405]) ).
cnf(i_0_19671,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)))),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(scs_inference,[],[i_0_15374,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_13839,i_0_19645,i_0_19192,i_0_19333,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406]) ).
cnf(i_0_19672,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)))),X2,X1) ),
inference(rename_variables,[],[i_0_11406]) ).
cnf(i_0_19673,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)))),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(scs_inference,[],[i_0_15374,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_13839,i_0_19645,i_0_19192,i_0_19333,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407]) ).
cnf(i_0_19674,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)))),X2,X1) ),
inference(rename_variables,[],[i_0_11407]) ).
cnf(i_0_19675,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)))),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_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
inference(scs_inference,[],[i_0_15374,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_13839,i_0_19645,i_0_19192,i_0_19333,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417]) ).
cnf(i_0_19676,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| 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)) ),
inference(rename_variables,[],[i_0_11417]) ).
cnf(i_0_19677,plain,
hAPP(c_Product__Type_Omap__pair(X1,X1,X2,X3,c_Fun_Oid(X1),c_Map_Omap__add(X4,X5,X6,c_Option_Ooption_OSome(X5))),X7) = hAPP(c_Product__Type_Omap__pair(X1,X1,X2,X3,c_Fun_Oid(X1),c_Option_Ooption_OSome(X5)),X7),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_13839,i_0_19645,i_0_19192,i_0_19333,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474]) ).
cnf(i_0_19678,plain,
hAPP(c_Map_Omap__add(X1,X2,X3,c_Option_Ooption_OSome(X2)),X4) = hAPP(c_Option_Ooption_OSome(X2),X4),
inference(rename_variables,[],[i_0_19343]) ).
cnf(i_0_19679,plain,
( hAPP(X1,hAPP(c_Product__Type_Osnd(X2,X3),X4)) != hAPP(X5,hAPP(c_Product__Type_Osnd(X2,X3),X4))
| 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) ),
inference(rename_variables,[],[i_0_11474]) ).
cnf(i_0_19680,plain,
hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,c_Map_Omap__add(X4,X5,X6,c_Option_Ooption_OSome(X5)),c_Fun_Oid(X3)),X7) = hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,c_Option_Ooption_OSome(X5),c_Fun_Oid(X3)),X7),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_13839,i_0_19645,i_0_19192,i_0_19333,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475]) ).
cnf(i_0_19681,plain,
hAPP(c_Map_Omap__add(X1,X2,X3,c_Option_Ooption_OSome(X2)),X4) = hAPP(c_Option_Ooption_OSome(X2),X4),
inference(rename_variables,[],[i_0_19343]) ).
cnf(i_0_19682,plain,
( hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),X4)) != hAPP(X5,hAPP(c_Product__Type_Ofst(X2,X3),X4))
| 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) ),
inference(rename_variables,[],[i_0_11475]) ).
cnf(i_0_19683,plain,
~ c_Finite__Set_Ofolding__image__simple(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),X4,c_Nat_OSuc),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_13839,i_0_19645,i_0_19192,i_0_19333,i_0_18009,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753]) ).
cnf(i_0_19684,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_18009]) ).
cnf(i_0_19685,plain,
( hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) = X3
| ~ c_Finite__Set_Ofolding__image__simple(X4,X2,X5,X3,X6,X1) ),
inference(rename_variables,[],[i_0_11753]) ).
cnf(i_0_19686,plain,
~ c_Finite__Set_Ofolding__image__simple__idem(X1,X2,c_List_Olist_OCons(X3),X4,X5,X6),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_13839,i_0_19645,i_0_19192,i_0_19333,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756]) ).
cnf(i_0_19687,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != c_List_Olist_ONil(X1),
inference(rename_variables,[],[i_0_17530]) ).
cnf(i_0_19688,plain,
( hAPP(hAPP(X1,X2),X2) = X2
| ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X1,X5,X6,X7) ),
inference(rename_variables,[],[i_0_11756]) ).
cnf(i_0_19689,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ORange(X3,X1),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X1),tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_13839,i_0_19645,i_0_19192,i_0_19333,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763]) ).
cnf(i_0_19690,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_16117]) ).
cnf(i_0_19691,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk323_4(X3,X1,X4,X2)),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_Relation_ORange(X1,X2),X3))) ),
inference(rename_variables,[],[i_0_11763]) ).
cnf(i_0_19692,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_Relation_ORange(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Wellfounded_Omax__ext(X1,X2)))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_13839,i_0_19645,i_0_19192,i_0_19665,i_0_19333,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764]) ).
cnf(i_0_19693,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(rename_variables,[],[i_0_19192]) ).
cnf(i_0_19694,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk322_4(X3,X1,X4,X2)),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_Relation_ORange(X1,X2),X3))) ),
inference(rename_variables,[],[i_0_11764]) ).
cnf(i_0_19695,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(X1),esk280_5(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2,X3,X1)),esk281_5(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2,X3,X1)),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_13839,i_0_19645,i_0_19275,i_0_19192,i_0_19665,i_0_19333,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824]) ).
cnf(i_0_19696,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)),X5))
| hAPP(hAPP(c_Set_Oinsert(X1),X3),X4) = hAPP(hAPP(c_Set_Oinsert(X1),esk280_5(X5,X4,X3,X2,X1)),esk281_5(X5,X4,X3,X2,X1)) ),
inference(rename_variables,[],[i_0_11824]) ).
cnf(i_0_19697,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(X1),esk278_5(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2,X3,X1)),esk279_5(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2,X3,X1)),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_13839,i_0_19645,i_0_19275,i_0_19192,i_0_19665,i_0_19333,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825]) ).
cnf(i_0_19698,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)),X5))
| hAPP(hAPP(c_Set_Oinsert(X1),X3),X4) = hAPP(hAPP(c_Set_Oinsert(X1),esk278_5(X5,X4,X3,X2,X1)),esk279_5(X5,X4,X3,X2,X1)) ),
inference(rename_variables,[],[i_0_11825]) ).
cnf(i_0_19699,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),X2)),c_Wellfounded_Ofinite__psubset(X1))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19363,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_13839,i_0_19645,i_0_19275,i_0_19192,i_0_19665,i_0_19333,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018]) ).
cnf(i_0_19700,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(rename_variables,[],[i_0_12018]) ).
cnf(i_0_19701,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ODomain(X1,X3),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X3),tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19363,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_13839,i_0_19645,i_0_19275,i_0_19192,i_0_19665,i_0_19333,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019]) ).
cnf(i_0_19702,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_16117]) ).
cnf(i_0_19703,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),esk327_4(X4,X2,X3,X1))),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_Relation_ODomain(X1,X2),X4))) ),
inference(rename_variables,[],[i_0_12019]) ).
cnf(i_0_19704,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),hAPP(c_Relation_ODomain(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel1(X1,X2)))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19363,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_13839,i_0_19645,i_0_19275,i_0_19192,i_0_19665,i_0_19333,i_0_12497,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020]) ).
cnf(i_0_19705,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(rename_variables,[],[i_0_12497]) ).
cnf(i_0_19706,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),esk326_4(X4,X2,X3,X1))),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_Relation_ODomain(X1,X2),X4))) ),
inference(rename_variables,[],[i_0_12020]) ).
cnf(i_0_19707,plain,
hAPP(hAPP(c_COMBB(tc_sum(X1,X2),X3,X1),c_Sum__Type_Osum_Osum__case(X1,X3,X2,X4,X5)),c_Sum__Type_OInl(X1,X2)) = X4,
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19363,i_0_12523,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_13839,i_0_19645,i_0_19275,i_0_19192,i_0_19665,i_0_19333,i_0_12497,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218]) ).
cnf(i_0_19708,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(rename_variables,[],[i_0_12523]) ).
cnf(i_0_19709,plain,
( c_Sum__Type_Osum_Osum__case(X1,X2,X3,X4,X5) != c_Sum__Type_Osum_Osum__case(X1,X2,X3,X6,X7)
| X4 = X6 ),
inference(rename_variables,[],[i_0_12218]) ).
cnf(i_0_19710,plain,
hAPP(hAPP(c_COMBB(tc_sum(X1,X2),X3,X2),c_Sum__Type_Osum_Osum__case(X1,X3,X2,X4,X5)),c_Sum__Type_OInr(X2,X1)) = X5,
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19363,i_0_12523,i_0_19708,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_13839,i_0_19645,i_0_19275,i_0_19192,i_0_19665,i_0_19333,i_0_12497,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219]) ).
cnf(i_0_19711,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(rename_variables,[],[i_0_12523]) ).
cnf(i_0_19712,plain,
( c_Sum__Type_Osum_Osum__case(X1,X2,X3,X4,X5) != c_Sum__Type_Osum_Osum__case(X1,X2,X3,X6,X7)
| X5 = X7 ),
inference(rename_variables,[],[i_0_12219]) ).
cnf(i_0_19713,plain,
hAPP(c_Set_Oimage(X1,X2,X3),X4) = hAPP(c_Set_Oimage(X1,X2,X3),esk117_5(X4,X3,X1,hAPP(c_Set_Oimage(X1,X2,X3),X4),X2)),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19363,i_0_12523,i_0_19708,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_13839,i_0_19645,i_0_19275,i_0_19192,i_0_19665,i_0_19333,i_0_12497,i_0_16324,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229]) ).
cnf(i_0_19714,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
inference(rename_variables,[],[i_0_16324]) ).
cnf(i_0_19715,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(X3,X1,X4),X5)))
| X2 = hAPP(c_Set_Oimage(X3,X1,X4),esk117_5(X5,X4,X3,X2,X1)) ),
inference(rename_variables,[],[i_0_12229]) ).
cnf(i_0_19716,plain,
~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X1,X2,tc_HOL_Obool,hAPP(c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5))),X4),X5)),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19363,i_0_12523,i_0_19708,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_13839,i_0_19645,i_0_19275,i_0_19192,i_0_19665,i_0_19333,i_0_12497,i_0_16324,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252]) ).
cnf(i_0_19717,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
inference(rename_variables,[],[i_0_19363]) ).
cnf(i_0_19718,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X2,X3),X4),X5)))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X2,X3,tc_HOL_Obool,X1),X4),X5)) ),
inference(rename_variables,[],[i_0_12252]) ).
cnf(i_0_19719,plain,
hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Orestrict__map(X1,X2,X3,c_Map_Oran(X4,X1,c_Option_Ooption_OSome(X1)))),X5),c_Option_Ooption_ONone(X2)) = c_Map_Orestrict__map(X1,X2,X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Map_Oran(X4,X1,c_Option_Ooption_OSome(X1))),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19363,i_0_12523,i_0_19708,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_13839,i_0_19645,i_0_19275,i_0_19192,i_0_19665,i_0_19333,i_0_12497,i_0_16324,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318]) ).
cnf(i_0_19720,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,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))))) ),
inference(rename_variables,[],[i_0_12318]) ).
cnf(i_0_19721,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) = hAPP(hAPP(c_List_Olist_OCons(X1),esk472_3(X4,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),X1)),esk473_3(X4,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),X1)),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19363,i_0_12523,i_0_19708,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19333,i_0_12497,i_0_16324,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351]) ).
cnf(i_0_19722,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_Olexord(X1,X3)))
| X2 = hAPP(hAPP(c_List_Olist_OCons(X1),esk472_3(X3,X2,X1)),esk473_3(X3,X2,X1)) ),
inference(rename_variables,[],[i_0_12351]) ).
cnf(i_0_19723,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Set_Oimage(X3,X1,X4),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19363,i_0_12523,i_0_19708,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19333,i_0_12497,i_0_16324,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406]) ).
cnf(i_0_19724,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_16117]) ).
cnf(i_0_19725,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk118_4(X2,X3,X1,X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(c_Set_Oimage(X1,X5,X3),X2))) ),
inference(rename_variables,[],[i_0_12406]) ).
cnf(i_0_19726,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Ovimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1))),X1)),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19363,i_0_12523,i_0_19708,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19333,i_0_12497,i_0_16324,i_0_12352,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412]) ).
cnf(i_0_19727,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(rename_variables,[],[i_0_12352]) ).
cnf(i_0_19728,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(rename_variables,[],[i_0_12412]) ).
cnf(i_0_19729,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19363,i_0_12523,i_0_19708,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19333,i_0_12497,i_0_16324,i_0_12352,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440]) ).
cnf(i_0_19730,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_16117]) ).
cnf(i_0_19731,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(rename_variables,[],[i_0_12440]) ).
cnf(i_0_19732,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Wellfounded_Oacc(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omax__ext(X1,X2)))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19363,i_0_12523,i_0_19708,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_12497,i_0_16324,i_0_12352,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441]) ).
cnf(i_0_19733,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(rename_variables,[],[i_0_19192]) ).
cnf(i_0_19734,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(rename_variables,[],[i_0_12441]) ).
cnf(i_0_19735,plain,
hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_Wellfounded_Oacc(tc_List_Olist(X1),c_List_Olistrel1(X1,X2)))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19363,i_0_12523,i_0_19708,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_12497,i_0_12529,i_0_16324,i_0_12352,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442]) ).
cnf(i_0_19736,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(rename_variables,[],[i_0_12529]) ).
cnf(i_0_19737,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk125_3(X2,X3,X1)),X3)),X2))
| hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2))) ),
inference(rename_variables,[],[i_0_12442]) ).
cnf(i_0_19738,plain,
hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X1,X2,tc_HOL_Obool,hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4))),X3),X4)),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_12497,i_0_12529,i_0_16324,i_0_12352,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555]) ).
cnf(i_0_19739,plain,
hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
inference(rename_variables,[],[i_0_19563]) ).
cnf(i_0_19740,plain,
( ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X2,X3),X4),X5)))
| hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X2,X3,tc_HOL_Obool,X1),X4),X5)) ),
inference(rename_variables,[],[i_0_12555]) ).
cnf(i_0_19741,plain,
hAPP(c_Option_Ooption_OSome(X1),X2) = hAPP(c_Option_Ooption_OSome(X1),esk438_5(hAPP(X3,X2),hAPP(c_Option_Ooption_OSome(X1),X2),X3,X4,X1)),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_12497,i_0_12529,i_0_16324,i_0_12352,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580]) ).
cnf(i_0_19742,plain,
( hAPP(hAPP(c_Option_Omap(X1,X2),X3),X4) != hAPP(c_Option_Ooption_OSome(X2),X5)
| X4 = hAPP(c_Option_Ooption_OSome(X1),esk438_5(X5,X4,X3,X2,X1)) ),
inference(rename_variables,[],[i_0_12580]) ).
cnf(i_0_19743,plain,
hAPP(c_Fun_Ooverride__on(X1,X2,X3,X4,c_Map_Oran(X5,X1,c_Option_Ooption_OSome(X1))),X6) = hAPP(X4,X6),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_12497,i_0_12529,i_0_16324,i_0_12352,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582]) ).
cnf(i_0_19744,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(c_Fun_Ooverride__on(X1,X4,X5,X6,X3),X2) = hAPP(X6,X2) ),
inference(rename_variables,[],[i_0_12582]) ).
cnf(i_0_19745,plain,
hAPP(X1,esk438_5(hAPP(X1,X2),hAPP(c_Option_Ooption_OSome(X3),X2),X1,X4,X3)) = hAPP(X1,X2),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_12497,i_0_12529,i_0_16324,i_0_12352,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583]) ).
cnf(i_0_19746,plain,
( hAPP(hAPP(c_Option_Omap(X1,X2),X3),X4) != hAPP(c_Option_Ooption_OSome(X2),X5)
| hAPP(X3,esk438_5(X5,X4,X3,X2,X1)) = X5 ),
inference(rename_variables,[],[i_0_12583]) ).
cnf(i_0_19747,plain,
hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Orestrict__map(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X4),c_Option_Ooption_ONone(X2)) = c_Map_Orestrict__map(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_12497,i_0_12529,i_0_16324,i_0_12352,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587]) ).
cnf(i_0_19748,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(rename_variables,[],[i_0_12587]) ).
cnf(i_0_19749,plain,
hAPP(c_Fun_Ooverride__on(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X5) = hAPP(X3,X5),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_12497,i_0_12529,i_0_16324,i_0_12352,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606]) ).
cnf(i_0_19750,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(c_Fun_Ooverride__on(X1,X4,X5,X6,X3),X2) = hAPP(X5,X2) ),
inference(rename_variables,[],[i_0_12606]) ).
cnf(i_0_19751,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),tc_HOL_Obool)),c_List_Olistrel1(tc_List_Olist(X1),c_List_Olistrel1(X1,c_Transitive__Closure_Ortrancl(X1,X2)))),c_List_Olistrel1(tc_List_Olist(X1),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X2))))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_12497,i_0_12529,i_0_13173,i_0_16324,i_0_12352,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671]) ).
cnf(i_0_19752,plain,
( ~ 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(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel1(X1,X2)),c_List_Olistrel1(X1,X3))) ),
inference(rename_variables,[],[i_0_12671]) ).
cnf(i_0_19753,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),tc_HOL_Obool)),c_List_Olistrel(tc_List_Olist(X1),c_List_Olistrel1(X1,c_Transitive__Closure_Ortrancl(X1,X2)))),c_List_Olistrel(tc_List_Olist(X1),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X2))))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_12497,i_0_12529,i_0_13173,i_0_16324,i_0_12352,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672]) ).
cnf(i_0_19754,plain,
( ~ 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(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel(X1,X2)),c_List_Olistrel(X1,X3))) ),
inference(rename_variables,[],[i_0_12672]) ).
cnf(i_0_19755,plain,
c_Fun_Oinj__on(X1,X2,X3,hAPP(c_Relation_OImage(X4,X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X1),tc_HOL_Obool))),X5)),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_12497,i_0_12529,i_0_13173,i_0_16324,i_0_12352,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686]) ).
cnf(i_0_19756,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk195_4(X2,X3,X4,X1)),X2))
| c_Fun_Oinj__on(X1,X4,X3,X2) ),
inference(rename_variables,[],[i_0_12686]) ).
cnf(i_0_19757,plain,
c_Fun_Oinj__on(X1,X2,X3,hAPP(c_Relation_ORange(X4,X1),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X1),tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_12497,i_0_12529,i_0_13173,i_0_16324,i_0_12352,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687]) ).
cnf(i_0_19758,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk194_4(X2,X3,X4,X1)),X2))
| c_Fun_Oinj__on(X1,X4,X3,X2) ),
inference(rename_variables,[],[i_0_12687]) ).
cnf(i_0_19759,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X3),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X3),tc_HOL_Obool)))),X4) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_12497,i_0_12529,i_0_13173,i_0_16324,i_0_12352,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703]) ).
cnf(i_0_19760,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk393_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(rename_variables,[],[i_0_12703]) ).
cnf(i_0_19761,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))),X3) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_12497,i_0_12529,i_0_13173,i_0_16324,i_0_12352,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704]) ).
cnf(i_0_19762,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_16117]) ).
cnf(i_0_19763,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk167_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(rename_variables,[],[i_0_12704]) ).
cnf(i_0_19764,plain,
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)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),X3),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_12497,i_0_12529,i_0_13173,i_0_16324,i_0_12352,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705]) ).
cnf(i_0_19765,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_16117]) ).
cnf(i_0_19766,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk392_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(rename_variables,[],[i_0_12705]) ).
cnf(i_0_19767,plain,
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)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),X3),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_12497,i_0_12529,i_0_13173,i_0_16324,i_0_12352,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706]) ).
cnf(i_0_19768,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_16117]) ).
cnf(i_0_19769,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk166_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(rename_variables,[],[i_0_12706]) ).
cnf(i_0_19770,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),X1)),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_12497,i_0_12529,i_0_13173,i_0_16310,i_0_16324,i_0_12352,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715]) ).
cnf(i_0_19771,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_16310]) ).
cnf(i_0_19772,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(rename_variables,[],[i_0_12715]) ).
cnf(i_0_19773,plain,
hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,X3),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_12497,i_0_12529,i_0_13173,i_0_16310,i_0_16324,i_0_12352,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729]) ).
cnf(i_0_19774,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_16117]) ).
cnf(i_0_19775,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk349_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(rename_variables,[],[i_0_12729]) ).
cnf(i_0_19776,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,tc_prod(tc_List_Olist(X2),tc_List_Olist(X2)),X3),c_List_Olistrel1(X2,c_Transitive__Closure_Ortrancl(X2,X4)))),hAPP(c_Set_Ovimage(X1,tc_prod(tc_List_Olist(X2),tc_List_Olist(X2)),X3),c_Transitive__Closure_Ortrancl(tc_List_Olist(X2),c_List_Olistrel1(X2,X4))))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_12497,i_0_12529,i_0_13173,i_0_16310,i_0_16324,i_0_12352,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754]) ).
cnf(i_0_19777,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(X4,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X4,X1,X5),X2)),hAPP(c_Set_Ovimage(X4,X1,X5),X3))) ),
inference(rename_variables,[],[i_0_12754]) ).
cnf(i_0_19778,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2)),X1,X3),c_List_Olistrel1(X2,c_Transitive__Closure_Ortrancl(X2,X4)))),hAPP(c_Set_Oimage(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2)),X1,X3),c_Transitive__Closure_Ortrancl(tc_List_Olist(X2),c_List_Olistrel1(X2,X4))))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_12497,i_0_12529,i_0_13173,i_0_16310,i_0_16324,i_0_12352,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755]) ).
cnf(i_0_19779,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(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X4,X5),X2)),hAPP(c_Set_Oimage(X1,X4,X5),X3))) ),
inference(rename_variables,[],[i_0_12755]) ).
cnf(i_0_19780,plain,
hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X1,X2,c_Map_Oran(X3,tc_prod(X1,X2),c_Option_Ooption_OSome(tc_prod(X1,X2)))),X4),X5)),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_12497,i_0_12529,i_0_13173,i_0_16310,i_0_16324,i_0_12352,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766]) ).
cnf(i_0_19781,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Oran(X3,X1,c_Option_Ooption_OSome(X1)))),
inference(rename_variables,[],[i_0_19385]) ).
cnf(i_0_19782,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))
| hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X1,X2,X5),X3),X4)) ),
inference(rename_variables,[],[i_0_12766]) ).
cnf(i_0_19783,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(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),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(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_12497,i_0_12529,i_0_13173,i_0_16310,i_0_17227,i_0_16324,i_0_12352,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769]) ).
cnf(i_0_19784,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),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)))) ),
inference(rename_variables,[],[i_0_12769]) ).
cnf(i_0_19785,plain,
hAPP(c_Relation_OImage(X1,X1,c_Transitive__Closure_Ortrancl(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(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_12497,i_0_12529,i_0_13173,i_0_15865,i_0_16310,i_0_17227,i_0_16324,i_0_12352,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770]) ).
cnf(i_0_19786,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(rename_variables,[],[i_0_15865]) ).
cnf(i_0_19787,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X2),X3)),X3))
| hAPP(c_Relation_OImage(X1,X1,c_Transitive__Closure_Ortrancl(X1,X2)),X3) = X3 ),
inference(rename_variables,[],[i_0_12770]) ).
cnf(i_0_19788,plain,
~ c_Typedef_Otype__definition(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_12497,i_0_12529,i_0_13173,i_0_15865,i_0_16310,i_0_17227,i_0_16324,i_0_12352,i_0_18009,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792]) ).
cnf(i_0_19789,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_16117]) ).
cnf(i_0_19790,plain,
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),X4))
| ~ c_Typedef_Otype__definition(X5,X1,X2,X6,X4) ),
inference(rename_variables,[],[i_0_12792]) ).
cnf(i_0_19791,plain,
~ c_Typedef_Otype__definition(X1,X2,X3,X4,hAPP(c_Nat_OSuc,hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_12497,i_0_12529,i_0_13173,i_0_15865,i_0_16310,i_0_17227,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821]) ).
cnf(i_0_19792,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_18010]) ).
cnf(i_0_19793,plain,
( hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = X4
| ~ c_Typedef_Otype__definition(X1,X2,X3,X5,X4) ),
inference(rename_variables,[],[i_0_12821]) ).
cnf(i_0_19794,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),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)))),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(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13173,i_0_15865,i_0_16310,i_0_17227,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826]) ).
cnf(i_0_19795,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(rename_variables,[],[i_0_12826]) ).
cnf(i_0_19796,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),c_Map_Oran(X3,X2,c_Option_Ooption_OSome(X2))),X4)),hAPP(X4,X5))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13173,i_0_15865,i_0_16310,i_0_17227,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879]) ).
cnf(i_0_19797,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| 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))) ),
inference(rename_variables,[],[i_0_12879]) ).
cnf(i_0_19798,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_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,c_Transitive__Closure_Ortrancl(X1,X2)))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X2))))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13173,i_0_15865,i_0_16310,i_0_17227,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880]) ).
cnf(i_0_19799,plain,
( ~ 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)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,X3))) ),
inference(rename_variables,[],[i_0_12880]) ).
cnf(i_0_19800,plain,
~ c_Typedef_Otype__definition(X1,X2,X3,c_Com_Ocom_OBODY,X4),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13173,i_0_15865,i_0_16310,i_0_17227,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912]) ).
cnf(i_0_19801,plain,
hAPP(c_Com_Ocom_OBODY,X1) != c_Com_Ocom_OLocal(X2,X3,X4),
inference(rename_variables,[],[i_0_17425]) ).
cnf(i_0_19802,plain,
( hAPP(X1,hAPP(X2,X3)) = X3
| ~ c_Typedef_Otype__definition(X4,X5,X2,X1,X6) ),
inference(rename_variables,[],[i_0_12912]) ).
cnf(i_0_19803,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Map_Odom(tc_prod(X1,X1),X3,c_Option_Ooption_OSome(X3))),c_Transitive__Closure_Ortrancl(X1,c_Map_Odom(tc_prod(X1,X1),X3,c_Option_Ooption_OSome(X3)))))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19386,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13173,i_0_15865,i_0_16310,i_0_17227,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917]) ).
cnf(i_0_19804,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Odom(X1,X3,c_Option_Ooption_OSome(X3)))),
inference(rename_variables,[],[i_0_19386]) ).
cnf(i_0_19805,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),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(rename_variables,[],[i_0_12917]) ).
cnf(i_0_19806,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ODomain(X1,X3),c_Map_Oran(X4,tc_prod(X1,X3),c_Option_Ooption_OSome(tc_prod(X1,X3)))))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19386,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13173,i_0_15865,i_0_16310,i_0_17227,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925]) ).
cnf(i_0_19807,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Oran(X3,X1,c_Option_Ooption_OSome(X1)))),
inference(rename_variables,[],[i_0_19385]) ).
cnf(i_0_19808,plain,
( ~ 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(X1),X3),hAPP(c_Relation_ODomain(X1,X2),X5))) ),
inference(rename_variables,[],[i_0_12925]) ).
cnf(i_0_19809,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ORange(X3,X1),c_Map_Oran(X4,tc_prod(X3,X1),c_Option_Ooption_OSome(tc_prod(X3,X1)))))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19386,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13173,i_0_15865,i_0_16310,i_0_17227,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927]) ).
cnf(i_0_19810,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Oran(X3,X1,c_Option_Ooption_OSome(X1)))),
inference(rename_variables,[],[i_0_19385]) ).
cnf(i_0_19811,plain,
( ~ 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(X2),X4),hAPP(c_Relation_ORange(X1,X2),X5))) ),
inference(rename_variables,[],[i_0_12927]) ).
cnf(i_0_19812,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(c_Relation_ODomain(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel1(X1,c_Transitive__Closure_Ortrancl(X1,X2)))),hAPP(c_Relation_ODomain(tc_List_Olist(X1),tc_List_Olist(X1)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X2))))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19386,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13173,i_0_15865,i_0_16310,i_0_17227,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941]) ).
cnf(i_0_19813,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_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X2),X3)),hAPP(c_Relation_ODomain(X1,X2),X4))) ),
inference(rename_variables,[],[i_0_12941]) ).
cnf(i_0_19814,plain,
~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),X3),X4)),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19386,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13173,i_0_15865,i_0_16310,i_0_17227,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956]) ).
cnf(i_0_19815,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_16117]) ).
cnf(i_0_19816,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X1,X2,X5),X3),X4)) ),
inference(rename_variables,[],[i_0_12956]) ).
cnf(i_0_19817,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Relation_OId__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19386,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13173,i_0_15865,i_0_16310,i_0_17227,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970]) ).
cnf(i_0_19818,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(rename_variables,[],[i_0_12970]) ).
cnf(i_0_19819,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Map_Oran(X3,X1,c_Option_Ooption_OSome(X1))),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_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Map_Oran(X3,X1,c_Option_Ooption_OSome(X1))),X5)),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13173,i_0_15865,i_0_16310,i_0_17227,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002]) ).
cnf(i_0_19820,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| 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)) ),
inference(rename_variables,[],[i_0_13002]) ).
cnf(i_0_19821,plain,
hBOOL(hAPP(hAPP(c_member(tc_sum(X1,X2)),hAPP(c_Sum__Type_OInl(X1,X2),X3)),c_Sum__Type_OPlus(X1,X2,c_Map_Oran(X4,X1,c_Option_Ooption_OSome(X1)),X5))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13173,i_0_15865,i_0_16310,i_0_17227,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011]) ).
cnf(i_0_19822,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| 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))) ),
inference(rename_variables,[],[i_0_13011]) ).
cnf(i_0_19823,plain,
hBOOL(hAPP(hAPP(c_member(tc_sum(X1,X2)),hAPP(c_Sum__Type_OInr(X2,X1),X3)),c_Sum__Type_OPlus(X1,X2,X4,c_Map_Oran(X5,X2,c_Option_Ooption_OSome(X2))))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13173,i_0_15865,i_0_16310,i_0_17227,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012]) ).
cnf(i_0_19824,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| 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))) ),
inference(rename_variables,[],[i_0_13012]) ).
cnf(i_0_19825,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),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13173,i_0_15865,i_0_19786,i_0_16310,i_0_17227,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012,i_0_13025]) ).
cnf(i_0_19826,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(rename_variables,[],[i_0_15865]) ).
cnf(i_0_19827,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3))
| 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))) ),
inference(rename_variables,[],[i_0_13025]) ).
cnf(i_0_19828,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),hAPP(c_List_Oset(tc_fun(X1,tc_HOL_Obool)),X2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(c_List_Oset(tc_fun(X1,tc_HOL_Obool)),c_List_Osublist(tc_fun(X1,tc_HOL_Obool),X2,X3))))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13173,i_0_13378,i_0_15865,i_0_19786,i_0_16310,i_0_17227,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012,i_0_13025,i_0_13026]) ).
cnf(i_0_19829,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(rename_variables,[],[i_0_13378]) ).
cnf(i_0_19830,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3))
| 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))) ),
inference(rename_variables,[],[i_0_13026]) ).
cnf(i_0_19831,plain,
hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2) = hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk389_2(hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2),X1)),esk389_2(hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2),X1)),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13781,i_0_13173,i_0_13378,i_0_15865,i_0_19786,i_0_16310,i_0_17227,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012,i_0_13025,i_0_13026,i_0_13047]) ).
cnf(i_0_19832,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(rename_variables,[],[i_0_13781]) ).
cnf(i_0_19833,plain,
( ~ 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)))))
| X2 = hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk389_2(X2,X1)),esk389_2(X2,X1)) ),
inference(rename_variables,[],[i_0_13047]) ).
cnf(i_0_19834,plain,
hAPP(c_Fun_Ocomp(X1,X2,X3,c_Sum__Type_OInl(X4,X5)),X6) != hAPP(c_Fun_Ocomp(X7,X2,X3,c_Sum__Type_OInr(X5,X4)),X8),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13781,i_0_13173,i_0_13378,i_0_15865,i_0_19786,i_0_16310,i_0_17227,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17284,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012,i_0_13025,i_0_13026,i_0_13047,i_0_13086]) ).
cnf(i_0_19835,plain,
hAPP(c_Sum__Type_OInl(X1,X2),X3) != hAPP(c_Sum__Type_OInr(X2,X1),X4),
inference(rename_variables,[],[i_0_17284]) ).
cnf(i_0_19836,plain,
( hAPP(X1,hAPP(X2,X3)) = hAPP(X4,hAPP(X5,X3))
| hAPP(c_Fun_Ocomp(X6,X7,X8,X1),X2) != hAPP(c_Fun_Ocomp(X9,X7,X8,X4),X5) ),
inference(rename_variables,[],[i_0_13086]) ).
cnf(i_0_19837,plain,
hAPP(hAPP(c_Fun_Ocomp(X1,X1,X2,c_Fun_Oid(X1)),X3),hAPP(c_Fun_Oid(X2),X4)) = hAPP(X3,X4),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_15370,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13781,i_0_13173,i_0_13378,i_0_15865,i_0_19786,i_0_16310,i_0_17227,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17284,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012,i_0_13025,i_0_13026,i_0_13047,i_0_13086,i_0_13091]) ).
cnf(i_0_19838,plain,
hAPP(c_Fun_Ocomp(X1,X2,X1,X3),c_Fun_Oid(X1)) = X3,
inference(rename_variables,[],[i_0_15370]) ).
cnf(i_0_19839,plain,
( hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5) != hAPP(c_Fun_Ocomp(X2,X2,X3,c_Fun_Oid(X2)),X6)
| hAPP(X4,hAPP(X5,X7)) = hAPP(X6,X7) ),
inference(rename_variables,[],[i_0_13091]) ).
cnf(i_0_19840,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(c_Relation_OField(tc_List_Olist(X1)),c_List_Olistrel1(X1,c_Transitive__Closure_Ortrancl(X1,X2)))),hAPP(c_Relation_OField(tc_List_Olist(X1)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X2))))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_15370,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13781,i_0_13173,i_0_13378,i_0_15865,i_0_19786,i_0_16310,i_0_17227,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17284,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012,i_0_13025,i_0_13026,i_0_13047,i_0_13086,i_0_13091,i_0_13141]) ).
cnf(i_0_19841,plain,
( ~ 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(X1,tc_HOL_Obool)),hAPP(c_Relation_OField(X1),X2)),hAPP(c_Relation_OField(X1),X3))) ),
inference(rename_variables,[],[i_0_13141]) ).
cnf(i_0_19842,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)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_15370,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13781,i_0_17107,i_0_13173,i_0_13378,i_0_15865,i_0_19786,i_0_16310,i_0_17227,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17284,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012,i_0_13025,i_0_13026,i_0_13047,i_0_13086,i_0_13091,i_0_13141,i_0_13163]) ).
cnf(i_0_19843,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)),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)) ),
inference(rename_variables,[],[i_0_13163]) ).
cnf(i_0_19844,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)),hAPP(c_List_Oset(X1),X2)),X3)),hAPP(c_List_Oset(X1),c_List_Osublist(X1,X2,X4))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(c_List_Oset(X1),c_List_Osublist(X1,X2,X4)))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_15370,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13781,i_0_17107,i_0_13173,i_0_13378,i_0_19829,i_0_15865,i_0_19786,i_0_16310,i_0_17227,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17284,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012,i_0_13025,i_0_13026,i_0_13047,i_0_13086,i_0_13091,i_0_13141,i_0_13163,i_0_13167]) ).
cnf(i_0_19845,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)),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)) ),
inference(rename_variables,[],[i_0_13167]) ).
cnf(i_0_19846,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),hAPP(c_Nat_OSuc,X1)),X1)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_15370,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13781,i_0_17107,i_0_13173,i_0_13378,i_0_19829,i_0_15865,i_0_19786,i_0_16310,i_0_19771,i_0_17227,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17284,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012,i_0_13025,i_0_13026,i_0_13047,i_0_13086,i_0_13091,i_0_13141,i_0_13163,i_0_13167,i_0_13192]) ).
cnf(i_0_19847,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(rename_variables,[],[i_0_13192]) ).
cnf(i_0_19848,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),c_Wellfounded_Oacc(tc_List_Olist(X1),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X2)))),c_Wellfounded_Oacc(tc_List_Olist(X1),c_List_Olistrel1(X1,c_Transitive__Closure_Ortrancl(X1,X2))))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_15370,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_13839,i_0_19645,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13781,i_0_17107,i_0_13173,i_0_13378,i_0_19829,i_0_15865,i_0_19786,i_0_16310,i_0_19771,i_0_17227,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17284,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012,i_0_13025,i_0_13026,i_0_13047,i_0_13086,i_0_13091,i_0_13141,i_0_13163,i_0_13167,i_0_13192,i_0_13201]) ).
cnf(i_0_19849,plain,
( ~ 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(X1,tc_HOL_Obool)),c_Wellfounded_Oacc(X1,X3)),c_Wellfounded_Oacc(X1,X2))) ),
inference(rename_variables,[],[i_0_13201]) ).
cnf(i_0_19850,plain,
c_Wellfounded_Owf(tc_prod(X1,X2),c_Recdef_Osame__fst(X1,X2,hAPP(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_fun(X4,tc_HOL_Obool))),X5),X6)),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_15370,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_13839,i_0_19645,i_0_19659,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13781,i_0_17107,i_0_13173,i_0_13378,i_0_19829,i_0_15865,i_0_19786,i_0_16310,i_0_19771,i_0_17227,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17284,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012,i_0_13025,i_0_13026,i_0_13047,i_0_13086,i_0_13091,i_0_13141,i_0_13163,i_0_13167,i_0_13192,i_0_13201,i_0_13203]) ).
cnf(i_0_19851,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4)),
inference(rename_variables,[],[i_0_13839]) ).
cnf(i_0_19852,plain,
( hBOOL(hAPP(X1,esk321_4(X2,X3,X4,X1)))
| c_Wellfounded_Owf(tc_prod(X2,X4),c_Recdef_Osame__fst(X2,X4,X1,X3)) ),
inference(rename_variables,[],[i_0_13203]) ).
cnf(i_0_19853,plain,
hAPP(X1,X2) = hAPP(X1,esk118_4(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)),X1,X3,hAPP(X1,X2))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_15370,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_14175,i_0_13839,i_0_19645,i_0_19659,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13781,i_0_17107,i_0_13173,i_0_13378,i_0_19829,i_0_15865,i_0_19786,i_0_16310,i_0_19771,i_0_17227,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17284,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012,i_0_13025,i_0_13026,i_0_13047,i_0_13086,i_0_13091,i_0_13141,i_0_13163,i_0_13167,i_0_13192,i_0_13201,i_0_13203,i_0_13329]) ).
cnf(i_0_19854,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Set_Oimage(X3,X1,X4),X5)))
| X2 = hAPP(X4,esk118_4(X5,X4,X3,X2)) ),
inference(rename_variables,[],[i_0_13329]) ).
cnf(i_0_19855,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),X2)))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_15370,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_14175,i_0_13839,i_0_19645,i_0_19659,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13781,i_0_17107,i_0_13173,i_0_13378,i_0_19829,i_0_15865,i_0_19786,i_0_16310,i_0_19771,i_0_17227,i_0_15425,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17284,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012,i_0_13025,i_0_13026,i_0_13047,i_0_13086,i_0_13091,i_0_13141,i_0_13163,i_0_13167,i_0_13192,i_0_13201,i_0_13203,i_0_13329,i_0_13359]) ).
cnf(i_0_19856,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(rename_variables,[],[i_0_15425]) ).
cnf(i_0_19857,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4)) ),
inference(rename_variables,[],[i_0_13359]) ).
cnf(i_0_19858,plain,
hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Map_Oran(X3,X1,c_Option_Ooption_OSome(X1))),hAPP(hAPP(c_Set_Oinsert(X1),X4),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),X2),c_Map_Oran(X3,X1,c_Option_Ooption_OSome(X1)))),hAPP(X2,X4)),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_15370,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_14175,i_0_13839,i_0_19645,i_0_19659,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13781,i_0_17107,i_0_13173,i_0_13378,i_0_19829,i_0_15865,i_0_19786,i_0_16310,i_0_19771,i_0_17227,i_0_15425,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17284,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012,i_0_13025,i_0_13026,i_0_13047,i_0_13086,i_0_13091,i_0_13141,i_0_13163,i_0_13167,i_0_13192,i_0_13201,i_0_13203,i_0_13329,i_0_13359,i_0_13387]) ).
cnf(i_0_19859,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_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)) ),
inference(rename_variables,[],[i_0_13387]) ).
cnf(i_0_19860,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),c_List_Osublist(X1,X3,X4)))),hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3)))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_15370,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_14175,i_0_13839,i_0_19645,i_0_19659,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13781,i_0_17107,i_0_13173,i_0_13378,i_0_19829,i_0_15865,i_0_19786,i_0_16310,i_0_19771,i_0_17227,i_0_15425,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17284,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012,i_0_13025,i_0_13026,i_0_13047,i_0_13086,i_0_13091,i_0_13141,i_0_13163,i_0_13167,i_0_13192,i_0_13201,i_0_13203,i_0_13329,i_0_13359,i_0_13387,i_0_13392]) ).
cnf(i_0_19861,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)),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3))) ),
inference(rename_variables,[],[i_0_13392]) ).
cnf(i_0_19862,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),c_List_Olistrel1(X1,c_Transitive__Closure_Ortrancl(X1,X2)))),hAPP(c_Set_OPow(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X2))))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_15370,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_14175,i_0_13839,i_0_19645,i_0_19659,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13781,i_0_17107,i_0_13173,i_0_13378,i_0_19829,i_0_15865,i_0_19786,i_0_16310,i_0_19771,i_0_17227,i_0_15425,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17284,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012,i_0_13025,i_0_13026,i_0_13047,i_0_13086,i_0_13091,i_0_13141,i_0_13163,i_0_13167,i_0_13192,i_0_13201,i_0_13203,i_0_13329,i_0_13359,i_0_13387,i_0_13392,i_0_13411]) ).
cnf(i_0_19863,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(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2)),hAPP(c_Set_OPow(X1),X3))) ),
inference(rename_variables,[],[i_0_13411]) ).
cnf(i_0_19864,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel1(X1,c_Transitive__Closure_Ortrancl(X1,X2)))),c_Predicate_OPowp(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X2))))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_15370,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_14175,i_0_13839,i_0_19645,i_0_19659,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13781,i_0_17107,i_0_13173,i_0_13378,i_0_19829,i_0_15865,i_0_19786,i_0_16310,i_0_19771,i_0_17227,i_0_15425,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17284,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012,i_0_13025,i_0_13026,i_0_13047,i_0_13086,i_0_13091,i_0_13141,i_0_13163,i_0_13167,i_0_13192,i_0_13201,i_0_13203,i_0_13329,i_0_13359,i_0_13387,i_0_13392,i_0_13411,i_0_13493]) ).
cnf(i_0_19865,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(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(X1,X2)),c_Predicate_OPowp(X1,X3))) ),
inference(rename_variables,[],[i_0_13493]) ).
cnf(i_0_19866,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_15370,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_14175,i_0_13839,i_0_19645,i_0_19659,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13781,i_0_17107,i_0_13173,i_0_13378,i_0_19829,i_0_15865,i_0_19786,i_0_16310,i_0_19771,i_0_17227,i_0_15425,i_0_19856,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17284,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012,i_0_13025,i_0_13026,i_0_13047,i_0_13086,i_0_13091,i_0_13141,i_0_13163,i_0_13167,i_0_13192,i_0_13201,i_0_13203,i_0_13329,i_0_13359,i_0_13387,i_0_13392,i_0_13411,i_0_13493,i_0_13598]) ).
cnf(i_0_19867,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(rename_variables,[],[i_0_15425]) ).
cnf(i_0_19868,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_member(X1),X2),X4)) ),
inference(rename_variables,[],[i_0_13598]) ).
cnf(i_0_19869,plain,
hAPP(hAPP(c_List_Otake(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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_15370,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_14175,i_0_13839,i_0_19645,i_0_19659,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13781,i_0_17107,i_0_13173,i_0_13378,i_0_19829,i_0_15865,i_0_19786,i_0_17497,i_0_16310,i_0_19771,i_0_17227,i_0_15425,i_0_19856,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17284,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012,i_0_13025,i_0_13026,i_0_13047,i_0_13086,i_0_13091,i_0_13141,i_0_13163,i_0_13167,i_0_13192,i_0_13201,i_0_13203,i_0_13329,i_0_13359,i_0_13387,i_0_13392,i_0_13411,i_0_13493,i_0_13598,i_0_13614]) ).
cnf(i_0_19870,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_17497]) ).
cnf(i_0_19871,plain,
( ~ 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))
| 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))) ),
inference(rename_variables,[],[i_0_13614]) ).
cnf(i_0_19872,plain,
c_Partial__Function_Oflat__lub(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = X2,
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_15370,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_14175,i_0_13839,i_0_19645,i_0_19659,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13781,i_0_17107,i_0_13173,i_0_13378,i_0_19829,i_0_15865,i_0_19786,i_0_17497,i_0_16310,i_0_19771,i_0_17227,i_0_15425,i_0_19856,i_0_19867,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17284,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012,i_0_13025,i_0_13026,i_0_13047,i_0_13086,i_0_13091,i_0_13141,i_0_13163,i_0_13167,i_0_13192,i_0_13201,i_0_13203,i_0_13329,i_0_13359,i_0_13387,i_0_13392,i_0_13411,i_0_13493,i_0_13598,i_0_13614,i_0_13664]) ).
cnf(i_0_19873,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(rename_variables,[],[i_0_15425]) ).
cnf(i_0_19874,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) = X3 ),
inference(rename_variables,[],[i_0_13664]) ).
cnf(i_0_19875,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Relation_OId__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_15370,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_14175,i_0_13839,i_0_19645,i_0_19659,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13781,i_0_17107,i_0_13173,i_0_13378,i_0_19829,i_0_15865,i_0_19786,i_0_17497,i_0_16310,i_0_19771,i_0_17227,i_0_15425,i_0_19856,i_0_19867,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17284,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012,i_0_13025,i_0_13026,i_0_13047,i_0_13086,i_0_13091,i_0_13141,i_0_13163,i_0_13167,i_0_13192,i_0_13201,i_0_13203,i_0_13329,i_0_13359,i_0_13387,i_0_13392,i_0_13411,i_0_13493,i_0_13598,i_0_13614,i_0_13664,i_0_13744]) ).
cnf(i_0_19876,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_16117]) ).
cnf(i_0_19877,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk178_3(X2,X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X3),c_Relation_OId__on(X1,X2))) ),
inference(rename_variables,[],[i_0_13744]) ).
cnf(i_0_19878,plain,
esk438_5(hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2),hAPP(c_Option_Ooption_OSome(X3),X2),hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X4,X3) = X2,
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_15370,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_14175,i_0_13839,i_0_19645,i_0_19659,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13781,i_0_17107,i_0_13173,i_0_13378,i_0_19829,i_0_15865,i_0_19786,i_0_17497,i_0_16310,i_0_19771,i_0_17227,i_0_15425,i_0_19856,i_0_19867,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17284,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012,i_0_13025,i_0_13026,i_0_13047,i_0_13086,i_0_13091,i_0_13141,i_0_13163,i_0_13167,i_0_13192,i_0_13201,i_0_13203,i_0_13329,i_0_13359,i_0_13387,i_0_13392,i_0_13411,i_0_13493,i_0_13598,i_0_13614,i_0_13664,i_0_13744,i_0_13750]) ).
cnf(i_0_19879,plain,
( 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)
| X2 = X3 ),
inference(rename_variables,[],[i_0_13750]) ).
cnf(i_0_19880,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),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_15370,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_14175,i_0_13839,i_0_19645,i_0_19659,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13781,i_0_17107,i_0_17410,i_0_13173,i_0_13378,i_0_19829,i_0_15865,i_0_19786,i_0_17497,i_0_16310,i_0_19771,i_0_17227,i_0_15425,i_0_19856,i_0_19867,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17284,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012,i_0_13025,i_0_13026,i_0_13047,i_0_13086,i_0_13091,i_0_13141,i_0_13163,i_0_13167,i_0_13192,i_0_13201,i_0_13203,i_0_13329,i_0_13359,i_0_13387,i_0_13392,i_0_13411,i_0_13493,i_0_13598,i_0_13614,i_0_13664,i_0_13744,i_0_13750,i_0_13805]) ).
cnf(i_0_19881,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(rename_variables,[],[i_0_13805]) ).
cnf(i_0_19882,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),c_List_Olists(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_15370,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_19876,i_0_14175,i_0_13839,i_0_19645,i_0_19659,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13781,i_0_17107,i_0_17410,i_0_13173,i_0_13378,i_0_19829,i_0_15865,i_0_19786,i_0_17497,i_0_16310,i_0_19771,i_0_17227,i_0_15425,i_0_19856,i_0_19867,i_0_16324,i_0_12352,i_0_18009,i_0_18010,i_0_17425,i_0_17284,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012,i_0_13025,i_0_13026,i_0_13047,i_0_13086,i_0_13091,i_0_13141,i_0_13163,i_0_13167,i_0_13192,i_0_13201,i_0_13203,i_0_13329,i_0_13359,i_0_13387,i_0_13392,i_0_13411,i_0_13493,i_0_13598,i_0_13614,i_0_13664,i_0_13744,i_0_13750,i_0_13805,i_0_13830]) ).
cnf(i_0_19883,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(rename_variables,[],[i_0_13830]) ).
cnf(i_0_19884,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),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3))),X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_15370,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_19876,i_0_14175,i_0_13839,i_0_19645,i_0_19659,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13781,i_0_17107,i_0_17410,i_0_13173,i_0_13378,i_0_19829,i_0_15865,i_0_19786,i_0_17497,i_0_16310,i_0_19771,i_0_17227,i_0_15425,i_0_19856,i_0_19867,i_0_16324,i_0_12352,i_0_13319,i_0_18009,i_0_18010,i_0_17425,i_0_17284,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012,i_0_13025,i_0_13026,i_0_13047,i_0_13086,i_0_13091,i_0_13141,i_0_13163,i_0_13167,i_0_13192,i_0_13201,i_0_13203,i_0_13329,i_0_13359,i_0_13387,i_0_13392,i_0_13411,i_0_13493,i_0_13598,i_0_13614,i_0_13664,i_0_13744,i_0_13750,i_0_13805,i_0_13830,i_0_13902]) ).
cnf(i_0_19885,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(rename_variables,[],[i_0_13319]) ).
cnf(i_0_19886,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(rename_variables,[],[i_0_13902]) ).
cnf(i_0_19887,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),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)))),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_15370,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_19876,i_0_14175,i_0_13839,i_0_19645,i_0_19659,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13781,i_0_17107,i_0_17410,i_0_13173,i_0_13378,i_0_19829,i_0_15865,i_0_19786,i_0_17497,i_0_16310,i_0_19771,i_0_17227,i_0_15425,i_0_19856,i_0_19867,i_0_16324,i_0_12352,i_0_13319,i_0_18009,i_0_18010,i_0_17425,i_0_17284,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012,i_0_13025,i_0_13026,i_0_13047,i_0_13086,i_0_13091,i_0_13141,i_0_13163,i_0_13167,i_0_13192,i_0_13201,i_0_13203,i_0_13329,i_0_13359,i_0_13387,i_0_13392,i_0_13411,i_0_13493,i_0_13598,i_0_13614,i_0_13664,i_0_13744,i_0_13750,i_0_13805,i_0_13830,i_0_13902,i_0_13907]) ).
cnf(i_0_19888,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_16117]) ).
cnf(i_0_19889,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk399_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(rename_variables,[],[i_0_13907]) ).
cnf(i_0_19890,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_HOL_Obool)),c_List_Olists(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel1(X1,c_Transitive__Closure_Ortrancl(X1,X2)))),c_List_Olists(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X2))))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_15370,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_19876,i_0_14175,i_0_13839,i_0_19645,i_0_19659,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13781,i_0_17107,i_0_17410,i_0_13173,i_0_13378,i_0_19829,i_0_15865,i_0_19786,i_0_17497,i_0_16310,i_0_19771,i_0_17227,i_0_15425,i_0_19856,i_0_19867,i_0_16324,i_0_12352,i_0_13319,i_0_18009,i_0_18010,i_0_17425,i_0_17284,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012,i_0_13025,i_0_13026,i_0_13047,i_0_13086,i_0_13091,i_0_13141,i_0_13163,i_0_13167,i_0_13192,i_0_13201,i_0_13203,i_0_13329,i_0_13359,i_0_13387,i_0_13392,i_0_13411,i_0_13493,i_0_13598,i_0_13614,i_0_13664,i_0_13744,i_0_13750,i_0_13805,i_0_13830,i_0_13902,i_0_13907,i_0_13940]) ).
cnf(i_0_19891,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(tc_List_Olist(X1),tc_HOL_Obool)),c_List_Olists(X1,X2)),c_List_Olists(X1,X3))) ),
inference(rename_variables,[],[i_0_13940]) ).
cnf(i_0_19892,plain,
hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),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))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_15370,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_19876,i_0_19888,i_0_14175,i_0_13839,i_0_19645,i_0_19659,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13781,i_0_17107,i_0_17410,i_0_13173,i_0_13378,i_0_19829,i_0_15865,i_0_19786,i_0_17497,i_0_16310,i_0_19771,i_0_17227,i_0_15425,i_0_19856,i_0_19867,i_0_16324,i_0_12352,i_0_13319,i_0_18009,i_0_18010,i_0_17425,i_0_17284,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012,i_0_13025,i_0_13026,i_0_13047,i_0_13086,i_0_13091,i_0_13141,i_0_13163,i_0_13167,i_0_13192,i_0_13201,i_0_13203,i_0_13329,i_0_13359,i_0_13387,i_0_13392,i_0_13411,i_0_13493,i_0_13598,i_0_13614,i_0_13664,i_0_13744,i_0_13750,i_0_13805,i_0_13830,i_0_13902,i_0_13907,i_0_13940,i_0_13976]) ).
cnf(i_0_19893,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(rename_variables,[],[i_0_13976]) ).
cnf(i_0_19894,plain,
esk335_1(X1) = hAPP(c_Int_ORep__Integ,esk306_1(esk335_1(X1))),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_15370,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_19876,i_0_19888,i_0_14175,i_0_13839,i_0_19645,i_0_19659,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13781,i_0_17107,i_0_17410,i_0_13173,i_0_13378,i_0_19829,i_0_15865,i_0_19786,i_0_17497,i_0_16310,i_0_19771,i_0_14931,i_0_17227,i_0_15425,i_0_19856,i_0_19867,i_0_16324,i_0_12352,i_0_13319,i_0_18009,i_0_18010,i_0_17425,i_0_17284,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012,i_0_13025,i_0_13026,i_0_13047,i_0_13086,i_0_13091,i_0_13141,i_0_13163,i_0_13167,i_0_13192,i_0_13201,i_0_13203,i_0_13329,i_0_13359,i_0_13387,i_0_13392,i_0_13411,i_0_13493,i_0_13598,i_0_13614,i_0_13664,i_0_13744,i_0_13750,i_0_13805,i_0_13830,i_0_13902,i_0_13907,i_0_13940,i_0_13976,i_0_13991]) ).
cnf(i_0_19895,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),c_Int_OInteg))
| X1 = hAPP(c_Int_ORep__Integ,esk306_1(X1)) ),
inference(rename_variables,[],[i_0_13991]) ).
cnf(i_0_19896,plain,
hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2)),
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_15370,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_19876,i_0_19888,i_0_14175,i_0_13839,i_0_19645,i_0_19659,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13781,i_0_17107,i_0_16591,i_0_17410,i_0_13173,i_0_13378,i_0_19829,i_0_15865,i_0_19786,i_0_17497,i_0_16310,i_0_19771,i_0_14931,i_0_17227,i_0_15425,i_0_19856,i_0_19867,i_0_16324,i_0_12352,i_0_13319,i_0_18009,i_0_18010,i_0_17425,i_0_17284,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012,i_0_13025,i_0_13026,i_0_13047,i_0_13086,i_0_13091,i_0_13141,i_0_13163,i_0_13167,i_0_13192,i_0_13201,i_0_13203,i_0_13329,i_0_13359,i_0_13387,i_0_13392,i_0_13411,i_0_13493,i_0_13598,i_0_13614,i_0_13664,i_0_13744,i_0_13750,i_0_13805,i_0_13830,i_0_13902,i_0_13907,i_0_13940,i_0_13976,i_0_13991,i_0_14060]) ).
cnf(i_0_19897,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| 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) ),
inference(rename_variables,[],[i_0_14060]) ).
cnf(i_0_19898,plain,
$false,
inference(scs_inference,[],[i_0_15374,i_0_19343,i_0_19678,i_0_19385,i_0_19781,i_0_19807,i_0_19810,i_0_19386,i_0_19363,i_0_19563,i_0_15370,i_0_12523,i_0_19708,i_0_16981,i_0_15176,i_0_19650,i_0_16117,i_0_19656,i_0_19662,i_0_19690,i_0_19702,i_0_19724,i_0_19730,i_0_19762,i_0_19765,i_0_19768,i_0_19774,i_0_19789,i_0_19815,i_0_19876,i_0_19888,i_0_14175,i_0_13839,i_0_19645,i_0_19659,i_0_19243,i_0_19275,i_0_19192,i_0_19665,i_0_19693,i_0_19333,i_0_19415,i_0_12497,i_0_12529,i_0_13781,i_0_17107,i_0_16591,i_0_17410,i_0_13173,i_0_13378,i_0_19829,i_0_15865,i_0_19786,i_0_17497,i_0_16310,i_0_19771,i_0_14931,i_0_17227,i_0_15425,i_0_19856,i_0_19867,i_0_16324,i_0_12352,i_0_13319,i_0_18009,i_0_18010,i_0_17425,i_0_17991,i_0_17284,i_0_17530,i_0_12321,i_0_13229,i_0_11286,i_0_11287,i_0_11317,i_0_11323,i_0_11376,i_0_11377,i_0_11403,i_0_11405,i_0_11406,i_0_11407,i_0_11417,i_0_11474,i_0_11475,i_0_11753,i_0_11756,i_0_11763,i_0_11764,i_0_11824,i_0_11825,i_0_12018,i_0_12019,i_0_12020,i_0_12218,i_0_12219,i_0_12229,i_0_12252,i_0_12318,i_0_12351,i_0_12406,i_0_12412,i_0_12440,i_0_12441,i_0_12442,i_0_12555,i_0_12580,i_0_12582,i_0_12583,i_0_12587,i_0_12606,i_0_12671,i_0_12672,i_0_12686,i_0_12687,i_0_12703,i_0_12704,i_0_12705,i_0_12706,i_0_12715,i_0_12729,i_0_12754,i_0_12755,i_0_12766,i_0_12769,i_0_12770,i_0_12792,i_0_12821,i_0_12826,i_0_12879,i_0_12880,i_0_12912,i_0_12917,i_0_12925,i_0_12927,i_0_12941,i_0_12956,i_0_12970,i_0_13002,i_0_13011,i_0_13012,i_0_13025,i_0_13026,i_0_13047,i_0_13086,i_0_13091,i_0_13141,i_0_13163,i_0_13167,i_0_13192,i_0_13201,i_0_13203,i_0_13329,i_0_13359,i_0_13387,i_0_13392,i_0_13411,i_0_13493,i_0_13598,i_0_13614,i_0_13664,i_0_13744,i_0_13750,i_0_13805,i_0_13830,i_0_13902,i_0_13907,i_0_13940,i_0_13976,i_0_13991,i_0_14060,i_0_14066]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWW293+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n006.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 06:34:31 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 38.94/22.22 % Version : CSE_E---1.7
% 38.94/22.22 % Problem : theBenchmark.p
% 38.94/22.22 % SZS status Theorem for theBenchmark.p
% 38.94/22.22 % SZS output start CNFRefutation
% See solution above
% 43.74/24.62 % Total time : 21.863s
%------------------------------------------------------------------------------